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# List of equations in classical mechanics
## Classical mechanics {#classical_mechanics}
### Generalized mechanics {#generalized_mechanics}
+----------------------------------------+----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------+--------------------+--------------------+
| Quantity (common name/s) | (Common) symbol/s | Defining equation | SI units | Dimension |
+========================================+==================================+===================================================================================================================================+====================+====================+
| Generalized coordinates | *q, Q* | | varies with choice | varies with choice |
+----------------------------------------+----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------+--------------------+--------------------+
| Generalized velocities | $\dot{q},\dot{Q}$ | $\dot{q}\equiv \mathrm{d}q/\mathrm{d}t$ | varies with choice | varies with choice |
+----------------------------------------+----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------+--------------------+--------------------+
| Generalized momenta | *p, P* | $p = \partial L /\partial \dot{q}$ | varies with choice | varies with choice |
+----------------------------------------+----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------+--------------------+--------------------+
| Lagrangian | *L* | $L(\mathbf{q},\mathbf{\dot{q}},t) = T(\mathbf{\dot{q}}) - V(\mathbf{q},\mathbf{\dot{q}},t)$ | J | M L^2^ T^−2^ |
| | | | | |
| | | where $\mathbf{q} = \mathbf{q}(t)$ and **p** = **p**(*t*) are vectors of the generalized coords and momenta, as functions of time | | |
+----------------------------------------+----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------+--------------------+--------------------+
| Hamiltonian | *H* | $H(\mathbf{p},\mathbf{q},t) = \mathbf{p}\cdot\mathbf{\dot{q}} - L(\mathbf{q},\mathbf{\dot{q}},t)$ | J | M L^2^ T^−2^ |
+----------------------------------------+----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------+--------------------+--------------------+
| Action, Hamilton\'s principal function | *S*, $\scriptstyle{\mathcal{S}}$ | $\mathcal{S} = \int_{t_1}^{t_2} L(\mathbf{q},\mathbf{\dot{q}},t) \mathrm{d}t$ | J s | M L^2^ T^−1^ |
+----------------------------------------+----------------------------------+-----------------------------------------------------------------------------------------------------------------------------------+--------------------+--------------------+
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# List of equations in classical mechanics
## Kinematics
In the following rotational definitions, the angle can be any angle about the specified axis of rotation. It is customary to use *θ*, but this does not have to be the polar angle used in polar coordinate systems. The unit axial vector
$\mathbf{\hat{n}} = \mathbf{\hat{e}}_r\times\mathbf{\hat{e}}_\theta$
defines the axis of rotation, $\scriptstyle \mathbf{\hat{e}}_r$ = unit vector in direction of `{{math|'''r'''}}`{=mediawiki}, $\scriptstyle \mathbf{\hat{e}}_\theta$ = unit vector tangential to the angle.
+--------------+-------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | Translation | Rotation |
+==============+=================================================================================================+====================================================================================================================================================================================+
| Velocity | Average: $\mathbf{v}_{\mathrm{average}} = {\Delta \mathbf{r} \over \Delta t}$ Instantaneous: | Angular velocity$\boldsymbol{\omega} = \mathbf{\hat{n}}\frac{{\rm d} \theta}{{\rm d} t}$Rotating rigid body$$\mathbf{v} = \boldsymbol{\omega} \times \mathbf{r}$$ |
| | | |
| | $\mathbf{v} = {d\mathbf{r} \over dt}$ | |
+--------------+-------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Acceleration | Average: $\mathbf{a}_{\mathrm{average}} = \frac{\Delta\mathbf{v}}{\Delta t}$ | Angular acceleration |
| | | |
| | Instantaneous: | $\boldsymbol{\alpha} = \frac{{\rm d} \boldsymbol{\omega}}{{\rm d} t} = \mathbf{\hat{n}}\frac{{\rm d}^2 \theta}{{\rm d} t^2}$ |
| | | |
| | $\mathbf{a} = \frac{d\mathbf{v}}{dt} = \frac{d^2\mathbf{r}}{dt^2}$ | Rotating rigid body: |
| | | |
| | | $\mathbf{a} = \boldsymbol{\alpha} \times \mathbf{r} + \boldsymbol{\omega} \times \mathbf{v}$ |
+--------------+-------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Jerk | Average: $\mathbf{j}_{\mathrm{average}} = \frac{\Delta\mathbf{a}}{\Delta t}$ | Angular jerk |
| | | |
| | Instantaneous: | $\boldsymbol{\zeta} = \frac{{\rm d} \boldsymbol{\alpha}}{{\rm d} t} = \mathbf{\hat{n}}\frac{{\rm d}^2 \omega}{{\rm d} t^2} = \mathbf{\hat{n}}\frac{{\rm d}^3 \theta}{{\rm d} t^3}$ |
| | | |
| | $\mathbf{j} = \frac{d\mathbf{a}}{dt} = \frac{d^2\mathbf{v}}{dt^2} = \frac{d^3\mathbf{r}}{dt^3}$ | Rotating rigid body: |
| | | |
| | | $\mathbf{j} = \boldsymbol{\zeta} \times \mathbf{r} + \boldsymbol{\alpha} \times \mathbf{a}$ |
+--------------+-------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
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# List of equations in classical mechanics
## Dynamics
+-----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------+
| | Translation | Rotation |
+=============================+===============================================================================================================================================================================================================================================+========================================================================================================================================================+
| Momentum | Momentum is the \"amount of translation\" | Angular momentum |
| | | |
| | $\mathbf{p} = m\mathbf{v}$ | Angular momentum is the \"amount of rotation\": |
| | | |
| | For a rotating rigid body: | $\mathbf{L} = \mathbf{r} \times \mathbf{p} = \mathbf{I} \cdot \boldsymbol{\omega}$ |
| | | |
| | $\mathbf{p} = \boldsymbol{\omega} \times \mathbf{m}$ | and the cross-product is a pseudovector i.e. if **r** and **p** are reversed in direction (negative), **L** is not. |
| | | |
| | | In general **I** is an order-2 tensor, see above for its components. The dot **·** indicates tensor contraction. |
+-----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------+
| Force and Newton\'s 2nd law | Resultant force acts on a system at the center of mass, equal to the rate of change of momentum: | Torque |
| | | |
| | $\begin{align} \mathbf{F} & = \frac{d\mathbf{p}}{dt} = \frac{d(m\mathbf{v})}{dt} \\ | Torque **τ** is also called moment of a force, because it is the rotational analogue to force: |
| | & = m\mathbf{a} + \mathbf{v}\frac{{\rm d}m}{{\rm d}t} \\ | |
| | \end{align}$ | $\boldsymbol{\tau} = \frac{{\rm d}\mathbf{L}}{{\rm d}t} = \mathbf{r}\times\mathbf{F} = \frac{{\rm d}(\mathbf{I} \cdot \boldsymbol{\omega})}{{\rm d}t}$ |
| | | |
| | For a number of particles, the equation of motion for one particle *i* is: | For rigid bodies, Newton\'s 2nd law for rotation takes the same form as for translation: |
| | | |
| | $\frac{\mathrm{d}\mathbf{p}_i}{\mathrm{d}t} = \mathbf{F}_{E} + \sum_{i \neq j} \mathbf{F}_{ij}$ | $\begin{align} |
| | | \boldsymbol{\tau} & = \frac{{\rm d}\mathbf{L}}{{\rm d}t} = \frac{{\rm d}(\mathbf{I}\cdot\boldsymbol{\omega})}{{\rm d}t} \\ |
| | where **p**~*i*~ = momentum of particle *i*, **F**~*ij*~ = force ***on*** particle *i* ***by*** particle *j*, and **F**~*E*~ = resultant external force (due to any agent not part of system). Particle *i* does not exert a force on itself. | & = \frac{{\rm d}\mathbf{I}}{{\rm d}t}\cdot\boldsymbol{\omega} + \mathbf{I}\cdot\boldsymbol{\alpha} \\ |
| | | \end{align}$ |
| | | |
| | | Likewise, for a number of particles, the equation of motion for one particle *i* is: |
| | | |
| | | $\frac{\mathrm{d}\mathbf{L}_i}{\mathrm{d}t} = \boldsymbol{\tau}_E + \sum_{i \neq j} \boldsymbol{\tau}_{ij}$ \|- valign=\"top\"\|-valign=\"top\" |
+-----------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------+
### Precession
The precession angular speed of a spinning top is given by:
$\boldsymbol{\Omega} = \frac{wr}{I\boldsymbol{\omega}}$
where *w* is the weight of the spinning flywheel.
## Energy
The mechanical work done by an external agent on a system is equal to the change in kinetic energy of the system:
### General work-energy theorem (translation and rotation) {#general_work_energy_theorem_translation_and_rotation}
The work done *W* by an external agent which exerts a force **F** (at **r**) and torque **τ** on an object along a curved path *C* is:
$W = \Delta T = \int_C \left ( \mathbf{F} \cdot \mathrm{d} \mathbf{r} + \boldsymbol{\tau} \cdot \mathbf{n} \, {\mathrm{d} \theta} \right )$
where θ is the angle of rotation about an axis defined by a unit vector **n**.
### Kinetic energy {#kinetic_energy}
The change in kinetic energy for an object initially traveling at speed $v_0$ and later at speed $v$ is: $\Delta E_k = W = \frac{1}{2} m(v^2 - {v_0}^2)$
### Elastic potential energy {#elastic_potential_energy}
For a stretched spring fixed at one end obeying Hooke\'s law, the elastic potential energy is
$\Delta E_p = \frac{1}{2} k(r_2-r_1)^2$
where *r*~2~ and *r*~1~ are collinear coordinates of the free end of the spring, in the direction of the extension/compression, and k is the spring constant.
## Euler\'s equations for rigid body dynamics {#eulers_equations_for_rigid_body_dynamics}
Euler also worked out analogous laws of motion to those of Newton, see Euler\'s laws of motion. These extend the scope of Newton\'s laws to rigid bodies, but are essentially the same as above. A new equation Euler formulated is:
$\mathbf{I} \cdot \boldsymbol{\alpha} + \boldsymbol{\omega} \times \left ( \mathbf{I} \cdot \boldsymbol{\omega} \right ) = \boldsymbol{\tau}$
where **I** is the moment of inertia tensor.
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## General planar motion {#general_planar_motion}
The previous equations for planar motion can be used here: corollaries of momentum, angular momentum etc. can immediately follow by applying the above definitions. For any object moving in any path in a plane,
$\mathbf{r} = \mathbf{r}(t) = r\hat\mathbf r$
the following general results apply to the particle.
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------+
| Kinematics | Dynamics |
+==================================================================================================================================================================================+===========================================================================================================================================+
| Position $\mathbf{r} =\mathbf{r}\left ( r,\theta, t \right ) = r \hat\mathbf r$ | |
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------+
| Velocity | Momentum $\mathbf{p} = m \left(\hat\mathbf r \frac{\mathrm{d} r}{\mathrm{d}t} + r \omega \hat\mathbf\theta \right)$ |
| | |
| $\mathbf{v} = \hat\mathbf r \frac{\mathrm{d} r}{\mathrm{d}t} + r \omega \hat\mathbf\theta$ | Angular momenta $\mathbf{L} = m \mathbf{r}\times \left(\hat\mathbf{r} \frac{\mathrm{d} r}{\mathrm{d}t} + r\omega\hat\mathbf\theta\right)$ |
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------+
| Acceleration | The centripetal force is |
| | |
| $\mathbf{a} =\left ( \frac{\mathrm{d}^2 r}{\mathrm{d}t^2} - r\omega^2\right )\hat\mathbf r + \left ( r \alpha + 2 \omega \frac{\mathrm{d}r}{{\rm d}t} \right )\hat\mathbf\theta$ | $\mathbf{F}_\bot = - m \omega^2 R \hat\mathbf r= - \omega^2 \mathbf{m}$ |
| | |
| | where again **m** is the mass moment, and the Coriolis force is |
| | |
| | $\mathbf{F}_c = 2\omega m \frac{{\rm d}r}{{\rm d}t} \hat\mathbf\theta = 2\omega m v \hat\mathbf\theta$ |
| | |
| | The Coriolis acceleration and force can also be written: |
| | |
| | $\mathbf{F}_c = m\mathbf{a}_c = -2 m \boldsymbol{ \omega \times v}$ |
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------+
### Central force motion {#central_force_motion}
For a massive body moving in a central potential due to another object, which depends only on the radial separation between the centers of masses of the two objects, the equation of motion is:
$\frac{d^2}{d\theta^2}\left(\frac{1}{\mathbf{r}}\right) + \frac{1}{\mathbf{r}} = -\frac{\mu\mathbf{r}^2}{\mathbf{l}^2}\mathbf{F}(\mathbf{r})$
## Equations of motion (constant acceleration) {#equations_of_motion_constant_acceleration}
These equations can be used only when acceleration is constant. If acceleration is not constant then the general calculus equations above must be used, found by integrating the definitions of position, velocity and acceleration (see above).
Linear motion Angular motion
-------------------------------------------------------------- ------------------------------------------------------------------------------------------------
$\mathbf{v-v_0}=\mathbf at$ $\boldsymbol{\omega - \omega_0} = \boldsymbol\alpha t$
$\mathbf{x - x_0} = \tfrac{1}{2}(\mathbf{v_0+v})t$ $\boldsymbol{\theta - \theta_0} = \tfrac{1}{2}(\boldsymbol{\omega_0 + \omega})t$
$\mathbf{x - x_0} = \mathbf v_0t+\tfrac{1}{2}\mathbf at^2$ $\boldsymbol{\theta - \theta_0} = \boldsymbol\omega _0 t + \tfrac{1}{2} \boldsymbol\alpha t^2$
$\mathbf x_{n^{th}} = \mathbf v_0+\mathbf a(n-\tfrac{1}{2})$ $\boldsymbol\theta_{n^{th}} =\boldsymbol\omega_0+\boldsymbol\alpha(n-\tfrac{1}{2})$
$v^2 - v_0^2 = 2\mathbf{a(x-x_0)}$ $\omega^2 - \omega_0^2 = 2\boldsymbol{\alpha(\theta-\theta_0)}$
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## Galilean frame transforms {#galilean_frame_transforms}
For classical (Galileo-Newtonian) mechanics, the transformation law from one inertial or accelerating (including rotation) frame (reference frame traveling at constant velocity - including zero) to another is the Galilean transform.
Unprimed quantities refer to position, velocity and acceleration in one frame F; primed quantities refer to position, velocity and acceleration in another frame F\' moving at translational velocity **V** or angular velocity **Ω** relative to F. Conversely F moves at velocity (---**V** or ---**Ω**) relative to F\'. The situation is similar for relative accelerations.
+---------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------+
| Motion of entities | Inertial frames | Accelerating frames |
+=============================================================================================+===========================================================================================================================================================================+=======================================================================================================+
| **Translation** | Relative position $\mathbf{r}' = \mathbf{r} + \mathbf{V}t$ | Relative accelerations $\mathbf{a}' = \mathbf{a} + \mathbf{A}$ |
| | | |
| **V** = Constant relative velocity between two inertial frames F and F\'.\ | Relative velocity $\mathbf{v}' = \mathbf{v} + \mathbf{V}$ | Apparent/fictitious forces $\mathbf{F}' = \mathbf{F} - \mathbf{F}_\mathrm{app}$ |
| **A** = (Variable) relative acceleration between two accelerating frames F and F\'.\ | | |
| | Equivalent accelerations $\mathbf{a}' = \mathbf{a}$ | |
+---------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------+
| **Rotation** | Relative angular position $\theta' = \theta + \Omega t$ Relative velocity $\boldsymbol{\omega}' = \boldsymbol{\omega} + \boldsymbol{\Omega}$ | Relative accelerations $\boldsymbol{\alpha}' = \boldsymbol{\alpha} + \boldsymbol{\Lambda}$ |
| | | |
| **Ω** = Constant relative angular velocity between two frames F and F\'.\ | Equivalent accelerations $\boldsymbol{\alpha}' = \boldsymbol{\alpha}$ | Apparent/fictitious torques $\boldsymbol{\tau}' = \boldsymbol{\tau} - \boldsymbol{\tau}_\mathrm{app}$ |
| **Λ** = (Variable) relative angular acceleration between two accelerating frames F and F\'. | | |
+---------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------+
| | Transformation of any vector **T** to a rotating frame $\frac{{\rm d}\mathbf{T}'}{{\rm d}t} = \frac{{\rm d}\mathbf{T}}{{\rm d}t} - \boldsymbol{\Omega} \times \mathbf{T}$ | |
+---------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------+
## Mechanical oscillators {#mechanical_oscillators}
SHM, DHM, SHO, and DHO refer to simple harmonic motion, damped harmonic motion, simple harmonic oscillator and damped harmonic oscillator respectively
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# Cursus honorum
The `{{langnf|la|'''cursus honorum'''|course of honors|paren=left}}`{=mediawiki}, or more colloquially \'ladder of offices\'; `{{IPA|la|ˈkʊrsʊs hɔˈnoːrũː|lang}}`{=mediawiki}) was the sequential order of public offices held by aspiring politicians in the Roman Republic and the early Roman Empire. It was designed for men of senatorial rank. The *cursus honorum* comprised a mixture of military and political administration posts; the ultimate prize for winning election to each \"rung\" in the sequence was to become one of the two consuls in a given year.
These rules were altered and flagrantly ignored in the course of the last century of the Republic. For example, Gaius Marius held consulships for five years in a row between 104 and 100 BC. He was consul seven times in all, also serving in 107 and 86. Officially presented as opportunities for public service, the offices often became mere opportunities for self-aggrandizement. The constitutional reforms of Sulla between 82 and 79 BC required a ten-year interval before holding the same office again for another term.
To have held each office at the youngest possible age (*suo anno*, \'in his year\') was considered a great political success. For instance, to miss out on a praetorship at 39 meant that one could not become consul at 42. Cicero expressed extreme pride not only in being a *\[\[novus homo\]\]* (\'new man\'; comparable to a \"self-made man\") who became consul even though none of his ancestors had ever served as a consul, but also in having become consul \"in his year\".
thumb\|upright=1.2\|The Roman *cursus honorum*
## Military service {#military_service}
Prior to entering political life and the *cursus honorum*, a young man of senatorial rank was expected to serve around ten years of military duty. The years of service were intended to be mandatory in order to qualify for political office.
Advancement and honors would improve his political prospects, and a successful military career might culminate in the office of military tribune, to which 24 men were elected by the Tribal Assembly each year. The rank of military tribune is sometimes described as the first office of the *cursus honorum*.
## Quaestor
The first official post was that of quaestor. Ever since the reforms of Sulla, candidates had to be at least 30 years old to hold the office. From the time of Augustus onwards, twenty quaestors served in the financial administration at Rome or as second-in-command to a governor in the provinces. They could also serve as the paymaster for a legion.
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# Cursus honorum
## Aedile
At 36 years of age, a promagistrate could stand for election to one of the aediles (pronounced `{{IPAc-en|ˈ|iː|d|aɪ|l}}`{=mediawiki} `{{respell|EE|dyle}}`{=mediawiki}, from *aedes*, \"temple edifice\") positions. Of these aediles, two were plebeian and two were patrician, with the patrician aediles called curule aediles. The plebeian aediles were elected by the Plebeian Council and the curule aediles were either elected by the Tribal Assembly or appointed by the reigning consul. The aediles had administrative responsibilities in Rome. They had to take care of the temples (whence their title, from the Latin *aedes*, \"temple\"), organize games, and be responsible for the maintenance of the public buildings in Rome. Moreover, they took charge of Rome\'s water and food supplies; in their capacity as market superintendents, they served sometimes as judges in mercantile affairs.
The aedile was the supervisor of public works; the words \"edifice\" and \"edification\" stem from the same root. He oversaw the public works, temples and markets. Therefore, the aediles would have been in some cooperation with the current censors, who had similar or related duties. Also, they oversaw the organization of festivals and games (*ludi*), which made this a very sought-after office for a career minded politician of the late Republic, as it was a good means of gaining popularity by staging spectacles. Curule aediles were added at a later date in the 4th century BC; their duties do not differ substantially from plebeian aediles. However, unlike plebeian aediles, curule aediles were allowed certain symbols of rank---the *sella curulis* or curule chair, for example---and only patricians could stand for election to curule aedile. This later changed, and both plebeians and patricians could stand for curule aedileship.
The elections for curule aedile were at first alternated between patricians and plebeians, until late in the 2nd century BC, when the practice was abandoned and both classes became free to run during all years.
While part of the *cursus honorum*, this step was optional and not required to hold future offices. Though the office was usually held after the quaestorship and before the praetorship, there are some cases with former praetors serving as aediles.
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# Cursus honorum
## Praetor
After serving either as quaestor or as aedile, a man of 39 years could run for praetor. During the reign of Augustus this requirement was lowered to 30, at the request of Gaius Maecenas. The number of praetors elected varied through history, generally increasing with time. During the republic, six or eight were generally elected each year to serve judicial functions throughout Rome and other governmental responsibilities. In the absence of the consuls, a praetor would be given command of the garrison in Rome or in Italy. Also, a praetor could exercise the functions of the consuls throughout Rome, but their main function was that of a judge. They would preside over trials involving criminal acts, grant court orders and validate \"illegal\" acts as acts of administering justice. A praetor was escorted by six lictors, and wielded *imperium*. After a term as praetor, the magistrate could serve as a provincial governor with the title of propraetor, wielding *propraetor imperium*, commanding the province\'s legions, and possessing ultimate authority within his province(s).
Two of the praetors were more prestigious than the others. The first was the Praetor Peregrinus, who was the chief judge in trials involving one or more foreigners. The other was the Praetor Urbanus, the chief judicial office in Rome. He had the power to overturn any verdict by any other courts, and served as judge in cases involving criminal charges against provincial governors. The Praetor Urbanus was not allowed to leave the city for more than ten days. If one of these two praetors was absent from Rome, the other would perform the duties of both.
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# Cursus honorum
## Consul
The office of consul was the most prestigious of all of the offices on the *cursus honorum*, and represented the summit of a successful career. The minimum age was 42. Years were identified by the names of the two consuls elected for a particular year; for instance, *M. Messalla et M. Pisone consulibus*, \"in the consulship of Messalla and Piso\", dates an event to 61 BC. Consuls were responsible for the city\'s political agenda, commanded large-scale armies and controlled important provinces. The consuls served for only a year (a restriction intended to limit the amassing of power by individuals) and could only rule when they agreed, because each consul could veto the other\'s decision.
The consuls would alternate monthly as the chairman of the Senate. They also were the supreme commanders in the Roman army, with each being granted two legions during their consular year. Consuls also exercised the highest juridical power in the Republic, being the only office with the power to override the decisions of the Praetor Urbanus. Only laws and the decrees of the Senate or the People\'s assembly limited their powers, and only the veto of a fellow consul or a tribune of the plebs could supersede their decisions.
A consul was escorted by twelve lictors, held *imperium* and wore the toga *praetexta*. Because the consul was the highest executive office within the Republic, they had the power to veto any action or proposal by any other magistrate, save that of the Tribune of the Plebs. After a consulship, a consul was assigned one of the more important provinces and acted as the governor in the same way that a propraetor did, only owning proconsular *imperium*. A second consulship could only be attempted after an interval of 10 years to prevent one man holding too much power.
## Governor
Although not part of the *cursus honorum*, upon completing a term as either praetor or consul, an officer was required to serve a term as propraetor and proconsul, respectively, in one of Rome\'s many provinces. These propraetors and proconsuls held near autocratic authority within their selected province or provinces. Because each governor held equal *imperium* to the equivalent magistrate, they were escorted by the same number of lictors (12) and could only be vetoed by a reigning consul or praetor. Their abilities to govern were only limited by the decrees of the Senate or the people\'s assemblies, and the Tribune of the Plebs was unable to veto their acts as long as the governor remained at least a mile outside of Rome.
## Censor
After a term as consul, the final step in the *cursus honorum* was the office of *censor*. This was the only office in the Roman Republic whose term was a period of eighteen months instead of the usual twelve. Censors were elected every five years and although the office held no military *imperium*, it was considered a great honour. The censors took a regular census of the people and then apportioned the citizens into voting classes on the basis of income and tribal affiliation. The censors enrolled new citizens in tribes and voting classes as well. The censors were also in charge of the membership roll of the Senate, every five years adding new senators who had been elected to the requisite offices. Censors could also remove unworthy members from the Senate. This ability was lost during the dictatorship of Sulla. Censors were also responsible for construction of public buildings and the moral status of the city.
Censors also had financial duties, in that they had to put out to tender projects that were to be financed by the state. Also, the censors were in charge of the leasing out of conquered land for public use and auction. Though this office owned no *imperium*, meaning no lictors for protection, they were allowed to wear the toga *praetexta*.
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# Cursus honorum
## Tribune of the Plebs {#tribune_of_the_plebs}
The office of Tribune of the Plebs was an important step in the political career of plebeians. Patricians could not hold the office. They were not an official step in the *cursus honorum*. The Tribune was an office first created to protect the right of the common man in Roman politics and served as the head of the Plebeian Council. In the mid-to-late Republic, however, plebeians were often just as, and sometimes more, wealthy and powerful than patricians. Those who held the office were granted sacrosanctity (the right to be legally protected from any physical harm), the power to rescue any plebeian from the hands of a patrician magistrate, and the right to veto any act or proposal of any magistrate, including another tribune of the people and the consuls. The tribune also had the power to exercise capital punishment against any person who interfered in the performance of his duties. The tribunes could even convene a Senate meeting and lay legislation before it and arrest magistrates. Their houses had to remain open for visitors even during the night, and they were not allowed to be more than a day\'s journey from Rome. Due to their unique power of sacrosanctity, the Tribune had no need for lictors for protection and owned no *imperium*, nor could they wear the toga *praetexta*. For a period after Sulla\'s reforms, a person who had held the office of Tribune of the Plebs could no longer qualify for any other office, and the powers of the tribunes were more limited, but these restrictions were subsequently lifted.
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# Cursus honorum
## *Princeps senatus* {#princeps_senatus}
Another office not officially a step in the *cursus honorum* was the *princeps senatus*, an extremely prestigious office for a patrician. The *princeps senatus* served as the leader of the Senate and was chosen to serve a five-year term by each pair of Censors every five years. Censors could, however, confirm a *princeps senatus* for a period of another five years. The *princeps senatus* was chosen from all Patricians who had served as a Consul, with former Censors usually holding the office. The office originally granted the holder the ability to speak first at session on the topic presented by the presiding magistrate, but eventually gained the power to open and close the senate sessions, decide the agenda, decide where the session should take place, impose order and other rules of the session, meet in the name of the senate with embassies of foreign countries, and write in the name of the senate letters and dispatches. This office, like the Tribune, did not own *imperium*, was not escorted by lictors, and could not wear the *toga praetexta*.
## Dictator and *magister equitum* {#dictator_and_magister_equitum}
Of all the offices within the Roman Republic, none granted as much power and authority as the position of dictator, known as the Master of the People. In times of emergency, the Senate would declare that a dictator was required, and the current consuls would appoint a dictator. This was the only decision that could not be vetoed by the Tribune of the Plebs. The dictator was the sole exception to the Roman legal principles of having multiple magistrates in the same office and being legally able to be held to answer for actions in office. Essentially by definition, only one dictator could serve at a time, and no dictator could ever be held legally responsible for any action during his time in office for any reason.
The dictator was the highest magistrate in degree of *imperium* and was attended by twenty-four lictors (as were the former Kings of Rome). Although his term lasted only six months instead of twelve (except for the Dictatorships of Sulla and Caesar), all other magistrates reported to the dictator (except for the tribunes of the plebs -- although they could not veto any of the dictator\'s acts), granting the dictator absolute authority in both civil and military matters throughout the Republic. The dictator was free from the control of the Senate in all that he did, could execute anyone without a trial for any reason, and could ignore any law in the performance of his duties. The dictator was the sole magistrate under the Republic that was truly independent in discharging his duties. All of the other offices were extensions of the Senate\'s executive authority and thus answerable to the Senate. Since the dictator exercised his own authority, he did not suffer this limitation, which was the cornerstone of the office\'s power.
When a dictator entered office, he appointed to serve as his second-in-command a *magister equitum*, the Master of the Horse, whose office ceased to exist once the dictator left office. The *magister equitum* held *praetorian imperium*, was attended by six lictors, and was charged with assisting the dictator in managing the State. When the dictator was away from Rome, the *magister equitum* usually remained behind to administer the city. The *magister equitum*, like the dictator, had unchallengeable authority in all civil and military affairs, with his decisions only being overturned by the dictator himself.
The dictatorship was definitively abolished in 44 BC after the assassination of Gaius Julius Caesar (*Lex Antonia*)
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# Craps
crap}} `{{redirect|Snake-eyes|other uses|Snake Eyes (disambiguation)}}`{=mediawiki} `{{Multiple issues|
{{Overly detailed|date=May 2020}}
{{Cleanup MOS|article|, , |date=December 2022}}
}}`{=mediawiki} `{{Infobox game
| title = Craps
| subtitle =
| image_link = Marines_and_sailors_attended_5th_annual_Casino_Royale_event_130928-M-WI309-003.jpg
| image_caption = A craps table with a game in progress
| image_size = 350px
| other_names = Seven-Eleven
| players =
| genre = [[Dice game]]
| ages =
| deck =
| origin =
| related =
| playing_time =
| random_chance = High
| skills =
| footnotes =
}}`{=mediawiki}
**Craps** is a dice game in which players bet on the outcomes of the roll of a pair of dice. Players can wager money against each other (playing \"street craps\") or against a bank (\"casino craps\"). Because it requires little equipment, \"street craps\" can be played in informal settings. While shooting craps, players may use slang terminology to place bets and actions.
## History
Craps developed in the United States from a simplification of the western European game of Hazard, also spelled Hazzard or Hasard. The origins of Hazard are obscure and may date to the Crusades; a detailed description of Hazard was provided by Edmond Hoyle in *Hoyle\'s Games, Improved* (1790). At approximately the same time (1788), \"Krabs\" was documented as a French variation on Hazard.
In aristocratic London, crabs was the epithet for the sum combinations of two and three for two rolled dice, which in Hazard are instant-losing numbers for the first dice roll, regardless of the shooter\'s selected main number. The name craps is derived from the corruption of this term crabs (or Krabs) to creps and then craps.
According to some accounts, Hazard was brought from London to New Orleans in approximately 1805 by the returning Bernard Xavier Philippe de Marigny de Mandeville, the young gambler and scion of a family of wealthy landowners in colonial Louisiana. Hazard allows the dice shooter to choose any number from five to nine as their \"main\" number; in a pamphlet published in 1933, Edward Tinker claimed that Marigny simplified the game by making the main always seven, which is the mathematically optimal choice, i.e., the choice with the lowest disadvantage for the shooter. However, more recent research indicates that Marigny played an unmodified version of Hazard, which had been played in America since at least the 1600s. Instead, John Scarne credits anonymous Black American inventors with simplifying and streamlining Hazard, increasing the pace of the game and adding a variety of wagers.
Regardless of who deserves credit for simplifying Hazard, the game initially was called Pass from the French word *pas* (meaning \"pace\" or \"step\"), and was popularized by the underclass starting in the early 19th century. Field hands taught their friends and deckhands, who carried the new game up the Mississippi River and its tributaries, although the game was never popular amongst the riverboat gamblers. Marigny gave the name Rue de Craps to a street in his new subdivision in New Orleans; in that city, craps experienced a resurgence of popularity in the late 1830s, but was not played in gaming houses until the 1890s. Budd Theobald credits the cultural exchange between attendants and railroad passengers on Pullman cars for popularizing the game, which eventually spread throughout America by the 1910s, when it was described as \"the gambling game of \[the country\]\" in *Foster\'s Complete Hoyle* (1914).
The craps numbers of 2, 3, and 12 are similarly derived from Hazard. If the main is seven, then the two-dice sum of twelve is added to the crabs as a losing number on the first dice roll. This condition is retained in the simplified game called Pass. All three losing numbers (2, 3, and 12) on the first roll of Pass are jointly called the craps numbers. The central game Pass gradually has been supplemented over the decades by many companion games and wagers which can be played simultaneously with Pass; these are now collectively known as craps.
Early versions of bank craps played in casinos made money either by charging a commission to shooters or offering short odds on the various wagers, primarily on the \"Pass line\" bet for the shooter to win against the house. In approximately 1907, a dicemaker named John H. Winn in Philadelphia introduced a layout which featured a space to wager on \"Don\'t Pass\" (i.e., for the shooter to lose) in addition to \"Pass\". Virtually all modern casinos use his innovation, which incentivizes casinos to use fair dice. As introduced by Winn, \"Don\'t Pass\" bets were taken with a 5 percent commission to ensure the house retained an edge in running the game; this was replaced by the Bar-3 push for \"Don\'t Pass\", and later by the Bar-12 (or Bar-2) push.
Craps exploded in popularity during World War II, which brought most young American men of every social class into the military. The street version of craps was popular among service members who often played it using a blanket as a shooting surface. Their military memories led to craps becoming the dominant casino game in postwar Las Vegas and the Caribbean.
After 1960, a few casinos in Europe, Australia, and Macau began offering craps, and, after 2004, online casinos extended the game\'s spread globally. Craps has been featured in a number of newer casinos, including the idea of expanding into formerly unavailable locals on the coastline.
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# Craps
## Bank craps {#bank_craps}
Bank craps or casino craps is played by one or more players betting against the casino rather than each other. Both the players and the dealers stand around a large rectangular craps table. Sitting is discouraged by most casinos unless a player has medical reasons for requiring a seat.
The basic flow of a single game is:
1. The *shooter* wagers to *pass* (win) and then makes an initial *come-out* roll with two six-sided dice.
```{=html}
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```
1. If the come-out roll is 7 or 11, that is a *natural* and the shooter has a *pass* (wins); the game is over.
2. If the come-out roll is 2, 3, or 12, that is a *crap* and the shooter has a *missout* (loses); the game is over.
3. If the come-out roll is any other number (4, 5, 6, 8, 9, or 10), that value becomes the shooter\'s *point*.
If a point has been set, the shooter continues to roll until either:
1. A subsequent roll matches the point and the shooter has a *pass* (wins); or
2. A subsequent roll is 7 and the shooter has a *missout* (loses).
Once a point is set and a missout occurs, the dice are passed to the person on the shooter\'s left, who becomes the new shooter.
### Craps table {#craps_table}
thumb\|center\|upright=4\|The layout of a craps table, sometimes called a *double-side dealer* Players use casino chips rather than cash to bet on the Craps \"layout\", a fabric surface which displays the various bets. The bets vary somewhat among casinos in availability, locations, and payouts. The tables roughly resemble bathtubs and come in various sizes. In some locations, chips may be called checks, tokens, or plaques.
Against one long side is the casino\'s table bank: as many as two thousand casino chips in stacks of 20. The opposite long side is usually a long mirror. The U-shaped ends of the table have duplicate layouts and standing room for approximately eight players. In the center of the layout is an additional group of side bets which are used by players from both ends. The vertical walls at each end are usually covered with a rubberized target surface covered with small pyramid shapes to randomize the dice which strike them. The top edges of the table walls have one or two horizontal grooves in which players may store their reserve chips.
The table is run by up to four casino employees: a ***boxman*** seated (usually the only seated employee) behind the casino\'s bank, who manages the chips, supervises the dealers, and handles \"coloring up\" players (exchanging small chip denominations for larger denominations in order to preserve the chips at a table); two ***base dealers**\'\' who stand to either side of the boxman and collect and pay bets to players around their half of the table; and a***stickman**\'\' who stands directly across the table from the boxman, takes and pays (or directs the base dealers to do so) the bets in the center of the table, announces the results of each roll (usually with a distinctive patter), and moves the dice across the layout with an elongated wooden stick.
Each employee also watches for mistakes by the others because of the sometimes large number of bets and frantic pace of the game. In smaller casinos or at quiet times of day, one or more of these employees may be missing, and have their job covered by another, or cause player capacity to be reduced.
Some smaller casinos have introduced \"mini-craps\" tables which are operated with only two dealers; rather than being two essentially identical sides and the center area, a single set of major bets is presented, split by the center bets. Responsibility of the dealers is adjusted: while the stickman continues to handle the center bets, it is the base dealer who handles all other bets (as well as cash and chip exchanges).
By contrast, in \"street craps\", there is no marked table and often the game is played with no back-stop against which the dice are to hit. Despite the name \"street craps\", this game is often played in houses, usually on an un-carpeted garage or kitchen floor. The wagers are made in cash, never in chips, and are usually thrown down onto the ground or floor by the players. There are no attendants, and so the progress of the game, fairness of the throws, and the way that the payouts are made for winning bets are self-policed by the players.
### Dice
thumb\|right\|upright=1.2\|These *perfect dice* from the Tropicana Atlantic City have been retired by drilling a hole completely through between the 1-6 faces; the four-digit serial number on the 6 face has been partially obliterated, but it started and ended with a 4. The dice used at casinos for craps and many other games are sometimes called *perfect* or *gambling house dice*. These are generally made from translucent extruded cellulose, with perfectly square edges each 3/4 ± in length, with pips drilled 17 ± deep and filled with opaque paint matching the density of cellulose, which ensures the dice remain balanced. The dice are buffed and polished to a high glossy finish after the pips are set, and the edges usually are left sharp, also called square or razor edge. To discourage cheating and dice substitution, each die carries a serial number and the casino\'s logo or name. New Jersey specifies the maximum size of the die is 0.775 in on a side.
Under New Jersey regulations, the shooter selects two dice from a set of at least five.
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# Craps
## Bank craps {#bank_craps}
### Rules of play {#rules_of_play}
Each casino may set which bets are offered and different payouts for them, though a core set of bets and payouts is typical. Players take turns rolling two dice and whoever is throwing the dice is called the \"shooter\". Players can bet on the various options by placing chips directly on the appropriately-marked sections of the layout, or asking the base dealer or stickman to do so, depending on which bet is being made.
While acting as the shooter, a player must have a bet on either the \"Pass\" or the \"Don\'t Pass\" line or both. \"Pass\" and \"Don\'t Pass\" are sometimes called \"Win\" and \"Lose\", \"Do\" and \"Don\'t\", or \"Right\" and \"Wrong\". The game is played in rounds and these \"Pass\" and \"Don\'t Pass\" bets are betting on the outcome of a single round. The shooter is presented with multiple dice (typically five) by the \"stickman\", and must choose two for the round. The remaining dice are returned to the stickman\'s bowl and are not used.
Each round has two phases: \"come-out\" and \"point\". Dice are passed to the left.
#### Phase 1 (Come-out) {#phase_1_come_out}
To start a round, the shooter makes one or more \"come-out\" rolls. While the come-out roll may specifically refer to the first roll of a new shooter, any roll where no point is established may be referred to as a come-out. By this definition the start of any new round regardless of whether it is the shooter\'s first toss can be referred to as a come-out roll. The shooter must shoot toward the farther back wall and is generally required to hit the farther back wall with both dice. Casinos may allow a few warnings before enforcing the dice to hit the back wall and are generally lenient if at least one die hits the back wall. Both dice must be tossed in one throw. If only one die is thrown the shot is invalid.
A come-out roll of 2, 3, or 12 is called \"craps\" or \"crapping out\", and anyone betting the Pass line loses. On the other hand, anyone betting the Don\'t Pass line on come out wins with a roll of 2 or 3 and ties (pushes) if a 12 is rolled; in some rules, the 2 pushes instead of the 12, in which case the 3 and 12 win a Don\'t Pass bet. Shooters may keep rolling after crapping out; the dice are only required to be passed if a shooter sevens out (rolls a seven after a point has been established). A come-out roll of 7 or 11 is a \"natural\"; the Pass line wins and Don\'t Pass loses. The other possible numbers are the point numbers: 4, 5, 6, 8, 9, and 10. If the shooter rolls one of these numbers on the come-out roll, this establishes the \"point\" -- to \"pass\" or \"win\", the point number must be rolled again before a seven.
#### Phase 2 (Point) {#phase_2_point}
The dealer flips a button to the \"On\" side and moves it to the point number signifying the second phase of the round. If the shooter \"hits\" the point value again (any value of the dice that sum to the point will do; the shooter does not have to exactly repeat the exact combination of the come-out roll) before rolling a seven, the Pass line wins and a new round starts. If the shooter rolls any seven before repeating the point number (a \"seven-out\"), the Pass line loses, the Don\'t Pass line wins, and the dice pass clockwise to the next new shooter for the next round. Once a point has been established, any multi-roll bets (including line bets and odds for Pass, Don\'t Pass, or both) are unaffected by the 2, 3, 11, or 12; the only numbers which affect the round are the established point, any specific bet on a number, or any 7. Any single roll bet is always affected (win or lose) by the outcome of any roll.
Phase 1 (\"Come-out\")
------------------------ --------------------- -------------------------------------------------------------
Come-out roll Initial outcome Subsequent roll(s), after point is established
2
2 Craps (Don\'t Pass) colspan=11 style=\"background:#faa;\" `{{N/A}}`{=mediawiki}
3 Craps (Don\'t Pass) colspan=11 style=\"background:#faa;\" `{{N/A}}`{=mediawiki}
4 Point 4 Reroll
5 Point 5 Reroll
6 Point 6 Reroll
7 Natural (Pass) colspan=11 style=\"background:#afa;\" `{{N/A}}`{=mediawiki}
8 Point 8 Reroll
9 Point 9 Reroll
10 Point 10 Reroll
11 Natural (Pass) colspan=11 style=\"background:#afa;\" `{{N/A}}`{=mediawiki}
12 Craps (Don\'t Pass) colspan=11 style=\"background:#faa;\" `{{N/A}}`{=mediawiki}
: Summary of rolls during a single round
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# Craps
## Bank craps {#bank_craps}
### Rules of play {#rules_of_play}
#### Basic wagering rules {#basic_wagering_rules}
Any player can make a bet on Pass or Don\'t Pass as long as a point has not been established, or Come or Don\'t Come as long as a point is established. All other bets, including an increase in odds behind the Pass and Don\'t Pass lines, may be made at any time. All bets other than Pass line and Come may be removed or reduced any time before the bet loses. This is known as \"taking it down\" in craps.
The maximum bet for Place, Buy, Lay, Pass, and Come bets are generally equal to table maximum. Lay bet maximum are equal to the table maximum win, so players wishing to lay the 4 or 10 may bet twice that amount of the table maximum for the win to be table maximum. Odds behind Pass, Come, Don\'t Pass, and Don\'t Come may be however larger than the odds offered allows and can be greater than the table maximum in some casinos. Don\'t odds are capped on the maximum allowed win. Some casino allow the odds bet itself to be larger than the maximum bet allowed as long as the win is capped at maximum odds. Single rolls bets can be lower than the table minimum, but the maximum bet allowed is also lower than the table maximum. The maximum allowed single roll bet is based on the maximum allowed win from a single roll.
In all the above scenarios, whenever the Pass line wins, the Don\'t Pass line loses, and vice versa, with one exception: on the come-out roll, a roll of 12 will cause Pass Line bets to lose, but Don\'t Pass bets are pushed (or \"barred\"), neither winning nor losing; this is done to establish a house edge for Don\'t Pass bets. (The same applies to \"Come\" and \"Don\'t Come\" bets, discussed below.)
### Joining a game {#joining_a_game}
A player wishing to play craps without being the shooter should approach the craps table and first check to see if the dealer\'s \"On\" button is on any of the point numbers.
- If the button has been turned to \"Off\", then the table is in the come-out phase, and a point has not been established.
- If the dealer\'s button is \"On\", the table is in the point phase where casinos will allow odds behind an existing Pass line to be bet. Some casino do not allow new Pass line bets while a point has been established. Some casinos will place the bet straddling the outer border of the Pass line so as to indicate that it is to be paid the same odds as a place bet, instead of just even money. Other casinos will take the bet on the Pass line after a point has been established, known as put betting, which is a disadvantage to the player (since the seven is the most common roll and likely to happen before the \"point\").
In either case, all single or multi-roll proposition bets may be placed in either of the two phases.
Between dice rolls there is a period for dealers to make payouts and collect losing bets, after which players can place new bets. The stickman monitors the action at a table and decides when to give the shooter the dice, after which no more betting is allowed.
When joining the game, one should place money on the table rather than passing it directly to a dealer. The dealer\'s exaggerated movements during the process of \"making change\" or \"change only\" (converting currency to an equivalent in casino cheques) are required so that any disputes can be later reviewed against security camera footage.
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# Craps
## Bank craps {#bank_craps}
### Rolling
The dealers will insist that the shooter roll with one hand and that the dice bounce off the far wall surrounding the table. These requirements are meant to keep the game fair (preventing switching the dice or making a \"controlled shot\"). If a die leaves the table, the shooter will usually be asked to select another die from the remaining three but can request permission to use the same die if it passes the boxman\'s inspection. This requirement exists to keep the game fair and reduce the chance of loaded dice.
### Names of rolls {#names_of_rolls}
+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
| | B:1\ | B:2\ | B:3\ | B:4\ | B:5\ | B:6\ |
| | `{{die|1}}`{=mediawiki} | `{{die|2}}`{=mediawiki} | `{{die|3}}`{=mediawiki} | `{{die|4}}`{=mediawiki} | `{{die|5}}`{=mediawiki} | `{{die|6}}`{=mediawiki} |
+=========================+=========================+=========================+=========================+=========================+=========================+=========================+
| A:1\ | Snake Eyes | | | | | |
| `{{die|1}}`{=mediawiki} | | | | | | |
+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
| A:2\ | Ace Deuce | Hard Four | | | | |
| `{{die|2}}`{=mediawiki} | | | | | | |
+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
| A:3\ | Easy Four | Five (Fever Five) | Hard Six | | | |
| `{{die|3}}`{=mediawiki} | | | | | | |
+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
| A:4\ | Five (Fever Five) | Easy Six | Natural/Seven Out | Hard Eight | | |
| `{{die|4}}`{=mediawiki} | | | | | | |
+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
| A:5\ | Easy Six | Natural/Seven Out | Easy Eight | Nine (Nina) | Hard Ten | \| |
| `{{die|5}}`{=mediawiki} | | | | | | |
+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
| A:6\ | Natural/Seven Out | Easy Eight | Nine (Nina) | Easy Ten | Yo (Yo-leven) | Boxcars/Midnight |
| `{{die|6}}`{=mediawiki} | | | | | | |
+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+-------------------------+
: Names of Rolls in Craps
There are many local variants of the calls made by the stickman for rolls during a craps game. These frequently incorporate a reminder to the dealers as to which bets to pay or collect.
Two --- \"Snake Eyes\", \"Two Craps Two\", \"Double Aces\", \"Loose Deuce\", \"Snickies\"
: The two ones that compose it look like a pair of small, beady eyes. During actual play, more common terms are \"two craps two\" during the comeout roll because the Pass line bet is lost on a comeout crap roll and/or because a bet on any craps would win. \"Aces; double the field\" would be a more common call when not on the comeout roll to remind the dealers to pay double on the field bets and encourage the field bettor to place subsequent bets and/or when no crap bets have been placed. Another name for the two is \"loose deuce\" or \"Snickies\" due to it sounding like \"Snake eyes\" but spoken with an accent.
Three --- \"Three Craps Three\", \"Ace Deuce\", \"Tracy\", \"Acey Deucy\"
: Typically called as \"three craps three\" during the comeout roll, or \"three, ace deuce, come away single\" when not on the comeout to signify the come bet has been lost and to pay single to any field bettors. Three may also be referred to as \"ace caught a deuce\", \"Tracy\", or even less often \"acey deucey\".
Four (hard) --- \"Little Joe\", \"Joe\", \"Little Dick\", \"Little Joe from Kokomo\", \"Little Joe on the Front Row\", \"Ballerina\"
: usually hard, is sometimes referred to as \"Little Joe from Kokomo\" or \"Little Joe on the front row\" or just \"Little Joe\". A hard four can be called a \"ballerina\" because it is two-two (\"tutu\").
Five --- \"Phoebe\", \"Fever in the South\", \"West Kentucky\", \"No Field Five\", \"Fever\"
: is frequently called \"no field five\" in casinos in which five is not one of the field rolls and thus not paid in the field bets. Other names for a five are \"fever\" and \"little Phoebe\".
Six --- \"Jimmie Hicks\", \"Jimmie Hicks from the Sticks\", \"666 Winner 6\", \"Sixty Days\", \"Sice\"
: may be referred to as \"Jimmie Hicks\" or \"Jimmie Hicks from the sticks\", examples of rhyming slang. On a win, the six is often called \"666 winner 6\" followed by \"came hard\" or \"came easy\".
Seven --- \"Six Ace\", \"Up Pops the Devil\", \"Up Jumped the Devil\", \"Big Red\", \"Seven Out\", \"Seven Out Seven\"
: rolled as 6--1 is sometimes called \"six ace\" or \"up pops the Devil\". Older dealers and players may use the term \"Big Red\" because craps tables once prominently featured a large red \"7\" in the center of the layout for the one-roll seven bet. During the comeout, the seven is called \"seven, front line winner\", frequently followed by \"pay the line\" and/or \"take the don\'ts\". After the point is established, a seven is typically called by simply \"7 out\" or \"7 out 7\"..
Eight (hard) --- \"Eighter from Decatur\", \"Ada from Decatur\", \"Square Pair\", \"Mom and Dad\", \"Ozzie and Harriet\"
: rolled the hard way, as opposed to an \"easy eight\", is sometimes called an \"eighter from Decatur\". It can also be known as a \"square pair\", \"mom and dad\", or \"Ozzie and Harriet\".
Nine --- \"Centerfield Nine\", \"Railroad Nine\", \"Jesse James\", \"Nina from Pasadena\", \"Nina at the Marina\", \"Niner from Carolina\", Old Mike\"
: is called a \"centerfield nine\" in casinos in which nine is one of the field rolls, because nine is the center number shown on the layout in such casinos (2--3--4--9--10--11--12). In Atlantic City, a 4--5 is called a \"railroad nine\". The 4--5 nine is also known as \"Jesse James\" because the outlaw Jesse James was killed by a .45 caliber pistol. Other names for the nine include \"Nina from Pasadena\", \"Nina at the Marina\", and \"niner from Carolina\". Nine can also be referred to as \"Old Mike\", named after NBA Hall-of-Famer Michael Jordan, who wore No. 9 in his FIBA international career, when players could only wear numbers 4 to 15.
Ten (hard) --- \"Big Dick\", \"Big Dick from Boston\", \"Big Dick the Ladies\' Friend\", \"Dos Equis\", \"Puppy Paws\", \"Pair of Sunflowers\", \"Big John\"
: the hard way is \"a hard ten\", \"dos equis\" (Spanish, meaning \"two X\'s\", because the pip arrangement on both dice on this roll resembles \"XX\"), or \"Hard ten -- a woman\'s best friend\", an example of both rhyming slang and sexual double entendre. Ten as a pair of 5\'s may also be known as \"puppy paws\" or \"a pair of sunflowers\" or \"Big Dick\" or \"Big John.\" Another slang for a hard ten is \"moose head\", because it resembles a moose\'s antlers. This phrase came from players in the Pittsburgh area.
Eleven --- \"Yo\", \"Yo-leven\", \"Six Five No Jive\"
: called out as \"yo\" or \"yo-leven\" to prevent being misheard as \"seven\". An older term for eleven is \"six five, no jive\" because it is a winning roll. During the comeout, eleven is typically followed by \"front line winner\". After the point is established, \"good field and come\" is often added.
Twelve --- \"Boxcars\", \"Midnight\", \"Double-action Field Traction\", \"12 Craps 12\"
: known as \"boxcars\" because the spots on the two dice that show 6--6 look like schematic drawings of railroad boxcars; it is also called \"midnight\", referring to twelve o\'clock; and also as \"double-action field traction\", because of the (standard) 2-to-1 pay on Field bets for this roll and the fact that the arrangement of the pips on the two dice, when laid end-to-end, resemble tire tracks. On tables that pay triple the field on a twelve roll, the stickman will often loudly exclaim \"triple\" either alone or in combination with \"12 craps 12\" or \"come away triple\".
Rolls of 4, 6, 8, and 10 are called \"hard\" or \"gag\", when rolled as a double, or \"easy\", when rolled with two different numbers. For example, rolls will be called \"six the hard way\", \"easy eight\", \"hard ten\", etc., because of their significance in center table bets known as the \"hard ways\". Hard way rolls are so named because there is only one way to roll them (i.e., the value on each die is the same when the number is rolled). Consequently, it is more likely to roll the number in different-number combinations (easy) rather than as a double (hard).
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# Craps
## Bet odds and summary {#bet_odds_and_summary}
: Note: Individual casinos may pay some of these bets at different payout ratios than those listed below. Some bets are listed more than once below -- the most common payout in North American casinos is listed first, followed by other known variants.
```{=html}
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```
: Note: \"True Odds\" do not vary.
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Bet | Type | True Odds | Odds Paid | House Edge | Single or Multi Roll | Win | Lose | Notes |
+=====================================+==========+==============+=========================+======================================================+======================+=============================================================================+=============================================================================+====================================================================================================================================================================================================================================================================================================================================================================+
| Pass / Come | Line | 251:244 | 1:1 | 1.41% | Multi | Come out roll: 7, 11. | Come out roll: 2, 3, 12. | Considered a \"contract bet\": once the point is established, the bet is locked until it wins or loses. See Optimal betting. Come uses only the come-out roll criteria (7, 11 to win \"come\") for a single roll after the point is established. |
| | | | | | | | | |
| | | | | | | Once the point is established: the point number (one of: 4, 5, 6, 8, 9, 10) | Once the point is established: 7 | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Don\'t Pass / Don\'t Come\ | Line | 976:949 | 1:1 | 1.36% | Multi | Come out roll: 2 (or 12, depending on Bar), 3 | Come out roll: 7, 11. | Controlled by the player: can be decreased at any time, but see Optimal betting. In some casinos, Bar-3 (1--2) is applied in lieu of either Bar-12 or Bar-2; this increases the house edge to 4.39%. Don\'t come uses only the come-out roll criteria (2, 3, 12 to win or tie \"don\'t come\", depending on Bar) for a single roll after the point is established. |
| (Bar-12 or Bar-2) | | | | | | | | |
| | | | | | | Tie: 12 (or 2, depending on Bar) | Once the point is established: the point number (one of: 4, 5, 6, 8, 9, 10) | |
| | | | | | | | | |
| | | | | | | Once the point is established: 7 | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Pass Odds / Come Odds | Line | Same as paid | 2:1 on 4,10; | 0% | Multi | Once the point is established: the point number (one of: 4, 5, 6, 8, 9, 10) | Once the point is established: 7 | Controlled by the player: can be increased or decreased at any time |
| | | | | | | | | |
| | | | 3:2 on 5,9; | | | | | |
| | | | | | | | | |
| | | | 6:5 on 6,8 | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Don\'t Pass Odds / Don\'t Come Odds | Line | Same as paid | 1:2 against 4,10; | 0% | Multi | Once the point is established: 7 | Once the point is established: the point number (one of: 4, 5, 6, 8, 9, 10) | Controlled by the player: can be increased or decreased at any time |
| | | | | | | | | |
| | | | 2:3 against 5,9; | | | | | |
| | | | | | | | | |
| | | | 5:6 against 6,8 | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | | | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Yo (11) | Prop | 17:1 | 15:1 | 11.11% | Single | 11 | Any other number | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| 3 | Prop | 17:1 | 15:1 | 11.11% | Single | 3 | Any other number | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| 2 | Prop | 35:1 | 30:1 | 13.89% | Single | 2 | Any other number | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| 12 | Prop | 35:1 | 30:1 | 13.89% | Single | 12 | Any other number | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Hi-Lo (2 or 12) | Prop | 17:1 | 15:1 | 11.11% | Single | 2 or 12 | Any other number | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Craps (2, 3, or 12) | Prop | 8:1 | 7:1 | 11.11% | Single | 2, 3, 12 | Any other number | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| C & E (the combined bet) | Prop | 5:1 | 3:1 on 2,3,12; | 11.11% | Single | 2, 3, 11, 12 | Any other number | |
| | | | | | | | | |
| | | | 7:1 on 11 | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Any 7 | Prop | 5:1 | 4:1 | 16.67% | Single | 7 | Any other number | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Field | Prop | 5:4 | 1:1 on 3,4,9,10,11; | 5.56% (2.78% if 12 pays 3:1, 0% if 2 and 12 pay 3:1) | Single | 2,3,4,9,10,11,12 | Any other number | Most common payout schedule. Some casinos pay 2:1 for 2 and 3:1 for 12, reducing house edge to 2.78%. A few pay both 2 and 12 at 3:1, eliminating the house edge. |
| | | | | | | | | |
| | | | 2:1 on 2,12 | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Horn (the combined bet) | Prop | 5:1 | 27:4 on 2,12; | 12.5% | Single | 2,3,11,12 | Any other number | |
| | | | | | | | | |
| | | | 3:1 on 3,11 | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Whirl/World (the combined bet) | Prop | 2:1 | 26:5 on 2,12; | 13.33% | Single | 2,3,7,11,12 | Any other number | |
| | | | | | | | | |
| | | | 11:5 on 3,11; | | | | | |
| | | | | | | | | |
| | | | 0:1 (push) on 7 | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | | | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Hard 4 / Hard 10 | Hard way | 8:1 | 7:1 | 11.11% | Multi | 4 as a pair (2-2) | 7 | In the UK and Australia, the payout is 7.5:1 lowering the house edge to 5.56%. |
| | | | | | | | | |
| | | | | | | 10 as a pair (5-5) | 4 as a non-pair (1--3) | |
| | | | | | | | | |
| | | | | | | | 10 as a non-pair (4--6) | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Hard 6 / Hard 8 | Hard way | 10:1 | 9:1 | 9.09% | Multi | 6 as a pair (3-3) | 7 | In the UK and Australia, the payout is 9.5:1 lowering the house edge to 4.55%. |
| | | | | | | | | |
| | | | | | | 8 as a pair (4-4) | 6 as a non-pair (1--5,2-4) | |
| | | | | | | | | |
| | | | | | | | 8 as a non-pair (2--6,3-5) | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Big 6 / Big 8 | Big 6/8 | 6:5 | 1:1 | 9.09% | Multi | 6/8 | 7 | Same true odds, better payout if the player places the 6/8 |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | | | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Place 4 / Place 10 | Place | 2:1 | 9:5 | 6.67% | Multi | 4/10 | 7 | Same true odds, better payout if the player buys the 4/10 |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Place 5 / Place 9 | Place | 3:2 | 7:5 | 4% | Multi | 5/9 | 7 | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Place 6 / Place 8 | Place | 6:5 | 7:6 | 1.52% | Multi | 6/8 | 7 | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | | | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Buy 4 / Buy 10 | Buy | 2:1 | 2:1 -5% of intended bet | 4.76% (1.67% if commission taken only on win) | Multi | 4/10 | 7 | Certain casinos such as Santa Ana Star Casino offer \"Free buy\" reducing house edge to 0% |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Buy 5 / Buy 9 | Buy | 3:2 | 3:2 -5% of intended bet | 4.76% (1.96% if commission taken only on win) | Multi | 5/9 | 7 | Same true odds, better payout if the player places the 5/9 |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Buy 6 / Buy 8 | Buy | 6:5 | 6:5 -5% of intended bet | 4.76% (2.22% if commission taken only on win) | Multi | 6/8 | 7 | Same true odds, better payout if the player places the 6/8 |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| | | | | | | | | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Lay 4 / Lay 10 | Lay | 1:2 | 1:2 -5% of intended win | 2.44% (1.67% if commission taken only on win) | Multi | 7 | 4/10 | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Lay 5 / Lay 9 | Lay | 2:3 | 2:3 -5% of intended win | 3.23% (2% if commission taken only on win) | Multi | 7 | 5/9 | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Lay 6 / Lay 8 | Lay | 5:6 | 5:6 -5% intended win | 4.00% (2.27% if commission taken only on win) | Multi | 7 | 6/8 | |
+-------------------------------------+----------+--------------+-------------------------+------------------------------------------------------+----------------------+-----------------------------------------------------------------------------+-----------------------------------------------------------------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
: Summary of wagers, true odds, and typical payouts
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# Craps
## Bet odds and summary {#bet_odds_and_summary}
The probability of dice combinations determine the odds of the payout. There are a total of 36 (6 × 6) possible combinations when rolling two dice. The following chart shows the dice combinations needed to roll each number. The two and twelve are the hardest to roll since only one combination of dice is possible. The game of craps is built around the dice roll of seven, since it is the most easily rolled dice combination.
thumb\|right\|upright=1.8\|Combinations of two dice, illustrated
Dice roll (sum) Possible dice combinations Probability
----------------- ---------------------------------------- ------------------------------
2 1--1
3 1--2, 2--1 =`{{frac|1|18}}`{=mediawiki}
4 1--3, 2--2, 3--1 =`{{frac|1|12}}`{=mediawiki}
5 1--4, 2--3, 3--2, 4--1 =`{{frac|1|9}}`{=mediawiki}
6 1--5, 2--4, 3--3, 4--2, 5--1
**7** **1--6, 2--5, 3--4, 4--3, 5--2, 6--1** =`{{frac|1|6}}`{=mediawiki}
8 2--6, 3--5, 4--4, 5--3, 6--2
9 3--6, 4--5, 5--4, 6--3 =`{{frac|1|9}}`{=mediawiki}
10 4--6, 5--5, 6--4 =`{{frac|1|12}}`{=mediawiki}
11 5--6, 6--5 =`{{frac|1|18}}`{=mediawiki}
12 6--6
: Combinations of two dice, with probability of occurrence
Viewed another way:
1 `{{die|1}}`{=mediawiki} 2 `{{die|2}}`{=mediawiki} 3 `{{die|3}}`{=mediawiki} 4 `{{die|4}}`{=mediawiki} 5 `{{die|5}}`{=mediawiki} 6 `{{die|6}}`{=mediawiki}
--------------------------- --------------------------- --------------------------- --------------------------- --------------------------- --------------------------- ---------------------------
1 `{{die|1}}`{=mediawiki} 2 3 4 5 6 **7**
2 `{{die|2}}`{=mediawiki} 3 4 5 6 **7** 8
3 `{{die|3}}`{=mediawiki} 4 5 6 **7** 8 9
4 `{{die|4}}`{=mediawiki} 5 6 **7** 8 9 10
5 `{{die|5}}`{=mediawiki} 6 **7** 8 9 10 11
6 `{{die|6}}`{=mediawiki} **7** 8 9 10 11 12
: Sum of two six-sided dice
The expected value of all bets is usually negative, such that the average player will always lose money. This is because the house always sets the paid odds to below the actual odds. The only exception is the \"odds\" bet that the player is allowed to make after a point is established on a pass/come Don\'t Pass/Don\'t Come bet (the odds portion of the bet has a long-term expected value of 0). However, this \"free odds\" bet cannot be made independently, so the expected value of the entire bet, including odds, is still negative. Since there is no correlation between die rolls, there is normally no possible long-term winning strategy in craps.
There are occasional promotional variants that provide either no house edge or even a player edge. One example is a field bet that pays 3:1 on 12 and 2:1 on either 3 or 11. Overall, given the 5:4 true odds of this bet, and the weighted average paid odds of approximately 7:5, the player has a 5% advantage on this bet. This is sometimes seen at casinos running limited-time incentives, in jurisdictions or gaming houses that require the game to be fair, or in layouts for use in informal settings using play money. No casino currently runs a craps table with a bet that yields a player edge full-time.
Maximizing the size of the odds bet in relation to the line bet will reduce, but never eliminate the house edge, and will increase variance. Most casinos have a limit on how large the odds bet can be in relation to the line bet, with single, double, and five times odds common. Some casinos offer 3--4--5 odds, referring to the maximum multiple of the line bet a player can place in odds for the points of 4 and 10, 5 and 9, and 6 and 8, respectively. During promotional periods, a casino may even offer 100× odds bets, which reduces the house edge to almost nothing, but dramatically increases variance, as the player will be betting in large betting units.
Since several of the multiple roll bets pay off in ratios of fractions on the dollar, it is important that the player bets in multiples that will allow a correct payoff in complete dollars. Normally, payoffs will be rounded down to the nearest dollar, resulting in a higher house advantage. These bets include all place bets, taking odds, and buying on numbers 6, 8, 5, and 9, as well as laying all numbers.
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# Craps
## Types of wagers {#types_of_wagers}
### Line bets {#line_bets}
The shooter is required to make either a Pass line bet or a Don\'t Pass bet if he wants to shoot. On the come out roll each player may only make one bet on the Pass or Don\'t Pass, but may bet both if desired. The Pass Line and Don\'t Pass bet is optional for any player not shooting. In rare cases, some casinos require all players to make a minimum Pass Line or Don\'t Pass bet (if they want to make any other bet), whether they are currently shooting or not.
\[\[<File:Craps> table diagram L.svg\|thumb\|right\|upright=2\|Left section of bank craps table, with spaces for common line and place bets. From top to bottom, these bets are:
- Don\'t Come (Bar-12) and Place 4 / 5 / 6 / 8 / 9 / 10
- Don\'t Pass (Bar-12) and Come
- Big 6, Big 8, and Field
- Don\'t Pass (Bar-12)
- Pass (wraps around to outside of diagram)
\]\]
#### Pass line {#pass_line}
The basic bet in craps is the Pass line bet, which is a bet for the shooter to win. This bet must be at least the table minimum and at most the table maximum.
- If the come-out roll is 7 or 11, the bet wins.
- If the come-out roll is 2, 3 or 12, the bet loses (known as \"crapping out\").
- If the roll is any other value, it establishes a point.
- If, with a point established, that point is rolled again before a 7, the bet wins.
- If, with a point established, a 7 is rolled before the point is rolled again (\"seven out\"), the bet loses.
The Pass line bet pays even money.
The Pass line bet is a contract bet. Once a Pass line bet is made, it is always working and cannot be turned \"Off\", taken down, or reduced until a decision is reached -- the point is made, or the shooter sevens out. A player may increase any corresponding odds (up to the table limit) behind the Pass line at any time after a point is established. Players may only bet the Pass line on the come out roll when no point has been established, unless the casino allows put betting where the player can bet Pass line or increase an existing Pass line bet whenever desired and may take odds immediately if the point is already on.
#### Don\'t Pass {#dont_pass}
A Don\'t Pass bet is a bet for the shooter to lose (\"seven out, line away\") and is almost the opposite of the Pass line bet. Like the Pass bet, this bet must be at least the table minimum and at most the table maximum.
- If the come-out roll is 3, the bet wins.
- If the come-out roll is 7 or 11, the bet loses.
- If the game is being played under \"Bar-12\" or \"Bar Sixes\":
- If the come-out roll is 2, the bet wins.
- If the come-out roll is 12, the bet is a push (neither won nor lost).
- Alternatively, if the game instead is played under \"Bar-2\" or \"Bar Aces\":
- If the come-out roll is 2, the bet is a push.
- If the come-out roll is 12, the bet wins.
- If the roll is any other value, it establishes a point.
- If, with a point established, a 7 is rolled before the point is rolled again (\"seven out\"), the bet wins.
- If, with a point established, that point is rolled again before a 7, the bet loses.
The Don\'t Pass bet pays even money.
The Don\'t Pass bet is a no-contract bet. After a point is established, a player may take down or reduce a Don\'t Pass bet and any corresponding odds at any time because odds of rolling a 7 before the point is in the player\'s favor. Once taken down or reduced, however, the Don\'t Pass bet may not be restored or increased. Because the shooter must have a line bet the shooter generally may not reduce a Don\'t Pass bet below the table minimum. In Las Vegas, a majority of casinos will allow the shooter to move the bet to the Pass line in lieu of taking it down; however, in other areas such as Pennsylvania and Atlantic City, this is not allowed. Even though players are allowed to remove the Don\'t Pass line bet after a point has been established, the bet cannot be turned \"Off\" without being removed. Players choosing to remove the Don\'t Pass line bet can no longer lay odds behind the Don\'t Pass line. The player can, however, still make standard lay bets on any of the point numbers (4, 5, 6, 8, 9, 10).
The casino chooses either Bar-2 or Bar-12, but not both. The push on 12 or 2 is mathematically necessary to maintain the house edge over the player. Other casinos allow the player to choose to either push on 2 (\"Bar Aces\") or push on 12 (\"Bar Sixes\") depending on where it is placed on the layout. Some older bank crap games used Bar-3 (\"Bar Ace-Deuce\"), which increases the house edge.
There are two different ways to calculate the odds and house edge of this bet. The summary table gives the numbers considering that the game ends in a push when a 12 is rolled, rather than being undetermined. Betting on Don\'t Pass is often called \"playing the dark side\", and it is considered by some players to be in poor taste, or even taboo, because it goes directly against conventional play, winning when most of the players lose.
#### Pass odds {#pass_odds}
If a 4, 5, 6, 8, 9, or 10 is thrown on the come-out roll (i.e., when a point is established), most casinos allow Pass line players to take odds by placing up to some predetermined multiple of the Pass line bet, behind the Pass line. This additional bet wins if the point is rolled again before a 7 is rolled (the point is made) and pays at the true odds:
- 2-to-1 if 4 or 10 is the point,
- 3-to-2 if 5 or 9 is the point, or
- 6-to-5 if 6 or 8 is the point.
Unlike the Pass line bet itself, the Pass line odds bet can be turned \"Off\" (not working), removed or reduced anytime before it loses. In Las Vegas, generally odds bets are required to be the table minimum. In Atlantic City and Pennsylvania, the combine odds and Pass bet must be table minimum so players can bet the minimum single unit on odds depending on the point. If the point is a 4 or 10, players can bet as little as \$1 on odds if the table minimum is low such as is \$5, \$10 or \$15. If the player requests the Pass odds be not working (\"Off\") and the shooter sevens-out or hits the point, the Pass line bet will be lost or doubled and the Pass odds returned.
Individual casinos (and sometimes tables within a casino) vary greatly in the maximum odds they offer, from single or double odds (one or two times the Pass line bet) up to 100× or even unlimited odds. A variation often seen is \"3-4-5× Odds\", where the maximum allowed odds bet depends on the point: three times if the point is 4 or 10; four times on points of 5 or 9; or five times on points of 6 or 8. This rule simplifies the calculation of winnings: a maximum Pass odds bet on a 3--4--5× table will always be paid at six times the Pass line bet regardless of the point.
As odds bets are paid at true odds, in contrast with the Pass line which is always even money, taking odds on a minimum Pass line bet lessens the house advantage compared with betting the same total amount on the Pass line only. A maximum odds bet on a minimum Pass line bet often gives the lowest house edge available in any game in the casino. However, the odds bet cannot be made independently, so the house retains an edge on the Pass line bet itself.
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# Craps
## Types of wagers {#types_of_wagers}
### Line bets {#line_bets}
#### Don\'t Pass odds {#dont_pass_odds}
If a player is playing Don\'t Pass instead of pass, they also may lay odds by placing chips behind the Don\'t Pass line. If a 7 comes before the point is rolled, the Don\'t Pass odds pay at true odds:
- 1-to-2 if 4 or 10 is the point,
- 2-to-3 if 5 or 9 is the point, or
- 5-to-6 if 6 or 8 is the point.
Typically the maximum lay bet will be expressed such that a player may win up to an amount equal to the maximum odds multiple at the table. If a player lays maximum odds with a point of 4 or 10 on a table offering five-times odds, he would be able to lay a maximum of ten times the amount of his Don\'t Pass bet. At 5× odds table, the maximum amount the combined bet can win will always be 6× the amount of the Don\'t Pass bet. Players can bet table minimum odds if desired and win less than table minimum.
Like the Don\'t Pass bet the odds can be removed or reduced. Unlike the Don\'t Pass bet itself, the Don\'t Pass odds can be turned \"Off\" (not working). In Las Vegas generally odds bets are required to be the table minimum. In Atlantic City and Pennsylvania, the combine lay odds and Don\'t Pass bet must be table minimum so players may bet as little as the minimum two units on odds depending on the point. If the point is a 4 or 10 players can bet as little as \$2 if the table minimum is low such as \$5, \$10 or \$15 tables. If the player requests the Don\'t Pass odds to be not working (\"Off\") and the shooter hits the point or sevens-out, the Don\'t Pass bet will be lost or doubled and the Don\'t Pass odds returned. Unlike a standard lay bet on a point, lay odds behind the Don\'t Pass line does not charge commission (vig).
#### Come bet {#come_bet}
A player making a Come bet is wagering on the first number that \"comes\" from the shooter\'s next roll, regardless of the table\'s phase. In other words, a Come bet can be considered as starting an entirely new Pass line bet, unique to that player.
- If a 7 or 11 is rolled on the shooter\'s next roll, the Come bet wins.
- If a 2, 3, or 12 is rolled on the shooter\'s next roll, the Come bet loses.
- If a 4, 5, 6, 8, 9, or 10 is rolled on the shooter\'s next roll, the number becomes the \"come-bet point\".
- The Come bet will be moved by the base dealer onto a box representing the same \"come-bet point\" number the shooter threw.
- If, with the Come-bet point established, that number is rolled during this second phase, the Come bet wins.
- If, with the Come-bet point established, a 7 is rolled during this second phase, the Come bet loses.
- The player is allowed to take odds on the Come-bet point, just like a Pass line bet.
The Come bet pays off at even money, like the Pass line bet.
Come bets can only be made after a point has been established since, on the come-out roll, a Come bet would be the same as a Pass line bet. Like the Pass line bet, each player may only make one Come bet per roll; this does not exclude a player from betting odds on an already established come-bet point. The Come bet must be at least the table minimum and at most the table maximum. Players may bet both the Come and Don\'t Come on the same roll if desired.
Also like a Pass line bet, the come bet is a contract bet and is always working, and cannot be turned \"Off\", removed or reduced until it wins or loses. However, the odds taken behind a Come bet can be turned \"Off\" (not working), removed or reduced anytime before the bet loses. In Las Vegas generally odds bets are required to be the table minimum. In Atlantic City and Pennsylvania, the combine odds and Pass bet must be table minimum so players can bet the minimum single unit depending on the point. If the point is a 4 or 10, players can bet as little as \$1 if the table minimum is low such as \$5, \$10, or \$15 minimums. If the player requests the Come odds to be not working (\"Off\") and the shooter sevens-out or hits the Come bet point, the Come bet will be lost or doubled and the Come odds returned. If the casino allows put betting a player may increase a Come bet after a point has been established and bet larger odds behind if desired. Put betting also allows a player to bet on a Come and take odds immediately on a point number without a Come bet point being established.
The dealer will place the odds on top of the come bet, but slightly off center in order to differentiate between the original bet and the odds. The second round wins if the shooter rolls the come bet point again before a seven. Winning come bets are paid the same as winning Pass line bets: even money for the original bet and true odds for the odds bet. If, instead, the seven is rolled before the come-bet point, the come bet (and any odds bet) loses.
Because of the come bet, if the shooter makes their point, a player can find themselves in the situation where they still have a come bet (possibly with odds on it) and the next roll is a come-out roll. In this situation, odds bets on the come wagers are usually presumed to be not working for the come-out roll. That means that if the shooter rolls a 7 on the come-out roll, any players with active come bets waiting for a come-bet point lose their initial wager but will have their odds bets returned to them.
If the come-bet point is rolled on the come-out roll, the odds do not win but the come bet does and the odds bet is returned (along with the come bet and its payoff). The player can tell the dealer that they want their odds working, such that if the shooter rolls a number that matches the come point, the odds bet will win along with the come bet, and if a seven is rolled, both lose.
Many players will use a come bet as \"insurance\" against sevening out: if the shooter rolls a seven, the come bet pays 1:1, offsetting the loss of the Pass line bet. The risk in this strategy is the situation where the shooter does not hit a seven for several rolls, leading to multiple come bets that will be lost if the shooter eventually sevens out.
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# Craps
## Types of wagers {#types_of_wagers}
### Line bets {#line_bets}
#### Don\'t Come bet {#dont_come_bet}
In the same way that a Come bet is similar to a Pass line bet, a Don\'t Come bet is similar to a Don\'t Pass bet. Like the Come, the Don\'t Come can only be bet after a point has already been established as it is the same as a Don\'t Pass line bet when no point is established. This bet must be at least the table minimum and at most the table maximum. A Don\'t Come bet is played in two phases, just like the Don\'t Pass line bet.
- If a 2 or 3 is rolled in the first phase, it wins.
- If a 7 or 11 is rolled, it loses.
- If a 12 is rolled, it is a push, assuming that Bar-12 is being followed; if Bar-2 is being followed, 2 instead is a push and 12 wins, in the same way as described above for the variants of the Don\'t Pass bet.
- If, instead, the roll is 4, 5, 6, 8, 9, or 10, this sets the Don\'t Come point.
- The base dealer will move the Don\'t Come bet onto a box representing the Don\'t Come point, i.e., the number the shooter threw.
- The second phase wins if the shooter rolls a seven before the Don\'t Come point.
Like the Don\'t Pass each player may only make one Don\'t Come bet per roll, this does not exclude a player from laying odds on an already established Don\'t Come points. Players may bet both the Don\'t Come and Come on the same roll if desired.
The player may lay odds on a Don\'t Come bet, just like a Don\'t Pass bet; in this case, the dealer (not the player) places the odds bet on top of the bet in the box, because of limited space, slightly offset to signify that it is an odds bet and not part of the original Don\'t Come bet. Lay odds behind a Don\'t Come are subject to the same rules as Don\'t Pass lay odds. Unlike a standard lay bet on a point, lay odds behind a Don\'t Come point does not charge commission (vig) and gives the player true odds. Like the Don\'t Pass line bet, Don\'t Come bets are no-contract, and can be removed or reduced after a Don\'t Come point has been established, but cannot be turned off (\"not working\") without being removed. A player may also call, \"No Action\" when a point is established, and the bet will not be moved to its point. This play is not to the player\'s advantage. If the bet is removed, the player can no longer lay odds behind the Don\'t Come point and cannot restore or increase the same Don\'t Come bet. Players must wait until next roll as long as a Pass line point has been established (players cannot bet Don\'t Come on come out rolls) before they can make a new Don\'t Come bet. Las Vegas casinos which allow put betting allows players to move the Don\'t Come directly to any Come point as a put; however, this is not allowed in Atlantic City or Pennsylvania. Unlike the Don\'t Come bet itself, the Don\'t Come odds can be turned \"Off\" (not working), removed, or reduced if desired. In Las Vegas, players generally must lay at least table minimum on odds if desired and win less than table minimum; in Atlantic City and Pennsylvania a player\'s combined bet must be at least table minimum, so depending on the point number players may lay as little as 2 minimum units (e.g. if the point is 4 or 10). If the player requests the Don\'t Come odds be not working (\"Off\") and the shooter hits the Don\'t Come point or sevens-out, the Don\'t Come bet will be lost or doubled and the Don\'t Come odds returned.
Winning Don\'t Come bets are paid the same as winning Don\'t Pass bets: even money for the original bet and true odds for the odds lay. Unlike come bets, the odds laid behind points established by Don\'t Come bets are always working including come out rolls unless the player specifies otherwise.
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# Craps
## Types of wagers {#types_of_wagers}
### Multi-roll bets {#multi_roll_bets}
These are bets that may not be settled on the first roll and may need one or more subsequent rolls before an outcome is determined.
Most multi-roll bets may fall into the situation where a point is made by the shooter before the outcome of the multi-roll bet is decided. These bets are often considered \"not working\" on the new come-out roll until the next point is established, unless the player calls the bet as \"working.\"
Casino rules vary on this; some of these bets may not be callable, while others may be considered \"working\" during the come-out. Dealers will usually announce if bets are working unless otherwise called off. If a non-working point number placed, bought or laid becomes the new point as the result of a come-out, the bet is usually refunded, or can be moved to another number for free.
#### Place
Players can bet any point number (4, 5, 6, 8, 9, 10) by placing their wager in the come area and telling the dealer how much and on what number(s), \"30 on the 6\", \"5 on the 5\", or \"25 on the 10\". These are typically \"Place Bets to Win\". These are bets that the number bet on will be rolled before a 7 is rolled, similar to the Pass odds bets. These bets are considered working bets, and will continue to be paid out each time a shooter rolls the number bet. On a come-out roll, a place bet is considered to be not in effect unless the player who made it specifies otherwise. This bet may be removed or reduced at any time until it loses; in the latter case, the player must abide by any table minimums.
Place bets to win pay out at slightly worse than the true odds: 9-to-5 on points 4 or 10, 7-to-5 on points 5 or 9, and 7-to-6 on points 6 or 8. The place bets on the outside numbers (4,5,9,10) should be made in units of \$5, (on a \$5 minimum table), in order to receive the correct exact payout of \$5 paying \$7 or \$5 paying \$9. The place bets on the 6 & 8 should be made in units of \$6, (on a \$5 minimum table), in order to receive the correct exact payout of \$6 paying \$7. For the 4 and 10, it is to the player\'s advantage to \'buy\' the bet (see below).
An alternative form, rarely offered by casinos, is the \"place bet to lose.\" This bet is the opposite of the place bet to win and pays off if a 7 is rolled before the specific point number. The place bet to lose typically carries a lower house edge than a place bet to win. Payouts are 4-to-5 on points 6 or 8, 5-to-8 on 5 or 9, and 5-to-11 on 4 or 10.
#### Buy
Players can also buy a bet which are paid at true odds, but a 5% commission is charged on the amount of the bet. Buy bets are placed with the shooter betting at a specific number will come out before a player sevens out. The buy bet must be at least table minimum excluding commission; however, some casinos require the minimum buy bet amount to be at least \$20 to match the \$1 charged on the 5% commission. Traditionally, the buy bet commission is paid no matter what, but in recent years a number of casinos have changed their policy to charge the commission only when the buy bet wins. Some casinos charge the commission as a one-time fee to buy the number; payouts are then always at true odds. Most casinos usually charge only \$1 for a \$25 green-chip bet (4% commission), or \$2 for \$50 (two green chips), reducing the house advantage a bit more. Players may remove or reduce this bet (bet must be at least table minimum excluding vig) anytime before it loses. Buy bets like place bets are not working when no point has been established unless the player specifies otherwise.
Where commission is charged only on wins, the commission is often deducted from the winning payoff---a winning \$25 buy bet on the 10 would pay \$49, for instance. The house edges stated in the table assume the commission is charged on all bets. They are reduced by at least a factor of two if commission is charged on winning bets only.
#### Lay
A lay bet is the opposite of a buy bet, where a player bets on a 7 to roll before the number that is laid. Players may only lay the 4, 5, 6, 8, 9, or 10 and may lay multiple numbers if desired. Just like the buy bet lay bets pay true odds, but because the lay bet is the opposite of the buy bet, the payout is reversed. Therefore, players get 1 to 2 for the numbers 4 and 10, 2 to 3 for the numbers 5 and 9, and 5 to 6 for the numbers 6 and 8. A 5% commission (vigorish, vig, juice) is charged up front on the possible winning amount. For example: A \$40 Lay Bet on the 4 would pay \$20 on a win. The 5% vig would be \$1 based on the \$20 win. (not \$2 based on the \$40 bet as the way buy bet commissions are figured.) Like the buy bet the commission is adjusted to suit the betting unit such that fraction of a dollar payouts are not needed. Casinos may charge the vig up front thereby requiring the player to pay a vig win or lose, other casinos may only take the vig if the bet wins. Taking vig only on wins lowers house edge. Players may removed or reduce this bet (bet must be at least table minimum) anytime before it loses. Some casinos in Las Vegas allow players to lay table minimum plus vig if desired and win less than table minimum. Lay bet maximums are equal to the table maximum win, so if a player wishes to lay the 4 or 10, he or she may bet twice at amount of the table maximum for the win to be table maximum. Other casinos require the minimum bet to win at \$20 even at the lowest minimum tables in order to match the \$1 vig, this requires a \$40 bet. Similar to buy betting, some casinos only take commission on win reducing house edge. Unlike place and buy bets, lay bets are always working even when no point has been established. The player must specify otherwise if he or she wishes to have the bet not working.
If a player is unsure of whether a bet is a single or multi-roll bet, it can be noted that all single-roll bets will be displayed on the playing surface in one color (usually red), while all multi-roll bets will be displayed in a different color (usually yellow).
#### Put
A put bet is a bet which allows players to increase or make a Pass line bet after a point has been established (after come-out roll). Players may make a put bet on the Pass line and take odds immediately or increase odds behind if a player decides to add money to an already existing Pass line bet. Put betting also allows players to increase an existing come bet for additional odds after a come point has been established or make a new come bet and take odds immediately behind if desired without a come bet point being established. If increased or added put bets on the Pass line and Come cannot be turned \"Off\", removed or reduced, but odds bet behind can be turned \"Off\", removed or reduced. The odds bet is generally required to be the table minimum. Player cannot put bet the Don\'t Pass or Don\'t Come. Put betting may give a larger house edge over place betting unless the casino offers high odds.
Put bets are generally allowed in Las Vegas, but not allowed in Atlantic City and Pennsylvania.
Put bets are better than place bets (to win) when betting more than 5-times odds over the flat bet portion of the put bet. For example, a player wants a \$30 bet on the six. Looking at two possible bets: 1) Place the six, or 2) Put the six with odds. A \$30 place bet on the six pays \$35 if it wins. A \$30 put bet would be a \$5 flat line bet plus \$25 (5-times) in odds, and also would pay \$35 if it wins. Now, with a \$60 bet on the six, the place bet wins \$70, where the put bet (\$5 + \$55 in odds) would pay \$71. The player needs to be at a table which not only allows put bets, but also high-times odds, to take this advantage.
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# Craps
## Types of wagers {#types_of_wagers}
### Multi-roll bets {#multi_roll_bets}
#### Hard way {#hard_way}
\[\[<File:Craps> table diagram C.svg\|thumb\|right\|upright=1.8\|Center section of craps table, with typical service bets, which in this generic diagram include, from top to bottom and left to right:
- Any seven
- Hard Six and Hard Ten
- Hard Eight and Hard Four
- Ace-Deuce (3), Snake Eyes (2), and Boxcars (12)
- Yo-leven (11) and Yo-leven (11)
- Any Craps (2, 3, or 12)
The C&E / E&C bets stand for Craps and Eleven (2, 3, 11, or 12).\]\] This bet can only be placed on the numbers 4, 6, 8, and 10. In order for this bet to win, the chosen number must be rolled the \"hard way\" (as doubles) before a 7 or any other non-double combination (\"easy way\") totaling that number is rolled. For example, a player who bets a hard 6 can only win by seeing a 3--3 roll come up before any 7 or any easy roll totaling 6 (4--2 or 5--1); otherwise, the player loses.
In Las Vegas casinos, this bet is generally working, including when no point has been established, unless the player specifies otherwise. In other casinos such as those in Atlantic City, hard ways are not working when the point is off unless the player requests to have it working on the come out roll.
Like single-roll bets, hard way bets can be lower than the table minimum; however, the maximum bet allowed is also lower than the table maximum. The minimum hard way bet can be a minimum one unit. For example, lower stake table minimums of \$5 or \$10, generally allow minimum hard ways bets of \$1. The maximum bet is based on the maximum allowed win from a single roll.
Easy way is not a specific bet offered in standard casinos, but a term used to define any number combination which has two ways to roll. For example, (6--4, 4--6) would be a \"10 easy\". The 4, 6, 8 or 10 can be made both hard and easy ways. Betting point numbers (which pays off on easy or hard rolls of that number) or single-roll (\"hop\") bets (e.g., \"hop the 2--4\" is a bet for the next roll to be an easy six rolled as a two and four) are methods of betting easy ways.
#### Big 6 and Big 8 {#big_6_and_big_8}
A player can wager on either the 6 or 8 being rolled before the shooter throws a seven. These wagers are usually avoided by experienced craps players since they create a large house edge by paying even money (1:1) while the true odds are 6:5; experienced players realize the house edge would be reduced by instead making place bets on the 6 or the 8, since those pay more (7:6) and are closer to the true odds. Some casinos (especially all those in Atlantic City) do not even offer the Big 6 & 8. The bets are located in the corners behind the Pass line, and bets may be placed directly by players.
The only real advantage offered by the Big 6 & 8 is that they can be bet for the table minimum, whereas a place bet minimum may sometimes be greater than the table minimum (e.g. \$6 place bet on a \$3 minimum game.) In addition place bets are usually not working, except by agreement, when the shooter is \"coming out\" i.e. shooting for a point, and Big 6 and 8 bets always work. Some modern layouts no longer show the Big 6/Big 8 bet.
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# Craps
## Types of wagers {#types_of_wagers}
### Single-roll bets {#single_roll_bets}
Single-roll (proposition) bets are resolved in one dice roll by the shooter. Most of these are called \"service bets\", and they are located at the center of most craps tables. Only the stickman or a dealer can place a service bet. Single-roll bets can be lower than the table minimum, but the maximum bet allowed is also lower than the table maximum. The maximum bet is based on the maximum allowed win from a single roll. The lowest single-roll bet can be a minimum one unit bet. For example, tables with minimums of \$5 or \$10 generally allow minimum single-roll bets of \$1. Single bets are always working by default unless the player specifies otherwise. The bets include:
2 (snake eyes, or Aces): Wins if shooter rolls a 2.\
3 (ace-deuce): Wins if the shooter rolls a 3.\
Yo: Wins if the shooter rolls 11.\
12 (boxcars, midnight, or cornrows): Wins if shooter rolls a 12.\
2 or 12 (hi-lo): Wins if shooter rolls a 2 or 12. The stickman places this bet on the line dividing the 2 and 12 bets.\
Any Craps (Three-Way): Wins if the shooter rolls 2, 3 or 12.\
C & E: A combined bet, a player is betting half their bet on craps (2,3,12) and the other half on 11 (yo). The combine payout is 3:1 on craps and 7:1 on 11 (yo). Another method of calculating the payout is to divide the total bet in half. The player would receive 7:1 minus half the total bet payout on half the total bet for craps and 15:1 minus half the total bet payout on half the total bet for 11 (yo). For example, using this method if a player were to bet \$2 on C & E, \$1 would receive 7:1 payout on craps minus \$1 for the bet on 11 so the total profit would be \$6. If an 11 was rolled the player would receive 15:1 minus \$1 for the bet on craps so the player\'s total profit is \$14. Both methods of calculation yield the same result so either method can be used. If a player wishes to take the bet down after a win the player would receive the whole bet not half even though only one of the two bets can win per roll. The minimum bet on C & E is double the lowest unit bet allowed at the table. So if the minimum single roll bet is \$1 the lowest C & E bet allowed would be \$2. Players are, however, able to make odd number bets larger than \$2 if desired. One of the two bets will always lose, the other may win.\
Any seven: A single roll bet which wins if the shooter rolls a 7 with 4:1 payout. This bet is also nicknamed Big Red, since the 7 on its betting space on the layout is usually large and red, and it is considered bad luck and a breach of etiquette among gamblers to speak the word \"seven\" at the table.\
Horn: This is a bet that involves betting on 1 unit each for 2, 3, 11, and 12 at the same time for the next roll. The bet is actually four separate bets, and pays off depending on which number is actually rolled. The combined payout is 27:4 for 2, 12 and 3:1 for 3, 11. Each individual bet has the same payout as a single bet on the specific numbers, 30:1 for 2 and 12 minus the other three bets, 15:1 for 3 and 11 minus the other three bets. If a player wins the bet he can take down all four bets instead of a single bet even though only one bet can win per roll. Many players, in order to eliminate the confusion of tossing four chips to the center of the table or having change made while bets are being placed, will make a five-unit Horn High bet, which is a four-way bet with the extra unit going to one specific number. For example, if one tosses a \$5 chip into the center and says \"horn high yo\", they are placing four \$1 bets on each of the horn numbers and the extra dollar will go on the yo (11). Horn bets are generally required to be in multiples of 4 or 5 with the minimum bet being 4 times the minimum unit allowed. For example, if the single roll minimum at the table is \$1 the Horn bet must be \$4 or more.\
Whirl or World: A five-unit bet that is a combination of a horn and any-seven bet, with the idea that if a seven is rolled the bet is a push, because the money won on the seven is lost on the horn portions of the bet. The combine odds are 26:5 on the 2, 12, 11:5 on the 3, 11, and a push on the 7. Like the C & E and Horn bet, if a player wishes to take down the bet after a win he or she would receive all five units back. The minimum bet is five of the minimum units. For example, if the minimum single roll bet is \$1, the minimum World/Whirl bet is \$5.\
On the Hop: (also Hop, or Hopping) A single roll bet on any particular combination of the two dice on the next roll including combinations whose sum is 7 (e.g. 4 and 3). For example, if someone bets on \"5 and 1\" on the hop, they are betting that the next roll will have a 5 on one die and a 1 on the other die. The bet pays 15:1 on easy ways (same as a bet on 3 or 11). Hard ways hop pays 30:1 (e.g., 3 and 3 on the hop, same as a bet on 2 or 12). The true odds are 17:1 and 35:1, resulting in a house edge of 11.11% and 13.89% respectively. When presented, hop bets are located at the center of the craps layout with the other proposition bets. If hop bets are not on the craps layout, they still may be bet on by players but they become the responsibility of the boxman to book the bet. Sometimes players may request to hop a whole number. In this case the money on the bet different combinations. For example, if a player says \"hop the tens\" (6--4, 5--5, 4--6) the player must give the dealer an even number bet so it can be divided among the hard and easy ways. If the player gives \$10, \$5 would be placed on the easy ways 10 with 15:1 odds and \$5 would be placed on the hard way with 30:1 odds. If a player wishes to \"hop the sevens\" there would be three different combinations and six possible ways to roll a 7 (6--1, 5--2, 4--3, 3--4, 2--5, 1--6) therefore the player should bet in multiples of 3 so the bet can be divided among each combination with a 15:1 payout minus the other two bets, otherwise if players does not bet in multiples of 3, they would specific which combination has additional units.\
Field: This bet is a wager that one of the numbers 2, 3, 4, 9, 10, 11, or 12 will appear on the next roll of the dice. This bet typically pays more (2:1 or 3:1) if 2 or 12 is rolled, and 1:1 if 3, 4, 9, 10, or 11 is rolled. The Field bet is a \"Self-Service\" Bet. Unlike the other proposition bets which are handled by the dealers or stickman, the field bet is placed directly by the player. Players identify their Field bets by placing them in the Field area directly in front of them or as close to their position as possible. The initial bet and/or any payouts can \"ride\" through several rolls until they lose, and are assumed to be \"riding\" by dealers. It is thus the player\'s responsibility to collect their bet and/or winnings immediately upon payout, before the next dice roll, if they do not wish to let it ride.
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# Craps
## Types of wagers {#types_of_wagers}
### Player bets {#player_bets}
Fire Bet: Before the shooter begins, some casinos will allow a bet known as a fire bet to be placed. A fire bet is a bet of as little as \$1 and generally up to a maximum of \$5 to \$10 sometimes higher, depending on casino, made in the hope that the next shooter will have a hot streak of setting and getting many points of different values. As different individual points are made by the shooter, they will be marked on the craps layout with a fire symbol.
The first three points will not pay out on the fire bet, but the fourth, fifth, and sixth will pay out at increasing odds. The fourth point pays at 24-to-1, the fifth point pays at 249-to-1, and the 6th point pays at 999-to-1. (The points must all be different numbers for them to count toward the fire bet.) For example, a shooter who successfully hits a point of 10 twice will only garner credit for the first one on the fire bet. Players must hit the established point in order for it to count toward the fire bet. The payout is determine by the number of points which have been established and hit after the shooter sevens out.
Bonus Craps: Prior to the initial \"come out roll\", players may place an optional wager (usually a \$1 minimum to a maximum \$25) on one or more of the three Bonus Craps wagers, \"All Small\", \"All Tall\", or \"All or Nothing at All.\" For players to win the \"All Small\" wager, the shooter must hit all five small numbers (2, 3, 4, 5, 6) before a seven is rolled; similarly, \"All Tall\" wins if all five high numbers (8, 9, 10, 11, 12) are hit before a seven is rolled.
These bets pay 35-for-1, for a house advantage of 7.76%. \"All or Nothing at All\" wins if the shooter hits all 10 numbers before a seven is rolled. This pays 176-for-1, for a house edge of 7.46%. For all three wagers, the order in which the numbers are hit does not matter. Whenever a seven is hit, including on the come out roll, all bonus bets lose, the bonus board is reset, and new bonus bets may be placed.
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# Craps
## Types of wagers {#types_of_wagers}
### Multiple different bets {#multiple_different_bets}
A player may wish to make multiple different bets. For example, a player may be wish to bet \$1 on all hard ways and the horn. If one of the bets win the dealer may automatically replenish the losing bet with profits from the winning bet. In this example, if the shooter rolls a hard 8 (pays 9:1), the horn loses. The dealer may return \$5 to the player and place the other \$4 on the horn bet which lost. If the player does not want the bet replenished, he or she should request any or all bets be taken down.
### Working and not working bets {#working_and_not_working_bets}
A working bet is a live bet. Bets may also be on the board, but not in play and therefore not working. Pass line and come bets are always working meaning the chips are in play and the player is therefore wagering live money. Other bets may be working or not working depending whether a point has been established or player\'s choice. Place and buy bets are working by default when a point is established and not working when the point is off unless the player specifies otherwise. Lay bets are always working even if a point has not been established unless the player requests otherwise. At any time, a player may wish to take any bet or bets out of play. The dealer will put an \"Off\" button on the player\'s specific bet or bets; this allows the player to keep his chips on the board without a live wager. For example, if a player decides not to wager a place bet mid-roll but wishes to keep the chips on the number, he or she may request the bet be \"not working\" or \"Off\". The chips remain on the table, but the player cannot win from or lose chips which are not working.
The opposite is also allowed. By default place and buy bets are not working without an established point; a player may wish to wager chips before a point has been established. In this case, the player would request the bet be working in which the dealer will place an \"On\" button on the specified chips.
### Betting variants {#betting_variants}
These variants depend on the casino and the table, and sometimes a casino will have different tables that use or omit these variants and others.
- 11 is a point number instead of a natural. Rolling an 11 still pays \"Yo\" center-table bets, but the Pass line does not automatically win (and the Don\'t Pass line does not automatically lose) when 11 is rolled on the come-out. Making the point pays 3:1 on Pass/Come odds bets (1:3 on Don\'t Pass/Come odds); all line bets are still even money. This substantially reduces the odds of a natural (from 8/36 to 6/36) and of making the point in general (since a 3:1 dog is added to the mix). All other things equal, the house edge on the Pass Line and Come bets for this play variation jumps dramatically to 9.75%.
- 12 pays 3:1 on the field. This is generally seen in rooms that have two different table minimums, on the tables with the higher minimums. The lower minimum ones will then have 2:1 odds. For example, the Mirage casino in Las Vegas features 3:1 odds.
- 11 pays 2:1 on the field. This variant is normally used when 12 pays 3:1, and neutralizes the house edge on the field.
- Big 6/8 are unavailable. These bets are equivalent to placing or buying 6 or 8 as points, which have better payout for the same real odds, so Big 6/8 are rarely used and many casinos simply omit them from the layout. Casinos in Atlantic City are even prohibited by law from offering Big 6/8 bets.
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# Craps
## Optimal betting {#optimal_betting}
When craps is played in a casino, all bets have a house advantage. That is, it can be shown mathematically that a player will (with 100% probability) lose all his or her money to the casino in the long run, while in the short run the player is more likely to lose money than make money. There may be players who are lucky and get ahead for a period of time, but in the long run these winning streaks are eroded away. One can slow, but not eliminate, one\'s average losses by only placing bets with the smallest house advantage.
The Pass/Don\'t Pass line, Come/Don\'t Come line, place 6, place 8, buy 4 and buy 10 (only under the casino rules where commission is charged only on wins) have the lowest house edge in the casino, and all other bets will, on average, lose money between three and twelve times faster because of the difference in house edges.
The place bets and buy bets differ from the Pass line and come line, in that place bets and buy bets can be removed at any time, since, while they are multi-roll bets, their odds of winning do not change from roll to roll, whereas Pass line bets and come line bets are a combination of different odds on their first roll and subsequent rolls. The first roll of a Pass line bet is 2:1 advantage for the player (8 wins, 4 losses), but it is \"paid for\" by subsequent rolls that are at the same disadvantage to the player as the Don\'t Pass bets were at an advantage. As such, they cannot profitably let the player take down the bet after the first roll. Players can bet or lay odds behind an established point depending on whether it was a Pass/Come or Don\'t Pass/Don\'t Come to lower house edge by receiving true odds on the point. Casinos which allow put betting allows players to increase or make new pass/come bets after the come-out roll. This bet generally has a higher house edge than place betting, unless the casino offers high odds.
Conversely, a player can take back (pick up) a Don\'t Pass or Don\'t Come bet after the first roll, but this cannot be recommended, because they already endured the disadvantaged part of the combination -- the first roll. On that come-out roll, they win just 3 times (2 and 3), while losing 8 of them (7 and 11) and pushing one (12) out of the 36 possible rolls. On the other 24 rolls that become a point, their Don\'t Pass bet is now to their advantage by 6:3 (4 and 10), 6:4 (5 and 9) and 6:5 (6 and 8). If a player chooses to remove the initial Don\'t Come and/or Don\'t Pass line bet, he or she can no longer lay odds behind the bet and cannot re-bet the same Don\'t Pass and/or Don\'t Come number (players must make a new Don\'t Pass or come bets if desired). However, players can still make standard lay bets odds on any of the point numbers (4,5,6,8,9,10).
Among these, and the remaining numbers and possible bets, there are a myriad of systems and progressions that can be used with many combinations of numbers.
An important alternative metric is house advantage per roll (rather than per bet), which may be expressed in loss per hour. The typical pace of rolls varies depending on the number of players, but 102 rolls per hour is a cited rate for a nearly full table. This same reference states that only \"29.6% of total rolls are come out rolls, on average\", so for this alternative metric, needing extra rolls to resolve the Pass line bet, for example, is factored. This number then permits calculation of rate of loss per hour, and per the 4 day/5 hour per day gambling trip:
- \$10 Pass line bets 0.42% per roll, \$4.28 per hour, \$86 per trip
- \$10 Place 6,8 bets 0.46% per roll, \$4.69 per hour, \$94 per trip
- \$10 Place 5,9 bets 1.11% per roll, \$11.32 per hour, \$226 per trip
- \$10 Place 4,10 bets 1.19% per roll, \$12.14 per hour, \$243 per trip
- \$1 Single Hardways 2.78% per roll, \$2.84 per hour, \$56.71 per trip
- \$1 All hardways 2.78% per roll, \$11.34 per hour, \$227 per trip
- \$5 All hardways 2.78% per roll, \$56.71 per hour, \$1134 per trip
- \$1 Craps only on come out 3.29% per roll, \$3.35 per hour, \$67.09 per trip
- \$1 Eleven only on come out 3.29% per roll, \$3.35 per hour, \$67.09 per trip
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# Craps
## Table rules {#table_rules}
Besides the rules of the game itself, a number of formal and informal rules are commonly applied in the table form of Craps, especially when played in a casino.
To reduce the potential opportunity for switching dice by sleight-of-hand, players are not supposed to handle the dice with more than one hand (such as shaking them in cupped hands before rolling) nor take the dice past the edge of the table. If a player wishes to change shooting hands, they may set the dice on the table, let go, then take them with the other hand.
When throwing the dice, the player is expected to hit the farthest wall at the opposite end of the table (these walls are typically augmented with pyramidal structures to ensure highly unpredictable bouncing after impact). Casinos will sometimes allow a roll that does not hit the opposite wall as long as the dice are thrown past the middle of the table; a very short roll will be nullified as a \"no roll\". The dice may not be slid across the table and must be tossed. These rules are intended to prevent dexterous players from physically influencing the outcome of the roll.
Players are generally asked not to throw the dice above a certain height (such as the eye level of the dealers). This is both for the safety of those around the table, and to eliminate the potential use of such a throw as a distraction device in order to cheat.
Dice are still considered \"in play\" if they land on players\' bets on the table, the dealer\'s working stacks, on the marker puck, or with one die resting on top of the other. The roll is invalid if either or both dice land in the boxman\'s bank, the stickman\'s bowl (where the extra three dice are kept between rolls), or in the rails around the top of the table where players chips are kept. If one or both dice hits a player or dealer and rolls back onto the table, the roll counts as long as the person being hit did not intentionally interfere with either of the dice, though some casinos will rule \"no roll\" for this situation. If one or both leave the table, it is also a \"no roll\", and the dice may either be replaced or examined by the boxman and returned to play.
Shooters may wish to \"set\" the dice to a particular starting configuration before throwing (such as showing a particular number or combination, stacking the dice, or spacing them to be picked up between different fingers), but if they do, they are often asked to be quick about it so as not to delay the game. Some casinos disallow such rituals to speed up the pace of the game. Some may also discourage or disallow unsanitary practices such as kissing or spitting on the dice.
In most casinos, players are not allowed to hand anything directly to dealers, and vice versa. Items such as cash, checks, and chips are exchanged by laying them down on the table; for example, when \"buying in\" (paying cash for chips), players are expected to place the cash on the layout: the dealer will take it and then place the chips in front of the player. This rule is enforced in order to allow the casino to easily monitor and record all transfers via overhead surveillance cameras, and to reduce the opportunity for cheating via sleight-of-hand.
Most casinos prohibit \"call bets\", and may have a warning such as \"No Call Bets\" printed on the layout to make this clear. This means a player may not call out a bet without also placing the corresponding chips on the table. Such a rule reduces the potential for misunderstanding in loud environments, as well as disputes over the amount that the player intended to bet after the outcome has been decided. Some casinos choose to allow call bets once players have bought-in. When allowed, they are usually made when a player wishes to bet at the last second, immediately before the dice are thrown, to avoid the risk of obstructing the roll.
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# Craps
## Etiquette
Craps is among the most social and most superstitious of all gambling games, which leads to an enormous variety of informal rules of etiquette that players may be expected to follow. An exhaustive list of these is beyond the scope of this article, but the guidelines below are most commonly given.
### Tips
Tipping the dealers is universal and expected in Craps. As in most other casino games, a player may simply place (or toss) chips onto the table and say, \"For the dealers\", \"For the crew\", *etc.* In craps, it is also common to place a bet for the dealers. This is usually done one of three ways: by placing an ordinary bet and simply declaring it for the dealers, as a \"two-way\", or \"on top\". A \"Two-Way\" is a bet for both parties: for example, a player may toss in two chips and say \"Two Way Hard Eight\", which will be understood to mean one chip for the player and one chip for the dealers. Players may also place a stack of chips for a bet as usual, but leave the top chip off-center and announce \"on top for the dealers\". The dealer\'s portion is often called a \"toke\" bet, which comes from the practice of using \$1 slot machine tokens to place dealer bets in some casinos.
In some cases, players may also tip each other, for example as a show of gratitude to the thrower for a roll on which they win a substantial bet.
### Superstition
Craps players routinely practice a wide range of superstitious behaviors, and may expect or demand these from other players as well.
Most prominently, it is universally considered bad luck to say the word \"seven\" (after the \"come-out\", a roll of 7 is a loss for \"pass\" bets). Dealers themselves often make significant efforts to avoid calling out the number. When necessary, participants may refer to seven with a \"nickname\" such as \"Big Red\" (or just \"Red\"), \"the S-word\", etc.
## Dice setting or dice control {#dice_setting_or_dice_control}
An approach to achieving an advantage is to \"set\" the dice in a particular orientation, and then throw them in such a manner that they do not tumble randomly. The theory is that given exactly the same throw from exactly the same starting configuration, the dice will tumble in the same way and therefore show the same or similar values every time.
Casinos take steps to prevent this. The dice are usually required to hit the back wall of the table, which is normally faced with a jagged angular texture such as pyramids, making controlled spins more difficult. There has been no independent evidence that such methods can be successfully applied in a real casino.
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# Craps
## Variants
Bank craps is a variation of the original craps game and is sometimes known as Las Vegas Craps. This variant is quite popular in Nevada gambling houses, and its availability online has now made it a globally played game. Bank craps uses a special table layout and all bets must be made against the house. In Bank Craps, the dice are thrown over a wire or a string that is normally stretched a few inches from the table\'s surface. The lowest house edge (for the Pass/Don\'t Pass) in this variation is around 1.4%. Generally, if the word \"craps\" is used without any modifier, it can be inferred to mean this version of the game, to which most of this article refers.
Crapless craps, also known as bastard craps, is a simple version of the original craps game, and is normally played as an online private game. The biggest difference between crapless craps and original craps is that the shooter (person throwing the dice) is at a far greater disadvantage and has a house edge of 5.38%. Another difference is that this is one of the craps games in which a player can bet on rolling a 2, 3, 11 or 12 before a 7 is thrown. In crapless craps, 2 and 12 have odds of 11:2 and have a house edge of 7.143% while 3 and 11 have odds of 11:4 with a house edge of 6.25%.
New York Craps is one of the variations of craps played mostly in the Eastern coast of the US, true to its name. History states that this game was actually found and played in casinos in Yugoslavia, the UK and the Bahamas. In this craps variant, the house edge is greater than Las Vegas Craps or Bank craps. The table layout is also different, and is called a double-end-dealer table. This variation is different from the original craps game in several ways, but the primary difference is that New York craps does not allow Come or Don\'t Come bets. New York Craps Players bet on box numbers like 4, 5, 6, 8, 9, or 10. The overall house edge in New York craps is 5%.
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# Craps
## Card-based variations {#card_based_variations}
In order to get around Californian laws barring the payout of a game being directly related to the roll of dice, Indian reservations have adapted the game to substitute cards for dice.
### Cards replacing dice {#cards_replacing_dice}
To replicate the original dice odds exactly without dice or possibility of card-counting, one scheme uses two shuffle machines each with just one deck of Ace through 6 each. Each machine selects one of the 6 cards at random and this is the roll. The selected cards are replaced and the decks are reshuffled for the next roll.
In one variation, two shoes are used, each containing some number of regular card decks that have been stripped down to just the Aces and deuces through sixes. The boxman simply deals one card from each shoe and that is the roll on which bets are settled. Since a card-counting scheme is easily devised to make use of the information of cards that have already been dealt, a relatively small portion (less than 50%) of each shoe is usually dealt in order to protect the house.
In a similar variation, cards representing dice are dealt directly from a continuous shuffling machine (CSM). Typically, the CSM will hold approximately 264 cards, or 44 sets of 1 through 6 spot cards. Two cards are dealt from the CSM for each roll. The game is played exactly as regular craps, but the roll distribution of the remaining cards in the CSM is slightly skewed from the normal symmetric distribution of dice.
Even if the dealer were to shuffle each roll back into the CSM, the effect of buffering a number of cards in the chute of the CSM provides information about the skew of the next roll. Analysis shows this type of game is biased towards the Don\'t Pass and Don\'t Come bets. A player betting Don\'t Pass and Don\'t Come every roll and laying 10x odds receives a 2% profit on the initial Don\'t Pass / Don\'t Come bet each roll. Using a counting system allows the player to attain a similar return at lower variance.
### Cards mapping physical dice {#cards_mapping_physical_dice}
In this game variation, one red deck and one blue deck of six cards each (A through 6), and a red die and a blue die are used. Each deck is shuffled separately, usually by machine. Each card is then dealt onto the layout, into the 6 red and 6 blue numbered boxes. The shooter then shoots the dice. The red card in the red-numbered box corresponding to the red die, and the blue card in the blue-numbered box corresponding to the blue die are then turned over to form the roll on which bets are settled.
Another variation uses a red and a blue deck of 36 custom playing cards each. Each card has a picture of a two-die roll on it -- from 1--1 to 6--6. The shooter shoots what looks like a red and a blue die, called \"cubes\". They are numbered such that they can never throw a pair, and that the blue one will show a higher value than the red one exactly half the time. One such scheme could be 222555 on the red die and 333444 on the blue die.
One card is dealt from the red deck and one is dealt from the blue deck. The shooter throws the \"cubes\" and the color of the cube that is higher selects the color of the card to be used to settle bets. On one such table, an additional one-roll prop bet was offered: If the card that was turned over for the \"roll\" was either 1--1 or 6--6, the other card was also turned over. If the other card was the \"opposite\" (6--6 or 1--1, respectively) of the first card, the bet paid 500:1 for this 647:1 proposition.
And additional variation uses a single set of 6 cards, and regular dice. The roll of the dice maps to the card in that position, and if a pair is rolled, then the mapped card is used twice, as a pair.
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# Craps
## Rules of play against other players (\"Street Craps\") {#rules_of_play_against_other_players_street_craps}
Recreational or informal playing of craps outside of a casino is referred to as street craps or private craps. The most notable difference between playing street craps and bank craps is that there is no bank or house to cover bets in street craps. Players must bet against each other by covering or fading each other\'s bets for the game to be played. If money is used instead of chips and depending on the laws of where it is being played, street craps can be an illegal form of gambling.
There are many variations of street craps. The simplest way is to either agree on or roll a number as the point, then roll the point again before rolling a seven. Unlike more complex proposition bets offered by casinos, street craps has more simplified betting options. The shooter is required to make either a Pass or a Don\'t Pass bet if he wants to roll the dice. Another player must choose to cover the shooter to create a stake for the game to continue.
If there are several players, the rotation of the player who must cover the shooter may change with the shooter (comparable to a blind in poker). The person covering the shooter will always bet against the shooter. For example, if the shooter made a \"Pass\" bet, the person covering the shooter would make a \"Don\'t Pass\" bet to win. Once the shooter is covered, other players may make Pass/Don\'t Pass bets, or any other proposition bets, as long as there is another player willing to cover.
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# Craps
## In popular culture {#in_popular_culture}
Due to the random nature of the game, in popular culture a **\"crapshoot\"** is often used to describe an action with an unpredictable outcome.
The prayer or invocation \"Baby needs a new pair of shoes!\" is associated with shooting craps.
### Floating craps {#floating_craps}
**Floating craps** is an illegal operation of craps. The term *floating* refers to the practice of the game\'s operators using portable tables and equipment to quickly move the game from location to location to stay ahead of the law enforcement authorities. The term may have originated in the 1930s when Benny Binion (later known for founding the downtown Las Vegas hotel Binion\'s) set up an illegal craps game utilizing tables created from portable crates for the Texas Centennial Exposition.
The 1950 Broadway musical *Guys and Dolls* features a major plot point revolving around a floating craps game.
In the 1950s and 1960s The Sands Hotel in Las Vegas had a craps table that floated in the swimming pool, as a joke reference to the notoriety of the term.
### Records
A Golden Arm is a craps player who rolls the dice for longer than one hour without losing. Likely the first known Golden Arm was Oahu native Stanley Fujitake, who rolled 118 times without sevening out in 3 hours and 6 minutes at the California Hotel and Casino on May 28, 1989.
The current record for length of a \"hand\" (successive rounds won by the same shooter) is 154 rolls including 25 passes by Patricia DeMauro of New Jersey, lasting 4 hours and 18 minutes, at the Borgata in Atlantic City, New Jersey, on May 23--24, 2009. She bested by over an hour the record held for almost 20 years -- that of Fujitake
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# Common Lisp
**Common Lisp** (**CL**) is a dialect of the Lisp programming language, published in American National Standards Institute (ANSI) standard document *ANSI INCITS 226-1994 (S2018)* (formerly *X3.226-1994 (R1999)*). The Common Lisp HyperSpec, a hyperlinked HTML version, has been derived from the ANSI Common Lisp standard.
The Common Lisp language was developed as a standardized and improved successor of Maclisp. By the early 1980s several groups were already at work on diverse successors to MacLisp: Lisp Machine Lisp (aka ZetaLisp), Spice Lisp, NIL and S-1 Lisp. Common Lisp sought to unify, standardise, and extend the features of these MacLisp dialects. Common Lisp is not an implementation, but rather a language specification. Several implementations of the Common Lisp standard are available, including free and open-source software and proprietary products. Common Lisp is a general-purpose, multi-paradigm programming language. It supports a combination of procedural, functional, and object-oriented programming paradigms. As a dynamic programming language, it facilitates evolutionary and incremental software development, with iterative compilation into efficient run-time programs. This incremental development is often done interactively without interrupting the running application.
It also supports optional type annotation and casting, which can be added as necessary at the later profiling and optimization stages, to permit the compiler to generate more efficient code. For instance, `fixnum` can hold an unboxed integer in a range supported by the hardware and implementation, permitting more efficient arithmetic than on big integers or arbitrary precision types. Similarly, the compiler can be told on a per-module or per-function basis which type of safety level is wanted, using *optimize* declarations.
Common Lisp includes CLOS, an object system that supports multimethods and method combinations. It is often implemented with a Metaobject Protocol.
Common Lisp is extensible through standard features such as *Lisp macros* (code transformations) and *reader macros* (input parsers for characters).
Common Lisp provides partial backwards compatibility with Maclisp and John McCarthy\'s original Lisp. This allows older Lisp software to be ported to Common Lisp.
## History
Work on Common Lisp started in 1981 after an initiative by ARPA manager Bob Engelmore to develop a single community standard Lisp dialect. Much of the initial language design was done via electronic mail. In 1982, Guy L. Steele Jr. gave the first overview of Common Lisp at the 1982 ACM Symposium on LISP and functional programming.
The first language documentation was published in 1984 as Common Lisp the Language (known as CLtL1), first edition. A second edition (known as CLtL2), published in 1990, incorporated many changes to the language, made during the ANSI Common Lisp standardization process: extended LOOP syntax, the Common Lisp Object System, the Condition System for error handling, an interface to the pretty printer and much more. But CLtL2 does not describe the final ANSI Common Lisp standard and thus is not a documentation of ANSI Common Lisp. The final ANSI Common Lisp standard then was published in 1994. Since then no update to the standard has been published. Various extensions and improvements to Common Lisp (examples are Unicode, Concurrency, CLOS-based IO) have been provided by implementations and libraries.
## Syntax
Common Lisp is a dialect of Lisp. It uses S-expressions to denote both code and data structure. Function calls, macro forms and special forms are written as lists, with the name of the operator first, as in these examples:
``` lisp
(+ 2 2) ; adds 2 and 2, yielding 4. The function's name is '+'. Lisp has no operators as such.
```
``` lisp
(defvar *x*) ; Ensures that a variable *x* exists,
; without giving it a value. The asterisks are part of
; the name, by convention denoting a special (global) variable.
; The symbol *x* is also hereby endowed with the property that
; subsequent bindings of it are dynamic, rather than lexical.
(setf *x* 42.1) ; Sets the variable *x* to the floating-point value 42.1
```
``` lisp
;; Define a function that squares a number:
(defun square (x)
(* x x))
```
``` lisp
;; Execute the function:
(square 3) ; Returns 9
```
``` lisp
;; The 'let' construct creates a scope for local variables. Here
;; the variable 'a' is bound to 6 and the variable 'b' is bound
;; to 4. Inside the 'let' is a 'body', where the last computed value is returned.
;; Here the result of adding a and b is returned from the 'let' expression.
;; The variables a and b have lexical scope, unless the symbols have been
;; marked as special variables (for instance by a prior DEFVAR).
(let ((a 6)
(b 4))
(+ a b)) ; returns 10
```
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# Common Lisp
## Data types {#data_types}
Common Lisp has many data types.
### Scalar types {#scalar_types}
*Number* types include integers, ratios, floating-point numbers, and complex numbers. Common Lisp uses bignums to represent numerical values of arbitrary size and precision. The ratio type represents fractions exactly, a facility not available in many languages. Common Lisp automatically coerces numeric values among these types as appropriate.
The Common Lisp *character* type is not limited to ASCII characters. Most modern implementations allow Unicode characters.
The *symbol* type is common to Lisp languages, but largely unknown outside them. A symbol is a unique, named data object with several parts: name, value, function, property list, and package. Of these, *value cell* and *function cell* are the most important. Symbols in Lisp are often used similarly to identifiers in other languages: to hold the value of a variable; however there are many other uses. Normally, when a symbol is evaluated, its value is returned. Some symbols evaluate to themselves, for example, all symbols in the keyword package are self-evaluating. Boolean values in Common Lisp are represented by the self-evaluating symbols T and NIL. Common Lisp has namespaces for symbols, called \'packages\'.
A number of functions are available for rounding scalar numeric values in various ways. The function `round` rounds the argument to the nearest integer, with halfway cases rounded to the even integer. The functions `truncate`, `floor`, and `ceiling` round towards zero, down, or up respectively. All these functions return the discarded fractional part as a secondary value. For example, `(floor -2.5)` yields −3, 0.5; `(ceiling -2.5)` yields −2, −0.5; `(round 2.5)` yields 2, 0.5; and `(round 3.5)` yields 4, −0.5.
### Data structures {#data_structures}
*Sequence* types in Common Lisp include lists, vectors, bit-vectors, and strings. There are many operations that can work on any sequence type.
As in almost all other Lisp dialects, *lists* in Common Lisp are composed of *conses*, sometimes called *cons cells* or *pairs*. A cons is a data structure with two slots, called its *car* and *cdr*. A list is a linked chain of conses or the empty list. Each cons\'s car refers to a member of the list (possibly another list). Each cons\'s cdr refers to the next cons---except for the last cons in a list, whose cdr refers to the `nil` value. Conses can also easily be used to implement trees and other complex data structures; though it is usually advised to use structure or class instances instead. It is also possible to create circular data structures with conses.
Common Lisp supports multidimensional *arrays*, and can dynamically resize *adjustable* arrays if required. Multidimensional arrays can be used for matrix mathematics. A *vector* is a one-dimensional array. Arrays can carry any type as members (even mixed types in the same array) or can be specialized to contain a specific type of members, as in a vector of bits. Usually, only a few types are supported. Many implementations can optimize array functions when the array used is type-specialized. Two type-specialized array types are standard: a *string* is a vector of characters, while a *bit-vector* is a vector of bits.
*Hash tables* store associations between data objects. Any object may be used as key or value. Hash tables are automatically resized as needed.
*Packages* are collections of symbols, used chiefly to separate the parts of a program into namespaces. A package may *export* some symbols, marking them as part of a public interface. Packages can use other packages.
*Structures*, similar in use to C structs and Pascal records, represent arbitrary complex data structures with any number and type of fields (called *slots*). Structures allow single-inheritance.
*Classes* are similar to structures, but offer more dynamic features and multiple-inheritance. (See CLOS). Classes have been added late to Common Lisp and there is some conceptual overlap with structures. Objects created of classes are called *Instances*. A special case is Generic Functions. Generic Functions are both functions and instances.
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# Common Lisp
## Data types {#data_types}
### Functions
Common Lisp supports first-class functions. For instance, it is possible to write functions that take other functions as arguments or return functions as well. This makes it possible to describe very general operations.
The Common Lisp library relies heavily on such higher-order functions. For example, the `sort` function takes a relational operator as an argument and key function as an optional keyword argument. This can be used not only to sort any type of data, but also to sort data structures according to a key.
``` lisp
;; Sorts the list using the > and < function as the relational operator.
(sort (list 5 2 6 3 1 4) #'>) ; Returns (6 5 4 3 2 1)
(sort (list 5 2 6 3 1 4) #'<) ; Returns (1 2 3 4 5 6)
```
``` lisp
;; Sorts the list according to the first element of each sub-list.
(sort (list '(9 A) '(3 B) '(4 C)) #'< :key #'first) ; Returns ((3 B) (4 C) (9 A))
```
The evaluation model for functions is very simple. When the evaluator encounters a form `(f a1 a2...)` then it presumes that the symbol named f is one of the following:
1. A special operator (easily checked against a fixed list)
2. A macro operator (must have been defined previously)
3. The name of a function (default), which may either be a symbol, or a sub-form beginning with the symbol `lambda`.
If f is the name of a function, then the arguments a1, a2, \..., an are evaluated in left-to-right order, and the function is found and invoked with those values supplied as parameters.
#### Defining functions {#defining_functions}
The macro `defun` defines functions where a function definition gives the name of the function, the names of any arguments, and a function body:
``` lisp
(defun square (x)
(* x x))
```
Function definitions may include compiler directives, known as *declarations*, which provide hints to the compiler about optimization settings or the data types of arguments. They may also include *documentation strings* (docstrings), which the Lisp system may use to provide interactive documentation:
``` lisp
(defun square (x)
"Calculates the square of the single-float x."
(declare (single-float x) (optimize (speed 3) (debug 0) (safety 1)))
(the single-float (* x x)))
```
Anonymous functions (function literals) are defined using `lambda` expressions, e.g. `(lambda (x) (* x x))` for a function that squares its argument. Lisp programming style frequently uses higher-order functions for which it is useful to provide anonymous functions as arguments.
Local functions can be defined with `flet` and `labels`.
``` lisp
(flet ((square (x)
(* x x)))
(square 3))
```
There are several other operators related to the definition and manipulation of functions. For instance, a function may be compiled with the `compile` operator. (Some Lisp systems run functions using an interpreter by default unless instructed to compile; others compile every function).
#### Defining generic functions and methods {#defining_generic_functions_and_methods}
The macro `defgeneric` defines generic functions. Generic functions are a collection of methods. The macro `defmethod` defines methods.
Methods can specialize their parameters over CLOS *standard classes*, *system classes*, *structure classes* or individual objects. For many types, there are corresponding *system classes*.
When a generic function is called, multiple-dispatch will determine the effective method to use.
``` lisp
(defgeneric add (a b))
```
``` lisp
(defmethod add ((a number) (b number))
(+ a b))
```
``` lisp
(defmethod add ((a vector) (b number))
(map 'vector (lambda (n) (+ n b)) a))
```
``` lisp
(defmethod add ((a vector) (b vector))
(map 'vector #'+ a b))
```
``` lisp
(defmethod add ((a string) (b string))
(concatenate 'string a b))
```
``` lisp
(add 2 3) ; returns 5
(add #(1 2 3 4) 7) ; returns #(8 9 10 11)
(add #(1 2 3 4) #(4 3 2 1)) ; returns #(5 5 5 5)
(add "COMMON " "LISP") ; returns "COMMON LISP"
```
Generic Functions are also a first class data type. There are many more features to Generic Functions and Methods than described above.
#### The function namespace {#the_function_namespace}
The namespace for function names is separate from the namespace for data variables. This is a key difference between Common Lisp and Scheme. For Common Lisp, operators that define names in the function namespace include `defun`, `flet`, `labels`, `defmethod` and `defgeneric`.
To pass a function by name as an argument to another function, one must use the `function` special operator, commonly abbreviated as `#'`. The first `sort` example above refers to the function named by the symbol `>` in the function namespace, with the code `#'>`. Conversely, to call a function passed in such a way, one would use the `funcall` operator on the argument.
Scheme\'s evaluation model is simpler: there is only one namespace, and all positions in the form are evaluated (in any order) -- not just the arguments. Code written in one dialect is therefore sometimes confusing to programmers more experienced in the other. For instance, many Common Lisp programmers like to use descriptive variable names such as *list* or *string* which could cause problems in Scheme, as they would locally shadow function names.
Whether a separate namespace for functions is an advantage is a source of contention in the Lisp community. It is usually referred to as the *Lisp-1 vs. Lisp-2 debate*. Lisp-1 refers to Scheme\'s model and Lisp-2 refers to Common Lisp\'s model. These names were coined in a 1988 paper by Richard P. Gabriel and Kent Pitman, which extensively compares the two approaches.
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# Common Lisp
## Data types {#data_types}
### Functions
#### Multiple return values {#multiple_return_values}
Common Lisp supports the concept of *multiple values*, where any expression always has a single *primary value*, but it might also have any number of *secondary values*, which might be received and inspected by interested callers. This concept is distinct from returning a list value, as the secondary values are fully optional, and passed via a dedicated side channel. This means that callers may remain entirely unaware of the secondary values being there if they have no need for them, and it makes it convenient to use the mechanism for communicating information that is sometimes useful, but not always necessary. For example,
- The `TRUNCATE` function rounds the given number to an integer towards zero. However, it also returns a remainder as a secondary value, making it very easy to determine what value was truncated. It also supports an optional divisor parameter, which can be used to perform Euclidean division trivially:
``` cl
(let ((x 1266778)
(y 458))
(multiple-value-bind (quotient remainder)
(truncate x y)
(format nil "~A divided by ~A is ~A remainder ~A" x y quotient remainder)))
;;;; => "1266778 divided by 458 is 2765 remainder 408"
```
- `GETHASH` returns the value of a key in an associative map, or the default value otherwise, and a secondary Boolean indicating whether the value was found. Thus code that does not care about whether the value was found or provided as the default can simply use it as-is, but when such distinction is important, it might inspect the secondary Boolean and react appropriately. Both use cases are supported by the same call and neither is unnecessarily burdened or constrained by the other. Having this feature at the language level removes the need to check for the existence of the key or compare it to null as would be done in other languages.
``` cl
(defun get-answer (library)
(gethash 'answer library 42))
(defun the-answer-1 (library)
(format nil "The answer is ~A" (get-answer library)))
;;;; Returns "The answer is 42" if ANSWER not present in LIBRARY
(defun the-answer-2 (library)
(multiple-value-bind (answer sure-p)
(get-answer library)
(if (not sure-p)
"I don't know"
(format nil "The answer is ~A" answer))))
;;;; Returns "I don't know" if ANSWER not present in LIBRARY
```
Multiple values are supported by a handful of standard forms, most common of which are the `MULTIPLE-VALUE-BIND` special form for accessing secondary values and `VALUES` for returning multiple values:
``` cl
(defun magic-eight-ball ()
"Return an outlook prediction, with the probability as a secondary value"
(values "Outlook good" (random 1.0)))
;;;; => "Outlook good"
;;;; => 0.3187
```
### Other types {#other_types}
Other data types in Common Lisp include:
- *Pathnames* represent files and directories in the filesystem. The Common Lisp pathname facility is more general than most operating systems\' file naming conventions, making Lisp programs\' access to files broadly portable across diverse systems.
- Input and output *streams* represent sources and sinks of binary or textual data, such as the terminal or open files.
- Common Lisp has a built-in pseudo-random number generator (PRNG). *Random state* objects represent reusable sources of pseudo-random numbers, allowing the user to seed the PRNG or cause it to replay a sequence.
- *Conditions* are a type used to represent errors, exceptions, and other \"interesting\" events to which a program may respond.
- *Classes* are first-class objects, and are themselves instances of classes called metaobject classes (metaclasses for short).
- *Readtables* are a type of object which control how Common Lisp\'s reader parses the text of source code. By controlling which readtable is in use when code is read in, the programmer can change or extend the language\'s syntax.
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# Common Lisp
## Scope
Like programs in many other programming languages, Common Lisp programs make use of names to refer to variables, functions, and many other kinds of entities. Named references are subject to scope.
The association between a name and the entity which the name refers to is called a binding.
Scope refers to the set of circumstances in which a name is determined to have a particular binding.
### Determiners of scope {#determiners_of_scope}
The circumstances which determine scope in Common Lisp include:
- the location of a reference within an expression. If it\'s the leftmost position of a compound, it refers to a special operator or a macro or function binding, otherwise to a variable binding or something else.
- the kind of expression in which the reference takes place. For instance, `(go x)` means transfer control to label `x`, whereas `(print x)` refers to the variable `x`. Both scopes of `x` can be active in the same region of program text, since tagbody labels are in a separate namespace from variable names. A special form or macro form has complete control over the meanings of all symbols in its syntax. For instance, in `(defclass x (a b) ())`, a class definition, the `(a b)` is a list of base classes, so these names are looked up in the space of class names, and `x` isn\'t a reference to an existing binding, but the name of a new class being derived from `a` and `b`. These facts emerge purely from the semantics of `defclass`. The only generic fact about this expression is that `defclass` refers to a macro binding; everything else is up to `defclass`.
- the location of the reference within the program text. For instance, if a reference to variable `x` is enclosed in a binding construct such as a `let` which defines a binding for `x`, then the reference is in the scope created by that binding.
- for a variable reference, whether or not a variable symbol has been, locally or globally, declared special. This determines whether the reference is resolved within a lexical environment, or within a dynamic environment.
- the specific instance of the environment in which the reference is resolved. An environment is a run-time dictionary which maps symbols to bindings. Each kind of reference uses its own kind of environment. References to lexical variables are resolved in a lexical environment, et cetera. More than one environment can be associated with the same reference. For instance, thanks to recursion or the use of multiple threads, multiple activations of the same function can exist at the same time. These activations share the same program text, but each has its own lexical environment instance.
To understand what a symbol refers to, the Common Lisp programmer must know what kind of reference is being expressed, what kind of scope it uses if it is a variable reference (dynamic versus lexical scope), and also the run-time situation: in what environment is the reference resolved, where was the binding introduced into the environment, et cetera.
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# Common Lisp
## Scope
### Kinds of environment {#kinds_of_environment}
#### Global
Some environments in Lisp are globally pervasive. For instance, if a new type is defined, it is known everywhere thereafter. References to that type look it up in this global environment.
#### Dynamic
One type of environment in Common Lisp is the dynamic environment. Bindings established in this environment have dynamic extent, which means that a binding is established at the start of the execution of some construct, such as a `let` block, and disappears when that construct finishes executing: its lifetime is tied to the dynamic activation and deactivation of a block. However, a dynamic binding is not just visible within that block; it is also visible to all functions invoked from that block. This type of visibility is known as indefinite scope. Bindings which exhibit dynamic extent (lifetime tied to the activation and deactivation of a block) and indefinite scope (visible to all functions which are called from that block) are said to have dynamic scope.
Common Lisp has support for dynamically scoped variables, which are also called special variables. Certain other kinds of bindings are necessarily dynamically scoped also, such as restarts and catch tags. Function bindings cannot be dynamically scoped using `flet` (which only provides lexically scoped function bindings), but function objects (a first-level object in Common Lisp) can be assigned to dynamically scoped variables, bound using `let` in dynamic scope, then called using `funcall` or `APPLY`.
Dynamic scope is extremely useful because it adds referential clarity and discipline to global variables. Global variables are frowned upon in computer science as potential sources of error, because they can give rise to ad-hoc, covert channels of communication among modules that lead to unwanted, surprising interactions.
In Common Lisp, a special variable which has only a top-level binding behaves just like a global variable in other programming languages. A new value can be stored into it, and that value simply replaces what is in the top-level binding. Careless replacement of the value of a global variable is at the heart of bugs caused by the use of global variables. However, another way to work with a special variable is to give it a new, local binding within an expression. This is sometimes referred to as \"rebinding\" the variable. Binding a dynamically scoped variable temporarily creates a new memory location for that variable, and associates the name with that location. While that binding is in effect, all references to that variable refer to the new binding; the previous binding is hidden. When execution of the binding expression terminates, the temporary memory location is gone, and the old binding is revealed, with the original value intact. Of course, multiple dynamic bindings for the same variable can be nested.
In Common Lisp implementations which support multithreading, dynamic scopes are specific to each thread of execution. Thus special variables serve as an abstraction for thread local storage. If one thread rebinds a special variable, this rebinding has no effect on that variable in other threads. The value stored in a binding can only be retrieved by the thread which created that binding. If each thread binds some special variable `*x*`, then `*x*` behaves like thread-local storage. Among threads which do not rebind `*x*`, it behaves like an ordinary global: all of these threads refer to the same top-level binding of `*x*`.
Dynamic variables can be used to extend the execution context with additional context information which is implicitly passed from function to function without having to appear as an extra function parameter. This is especially useful when the control transfer has to pass through layers of unrelated code, which simply cannot be extended with extra parameters to pass the additional data. A situation like this usually calls for a global variable. That global variable must be saved and restored, so that the scheme doesn\'t break under recursion: dynamic variable rebinding takes care of this. And that variable must be made thread-local (or else a big mutex must be used) so the scheme doesn\'t break under threads: dynamic scope implementations can take care of this also.
In the Common Lisp library, there are many standard special variables. For instance, all standard I/O streams are stored in the top-level bindings of well-known special variables. The standard output stream is stored in \*standard-output\*.
Suppose a function foo writes to standard output:
``` lisp
(defun foo ()
(format t "Hello, world"))
```
To capture its output in a character string, \*standard-output\* can be bound to a string stream and called:
``` lisp
(with-output-to-string (*standard-output*)
(foo))
```
` -> "Hello, world" ; gathered output returned as a string`
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# Common Lisp
## Scope
### Kinds of environment {#kinds_of_environment}
#### Lexical
Common Lisp supports lexical environments. Formally, the bindings in a lexical environment have lexical scope and may have either an indefinite extent or dynamic extent, depending on the type of namespace. Lexical scope means that visibility is physically restricted to the block in which the binding is established. References which are not textually (i.e. lexically) embedded in that block simply do not see that binding.
The tags in a TAGBODY have lexical scope. The expression (GO X) is erroneous if it is not embedded in a TAGBODY which contains a label X. However, the label bindings disappear when the TAGBODY terminates its execution, because they have dynamic extent. If that block of code is re-entered by the invocation of a lexical closure, it is invalid for the body of that closure to try to transfer control to a tag via GO:
``` lisp
(defvar *stashed*) ;; will hold a function
(tagbody
(setf *stashed* (lambda () (go some-label)))
(go end-label) ;; skip the (print "Hello")
some-label
(print "Hello")
end-label)
-> NIL
```
When the TAGBODY is executed, it first evaluates the setf form which stores a function in the special variable \*stashed\*. Then the (go end-label) transfers control to end-label, skipping the code (print \"Hello\"). Since end-label is at the end of the tagbody, the tagbody terminates, yielding NIL. Suppose that the previously remembered function is now called:
``` lisp
(funcall *stashed*) ;; Error!
```
This situation is erroneous. One implementation\'s response is an error condition containing the message, \"GO: tagbody for tag SOME-LABEL has already been left\". The function tried to evaluate (go some-label), which is lexically embedded in the tagbody, and resolves to the label. However, the tagbody isn\'t executing (its extent has ended), and so the control transfer cannot take place.
Local function bindings in Lisp have lexical scope, and variable bindings also have lexical scope by default. By contrast with GO labels, both of these have indefinite extent. When a lexical function or variable binding is established, that binding continues to exist for as long as references to it are possible, even after the construct which established that binding has terminated. References to lexical variables and functions after the termination of their establishing construct are possible thanks to lexical closures.
Lexical binding is the default binding mode for Common Lisp variables. For an individual symbol, it can be switched to dynamic scope, either by a local declaration, by a global declaration. The latter may occur implicitly through the use of a construct like DEFVAR or DEFPARAMETER. It is an important convention in Common Lisp programming that special (i.e. dynamically scoped) variables have names which begin and end with an asterisk sigil `*` in what is called the \"earmuff convention\". If adhered to, this convention effectively creates a separate namespace for special variables, so that variables intended to be lexical are not accidentally made special.
Lexical scope is useful for several reasons.
Firstly, references to variables and functions can be compiled to efficient machine code, because the run-time environment structure is relatively simple. In many cases it can be optimized to stack storage, so opening and closing lexical scopes has minimal overhead. Even in cases where full closures must be generated, access to the closure\'s environment is still efficient; typically each variable becomes an offset into a vector of bindings, and so a variable reference becomes a simple load or store instruction with a base-plus-offset addressing mode.
Secondly, lexical scope (combined with indefinite extent) gives rise to the lexical closure, which in turn creates a whole paradigm of programming centered around the use of functions being first-class objects, which is at the root of functional programming.
Thirdly, perhaps most importantly, even if lexical closures are not exploited, the use of lexical scope isolates program modules from unwanted interactions. Due to their restricted visibility, lexical variables are private. If one module A binds a lexical variable X, and calls another module B, references to X in B will not accidentally resolve to the X bound in A. B simply has no access to X. For situations in which disciplined interactions through a variable are desirable, Common Lisp provides special variables. Special variables allow for a module A to set up a binding for a variable X which is visible to another module B, called from A. Being able to do this is an advantage, and being able to prevent it from happening is also an advantage; consequently, Common Lisp supports both lexical and dynamic scope.
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# Common Lisp
## Macros
A *macro* in Lisp superficially resembles a function in usage. However, rather than representing an expression which is evaluated, it represents a transformation of the program source code. The macro gets the source it surrounds as arguments, binds them to its parameters and computes a new source form. This new form can also use a macro. The macro expansion is repeated until the new source form does not use a macro. The final computed form is the source code executed at runtime.
Typical uses of macros in Lisp:
- new control structures (example: looping constructs, branching constructs)
- scoping and binding constructs
- simplified syntax for complex and repeated source code
- top-level defining forms with compile-time side-effects
- data-driven programming
- embedded domain specific languages (examples: SQL, HTML, Prolog)
- implicit finalization forms
Various standard Common Lisp features also need to be implemented as macros, such as:
- the standard `setf` abstraction, to allow custom compile-time expansions of assignment/access operators
- `with-accessors`, `with-slots`, `with-open-file` and other similar `WITH` macros
- Depending on implementation, `if` or `cond` is a macro built on the other, the special operator; `when` and `unless` consist of macros
- The powerful `loop` domain-specific language
Macros are defined by the *defmacro* macro. The special operator *macrolet* allows the definition of local (lexically scoped) macros. It is also possible to define macros for symbols using *define-symbol-macro* and *symbol-macrolet*.
Paul Graham\'s book On Lisp describes the use of macros in Common Lisp in detail. Doug Hoyte\'s book Let Over Lambda extends the discussion on macros, claiming \"Macros are the single greatest advantage that lisp has as a programming language and the single greatest advantage of any programming language.\" Hoyte provides several examples of iterative development of macros.
### Example using a macro to define a new control structure {#example_using_a_macro_to_define_a_new_control_structure}
Macros allow Lisp programmers to create new syntactic forms in the language. One typical use is to create new control structures. The example macro provides an `until` looping construct. The syntax is:
``` text
(until test form*)
```
The macro definition for *until*:
``` lisp
(defmacro until (test &body body)
(let ((start-tag (gensym "START"))
(end-tag (gensym "END")))
`(tagbody ,start-tag
(when ,test (go ,end-tag))
(progn ,@body)
(go ,start-tag)
,end-tag)))
```
*tagbody* is a primitive Common Lisp special operator which provides the ability to name tags and use the *go* form to jump to those tags. The backquote *\`* provides a notation that provides code templates, where the value of forms preceded with a comma are filled in. Forms preceded with comma and at-sign are *spliced* in. The tagbody form tests the end condition. If the condition is true, it jumps to the end tag. Otherwise, the provided body code is executed and then it jumps to the start tag.
An example of using the above *until* macro:
``` lisp
(until (= (random 10) 0)
(write-line "Hello"))
```
The code can be expanded using the function *macroexpand-1*. The expansion for the above example looks like this:
``` lisp
(TAGBODY
#:START1136
(WHEN (ZEROP (RANDOM 10))
(GO #:END1137))
(PROGN (WRITE-LINE "hello"))
(GO #:START1136)
#:END1137)
```
During macro expansion the value of the variable *test* is *(= (random 10) 0)* and the value of the variable *body* is *((write-line \"Hello\"))*. The body is a list of forms.
Symbols are usually automatically upcased. The expansion uses the TAGBODY with two labels. The symbols for these labels are computed by GENSYM and are not interned in any package. Two *go* forms use these tags to jump to. Since *tagbody* is a primitive operator in Common Lisp (and not a macro), it will not be expanded into something else. The expanded form uses the *when* macro, which also will be expanded. Fully expanding a source form is called *code walking*.
In the fully expanded (*walked*) form, the *when* form is replaced by the primitive *if*:
``` lisp
(TAGBODY
#:START1136
(IF (ZEROP (RANDOM 10))
(PROGN (GO #:END1137))
NIL)
(PROGN (WRITE-LINE "hello"))
(GO #:START1136))
#:END1137)
```
All macros must be expanded before the source code containing them can be evaluated or compiled normally. Macros can be considered functions that accept and return S-expressions -- similar to abstract syntax trees, but not limited to those. These functions are invoked before the evaluator or compiler to produce the final source code. Macros are written in normal Common Lisp, and may use any Common Lisp (or third-party) operator available.
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# Common Lisp
## Macros
### Variable capture and shadowing {#variable_capture_and_shadowing}
Common Lisp macros are capable of what is commonly called *variable capture*, where symbols in the macro-expansion body coincide with those in the calling context, allowing the programmer to create macros wherein various symbols have special meaning. The term *variable capture* is somewhat misleading, because all namespaces are vulnerable to unwanted capture, including the operator and function namespace, the tagbody label namespace, catch tag, condition handler and restart namespaces.
*Variable capture* can introduce software defects. This happens in one of the following two ways:
- In the first way, a macro expansion can inadvertently make a symbolic reference which the macro writer assumed will resolve in a global namespace, but the code where the macro is expanded happens to provide a local, shadowing definition which steals that reference. Let this be referred to as type 1 capture.
- The second way, type 2 capture, is just the opposite: some of the arguments of the macro are pieces of code supplied by the macro caller, and those pieces of code are written such that they make references to surrounding bindings. However, the macro inserts these pieces of code into an expansion which defines its own bindings that accidentally captures some of these references.
The Scheme dialect of Lisp provides a macro-writing system which provides the referential transparency that eliminates both types of capture problem. This type of macro system is sometimes called \"hygienic\", in particular by its proponents (who regard macro systems which do not automatically solve this problem as unhygienic).
In Common Lisp, macro hygiene is ensured one of two different ways.
One approach is to use gensyms: guaranteed-unique symbols which can be used in a macro-expansion without threat of capture. The use of gensyms in a macro definition is a manual chore, but macros can be written which simplify the instantiation and use of gensyms. Gensyms solve type 2 capture easily, but they are not applicable to type 1 capture in the same way, because the macro expansion cannot rename the interfering symbols in the surrounding code which capture its references. Gensyms could be used to provide stable aliases for the global symbols which the macro expansion needs. The macro expansion would use these secret aliases rather than the well-known names, so redefinition of the well-known names would have no ill effect on the macro.
Another approach is to use packages. A macro defined in its own package can simply use internal symbols in that package in its expansion. The use of packages deals with type 1 and type 2 capture.
However, packages don\'t solve the type 1 capture of references to standard Common Lisp functions and operators. The reason is that the use of packages to solve capture problems revolves around the use of private symbols (symbols in one package, which are not imported into, or otherwise made visible in other packages). Whereas the Common Lisp library symbols are external, and frequently imported into or made visible in user-defined packages.
The following is an example of unwanted capture in the operator namespace, occurring in the expansion of a macro:
``` lisp
;; expansion of UNTIL makes liberal use of DO
(defmacro until (expression &body body)
`(do () (,expression) ,@body))
;; macrolet establishes lexical operator binding for DO
(macrolet ((do (...) ... something else ...))
(until (= (random 10) 0) (write-line "Hello")))
```
The `until` macro will expand into a form which calls `do` which is intended to refer to the standard Common Lisp macro `do`. However, in this context, `do` may have a completely different meaning, so `until` may not work properly.
Common Lisp solves the problem of the shadowing of standard operators and functions by forbidding their redefinition. Because it redefines the standard operator `do`, the preceding is actually a fragment of non-conforming Common Lisp, which allows implementations to diagnose and reject it.
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# Common Lisp
## Condition system {#condition_system}
The *condition system* is responsible for exception handling in Common Lisp. It provides *conditions*, *handler*s and *restart*s. *Condition*s are objects describing an exceptional situation (for example an error). If a *condition* is signaled, the Common Lisp system searches for a *handler* for this condition type and calls the handler. The *handler* can now search for restarts and use one of these restarts to automatically repair the current problem, using information such as the condition type and any relevant information provided as part of the condition object, and call the appropriate restart function.
These restarts, if unhandled by code, can be presented to users (as part of a user interface, that of a debugger for example), so that the user can select and invoke one of the available restarts. Since the condition handler is called in the context of the error (without unwinding the stack), full error recovery is possible in many cases, where other exception handling systems would have already terminated the current routine. The debugger itself can also be customized or replaced using the `*debugger-hook*` dynamic variable. Code found within *unwind-protect* forms such as finalizers will also be executed as appropriate despite the exception.
In the following example (using Symbolics Genera) the user tries to open a file in a Lisp function *test* called from the Read-Eval-Print-LOOP (REPL), when the file does not exist. The Lisp system presents four restarts. The user selects the *Retry OPEN using a different pathname* restart and enters a different pathname (lispm-init.lisp instead of lispm-int.lisp). The user code does not contain any error handling code. The whole error handling and restart code is provided by the Lisp system, which can handle and repair the error without terminating the user code.
``` text
Command: (test ">zippy>lispm-int.lisp")
Error: The file was not found.
For lispm:>zippy>lispm-int.lisp.newest
LMFS:OPEN-LOCAL-LMFS-1
Arg 0: #P"lispm:>zippy>lispm-int.lisp.newest"
s-A, <Resume>: Retry OPEN of lispm:>zippy>lispm-int.lisp.newest
s-B: Retry OPEN using a different pathname
s-C, <Abort>: Return to Lisp Top Level in a TELNET server
s-D: Restart process TELNET terminal
-> Retry OPEN using a different pathname
Use what pathname instead [default lispm:>zippy>lispm-int.lisp.newest]:
lispm:>zippy>lispm-init.lisp.newest
...the program continues
```
## Common Lisp Object System (CLOS) {#common_lisp_object_system_clos}
Common Lisp includes a toolkit for object-oriented programming, the Common Lisp Object System or CLOS. Peter Norvig explains how many Design Patterns are simpler to implement in a dynamic language with the features of CLOS (Multiple Inheritance, Mixins, Multimethods, Metaclasses, Method combinations, etc.). Several extensions to Common Lisp for object-oriented programming have been proposed to be included into the ANSI Common Lisp standard, but eventually CLOS was adopted as the standard object-system for Common Lisp. CLOS is a dynamic object system with multiple dispatch and multiple inheritance, and differs radically from the OOP facilities found in static languages such as C++ or Java. As a dynamic object system, CLOS allows changes at runtime to generic functions and classes. Methods can be added and removed, classes can be added and redefined, objects can be updated for class changes and the class of objects can be changed.
CLOS has been integrated into ANSI Common Lisp. Generic functions can be used like normal functions and are a first-class data type. Every CLOS class is integrated into the Common Lisp type system. Many Common Lisp types have a corresponding class. There is more potential use of CLOS for Common Lisp. The specification does not say whether conditions are implemented with CLOS. Pathnames and streams could be implemented with CLOS. These further usage possibilities of CLOS for ANSI Common Lisp are not part of the standard. Actual Common Lisp implementations use CLOS for pathnames, streams, input--output, conditions, the implementation of CLOS itself and more.
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# Common Lisp
## Compiler and interpreter {#compiler_and_interpreter}
A Lisp interpreter directly executes Lisp source code provided as Lisp objects (lists, symbols, numbers, \...) read from s-expressions. A Lisp compiler generates bytecode or machine code from Lisp source code. Common Lisp allows both individual Lisp functions to be compiled in memory and the compilation of whole files to externally stored compiled code (*fasl* files).
Several implementations of earlier Lisp dialects provided both an interpreter and a compiler. Unfortunately often the semantics were different. These earlier Lisps implemented lexical scoping in the compiler and dynamic scoping in the interpreter. Common Lisp requires that both the interpreter and compiler use lexical scoping by default. The Common Lisp standard describes both the semantics of the interpreter and a compiler. The compiler can be called using the function *compile* for individual functions and using the function *compile-file* for files. Common Lisp allows type declarations and provides ways to influence the compiler code generation policy. For the latter various optimization qualities can be given values between 0 (not important) and 3 (most important): *speed*, *space*, *safety*, *debug* and *compilation-speed*.
There is also a function to evaluate Lisp code: `eval`. `eval` takes code as pre-parsed s-expressions and not, like in some other languages, as text strings. This way code can be constructed with the usual Lisp functions for constructing lists and symbols and then this code can be evaluated with the function `eval`. Several Common Lisp implementations (like Clozure CL and SBCL) are implementing `eval` using their compiler. This way code is compiled, even though it is evaluated using the function `eval`.
The file compiler is invoked using the function *compile-file*. The generated file with compiled code is called a *fasl* (from *fast load*) file. These *fasl* files and also source code files can be loaded with the function *load* into a running Common Lisp system. Depending on the implementation, the file compiler generates byte-code (for example for the Java Virtual Machine), C language code (which then is compiled with a C compiler) or, directly, native code.
Common Lisp implementations can be used interactively, even though the code gets fully compiled. The idea of an Interpreted language thus does not apply for interactive Common Lisp.
The language makes a distinction between read-time, compile-time, load-time, and run-time, and allows user code to also make this distinction to perform the wanted type of processing at the wanted step.
Some special operators are provided to especially suit interactive development; for instance, `defvar` will only assign a value to its provided variable if it wasn\'t already bound, while `defparameter` will always perform the assignment. This distinction is useful when interactively evaluating, compiling and loading code in a live image.
Some features are also provided to help writing compilers and interpreters. Symbols consist of first-level objects and are directly manipulable by user code. The `progv` special operator allows to create lexical bindings programmatically, while packages are also manipulable. The Lisp compiler is available at runtime to compile files or individual functions. These make it easy to use Lisp as an intermediate compiler or interpreter for another language.
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# Common Lisp
## Code examples {#code_examples}
### Birthday paradox {#birthday_paradox}
The following program calculates the smallest number of people in a room for whom the probability of unique birthdays is less than 50% (the birthday paradox, where for 1 person the probability is obviously 100%, for 2 it is 364/365, etc.). The answer is 23.
In Common Lisp, by convention, constants are enclosed with + characters.
``` lisp
(defconstant +year-size+ 365)
(defun birthday-paradox (probability number-of-people)
(let ((new-probability (* (/ (- +year-size+ number-of-people)
+year-size+)
probability)))
(if (< new-probability 0.5)
(1+ number-of-people)
(birthday-paradox new-probability (1+ number-of-people)))))
```
Calling the example function using the REPL (Read Eval Print Loop):
``` text
CL-USER > (birthday-paradox 1.0 1)
23
```
### Sorting a list of person objects {#sorting_a_list_of_person_objects}
We define a class `person` and a method for displaying the name and age of a person. Next we define a group of persons as a list of `person` objects. Then we iterate over the sorted list.
``` lisp
(defclass person ()
((name :initarg :name :accessor person-name)
(age :initarg :age :accessor person-age))
(:documentation "The class PERSON with slots NAME and AGE."))
(defmethod display ((object person) stream)
"Displaying a PERSON object to an output stream."
(with-slots (name age) object
(format stream "~a (~a)" name age)))
(defparameter *group*
(list (make-instance 'person :name "Bob" :age 33)
(make-instance 'person :name "Chris" :age 16)
(make-instance 'person :name "Ash" :age 23))
"A list of PERSON objects.")
(dolist (person (sort (copy-list *group*)
#'>
:key #'person-age))
(display person *standard-output*)
(terpri))
```
It prints the three names with descending age.
``` text
Bob (33)
Ash (23)
Chris (16)
```
### Exponentiating by squaring {#exponentiating_by_squaring}
Use of the LOOP macro is demonstrated:
``` lisp
(defun power (x n)
(loop with result = 1
while (plusp n)
when (oddp n) do (setf result (* result x))
do (setf x (* x x)
n (truncate n 2))
finally (return result)))
```
Example use:
``` lisp
CL-USER > (power 2 200)
1606938044258990275541962092341162602522202993782792835301376
```
Compare with the built in exponentiation:
``` lisp
CL-USER > (= (expt 2 200) (power 2 200))
T
```
### Find the list of available shells {#find_the_list_of_available_shells}
WITH-OPEN-FILE is a macro that opens a file and provides a stream. When the form is returning, the file is automatically closed. FUNCALL calls a function object. The LOOP collects all lines that match the predicate.
``` lisp
(defun list-matching-lines (file predicate)
"Returns a list of lines in file, for which the predicate applied to
the line returns T."
(with-open-file (stream file)
(loop for line = (read-line stream nil nil)
while line
when (funcall predicate line)
collect it)))
```
The function AVAILABLE-SHELLS calls the above function LIST-MATCHING-LINES with a pathname and an anonymous function as the predicate. The predicate returns the pathname of a shell or NIL (if the string is not the filename of a shell).
``` lisp
(defun available-shells (&optional (file #p"/etc/shells"))
(list-matching-lines
file
(lambda (line)
(and (plusp (length line))
(char= (char line 0) #\/)
(pathname
(string-right-trim '(#\space #\tab) line))))))
```
Example results (on Mac OS X 10.6):
``` lisp
CL-USER > (available-shells)
(#P"/bin/bash" #P"/bin/csh" #P"/bin/ksh" #P"/bin/sh" #P"/bin/tcsh" #P"/bin/zsh")
```
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# Common Lisp
## Comparison with other Lisps {#comparison_with_other_lisps}
Common Lisp is most frequently compared with, and contrasted to, Scheme---if only because they are the two most popular Lisp dialects. Scheme predates CL, and comes not only from the same Lisp tradition but from some of the same engineers---Guy Steele, with whom Gerald Jay Sussman designed Scheme, chaired the standards committee for Common Lisp.
Common Lisp is a general-purpose programming language, in contrast to Lisp variants such as Emacs Lisp and AutoLISP which are extension languages embedded in particular products (GNU Emacs and AutoCAD, respectively). Unlike many earlier Lisps, Common Lisp (like Scheme) uses lexical variable scope by default for both interpreted and compiled code.
Most of the Lisp systems whose designs contributed to Common Lisp---such as ZetaLisp and Franz Lisp---used dynamically scoped variables in their interpreters and lexically scoped variables in their compilers. Scheme introduced the sole use of lexically scoped variables to Lisp; an inspiration from ALGOL 68. CL supports dynamically scoped variables as well, but they must be explicitly declared as \"special\". There are no differences in scoping between ANSI CL interpreters and compilers.
Common Lisp is sometimes termed a *Lisp-2* and Scheme a *Lisp-1*, referring to CL\'s use of separate namespaces for functions and variables. (In fact, CL has *many* namespaces, such as those for go tags, block names, and `loop` keywords). There is a long-standing controversy between CL and Scheme advocates over the tradeoffs involved in multiple namespaces. In Scheme, it is (broadly) necessary to avoid giving variables names that clash with functions; Scheme functions frequently have arguments named `lis`, `lst`, or `lyst` so as not to conflict with the system function `list`. However, in CL it is necessary to explicitly refer to the function namespace when passing a function as an argument---which is also a common occurrence, as in the `sort` example above.
CL also differs from Scheme in its handling of Boolean values. Scheme uses the special values #t and #f to represent truth and falsity. CL follows the older Lisp convention of using the symbols T and NIL, with NIL standing also for the empty list. In CL, *any* non-NIL value is treated as true by conditionals, such as `if`, whereas in Scheme all non-#f values are treated as true. These conventions allow some operators in both languages to serve both as predicates (answering a Boolean-valued question) and as returning a useful value for further computation, but in Scheme the value \'() which is equivalent to NIL in Common Lisp evaluates to true in a Boolean expression.
Lastly, the Scheme standards documents require tail-call optimization, which the CL standard does not. Most CL implementations do offer tail-call optimization, although often only when the programmer uses an optimization directive. Nonetheless, common CL coding style does not favor the ubiquitous use of recursion that Scheme style prefers---what a Scheme programmer would express with tail recursion, a CL user would usually express with an iterative expression in `do`, `dolist`, `loop`, or (more recently) with the `iterate` package.
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# Common Lisp
## Implementations
See the Category Common Lisp implementations.
Common Lisp is defined by a specification (like Ada and C) rather than by one implementation (like Perl). There are many implementations, and the standard details areas in which they may validly differ.
In addition, implementations tend to come with extensions, which provide functionality not covered in the standard:
- Interactive Top-Level (REPL)
- Garbage Collection
- Debugger, Stepper and Inspector
- Weak data structures (hash tables)
- Extensible sequences
- Extensible LOOP
- Environment access
- CLOS Meta-object Protocol
- CLOS based extensible streams
- CLOS based Condition System
- Network streams
- Persistent CLOS
- Unicode support
- Foreign-Language Interface (often to C)
- Operating System interface
- Java Interface
- Threads and Multiprocessing
- Application delivery (applications, dynamic libraries)
- Saving of images
Free and open-source software libraries have been created to support extensions to Common Lisp in a portable way, and are most notably found in the repositories of the Common-Lisp.net and CLOCC (Common Lisp Open Code Collection) projects.
Common Lisp implementations may use any mix of native code compilation, byte code compilation or interpretation. Common Lisp has been designed to support incremental compilers, file compilers and block compilers. Standard declarations to optimize compilation (such as function inlining or type specialization) are proposed in the language specification. Most Common Lisp implementations compile source code to native machine code. Some implementations can create (optimized) stand-alone applications. Others compile to interpreted bytecode, which is less efficient than native code, but eases binary-code portability. Some compilers compile Common Lisp code to C code. The misconception that Lisp is a purely interpreted language is most likely because Lisp environments provide an interactive prompt and that code is compiled one-by-one, in an incremental way. With Common Lisp incremental compilation is widely used.
Some Unix-based implementations (CLISP, SBCL) can be used as a scripting language; that is, invoked by the system transparently in the way that a Perl or Unix shell interpreter is.
### List of implementations {#list_of_implementations}
#### Commercial implementations {#commercial_implementations}
Allegro Common Lisp: for Microsoft Windows, FreeBSD, Linux, Apple macOS and various UNIX variants. Allegro CL provides an Integrated Development Environment (IDE) (for Windows and Linux) and extensive capabilities for application delivery.\
Liquid Common Lisp: formerly called Lucid Common Lisp. Only maintenance, no new releases.\
LispWorks: for Microsoft Windows, FreeBSD, Linux, Apple macOS, iOS, Android and various UNIX variants. LispWorks provides an Integrated Development Environment (IDE) (available for most platforms, but not for iOS and Android) and extensive capabilities for application delivery.\
mocl: for iOS, Android and macOS.\
Open Genera: for DEC Alpha.\
Scieneer Common Lisp: which is designed for high-performance scientific computing.
#### Freely redistributable implementations {#freely_redistributable_implementations}
Armed Bear Common Lisp (ABCL): A CL implementation that runs on the Java Virtual Machine. It includes a compiler to Java byte code, and allows access to Java libraries from CL. It was formerly just a component of the Armed Bear J Editor.\
Clasp: A LLVM based implementation that seamlessly interoperates with C++ libraries. Runs on several Unix and Unix-like systems (including macOS).\
CLISP: A bytecode-compiling implementation, portable and runs on several Unix and Unix-like systems (including macOS), as well as Microsoft Windows and several other systems.\
Clozure CL (CCL): Originally a free and open-source fork of Macintosh Common Lisp. As that history implies, CCL was written for the Macintosh, but Clozure CL now runs on macOS, FreeBSD, Linux, Solaris and Windows. 32 and 64 bit x86 ports are supported on each platform. Additionally there are Power PC ports for Mac OS and Linux. CCL was previously known as OpenMCL, but that name is no longer used, to avoid confusion with the open source version of Macintosh Common Lisp.\
CMUCL: Originally from Carnegie Mellon University, now maintained as free and open-source software by a group of volunteers. CMUCL uses a fast native-code compiler. It is available on Linux and BSD for Intel x86; Linux for Alpha; macOS for Intel x86 and PowerPC; and Solaris, IRIX, and HP-UX on their native platforms.\
Corman Common Lisp: for Microsoft Windows. In January 2015 Corman Lisp has been published under MIT license.\
Embeddable Common Lisp (ECL): ECL includes a bytecode interpreter and compiler. It can also compile Lisp code to machine code via a C compiler. ECL then compiles Lisp code to C, compiles the C code with a C compiler and can then load the resulting machine code. It is also possible to embed ECL in C programs, and C code into Common Lisp programs.\
GNU Common Lisp (GCL): The GNU Project\'s Lisp compiler. Not yet fully ANSI-compliant, GCL is however the implementation of choice for several large projects including the mathematical tools Maxima, AXIOM and (historically) ACL2. GCL runs on Linux under eleven different architectures, and also under Windows, Solaris, and FreeBSD.\
Macintosh Common Lisp (MCL): Version 5.2 for Apple Macintosh computers with a PowerPC processor running Mac OS X is open source. RMCL (based on MCL 5.2) runs on Intel-based Apple Macintosh computers using the Rosetta binary translator from Apple.\
ManKai Common Lisp (MKCL): A branch of ECL. MKCL emphasises reliability, stability and overall code quality through a heavily reworked, natively multi-threaded, runtime system. On Linux, MKCL features a fully POSIX compliant runtime system.\
Movitz: Implements a Lisp environment for x86 computers without relying on any underlying OS.\
Poplog: Poplog implements a version of CL, with POP-11, and optionally Prolog, and Standard ML (SML), allowing mixed language programming. For all, the implementation language is POP-11, which is compiled incrementally. It also has an integrated Emacs-like editor that communicates with the compiler.\
Steel Bank Common Lisp (SBCL): A branch from CMUCL. \"Broadly speaking, SBCL is distinguished from CMU CL by a greater emphasis on maintainability.\"{{cite web
`|url=`[`http://sbcl.sourceforge.net/history.html`](http://sbcl.sourceforge.net/history.html)\
`|title=History and Copyright |work=Steel Bank Common Lisp`
}}
SBCL runs on the platforms CMUCL does, except HP/UX; in addition, it runs on Linux for AMD64, PowerPC, SPARC, MIPS, Windows x86 and AMD64. SBCL does not use an interpreter by default; all expressions are compiled to native code unless the user switches the interpreter on. The SBCL compiler generates fast native code according to a previous version of The Computer Language Benchmarks Game.
Ufasoft Common Lisp: port of CLISP for windows platform with core written in C++.
#### Other implementations {#other_implementations}
Austin Kyoto Common Lisp: an evolution of Kyoto Common Lisp by Bill Schelter\
Butterfly Common Lisp: an implementation written in Scheme for the BBN Butterfly multi-processor computer\
CLICC: a Common Lisp to C compiler\
CLOE: Common Lisp for PCs by Symbolics\
Codemist Common Lisp: used for the commercial version of the computer algebra system Axiom\
ExperCommon Lisp: an early implementation for the Apple Macintosh by ExperTelligence\
Golden Common Lisp: an implementation for the PC by GoldHill Inc.\
Ibuki Common Lisp: a commercialized version of Kyoto Common Lisp\
Kyoto Common Lisp: the first Common Lisp compiler that used C as a target language. GCL, ECL and MKCL originate from this Common Lisp implementation.\
L: a small version of Common Lisp for embedded systems developed by IS Robotics, now iRobot\
Lisp Machines (from Symbolics, TI and Xerox): provided implementations of Common Lisp in addition to their native Lisp dialect (Lisp Machine Lisp or Interlisp). CLOS was also available. Symbolics provides an enhanced version Common Lisp.\
Procyon Common Lisp: an implementation for Windows and Mac OS, used by Franz for their Windows port of Allegro CL\
Star Sapphire Common LISP: an implementation for the PC\
SubL: a variant of Common Lisp used for the implementation of the Cyc knowledge-based system\
Top Level Common Lisp: an early implementation for concurrent execution\
WCL: a shared library implementation\
VAX Common Lisp: Digital Equipment Corporation\'s implementation that ran on VAX systems running VMS or ULTRIX\
XLISP: an implementation written by David Betz
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# Common Lisp
## Applications
Common Lisp is used to develop research applications (often in Artificial Intelligence), for rapid development of prototypes or for deployed applications.
Common Lisp is used in many commercial applications, including the Yahoo! Store web-commerce site, which originally involved Paul Graham and was later rewritten in C++ and Perl. Other notable examples include:
- ACT-R, a cognitive architecture used in a large number of research projects.
- Authorizer\'s Assistant, a large rule-based system used by American Express, analyzing credit requests.
- Cyc, a long running project to create a knowledge-based system that provides a huge amount of common sense knowledge.
- Gensym G2, a real-time expert system and business rules engine
- Genworks GDL, based on the open-source Gendl kernel.
- The development environment for the *Jak and Daxter* video game series, developed by Naughty Dog.
- ITA Software\'s low fare search engine, used by travel websites such as Orbitz and Kayak.com and airlines such as American Airlines, Continental Airlines and US Airways.
- Mirai, a 3D graphics suite.
- Opusmodus is a music composition system based on Common Lisp, used in Computer assisted composition.
- Prototype Verification System (PVS), a mechanized environment for formal specification and verification.
- PWGL is a sophisticated visual programming environment based on Common Lisp, used in Computer assisted composition and sound synthesis.
- Piano, a complete aircraft analysis suite, written in Common Lisp, used by companies like Boeing, Airbus, and Northrop Grumman.
- Grammarly, an English-language writing-enhancement platform, has its core grammar engine written in Common Lisp.
- The Dynamic Analysis and Replanning Tool (DART), which is said to alone have paid back during the years from 1991 to 1995 for all thirty years of DARPA investments in AI research.
- NASA\'s Jet Propulsion Lab\'s \"Deep Space 1\", an award-winning Common Lisp program for autopiloting the Deep Space One spaceship.
- SigLab, a Common Lisp platform for signal processing used in missile defense, built by Raytheon.
- NASA\'s Mars Pathfinder Mission Planning System.
- SPIKE, a scheduling system for Earth or space based observatories and satellites, notably the Hubble Space Telescope, written in Common Lisp.
- Common Lisp has been used for prototyping the garbage collector of Microsoft\'s .NET Common Language Runtime.
- The original version of Reddit, though the developers later switched to Python due to the lack of libraries for Common Lisp, according to an official blog post by Reddit co-founder Steve Huffman. The reddit v1 source code has been open-sourced and modernized.
There also exist open-source applications written in Common Lisp, such as:
- ACL2, a full-featured automated theorem prover for an applicative variant of Common Lisp.
- Axiom, a sophisticated computer algebra system.
- Maxima, a sophisticated computer algebra system, based on Macsyma.
- OpenMusic, an object-oriented visual programming environment based on Common Lisp, used in computer assisted composition.
- Pgloader, a data loader for PostgreSQL, which was re-written from Python to Common Lisp.
- Stumpwm, a tiling, keyboard driven X11 Window Manager written entirely in Common Lisp
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# Color code
A **color code** is a system for encoding and representing non-color information with colors to facilitate communication. This information tends to be categorical (representing unordered/qualitative categories) though may also be sequential (representing an ordered/quantitative variable).
## History
The earliest examples of color codes in use are for long-distance communication by use of flags, as in semaphore communication. The United Kingdom adopted a color code scheme for such communication wherein red signified danger and white signified safety, with other colors having similar assignments of meaning.
As chemistry and other technologies advanced, it became expedient to use coloration as a signal for telling apart things that would otherwise be confusingly similar, such as wiring in electrical and electronic devices, and pharmaceutical pills.
## Encoded Variable {#encoded_variable}
A color code encodes a variable, which may have different representations, where the color code type should match the variable type:
- Categorical variable -- the variable may represent discrete values of unordered qualitative data (e.g. blood type)
- Binary variables are typically treated as a categorical variable (e.g. sex)
- Quantitative variable -- the variable represents ordered, quantitative data (e.g. age)
- Discrete quantitative data (e.g. the 6 sides of a die: 1,2,3,4,5,6) are sometimes treated as a categorical variable, despite the ordered nature.
## Types
The types of color code are:
- **Categorical** -- the colors are unordered, but are chosen to maximize saliency of the colors, by maximizing color difference between all color pair permutations.
- **Continuous** -- the colors are ordered and form a smooth color gradient.
- **Discrete** -- only a subset of a continuous color code are used (still ordered), where each is distinguishable from the others.
### Categorical
When color is the only varied attribute, the color code is *unidimensional*. When other attributes are varied (e.g. shape, size), the code is *multidimensional*, where the dimensions can be *independent* (each encoding separate variables) or *redundant* (encoding the same variable). Partial redundancy sees one variable as a subset of another. For example, playing card suits are multidimensional with color (black, red) and shape (club, diamond, heart, spade), which are partially redundant since clubs and spades are always black and diamonds and hearts are always red. Tasks using categorical color codes can be classified as identification tasks, where a single stimulus is shown and must be identified (connotatively or denotatively), versus search tasks, where a color stimulus must be found within a field of heterogenous stimuli. Performance in these tasks is measured by speed and/or accuracy.
The ideal color scheme for a categorical color code depends on whether speed or accuracy is more important. Despite humans being able to distinguish 150 distinct colors along the hue dimension during comparative task, evidence supports that color schemes where colors differ only by hue (equal luminosity and colorfulness) should have a maximum of eight categories with optimized stimulus spacing along the hue dimension, though this would not be color blind accessible. The IALA recommends categorical color codes in seven colors: red, orange, yellow, green, blue, white and black. Adding redundant coding of luminosity and colorfulness adds information and increases speed and accuracy of color decoding tasks. Color codes are superior to others (encoding to letters, shape, size, etc.) in certain types of tasks. Adding color as a redundant attribute to a numeral or letter encoding in search tasks decreased time by 50--75%,`{{r|CHRIST75|at=Fig9}}`{=mediawiki} but in unidimensional identification tasks, using alphanumeric or line inclination codes caused less errors than color codes.`{{r|1=JONES62|2=CHRIST75|p2=19}}`{=mediawiki}
Several studies demonstrate a subjective preference for color codes over achromatic codes (e.g. shapes), even in studies where color coding did not increase performance over achromatic coding.`{{r|CHRIST75|p=18}}`{=mediawiki} Subjects reported the tasks as less monotonous and less inducing of eye strain and fatigue.`{{r|CHRIST75|p=18}}`{=mediawiki}
The ability to discriminate color differences decreases rapidly as the visual angle subtends less than 12\' (0.2° or \~2 mm at a viewing distance of 50 cm), so color stimulus of at least 3 mm in diameter or thickness is recommended when the color is on paper or on a screen. Under normal conditions, colored backgrounds do not affect the interpretation of color codes, but chromatic (and/or low) illumination of surface color code can degrade performance.
## Criticism
Color codes present some potential problems. On forms and signage, the use of color can distract from black and white text.
Color codes are often designed without consideration for accessibility to color blind and blind people, and may even be inaccessible for those with normal color vision, since use of many colors to code many variables can lead to use of confusingly similar colors. Only 15--40% of the colorblind can correctly name surface color codes with 8--10 color categories, most of which test as mildly colorblind. This finding uses ideal illumination; when dimmer illumination is used, performance drops sharply.
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# Color code
## Examples
Systems incorporating color-coding include:
- In electricity:
- 25-pair color code -- telecommunications wiring
- ANSI Z535
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# Charles Robert Malden
**Charles Robert Malden** (9 August 1797 -- 23 May 1855) was a nineteenth-century British naval officer, surveyor and educator. He is the discoverer of Malden Island in the central Pacific, which is named in his honour. He also founded Windlesham House School at Brighton, England.
## Biography
Malden was born in Putney, Surrey, son of Jonas Malden, a surgeon. He entered British naval service at the age of 11 on 22 June 1809. He served nine years as a volunteer 1st class, midshipman, and shipmate, including one year in the English Channel and Bay of Biscay (1809), four years at the Cape of Good Hope and in the East Indies (1809--14), two and a half years on the North American and West Indian stations (1814--16), and a year and a half in the Mediterranean (1817--18). He was present at the capture of Mauritius and Java, and at the battles of Baltimore and New Orleans.
He passed the examination in the elements of mathematics and the theory of navigation at the Royal Naval Academy on 2--4 September 1816, and became a 1st Lieutenant on 1 September 1818. In eight years of active service as an officer, he served two and a half years in a surveying ship in the Mediterranean (1818--21), one and a half years in a surveying sloop in the English Channel and off the coast of Ireland (1823--24), and one and a half years as Surveyor of the frigate `{{HMS|Blonde|1819|6}}`{=mediawiki} during a voyage (1824--26) to and from the Hawaiian Islands (then known as the \"Sandwich islands\"). In Hawaii he surveyed harbours which, he noted, were \"said not to exist by Captains Cook and Vancouver.\" On the return voyage he discovered and explored uninhabited Malden Island in the central Pacific on 30 July 1825. After his return he left active service but remained at half pay. He served for several years as hydrographer to King William IV.
He married Frances Cole, daughter of Rev. William Hodgson Cole, rector of West Clandon and Vicar of Wonersh, near Guildford, Surrey, on 8 April 1828. Malden became the father of seven sons and a daughter.
From 1830 to 1836 he took pupils for the Royal Navy at Ryde, Isle of Wight. He purchased the school of Henry Worsley at Newport, Isle of Wight, in December 1836, reopened it as a preparatory school on 20 February 1837, and moved it to Montpelier Road in Brighton in December 1837. He built the Windlesham House School at Brighton in 1844, and conducted the school until his death there in 1855. He was succeeded as headmaster by his son Henry Charles Malden
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# Canonization
`{{Use dmy dates|date=October 2020}}`{=mediawiki} `{{Use American English|date=February 2016}}`{=mediawiki}
**Canonization** is the declaration of a deceased person as an officially recognized saint, specifically, the official act of a Christian communion declaring a person worthy of public veneration and entering their name in the canon catalogue of saints, or authorized list of that communion\'s recognized saints.
## Catholic Church {#catholic_church}
`{{Catholic canon law}}`{=mediawiki} Canonization is a papal declaration that the Catholic faithful may venerate a particular deceased member of the church. Popes began making such decrees in the tenth century. Up to that point, the local bishops governed the veneration of holy men and women within their own dioceses; and there may have been, for any particular saint, no formal decree at all. In subsequent centuries, the procedures became increasingly regularized and the Popes began restricting to themselves the right to declare someone a Catholic saint. In contemporary usage, the term is understood to refer to the act by which any Christian church declares that a person who has died is a saint, upon which declaration the person is included in the list of recognized saints, called the \"canon\".
### Biblical roots {#biblical_roots}
In the Roman Martyrology, the following entry is given for the Penitent Thief: \"At Jerusalem, the commemoration of the good Thief, who confessed Christ on the cross, and deserved to hear from Him these words: \'This day thou shalt be with Me in paradise.\'
### Historical development {#historical_development}
The Roman Canon, the historical Eucharistic Prayer or Anaphora of Canon of the Roman Rite contains only the names of apostles and martyrs, along with that of the Blessed Virgin Mary and, since 1962, that of Saint Joseph her spouse.
By the fourth century, however, \"confessors\"---people who had confessed their faith not by dying but by word and life---began to be venerated publicly. Examples of such people are Saint Hilarion and Saint Ephrem the Syrian in the East, and Saint Martin of Tours and Saint Hilary of Poitiers in the West. Their names were inserted in the diptychs, the lists of saints explicitly venerated in the liturgy, and their tombs were honoured in like manner as those of the martyrs. Since the witness of their lives was not as unequivocal as that of the martyrs, they were venerated publicly only with the approval by the local bishop. This process is often referred to as \"local canonization\".
This approval was required even for veneration of a reputed martyr. In his history of the Donatist heresy, Saint Optatus recounts that at Carthage a Catholic matron, named Lucilla, incurred the censures of the Church for having kissed the relics of a reputed martyr whose claims to martyrdom had not been juridically proved. And Saint Cyprian (died 258) recommended that the utmost diligence be observed in investigating the claims of those who were said to have died for the faith. All the circumstances accompanying the martyrdom were to be inquired into; the faith of those who suffered, and the motives that animated them were to be rigorously examined, in order to prevent the recognition of undeserving persons. Evidence was sought from the court records of the trials or from people who had been present at the trials.
Augustine of Hippo (died 430) tells of the procedure which was followed in his day for the recognition of a martyr. The bishop of the diocese in which the martyrdom took place set up a canonical process for conducting the inquiry with the utmost severity. The acts of the process were sent either to the metropolitan or primate, who carefully examined the cause, and, after consultation with the suffragan bishops, declared whether the deceased was worthy of the name of \"martyr\" and public veneration.
Though not \"canonizations\" in the narrow sense, acts of formal recognition, such as the erection of an altar over the saint\'s tomb or transferring the saint\'s relics to a church, were preceded by formal inquiries into the sanctity of the person\'s life and the miracles attributed to that person\'s intercession.
Such acts of recognition of a saint were authoritative, in the strict sense, only for the diocese or ecclesiastical province for which they were issued, but with the spread of the fame of a saint, were often accepted elsewhere also.
### Nature
In the Catholic Church, both in the Latin and the constituent Eastern churches, the act of canonization is reserved to the Apostolic See and occurs at the conclusion of a long process requiring extensive proof that the candidate for canonization lived and died in such an exemplary and holy way that they are worthy to be recognized as a saint. The Church\'s official recognition of sanctity implies that the person is now in Heaven and that they may be publicly invoked and mentioned officially in the liturgy of the Church, including in the Litany of the Saints.
In the Catholic Church, canonization is a decree that allows universal veneration of the saint. For permission to venerate merely locally, only beatification is needed.
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# Canonization
## Catholic Church {#catholic_church}
### Procedure prior to reservation to the Apostolic See {#procedure_prior_to_reservation_to_the_apostolic_see}
For several centuries the bishops, or in some places only the primates and patriarchs, could grant martyrs and confessors public ecclesiastical honor; such honor, however, was always decreed only for the local territory of which the grantors had jurisdiction. Only acceptance of the *cultus* by the Pope made the *cultus* universal, because he alone can rule the universal Catholic Church. Abuses, however, crept into this discipline, due as well to indiscretions of popular fervor as to the negligence of some bishops in inquiring into the lives of those whom they permitted to be honoured as saints.
In the Medieval West, the Apostolic See was asked to intervene in the question of canonizations so as to ensure more authoritative decisions. The canonization of Saint Udalric, Bishop of Augsburg by Pope John XV in 993 was the first undoubted example of papal canonization of a saint from outside of Rome being declared worthy of liturgical veneration for the entire church.
Thereafter, recourse to the judgment of the Pope occurred more frequently. Toward the end of the 11th century, the Popes began asserting their exclusive right to authorize the veneration of a saint against the older rights of bishops to do so for their dioceses and regions. Popes therefore decreed that the virtues and miracles of persons proposed for public veneration should be examined in councils, more specifically in general councils. Pope Urban II, Pope Calixtus II, and Pope Eugene III conformed to this discipline.
### Exclusive reservation to the Apostolic See {#exclusive_reservation_to_the_apostolic_see}
Hugh de Boves, Archbishop of Rouen, canonized Walter of Pontoise, or St. Gaultier, in 1153, the final saint in Western Europe to be canonized by an authority other than the Pope: \"The last case of canonization by a metropolitan is said to have been that of St. Gaultier, or Gaucher, \[A\]bbot of Pontoise, by the Archbishop of Rouen. A decree of Pope Alexander III \[in\] 1170 gave the prerogative to the \[P\]ope thenceforth, so far as the Western Church was concerned.\" In a decretal of 1173, Pope Alexander III reprimanded some bishops for permitting veneration of a man who was merely killed while intoxicated, prohibited veneration of the man, and most significantly decreed that \"you shall not therefore presume to honor him in the future; for, even if miracles were worked through him, it is not lawful for you to venerate him as a saint without the authority of the Catholic Church.\" Theologians disagree as to the full import of the decretal of Pope Alexander III: either a new law was instituted, in which case the Pope then for the first time reserved the right of beatification to himself, or an existing law was confirmed.
However, the procedure initiated by the decretal of Pope Alexander III was confirmed by a bull of Pope Innocent III issued on the occasion of the canonization of Cunigunde of Luxembourg in 1200. The bull of Pope Innocent III resulted in increasingly elaborate inquiries to the Apostolic See concerning canonizations. Because the decretal of Pope Alexander III did not end all controversy and some bishops did not obey it in so far as it regarded beatification, the right of which they had certainly possessed hitherto, Pope Urban VIII issued the Apostolic letter *Caelestis Hierusalem cives* of 5 July 1634 that exclusively reserved to the Apostolic See both its immemorial right of canonization and that of beatification. He further regulated both of these acts by issuing his *Decreta servanda in beatificatione et canonizatione Sanctorum* on 12 March 1642.
### Procedure from 1734 to 1738 to 1983 {#procedure_from_1734_to_1738_to_1983}
In his *De Servorum Dei beatificatione et de Beatorum canonizatione* of five volumes the eminent canonist Prospero Lambertini (1675--1758), who later became Pope Benedict XIV, elaborated on the procedural norms of Pope Urban VIII\'s Apostolic letter *Caelestis Hierusalem cives* of 1634 and *Decreta servanda in beatificatione et canonizatione Sanctorum* of 1642, and on the conventional practice of the time. His work published from 1734 to 1738 governed the proceedings until 1917. The article \"Beatification and canonization process in 1914\" describes the procedures followed until the promulgation of the *Codex* of 1917. The substance of *De Servorum Dei beatifιcatione et de Beatorum canonizatione* was incorporated into the *Codex Iuris Canonici* (*Code of Canon Law*) of 1917, which governed until the promulgation of the revised *Codex Iuris Canonici* in 1983 by Pope John Paul II. Prior to promulgation of the revised *Codex* in 1983, Pope Paul VI initiated a simplification of the procedures.
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# Canonization
## Catholic Church {#catholic_church}
### Since 1983 {#since_1983}
The Apostolic constitution *Divinus Perfectionis Magister* of Pope John Paul II of 25 January 1983 and the norms issued by the Congregation for the Causes of Saints on 7 February 1983 to implement the constitution in dioceses, continued the simplification of the process initiated by Pope Paul VI. Contrary to popular belief, the reforms did not eliminate the office of the Promoter of the Faith (Latin: *Promotor Fidei*), popularly known as the Devil\'s advocate, whose office is to question the material presented in favor of canonization. The reforms were intended to reduce the adversarial nature of the process. In November 2012 Pope Benedict XVI appointed Monsignor Carmello Pellegrino as Promoter of the Faith.
Candidates for canonization undergo the following process: `{{ordered list
| [[Servant of God]] (''Servus Dei''): The process of canonization commences at the diocesan level. A [[bishop]] with jurisdiction, usually the bishop of the place where the candidate died or is buried, although another ordinary can be given this authority, gives permission to open an investigation into the virtues of the individual in response to a petition of members of the faithful, either actually or ''[[pro forma]]''.<ref>Pope John Paul II, [https://www.vatican.va/holy_father/john_paul_ii/apost_constitutions/documents/hf_jp-ii_apc_25011983_divinus-perfectionis-magister_en.html ''Divinus Perfectionis Magister''] (25 January 1983), Art. 1, Sec. 1.</ref> This investigation usually commences no sooner than five years after the death of the person being investigated.<ref>Pietro Cardinal Palazzini, [https://www.vatican.va/roman_curia/congregations/csaints/documents/rc_con_csaints_doc_07021983_norme_en.html ''Norms to be observed in inquiries made by bishops in the causes of saints''], 1983 {{webarchive |url=https://web.archive.org/web/20061022065149/https://www.vatican.va/roman_curia/congregations/csaints/documents/rc_con_csaints_doc_07021983_norme_en.html |date=22 October 2006 }}, §9(a).</ref> The [[Pope]], ''qua'' Bishop of Rome, may also open a process and has the authority to waive the waiting period of five years, e.g., as was done for [[St. Teresa of Calcutta]] by [[Pope John Paul II]],<ref>[https://www.vatican.va/news_services/liturgy/saints/ns_lit_doc_20031019_madre-teresa_en.html ''Mother Teresa of Calcutta (1910–1997), Biography''], Office of Papal Liturgical Celebrations, Internet Office of the Holy See</ref> and for [[Lúcia Santos]] and for [[Pope John Paul II]] himself by [[Pope Benedict XVI]].<ref>{{cite web|url=http://www.zenit.org/article-21764?l=english|title=Sister Lucia's Beatification Process to Begin|work=ZENIT – The World Seen from Rome|access-date=4 October 2014|url-status=dead|archive-url=https://web.archive.org/web/20120927020314/http://www.zenit.org/article-21764?l=english|archive-date=27 September 2012}}</ref><ref>[[Cardinal (Catholicism)|Cardinal]] [[José Saraiva Martins]], [[Claretians|CMF]], [https://www.vatican.va/roman_curia/congregations/csaints/documents/rc_con_csaints_doc_20050509_rescritto-gpii_en.html ''Response of His Holiness Benedict XVI for the Examination of the Cause for Beatification and Canonization of the Servant of God John Paul II''], 2005 {{webarchive |url=https://web.archive.org/web/20090105024819/https://www.vatican.va/roman_curia/congregations/csaints/documents/rc_con_csaints_doc_20050509_rescritto-gpii_en.html |date=5 January 2009 }}</ref> Normally, an association to promote the cause of the candidate is instituted, an exhaustive search of the candidate's writings, speeches, and sermons is undertaken, a detailed biography is written, and eyewitness accounts are collected. When sufficient evidence has been collected, the local bishop presents the investigation of the candidate, who is titled "Servant of God" ([[Latin]]: ''Servus Dei''), to the [[Congregation for the Causes of the Saints]] of the [[Roman Curia]], where the cause is assigned a [[postulator]], whose office is to collect further evidence of the life of the Servant of God. Religious orders that regularly deal with the Congregation often designate their own Postulator General. At some time, permission is then granted for the body of the Servant of God to be exhumed and examined. A certification ''non-cultus'' is made that no superstitious or heretical worship, or improper cult of the Servant of God or her/his tomb has emerged, and relics are taken and preserved.
| [[Venerable]] (''Venerabilis''; abbreviated "Ven.") or "Heroic in Virtue": When sufficient evidence has been collected, the Congregation recommends to the [[Pope]] that he proclaim the [[heroic virtue]] of the Servant of God; that is, that the Servant of God exercised "to a heroic degree" the [[theological virtues]] of faith, hope, and charity and the [[cardinal virtues]] of prudence, justice, fortitude, and temperance. From this time the one said to be "heroic in virtue" is entitled "[[Venerable]]" ([[Latin]]: ''Venerabilis''). A Venerable does not yet have a [[feast day]], permission to erect churches in their honor has not yet been granted, and the Church does not yet issue a statement on their probable or certain presence in [[Heaven]], but [[prayer card]]s and other materials may be printed to encourage the faithful to pray for a [[miracle]] wrought by their intercession as a sign of God's will that the person be canonized.
| [[Beatification|Blessed]] (''Beatus'' or ''Beata''; abbreviated "Bl."): Beatification is a statement of the Church that it is "worthy of belief" that the Venerable is in [[Heaven]] and saved. Attaining this grade depends on whether the Venerable is a [[martyr]]:{{bulleted list
| For a martyr, the [[Pope]] has only to make a declaration of martyrdom, which is a certification that the Venerable gave their life voluntarily as a witness of the Faith or in an [[act of heroic charity]] for others.
| For a non-martyr, all of them being denominated "confessors" because they "confessed", i.e., bore witness to the Faith by how they lived, proof is required of the occurrence of a [[miracle]] through the intercession of the Venerable; that is, that God granted a sign that the person is enjoying the [[beatific vision]] by performing a miracle for which the Venerable interceded. Presently, these miracles are almost always miraculous cures of infirmity, because these are the easiest to judge given the Church's evidentiary requirements for miracles; e.g., a patient was sick with an illness for which no cure was known; prayers were directed to the Venerable; the patient was cured; the cure was spontaneous, instantaneous, complete, and enduring; and physicians cannot discover any natural explanation for the cure.
}}
The satisfaction of the applicable conditions permits [[beatification]], which then bestows on the Venerable the title of "Blessed" ([[Latin]]: ''Beatus'' or ''Beata''). A [[feast day]] will be designated, but its observance is ordinarily only permitted for the Blessed's home [[diocese]], to specific locations associated with them, or to the churches or houses of the Blessed's religious order if they belonged to one. Parishes may not normally be named in honor of ''beati''.
| [[Saint]] (''Sanctus'' or ''Sancta''; abbreviated "St." or "S."): To be canonized as a saint, ordinarily at least two miracles must have been performed through the intercession of the Blessed after their death, but for ''beati'' confessors, i.e., ''beati'' who were not declared martyrs, only one miracle is required, ordinarily being additional to that upon which beatification was premised. Very rarely, a Pope may waive the requirement for a second miracle after beatification if he, the [[College of Cardinals|Sacred College of Cardinals]], and the [[Congregation for the Causes of Saints]] all agree that the Blessed lived a life of great merit proven by certain actions. This extraordinary procedure was used in [[Pope Francis]]' canonization of [[Pope John XXIII]], who convoked the first part of the [[Second Vatican Council]].
}}`{=mediawiki}
Canonization is a statement of the Church that the person certainly enjoys the beatific vision of Heaven. The title of \"Saint\" (Latin: *Sanctus* or *Sancta*) is then proper, reflecting that the saint is a refulgence of the holiness (*sanctitas*) of God himself, which alone comes from God\'s gift. The saint is assigned a feast day which may be celebrated anywhere in the universal Church, although it is not necessarily added to the General Roman Calendar or local calendars as an \"obligatory\" feast; parish churches may be erected in their honor; and the faithful may freely celebrate and honor the saint.
Although recognition of sainthood by the Pope does not directly concern a fact of Divine revelation, nonetheless it must be \"definitively held\" by the faithful as *infallible* pursuant to, at the least, the Universal Magisterium of the Church, because it is a truth related to revelation by historical necessity.
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# Canonization
## Catholic Church {#catholic_church}
### Equipollent canonization {#equipollent_canonization}
Popes have several times permitted to the universal Church, without executing the ordinary judicial process of canonization described above, the veneration as a saint, the \"*cultus*\" of one long venerated as such locally. This act of a Pope is denominated \"equipollent\" or \"equivalent canonization\" and \"confirmation of *cultus*\". In such cases, there is no need to have a miracle attributed to the saint to allow their canonization. According to the rules Pope Benedict XIV (*regnat* 17 August 1740 -- 3 May 1758) instituted, there are three conditions for an equipollent canonization: (1) existence of an ancient *cultus* of the person, (2) a general and constant attestation to the virtues or martyrdom of the person by credible historians, and (3) uninterrupted fame of the person as a worker of miracles.
## Protestant denominations {#protestant_denominations}
The majority of Protestant denominations do not formally recognize saints because the Bible uses the term in a way that suggests all Christians are saints. However, some denominations do, as shown below.
### Anglican Communion {#anglican_communion}
The Church of England, the Mother Church of the Anglican Communion, canonized Charles I as a saint, in the Convocations of Canterbury and York of 1660.
### United Methodist Church {#united_methodist_church}
The General Conference of the United Methodist Church has formally declared individuals *martyrs*, including Dietrich Bonhoeffer (in 2008) and Martin Luther King Jr. (in 2012).
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# Canonization
## Eastern Orthodox Church {#eastern_orthodox_church}
Various terms are used for canonization by the autocephalous Eastern Orthodox Churches: канонизация (\"canonization\") or прославление (\"glorification\", in the Russian Orthodox Church), კანონიზაცია (*kanonizats'ia*, Georgian Orthodox Church), канонизација (Serbian Orthodox Church), *canonizare* (Romanian Orthodox Church), and Канонизация (Bulgarian Orthodox Church). Additional terms are used for canonization by other autocephalous Eastern Orthodox Churches: *αγιοκατάταξη* (Katharevousa: *ἁγιοκατάταξις*) *agiokatataxi/agiokatataxis*, \"ranking among saints\" (Ecumenical Patriarchate of Constantinople, Church of Cyprus, Church of Greece), *kanonizim* (Albanian Orthodox Church), *kanonizacja* (Polish Orthodox Church), and *kanonizace/kanonizácia* (Czech and Slovak Orthodox Church).
The Orthodox Church in America, an Eastern Orthodox Church partly recognized as autocephalous, uses the term \"glorification\" for the official recognition of a person as a saint.
## Oriental Orthodox Church {#oriental_orthodox_church}
Within the Armenian Apostolic Church, part of Oriental Orthodoxy, there had been discussions since the 1980s about canonizing the victims of the Armenian genocide. On 23 April 2015, all of the victims of the genocide were canonized
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# Carboxylic acid
In organic chemistry, a **carboxylic acid** is an organic acid that contains a **carboxyl group** (`{{chem2|\sC(\dO)\sOH}}`{=mediawiki}) attached to an R-group. The general formula of a carboxylic acid is often written as **`{{chem2|R\sCOOH}}`{=mediawiki}** or **`{{chem2|R\sCO2H}}`{=mediawiki}**, sometimes as `{{chem2|R\sC(O)OH}}`{=mediawiki} with R referring to an organyl group (e.g., alkyl, alkenyl, aryl), or hydrogen, or other groups. Carboxylic acids occur widely. Important examples include the amino acids and fatty acids. Deprotonation of a carboxylic acid gives a carboxylate anion.
## Examples and nomenclature {#examples_and_nomenclature}
Carboxylic acids are commonly identified by their trivial names. They often have the suffix *-ic acid*. `{{anchor|-oic}}`{=mediawiki}IUPAC-recommended names also exist; in this system, carboxylic acids have an *-oic acid* suffix. For example, butyric acid (`{{chem2|CH3CH2CH2CO2H}}`{=mediawiki}) is butanoic acid by IUPAC guidelines. For nomenclature of complex molecules containing a carboxylic acid, the carboxyl can be considered position one of the parent chain even if there are other substituents, such as 3-chloropropanoic acid. Alternately, it can be named as a \"carboxy\" or \"carboxylic acid\" substituent on another parent structure, such as 2-carboxyfuran.
The carboxylate anion (`{{chem2|R\sCOO−}}`{=mediawiki} or `{{chem2|R\sCO2−}}`{=mediawiki}) of a carboxylic acid is usually named with the suffix *-ate*, in keeping with the general pattern of *-ic acid* and *-ate* for a conjugate acid and its conjugate base, respectively. For example, the conjugate base of acetic acid is acetate.
Carbonic acid, which occurs in bicarbonate buffer systems in nature, is not generally classed as one of the carboxylic acids, despite it having a moiety that looks like a COOH group.
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| Carbon\ | Common name | IUPAC name | Chemical formula | Common location or use |
| atoms | | | | |
+=========+===================+====================+==================+==================================================================+
| 1 | Formic acid | Methanoic acid | HCOOH | Insect stings |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 2 | Acetic acid | Ethanoic acid | | Vinegar |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 3 | Propionic acid | Propanoic acid | | Preservative for stored grains, body odour, milk, butter, cheese |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 4 | Butyric acid | Butanoic acid | | Butter |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 5 | Valeric acid | Pentanoic acid | | Valerian plant |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 6 | Caproic acid | Hexanoic acid | | Goat fat |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 7 | Enanthic acid | Heptanoic acid | | Fragrance |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 8 | Caprylic acid | Octanoic acid | | Coconuts |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 9 | Pelargonic acid | Nonanoic acid | | Pelargonium plant |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 10 | Capric acid | Decanoic acid | | Coconut and Palm kernel oil |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 11 | Undecylic acid | Undecanoic acid | | Anti-fungal agent |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 12 | Lauric acid | Dodecanoic acid | | Coconut oil and hand wash soaps |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 13 | Tridecylic acid | Tridecanoic acid | | Plant metabolite |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 14 | Myristic acid | Tetradecanoic acid | | Nutmeg |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 15 | Pentadecylic acid | Pentadecanoic acid | | Milk fat |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 16 | Palmitic acid | Hexadecanoic acid | | Palm oil |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 17 | Margaric acid | Heptadecanoic acid | | Pheromone in various animals |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 18 | Stearic acid | Octadecanoic acid | | Chocolate, waxes, soaps, and oils |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 19 | Nonadecylic acid | Nonadecanoic acid | | Fats, vegetable oils, pheromone |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
| 20 | Arachidic acid | Icosanoic acid | | Peanut oil |
+---------+-------------------+--------------------+------------------+------------------------------------------------------------------+
: Straight-chain, saturated carboxylic acids (alkanoic acids)
Compound class Members
---------------------------------- ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
unsaturated monocarboxylic acids acrylic acid (2-propenoic acid) -- `{{chem2|CH2\dCH\sCOOH}}`{=mediawiki}, used in polymer synthesis
Fatty acids medium to long-chain saturated and unsaturated monocarboxylic acids, with even number of carbons; examples: docosahexaenoic acid and eicosapentaenoic acid (nutritional supplements)
Amino acids the building-blocks of proteins
Keto acids acids of biochemical significance that contain a ketone group; examples: acetoacetic acid and pyruvic acid
Aromatic carboxylic acids containing at least one aromatic ring; examples: benzoic acid -- the sodium salt of benzoic acid is used as a food preservative; salicylic acid -- a beta-hydroxy type found in many skin-care products; phenyl alkanoic acids -- the class of compounds where a phenyl group is attached to a carboxylic acid
Dicarboxylic acids containing two carboxyl groups; examples: adipic acid the monomer used to produce nylon and aldaric acid -- a family of sugar acids
Tricarboxylic acids containing three carboxyl groups; examples: citric acid -- found in citrus fruits and isocitric acid
Alpha hydroxy acids containing a hydroxy group in the first position; examples: glyceric acid, glycolic acid and lactic acid (2-hydroxypropanoic acid) -- found in sour milk, tartaric acid -- found in wine
Beta hydroxy acids containing a hydroxy group in the second position
Omega hydroxy acids containing a hydroxy group beyond the first or second position
Divinylether fatty acids containing a doubly unsaturated carbon chain attached via an ether bond to a fatty acid, found in some plants
: Other carboxylic acids
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# Carboxylic acid
## Physical properties {#physical_properties}
### Solubility
Carboxylic acids are polar. Because they are both hydrogen-bond acceptors (the carbonyl `{{chem2|\sC(\dO)\s}}`{=mediawiki}) and hydrogen-bond donors (the hydroxyl `{{chem2|\sOH}}`{=mediawiki}), they also participate in hydrogen bonding. Together, the hydroxyl and carbonyl group form the functional group carboxyl. Carboxylic acids usually exist as dimers in nonpolar media due to their tendency to \"self-associate\". Smaller carboxylic acids (1 to 5 carbons) are soluble in water, whereas bigger carboxylic acids have limited solubility due to the increasing hydrophobic nature of the alkyl chain. These longer chain acids tend to be soluble in less-polar solvents such as ethers and alcohols. Aqueous sodium hydroxide and carboxylic acids, even hydrophobic ones, react to yield water-soluble sodium salts. For example, enanthic acid has a low solubility in water (0.2 g/L), but its sodium salt is very soluble in water.
:
### Boiling points {#boiling_points}
Carboxylic acids tend to have higher boiling points than water, because of their greater surface areas and their tendency to form stabilized dimers through hydrogen bonds. For boiling to occur, either the dimer bonds must be broken or the entire dimer arrangement must be vaporized, increasing the enthalpy of vaporization requirements significantly.
:
### Acidity
Carboxylic acids are Brønsted--Lowry acids because they are proton (H^+^) donors. They are the most common type of organic acid.
Carboxylic acids are typically weak acids, meaning that they only partially dissociate into `{{chem2|[H3O]+}}`{=mediawiki} cations and `{{chem2|R\sCO2−}}`{=mediawiki} anions in neutral aqueous solution. For example, at room temperature, in a 1-molar solution of acetic acid, only 0.001% of the acid are dissociated (i.e. 10^−5^ moles out of 1 mol). Electron-withdrawing substituents such as trifluoromethyl (`{{chem2|\sCF3}}`{=mediawiki}) give stronger acids (the p*K*~a~ of acetic acid is 4.76 whereas trifluoroacetic acid, with a trifluoromethyl substituent, has a p*K*~a~ of 0.23). Electron-donating substituents give weaker acids (the p*K*~a~ of formic acid is 3.75 whereas acetic acid, with a methyl substituent, has a p*K*~a~ of 4.76)
Carboxylic acid p*K*~a~
-------------------------------------------------------------------------------------------------- ---------
Formic acid (`{{chem2|HCO2H}}`{=mediawiki}) 3.75
Chloroformic acid (`{{chem2|ClCO2H}}`{=mediawiki}) 0.27
Acetic acid (`{{chem2|CH3CO2H}}`{=mediawiki}) 4.76
Glycine (`{{chem2|NH2CH2CO2H}}`{=mediawiki}) 2.34
Fluoroacetic acid (`{{chem2|FCH2CO2H}}`{=mediawiki}) 2.586
Difluoroacetic acid (`{{chem2|F2CHCO2H}}`{=mediawiki}) 1.33
Trifluoroacetic acid (`{{chem2|CF3CO2H}}`{=mediawiki}) 0.23
Chloroacetic acid (`{{chem2|ClCH2CO2H}}`{=mediawiki}) 2.86
Dichloroacetic acid (`{{chem2|Cl2CHCO2H}}`{=mediawiki}) 1.29
Trichloroacetic acid (`{{chem2|CCl3CO2H}}`{=mediawiki}) 0.65
Benzoic acid (`{{chem2|C6H5\sCO2H}}`{=mediawiki}) 4.2
2-Nitrobenzoic acid (*ortho*-`{{chem2|C6H4(NO2)CO2H}}`{=mediawiki}) 2.16
Oxalic acid (`{{chem2|HO\sC(\dO)\sC(\dO)\sOH}}`{=mediawiki}) (first dissociation) 1.27
Hydrogen oxalate (`{{chem2|HO\sC(\dO)\sCO2−}}`{=mediawiki}) (second dissociation of oxalic acid) 4.14
Deprotonation of carboxylic acids gives carboxylate anions; these are resonance stabilized, because the negative charge is delocalized over the two oxygen atoms, increasing the stability of the anion. Each of the carbon--oxygen bonds in the carboxylate anion has a partial double-bond character. The carbonyl carbon\'s partial positive charge is also weakened by the −^1^/~2~ negative charges on the 2 oxygen atoms.
### Odour
Carboxylic acids often have strong sour odours. Esters of carboxylic acids tend to have fruity, pleasant odours, and many are used in perfume.
### Characterization
Carboxylic acids are readily identified as such by infrared spectroscopy. They exhibit a sharp band associated with vibration of the C=O carbonyl bond (*ν*~C=O~) between 1680 and 1725 cm^−1^. A characteristic *ν*~O--H~ band appears as a broad peak in the 2500 to 3000 cm^−1^ region. By ^1^H NMR spectrometry, the hydroxyl hydrogen appears in the 10--13 ppm region, although it is often either broadened or not observed owing to exchange with traces of water.
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# Carboxylic acid
## Occurrence and applications {#occurrence_and_applications}
Many carboxylic acids are produced industrially on a large scale. They are also frequently found in nature. Esters of fatty acids are the main components of lipids and polyamides of aminocarboxylic acids are the main components of proteins.
Carboxylic acids are used in the production of polymers, pharmaceuticals, solvents, and food additives. Industrially important carboxylic acids include acetic acid (component of vinegar, precursor to solvents and coatings), acrylic and methacrylic acids (precursors to polymers, adhesives), adipic acid (polymers), citric acid (a flavor and preservative in food and beverages), ethylenediaminetetraacetic acid (chelating agent), fatty acids (coatings), maleic acid (polymers), propionic acid (food preservative), terephthalic acid (polymers). Important carboxylate salts are soaps.
## Synthesis
### Industrial routes {#industrial_routes}
In general, industrial routes to carboxylic acids differ from those used on a smaller scale because they require specialized equipment.
- Carbonylation of alcohols as illustrated by the Cativa process for the production of acetic acid. Formic acid is prepared by a different carbonylation pathway, also starting from methanol.
- Oxidation of aldehydes with air using cobalt and manganese catalysts. The required aldehydes are readily obtained from alkenes by hydroformylation.
- Oxidation of hydrocarbons using air. For simple alkanes, this method is inexpensive but not selective enough to be useful. Allylic and benzylic compounds undergo more selective oxidations. Alkyl groups on a benzene ring are oxidized to the carboxylic acid, regardless of its chain length. Benzoic acid from toluene, terephthalic acid from *para*-xylene, and phthalic acid from *ortho*-xylene are illustrative large-scale conversions. Acrylic acid is generated from propene.
- Oxidation of ethene using silicotungstic acid catalyst.
- Base-catalyzed dehydrogenation of alcohols.
- Carbonylation coupled to the addition of water. This method is effective and versatile for alkenes that generate secondary and tertiary carbocations, e.g. isobutylene to pivalic acid. In the Koch reaction, the addition of water and carbon monoxide to alkenes or alkynes is catalyzed by strong acids. Hydrocarboxylations involve the simultaneous addition of water and CO. Such reactions are sometimes called \"Reppe chemistry.\"
:
- Hydrolysis of triglycerides obtained from plant or animal oils. These methods of synthesizing some long-chain carboxylic acids are related to soap making.
- Fermentation of ethanol. This method is used in the production of vinegar.
- The Kolbe--Schmitt reaction provides a route to salicylic acid, precursor to aspirin.
### Laboratory methods {#laboratory_methods}
Preparative methods for small scale reactions for research or for production of fine chemicals often employ expensive consumable reagents.
- Oxidation of primary alcohols or aldehydes with strong oxidants such as potassium dichromate, Jones reagent, potassium permanganate, or sodium chlorite. The method is more suitable for laboratory conditions than the industrial use of air, which is \"greener\" because it yields less inorganic side products such as chromium or manganese oxides.
- Oxidative cleavage of olefins by ozonolysis, potassium permanganate, or potassium dichromate.
- Hydrolysis of nitriles, esters, or amides, usually with acid- or base-catalysis.
- Carbonation of a Grignard reagent and organolithium reagents:
:
:
- Halogenation followed by hydrolysis of methyl ketones in the haloform reaction
- Base-catalyzed cleavage of non-enolizable ketones, especially aryl ketones:
:
### Less-common reactions {#less_common_reactions}
Many reactions produce carboxylic acids but are used only in specific cases or are mainly of academic interest.
- Disproportionation of an aldehyde in the Cannizzaro reaction
- Rearrangement of diketones in the benzilic acid rearrangement
- Involving the generation of benzoic acids are the von Richter reaction from nitrobenzenes and the Kolbe--Schmitt reaction from phenols.
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# Carboxylic acid
## Reactions
### Acid-base reactions {#acid_base_reactions}
Carboxylic acids react with bases to form carboxylate salts, in which the hydrogen of the hydroxyl (--OH) group is replaced with a metal cation. For example, acetic acid found in vinegar reacts with sodium bicarbonate (baking soda) to form sodium acetate, carbon dioxide, and water:
:
### Conversion to esters, amides, anhydrides {#conversion_to_esters_amides_anhydrides}
Widely practiced reactions convert carboxylic acids into esters, amides, carboxylate salts, acid chlorides, and alcohols. Their conversion to esters is widely used, e.g. in the production of polyesters. Likewise, carboxylic acids are converted into amides, but this conversion typically does not occur by direct reaction of the carboxylic acid and the amine. Instead esters are typical precursors to amides. The conversion of amino acids into peptides is a significant biochemical process that requires ATP.
Converting a carboxylic acid to an amide is possible, but not straightforward. Instead of acting as a nucleophile, an amine will react as a base in the presence of a carboxylic acid to give the ammonium carboxylate salt. Heating the salt to above 100 °C will drive off water and lead to the formation of the amide. This method of synthesizing amides is industrially important, and has laboratory applications as well. In the presence of a strong acid catalyst, carboxylic acids can condense to form acid anhydrides. The condensation produces water, however, which can hydrolyze the anhydride back to the starting carboxylic acids. Thus, the formation of the anhydride via condensation is an equilibrium process.
Under acid-catalyzed conditions, carboxylic acids will react with alcohols to form esters via the Fischer esterification reaction, which is also an equilibrium process. Alternatively, diazomethane can be used to convert an acid to an ester. While esterification reactions with diazomethane often give quantitative yields, diazomethane is only useful for forming methyl esters.
### Reduction
Like esters, most carboxylic acids can be reduced to alcohols by hydrogenation, or using hydride transferring agents such as lithium aluminium hydride. Strong alkyl transferring agents, such as organolithium compounds but not Grignard reagents, will reduce carboxylic acids to ketones along with transfer of the alkyl group.
The Vilsmaier reagent (*N*,*N*-Dimethyl(chloromethylene)ammonium chloride; `{{chem2|[ClHC\dN+(CH3)2]Cl−}}`{=mediawiki}) is a highly chemoselective agent for carboxylic acid reduction. It selectively activates the carboxylic acid to give the carboxymethyleneammonium salt, which can be reduced by a mild reductant like lithium tris(*t*-butoxy)aluminum hydride to afford an aldehyde in a one pot procedure. This procedure is known to tolerate reactive carbonyl functionalities such as ketone as well as moderately reactive ester, olefin, nitrile, and halide moieties.
### Conversion to acyl halides {#conversion_to_acyl_halides}
The hydroxyl group on carboxylic acids may be replaced with a chlorine atom using thionyl chloride to give acyl chlorides. In nature, carboxylic acids are converted to thioesters. Thionyl chloride can be used to convert carboxylic acids to their corresponding acyl chlorides. First, carboxylic acid **1** attacks thionyl chloride, and chloride ion leaves. The resulting oxonium ion **2** is activated towards nucleophilic attack and has a good leaving group, setting it apart from a normal carboxylic acid. In the next step, **2** is attacked by chloride ion to give tetrahedral intermediate **3**, a chlorosulfite. The tetrahedral intermediate collapses with the loss of sulfur dioxide and chloride ion, giving protonated acyl chloride **4**. Chloride ion can remove the proton on the carbonyl group, giving the acyl chloride **5** with a loss of HCl.
Phosphorus(III) chloride (PCl~3~) and phosphorus(V) chloride (PCl~5~) will also convert carboxylic acids to acid chlorides, by a similar mechanism. One equivalent of PCl~3~ can react with three equivalents of acid, producing one equivalent of H~3~PO~3~, or phosphorus acid, in addition to the desired acid chloride. PCl~5~ reacts with carboxylic acids in a 1:1 ratio, and produces phosphorus(V) oxychloride (POCl~3~) and hydrogen chloride (HCl) as byproducts.
### Reactions with carbanion equivalents {#reactions_with_carbanion_equivalents}
Carboxylic acids react with Grignard reagents and organolithiums to form ketones. The first equivalent of nucleophile acts as a base and deprotonates the acid. A second equivalent will attack the carbonyl group to create a geminal alkoxide dianion, which is protonated upon workup to give the hydrate of a ketone. Because most ketone hydrates are unstable relative to their corresponding ketones, the equilibrium between the two is shifted heavily in favor of the ketone. For example, the equilibrium constant for the formation of acetone hydrate from acetone is only 0.002. The carboxylic group is the most acidic in organic compounds.
### Specialized reactions {#specialized_reactions}
- As with all carbonyl compounds, the protons on the α-carbon are labile due to keto--enol tautomerization. Thus, the α-carbon is easily halogenated in the Hell--Volhard--Zelinsky halogenation.
- The Schmidt reaction converts carboxylic acids to amines.
- Carboxylic acids are decarboxylated in the Hunsdiecker reaction.
- The Dakin--West reaction converts an amino acid to the corresponding amino ketone.
- In the Barbier--Wieland degradation, a carboxylic acid on an aliphatic chain having a simple methylene bridge at the alpha position can have the chain shortened by one carbon. The inverse procedure is the Arndt--Eistert synthesis, where an acid is converted into acyl halide, which is then reacted with diazomethane to give one additional methylene in the aliphatic chain.
- Many acids undergo oxidative decarboxylation. Enzymes that catalyze these reactions are known as carboxylases (EC 6.4.1) and decarboxylases (EC 4.1.1).
- Carboxylic acids are reduced to aldehydes via the ester and DIBAL, via the acid chloride in the Rosenmund reduction and via the thioester in the Fukuyama reduction.
- In ketonic decarboxylation carboxylic acids are converted to ketones.
- Organolithium reagents (\>2 equiv) react with carboxylic acids to give a dilithium 1,1-diolate, a stable tetrahedral intermediate which decomposes to give a ketone upon acidic workup.
- The Kolbe electrolysis is an electrolytic, decarboxylative dimerization reaction. It gets rid of the carboxyl groups of two acid molecules, and joins the remaining fragments together.
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# Carboxylic acid
## Carboxyl radical {#carboxyl_radical}
The carboxyl radical, •COOH, only exists briefly. The acid dissociation constant of •COOH has been measured using electron paramagnetic resonance spectroscopy. The carboxyl group tends to dimerise to form oxalic acid
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# Chernobyl
**Chernobyl**, officially called **Chornobyl**, is a partially abandoned city in Vyshhorod Raion, Kyiv Oblast, Ukraine. It is located within the Chernobyl Exclusion Zone, 90 km to the north of Kyiv and 160 km to the southwest of Gomel in neighbouring Belarus. Prior to being evacuated in the aftermath of the Chernobyl disaster in 1986, it was home to approximately 14,000 residents---considerably less than adjacent Pripyat, which was completely abandoned following the incident. Since then, although living anywhere within the Chernobyl Exclusion Zone is technically illegal, Ukrainian authorities have tolerated those who have taken up living in some of the city\'s less irradiated areas; Chernobyl\'s 2020 population estimate was 150 people.
First mentioned as a ducal hunting lodge in Kievan Rus\' in 1193, the city has changed hands multiple times over the course of its history. In the 16th century, Jews began moving into Chernobyl, and at the end of the 18th century, it had become a major centre of Hasidic Judaism under the Twersky dynasty. During the early 20th century, pogroms and associated emigration caused the local Jewish community to dwindle significantly. By World War II, all remaining Jews in the city were murdered by Nazi Germany as part of the Holocaust.
In 1972, Chernobyl rose to prominence in the Soviet Union when it was selected as the site of the Chernobyl Nuclear Power Plant; Pripyat was constructed nearby to house the facility\'s workers. Located 15 km to the north of Chernobyl proper, it opened in 1977. On 5 May 1986, nine days after Reactor No. 4 at the Chernobyl Nuclear Power Plant exploded, the Soviet government began evacuating the residents of both Chernobyl and Pripyat in preparation for the liquidators\' management of the disaster. Following their subsequent settlement in the newly purpose-built city of Slavutych, most of the evacuees never returned. From 1923 onwards, Chernobyl had been the administrative centre of Chernobyl Raion, which was dissolved and merged with Ivankiv Raion in 1988, owing to widespread radioactive contamination in the region. Ivankiv Raion, in turn, was dissolved and merged with Vyshhorod Raion during Ukraine\'s 2020 administrative reform.
Workers on watch and administrative personnel of the Chernobyl Exclusion Zone are stationed in the city, which has two general stores and a hotel. Though the city\'s atmosphere remained calm after the disaster was contained, the beginning of the Russian invasion of Ukraine in February 2022 sparked international concern about the stability of Ukrainian nuclear facilities, especially pursuant to reports that Russia\'s occupation of the Chernobyl Exclusion Zone until April 2022 had caused a spike in radiation levels.
## Etymology
The city\'s name is the same as one of the Ukrainian names for *Artemisia vulgaris*, mugwort or common wormwood: *label=none* (or more commonly *полин звичайний* `{{transliteration|uk|polýn zvycháynyy}}`{=mediawiki}, \'common artemisia\'). The name is inherited from `{{proto|slavic|čьrnobylъ}}`{=mediawiki} or `{{proto|slavic|čьrnobyl}}`{=mediawiki}, a compound of `{{proto|slavic|čьrnъ|black}}`{=mediawiki} + `{{proto|slavic|bylь|grass}}`{=mediawiki}, the parts related to *links=no* and *било* `{{transliteration|uk|byló}}`{=mediawiki}, \'stalk\', so named in distinction to the lighter-stemmed wormwood *A. absinthium*.
The name in languages used nearby is:
- , `{{IPA|uk|tʃorˈnɔbɪlʲ|pron|uk-чорнобиль.ogg}}`{=mediawiki}
- , `{{IPA|be|t͡ʂarˈnɔbɨlʲ|pron}}`{=mediawiki}
- , `{{IPA|ru|tɕɪrˈnobɨlʲ|pron}}`{=mediawiki}.
The name in languages formerly used in the area is:
- , `{{IPA|pl|tʂarˈnɔbɨl|pron}}`{=mediawiki}
- , `{{IPA|yi|tʃɛrˈnɔbl̩|pron}}`{=mediawiki}.
In English, the Russian-derived spelling *Chernobyl* has been commonly used, but some style guides recommend the spelling *Chornobyl*, or the use of romanized Ukrainian names for Ukrainian places generally.
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# Chernobyl
## History
The Polish Geographical Dictionary of the Kingdom of Poland of 1880--1902 states that the time the city was founded is not known.
### Identity of Ptolemy\'s \"Azagarium\" {#identity_of_ptolemys_azagarium}
Some older geographical dictionaries and descriptions of modern Eastern Europe mention \"Czernobol\" (Chernobyl) with reference to Ptolemy\'s world map (2nd century AD). Czernobol is identified as Azagarium \"oppidium Sarmatiae\" (Lat., \"a city in Sarmatia\"), by the 1605 *Lexicon geographicum* of Filippo Ferrari and the 1677 *Lexicon Universale* of Johann Jakob Hofmann. According to the *Dictionary of Ancient Geography* of Alexander Macbean (London, 1773), Azagarium is \"a town of Sarmatia Europaea, on the Borysthenes\" (Dnieper), 36° East longitude and 50°40\' latitude. The city is \"now supposed to be *Czernobol*, a town of Poland, in Red Russia \[Red Ruthenia\], in the Palatinate of Kiow \[Kiev Voivodeship\], not far from the Borysthenes.\"
Whether Azagarium is indeed Czernobol is debatable. The question of Azagarium\'s correct location was raised in 1842 by Habsburg-Slovak historian, Pavel Jozef Šafárik, who published a book titled \"Slavic Ancient History\" (\"Sławiańskie starożytności\"), where he claimed Azagarium to be the hill of Zaguryna, which he found on an old Russian map \"Bolzoj czertez\" (Big drawing)`{{dubious|Azagarium|reason=What is this "Big drawing"? The name of the map, or what?|date=September 2020}}`{=mediawiki} near the city of Pereiaslav, now in central Ukraine.
In 2019, Ukrainian architect Boris Yerofalov-Pylypchak published a book, *Roman Kyiv or Castrum Azagarium at Kyiv-Podil*.
### Kievan Rus\' and post-medieval era (880--1793) {#kievan_rus_and_post_medieval_era_8801793}
The archaeological excavations that were conducted in 2005--2008 found a cultural layer from the 10--12th centuries AD, which predates the first documentary mention of Chernobyl.
Around the 12th century Chernobyl was part of the land of Kievan Rus′. The first known mention of the settlement as Chernobyl is from an 1193 charter, which describes it as a hunting lodge of Knyaz Rurik Rostislavich. In 1362 it was a crown village of the Grand Duchy of Lithuania. Around that time the town had own castle which was ruined at least on two occasions in 1473 and 1482. The Chernobyl castle was rebuilt in the first quarter of the 16th century being located nearby the settlement in a hard to reach area. With revival of the castle, Chernobyl became a county seat. In 1552 it accounted for 196 buildings with 1,372 residents, out of which over 1,160 were considered city dwellers. In the city were developing various crafts professions such as blacksmith, cooper among others. Near Chernobyl has been excavated bog iron, out of which was produced iron. The village was granted to Filon Kmita, a captain of the royal cavalry, as a fiefdom in 1566. Following the Union of Lublin, the province where Chernobyl is located was transferred to the Crown of the Kingdom of Poland in 1569. Under the Polish Crown, Chernobyl became a seat of eldership (starostwo). During that period Chernobyl was inhabited by Ukrainian peasants, some Polish people and a relatively large number of Jews. Jews were brought to Chernobyl by Filon Kmita, during the Polish campaign of colonization. The first mentioning of Jewish community in Chernobyl is in the 17th century. In 1600 the first Roman Catholic church was built in the town. Local population was persecuted for holding Eastern Orthodox rite services. The traditionally Eastern Orthodox Ukrainian peasantry around the town were forcibly converted, by Poland, to the Ruthenian Uniate Church. In 1626, during the Counter-Reformation, a Dominican church and monastery were founded by Lukasz Sapieha. A group of Old Catholics opposed the decrees of the Council of Trent.`{{clarify|date=June 2017}}`{=mediawiki} The Chernobyl residents actively supported the Khmelnytsky Uprising (1648--1657).
With the signing of the Truce of Andrusovo in 1667, Chernobyl was secured after`{{dubious|What is the meaning of "was secured after the Sapieha family" in proper English?|date=September 2020}}`{=mediawiki} the Sapieha family. Sometime in the 18th century, the place was passed on to the Chodkiewicz family. In the mid-18th century the area around Chernobyl was engulfed in a number of peasant riots, which caused Prince Riepnin to write from Warsaw to Major General Krechetnikov, requesting hussars to be sent from Kharkiv to deal with the uprising near Chernobyl in 1768. The 8th Lithuanian Infantry Regiment was stationed in the town in 1791. By the end of the 18th century, the town accounted for 2,865 residents and had 642 buildings.
### Imperial Russian era (1793--1917) {#imperial_russian_era_17931917}
Following the Second Partition of Poland, in 1793 Chernobyl was annexed by the Russian Empire and became part of Radomyshl county (*uezd*) as a supernumerary town (\"zashtatny gorod\"). Many of the Uniate Church converts returned to Eastern Orthodoxy.
In 1832, following the failed Polish November Uprising, the Dominican monastery was sequestrated. The church of the Old Catholics was disbanded in 1852.
Until the end of the 19th century, Chernobyl was a privately owned city that belonged to the Chodkiewicz family. In 1896 they sold the city to the state, but until 1910 they owned a castle and a house in the city.
#### Hasidic Jewish dynasty of Chernobyl {#hasidic_jewish_dynasty_of_chernobyl}
In the second half of the 18th century, Chernobyl became a major centre of Hasidic Judaism. The Chernobyl Hasidic dynasty had been founded by Rabbi Menachem Nachum Twersky. The Jewish population suffered greatly from pogroms in October 1905 and in March--April 1919; many Jews were killed or robbed at the instigation of the Russian nationalist Black Hundreds. When the Twersky Dynasty left Chernobyl in 1920, it ceased to exist as a center of Hasidism.
Chernobyl had a population of 10,800 in 1898, including 7,200 Jews. In the beginning of March 1918 Chernobyl was occupied in World War I by German forces in accordance with the Treaty of Brest-Litovsk
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# Chernobyl
## History
### Soviet era (1920--1991) {#soviet_era_19201991}
Ukrainians and Bolsheviks fought over the city in the ensuing Civil War. In the Polish--Soviet War of 1919--20, Chernobyl was taken first by the Polish Army and then by the cavalry of the Red Army. From 1921 onwards, it was officially incorporated into the Ukrainian SSR.
#### Holodomor
Between 1929 and 1933, Chernobyl suffered from killings during Stalin\'s collectivization campaign. It was also affected by the famine that resulted from Stalin\'s policies. The Polish and German community of Chernobyl was deported to Kazakhstan in 1936, during the Frontier Clearances.
#### World War II and the Holocaust {#world_war_ii_and_the_holocaust}
During World War II, Chernobyl was occupied by the German Army from 25 August 1941 to 17 November 1943. When the Germans arrived, only 400 Jews remained in Chernobyl; they were murdered during the Holocaust.
#### Chernobyl Nuclear Power Plant {#chernobyl_nuclear_power_plant}
In 1972, the Duga-1 radio receiver, part of the larger Duga over-the-horizon radar array, began construction 11 km west-northwest of Chernobyl. It was the origin of the Russian Woodpecker and was designed as part of an anti-ballistic missile early-warning radar network.
On 15 August 1972, the Chernobyl Nuclear Power Plant (officially the Vladimir Ilyich Lenin Nuclear Power Plant) began construction about 15 km northwest of Chernobyl. The plant was built alongside Pripyat, an \"atomograd\" city founded on 4 February 1970 that was intended to serve the nuclear power plant. The decision to build the power plant was adopted by the Central Committee of the Communist Party of the Soviet Union and the Council of Ministers of the Soviet Union on recommendations of the State Planning Committee that the Ukrainian SSR be its location. It was the first nuclear power plant to be built in Ukraine.
#### 26 April 1986: Chernobyl disaster {#april_1986_chernobyl_disaster}
After the nuclear disaster at the Chernobyl Nuclear Power Plant; the worst nuclear disaster in history, the city of Chernobyl was evacuated on 5 May 1986. Along with the residents of the nearby city of Pripyat, built as a home for the plant\'s workers, the population was relocated to the newly built city of Slavutych. While Pripyat remains completely abandoned with no remaining inhabitants, Chernobyl has since hosted a small population.
### Independent Ukrainian era (1991--present) {#independent_ukrainian_era_1991present}
With the dissolution of the Soviet Union in 1991, Chernobyl remained part of Ukraine within the Chernobyl Exclusion Zone which Ukraine inherited from the Soviet Union.
#### 2022 Russian occupation of Chernobyl {#russian_occupation_of_chernobyl}
During the Russian invasion of Ukraine, Russian forces captured the city on 24 February. Following the capture of Chernobyl, the Russian army used the city as a staging point for attacks on Kyiv. Ukrainian officials reported that the radiation levels in the city had started to rise due to recent military activity causing radioactive dust to ascend into the air. Hundreds of Russian soldiers were suffering from radiation poisoning after digging trenches in a contaminated area, and one died. On 31 March it was reported that Russian forces had left the exclusion zone. Ukrainian authorities reasserted control over the area on 2 April.
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# Chernobyl
## Geography
Chernobyl is located about 90 km north of Kyiv, and 160 km southwest of the Belarusian city of Gomel.
### Climate
Chernobyl has a humid continental climate (Dfb) with very warm, wet summers with cool nights and long, cold, and snowy winters.`{{Weather box
|location = Chernobyl, 127 m asl (1981–2010 normals, extremes 1955–present)
|collapsed =
|metric first = Yes
|single line = Yes
|Jan record high C = 11.5
|Feb record high C = 17.0
|Mar record high C = 22.6
|Apr record high C = 26.6
|May record high C = 32.9
|Jun record high C = 34.0
|Jul record high C = 35.2
|Aug record high C = 36.3
|Sep record high C = 35.9
|Oct record high C = 26.3
|Nov record high C = 19.6
|Dec record high C = 11.3
|year record high C = 36.3
|Jan high C = -0.8
|Feb high C = 0.1
|Mar high C = 6.0
|Apr high C = 14.5
|May high C = 21.0
|Jun high C = 23.7
|Jul high C = 25.7
|Aug high C = 25.0
|Sep high C = 18.9
|Oct high C = 12.4
|Nov high C = 4.2
|Dec high C = -0.3
|year high C = 12.5
|Jan mean C = -3.5
|Feb mean C = -3.4
|Mar mean C = 1.5
|Apr mean C = 8.9
|May mean C = 14.9
|Jun mean C = 17.9
|Jul mean C = 19.9
|Aug mean C = 18.8
|Sep mean C = 13.4
|Oct mean C = 7.7
|Nov mean C = 1.4
|Dec mean C = -2.8
|year mean C = 7.9
|Jan low C = -6.1
|Feb low C = -6.7
|Mar low C = -2.3
|Apr low C = 3.9
|May low C = 9.1
|Jun low C = 12.3
|Jul low C = 14.5
|Aug low C = 13.3
|Sep low C = 8.7
|Oct low C = 3.8
|Nov low C = -1.1
|Dec low C = -5.2
|year low C = 3.7
|Jan record low C = -29.7
|Feb record low C = -32.8
|Mar record low C = -20.0
|Apr record low C = -9.0
|May record low C = -6.0
|Jun record low C = 2.2
|Jul record low C = 6.2
|Aug record low C = 0.0
|Sep record low C = -1.6
|Oct record low C = -10.5
|Nov record low C = -20.0
|Dec record low C = -30.8
|year record low C = -32.8
|precipitation colour = green
|Jan precipitation mm = 34.0
|Feb precipitation mm = 36.8
|Mar precipitation mm = 35.6
|Apr precipitation mm = 40.0
|May precipitation mm = 60.8
|Jun precipitation mm = 73.2
|Jul precipitation mm = 79.5
|Aug precipitation mm = 55.3
|Sep precipitation mm = 56.3
|Oct precipitation mm = 42.2
|Nov precipitation mm = 47.7
|Dec precipitation mm = 42.6
|year precipitation mm = 604.0
|unit precipitation days = 1.0 mm
|Jan precipitation days = 8.1
|Feb precipitation days = 8.9
|Mar precipitation days = 8.1
|Apr precipitation days = 7.5
|May precipitation days = 8.7
|Jun precipitation days = 10.2
|Jul precipitation days = 9.2
|Aug precipitation days = 7.1
|Sep precipitation days = 8.7
|Oct precipitation days = 7.4
|Nov precipitation days = 8.7
|Dec precipitation days = 9.1
|year precipitation days = 101.7
|Jan humidity = 83.5
|Feb humidity = 79.8
|Mar humidity = 74.7
|Apr humidity = 66.7
|May humidity = 66.0
|Jun humidity = 70.4
|Jul humidity = 72.8
|Aug humidity = 72.3
|Sep humidity = 77.8
|Oct humidity = 80.8
|Nov humidity = 85.3
|Dec humidity = 85.9
|year humidity = 76.3
|source 1 = [[NOAA]]<ref name=WMOCLINO>{{cite web
| archive-url = https://web.archive.org/web/20210717143555/https://www.ncei.noaa.gov/pub/data/normals/WMO/1981-2010/RA-VI/Ukraine/12.6.%20WMO_Normals_Excel_Template%20%282%29.xls
| archive-date = 17 July 2021
| url = https://www.ncei.noaa.gov/pub/data/normals/WMO/1981-2010/RA-VI/Ukraine/12.6.%20WMO_Normals_Excel_Template%20(2).xls
| format = XLS
| title = World Meteorological Organization Climate Normals for 1981–2010
| publisher = [[NCEI|National Centers for Environmental Information]]
| access-date = 17 July 2021}}</ref>
|source 2 = Météo Climat (extremes)<ref>{{cite web|url=http://meteo-climat-bzh.dyndns.org/station-1986.php|title=Weather extremes for Tchernobyl|publisher=Météo Climat|language=fr|access-date=17 July 2021|archive-date=13 October 2020|archive-url=https://web.archive.org/web/20201013210112/http://meteo-climat-bzh.dyndns.org/station-1986.php|url-status=live}}</ref>
}}`{=mediawiki}
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# Chernobyl
## Aftermath of the Chernobyl disaster and evacuation {#aftermath_of_the_chernobyl_disaster_and_evacuation}
*Main article: Chernobyl disaster, Effects of the Chernobyl disaster*
On 26 April 1986, one of the reactors at the Chernobyl Nuclear Power Plant exploded after a scheduled test on the reactor was carried out improperly by plant operators. The resulting loss of control was due to design flaws of the RBMK reactor, which made it unstable when operated at low power, and prone to thermal runaway where increases in temperature increase reactor power output.
Chernobyl city was evacuated nine days after the disaster. The level of contamination with caesium-137 was around 555 kBq/m^2^ (surface ground deposition in 1986).
Later analyses concluded that, even with very conservative estimates, relocation of the city (or of any area below 1500 kBq/m^2^) could not be justified on the grounds of radiological health. This however does not account for the uncertainty in the first few days of the accident about further depositions and weather patterns. Moreover, an earlier short-term evacuation could have averted more significant doses from short-lived isotope radiation (specifically iodine-131, which has a half-life of eight days). The long-term health effects of the Chernobyl disaster are a subject of some controversy.
In 1998, average caesium-137 doses from the accident (estimated at 1--2 mSv per year) did not exceed those from other sources of exposure. Current effective caesium-137 dose rates as of 2019 are 200--250 nSv/h, or roughly 1.7--2.2 mSv per year, which is comparable to the worldwide average background radiation from natural sources.
The base of operations for the administration and monitoring of the Chernobyl Exclusion Zone was moved from Pripyat to Chernobyl. Chernobyl currently contains offices for the State Agency of Ukraine on the Exclusion Zone Management and accommodations for visitors. Apartment blocks have been repurposed as accommodations for employees of the State Agency. The length of time that workers may spend within the Chernobyl Exclusion Zone is restricted by regulations that have been implemented to limit radiation exposure. Today, visits are allowed to Chernobyl but limited by strict rules.
In 2003, the United Nations Development Programme launched a project, called the Chernobyl Recovery and Development Programme (CRDP), for the recovery of the affected areas. The main goal of the CRDP\'s activities is supporting the efforts of the Government of Ukraine to mitigate the long-term social, economic, and ecological consequences of the Chernobyl disaster.
The city has become overgrown and many types of animals live there. According to census information collected over an extended period of time, it is estimated that more mammals live there now than before the disaster.
Notably, Mikhail Gorbachev, the final leader of the Soviet Union, stated in respect to the Chernobyl disaster that, \"More than anything else, (Chernobyl) opened the possibility of much greater freedom of expression, to the point that the (Soviet) system as we knew it could no longer continue
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# Christoph Ludwig Agricola
**Christoph Ludwig Agricola** (5 November 1665 -- 8 August 1724) was a German landscape painter and etcher. He was born and died in Regensburg (Ratisbon).
## Life and career {#life_and_career}
Christoph Ludwig Agricola was born on 5 November 1665 in Regensburg in Germany. He trained, as many painters of the period did, by studying nature.
He spent a great part of his life in travel visiting England, the Netherlands and France, and residing for a considerable period in Naples, where he may have been influenced by Nicolas Poussin. He also stayed in Venice for several years around 1712, where he painted many works for Zaccaria Sagredo.
He died in Regensburg in 1724.
## Work
Although he primarily worked in gouache and oils, documentary sources show that he also produced a small number of etchings. He was a good draughtsman, used warm lighting and exhibited a warm, masterly brushstroke.
His numerous landscapes, chiefly cabinet pictures, are remarkable for their fidelity to nature, and especially for their skilful representation of varied phases of climate, especially nocturnal scenes and weather phenomena like thunderstorms. In composition, his style shows the influence of Nicolas Poussin: Agricola\'s work often displays idealistic scenes like Poussin\'s work. In light and colour Agricola\'s work resembles that of Claude Lorrain. His compositions often include ruins of ancient buildings in the foreground, but his favourite foreground figures were men dressed in Oriental attire. He also produced a series of etchings of birds.
His pictures can be found in Dresden, Braunschweig, Vienna, Florence, Naples and many other locations in Germany and Italy.
## Legacy
He probably tutored the artist Johann Theile and had a strong influence on him. Art historians have also noted that the work of the landscape painter Christian Johann Bendeler (1699--1728) was influenced by Agricola.
## Gallery
<File:Christoph> Ludwig Agricola (zugeschr.) - Eine Flusslandschaft mit Anglern.jpg\|*River landscape* <File:Christoph> Ludwig Agricola - Großer Hänfling und Schopfmeise.jpg\|*Greater Redpole and crested titmous; Bluethroat* <File:Christoph> Ludwig Agricola (Umkreis) - Räuber schießen auf Reisende.jpg\|*Bandits Shooting at Travellers* <File:Christoph> Ludwig Agricola - Trappe un Elster in exotischer Landschaft.jpg\|*A bustard and a magpie in an exotic landscape* <File:Christoph> Ludwig Agricola - Ein Vogel auf einem Ast.jpg\|*A bird seated on a branch* <File:Wintergezicht> met ijsvermaak, RP-T-1898-A-3549.jpg\|*Winter face with ice entertainment* <File:Christoph> Ludwig Agricola - Singvogel auf einem Nadelbaum
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# Cardinal number
In mathematics, a **cardinal number**, or **cardinal** for short, is what is commonly called the number of elements of a set. In the case of a finite set, its cardinal number, or cardinality is therefore a natural number. For dealing with the case of infinite sets, the infinite cardinal numbers have been introduced, which are often denoted with the Hebrew letter $\aleph$ (aleph) marked with subscript indicating their rank among the infinite cardinals.
Cardinality is defined in terms of bijective functions. Two sets have the same cardinality if, and only if, there is a one-to-one correspondence (bijection) between the elements of the two sets. In the case of finite sets, this agrees with the intuitive notion of number of elements. In the case of infinite sets, the behavior is more complex. A fundamental theorem due to Georg Cantor shows that it is possible for two infinite sets to have different cardinalities, and in particular the cardinality of the set of real numbers is greater than the cardinality of the set of natural numbers. It is also possible for a proper subset of an infinite set to have the same cardinality as the original set---something that cannot happen with proper subsets of finite sets.
There is a transfinite sequence of cardinal numbers:
$$0, 1, 2, 3, \ldots, n, \ldots ; \aleph_0, \aleph_1, \aleph_2, \ldots, \aleph_{\alpha}, \ldots.\$$ This sequence starts with the natural numbers including zero (finite cardinals), which are followed by the aleph numbers. The aleph numbers are indexed by ordinal numbers. If the axiom of choice is true, this transfinite sequence includes every cardinal number. If the axiom of choice is not true (see `{{slink|Axiom of choice#Independence}}`{=mediawiki}), there are infinite cardinals that are not aleph numbers.
Cardinality is studied for its own sake as part of set theory. It is also a tool used in branches of mathematics including model theory, combinatorics, abstract algebra and mathematical analysis. In category theory, the cardinal numbers form a skeleton of the category of sets.
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# Cardinal number
## History
The notion of cardinality, as now understood, was formulated by Georg Cantor, the originator of set theory, in 1874--1884. Cardinality can be used to compare an aspect of finite sets. For example, the sets {1,2,3} and {4,5,6} are not *equal*, but have the *same cardinality*, namely three. This is established by the existence of a bijection (i.e., a one-to-one correspondence) between the two sets, such as the correspondence {1→4, 2→5, 3→6}.
Cantor applied his concept of bijection to infinite sets (for example the set of natural numbers **N** = {0, 1, 2, 3, \...}). Thus, he called all sets having a bijection with **N** *denumerable (countably infinite) sets*, which all share the same cardinal number. This cardinal number is called $\aleph_0$, aleph-null. He called the cardinal numbers of infinite sets transfinite cardinal numbers.
Cantor proved that any unbounded subset of **N** has the same cardinality as **N**, even though this might appear to run contrary to intuition. He also proved that the set of all ordered pairs of natural numbers is denumerable; this implies that the set of all rational numbers is also denumerable, since every rational can be represented by a pair of integers. He later proved that the set of all real algebraic numbers is also denumerable. Each real algebraic number *z* may be encoded as a finite sequence of integers, which are the coefficients in the polynomial equation of which it is a solution, i.e. the ordered n-tuple (*a*~0~, *a*~1~, \..., *a~n~*), *a~i~* ∈ **Z** together with a pair of rationals (*b*~0~, *b*~1~) such that *z* is the unique root of the polynomial with coefficients (*a*~0~, *a*~1~, \..., *a~n~*) that lies in the interval (*b*~0~, *b*~1~).
In his 1874 paper \"On a Property of the Collection of All Real Algebraic Numbers\", Cantor proved that there exist higher-order cardinal numbers, by showing that the set of real numbers has cardinality greater than that of **N**. His proof used an argument with nested intervals, but in an 1891 paper, he proved the same result using his ingenious and much simpler diagonal argument. The new cardinal number of the set of real numbers is called the cardinality of the continuum and Cantor used the symbol $\mathfrak{c}$ for it.
Cantor also developed a large portion of the general theory of cardinal numbers; he proved that there is a smallest transfinite cardinal number ($\aleph_0$, aleph-null), and that for every cardinal number there is a next-larger cardinal
$$(\aleph_1, \aleph_2, \aleph_3, \ldots).$$
His continuum hypothesis is the proposition that the cardinality $\mathfrak{c}$ of the set of real numbers is the same as $\aleph_1$. This hypothesis is independent of the standard axioms of mathematical set theory, that is, it can neither be proved nor disproved from them. This was shown in 1963 by Paul Cohen, complementing earlier work by Kurt Gödel in 1940.
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Cardinal number
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# Cardinal number
## Motivation
In informal use, a cardinal number is what is normally referred to as a *counting number*, provided that 0 is included: 0, 1, 2, \.... They may be identified with the natural numbers beginning with 0. The counting numbers are exactly what can be defined formally as the finite cardinal numbers. Infinite cardinals only occur in higher-level mathematics and logic.
More formally, a non-zero number can be used for two purposes: to describe the size of a set, or to describe the position of an element in a sequence. For finite sets and sequences it is easy to see that these two notions coincide, since for every number describing a position in a sequence we can construct a set that has exactly the right size. For example, 3 describes the position of \'c\' in the sequence \<\'a\',\'b\',\'c\',\'d\',\...\>, and we can construct the set {a,b,c}, which has 3 elements.
However, when dealing with infinite sets, it is essential to distinguish between the two, since the two notions are in fact different for infinite sets. Considering the position aspect leads to ordinal numbers, while the size aspect is generalized by the cardinal numbers described here.
The intuition behind the formal definition of cardinal is the construction of a notion of the relative size or \"bigness\" of a set, without reference to the kind of members which it has. For finite sets this is easy; one simply counts the number of elements a set has. In order to compare the sizes of larger sets, it is necessary to appeal to more refined notions.
A set *Y* is at least as big as a set *X* if there is an injective mapping from the elements of *X* to the elements of *Y*. An injective mapping identifies each element of the set *X* with a unique element of the set *Y*. This is most easily understood by an example; suppose we have the sets *X* = {1,2,3} and *Y* = {a,b,c,d}, then using this notion of size, we would observe that there is a mapping:
: 1 → a
: 2 → b
: 3 → c
which is injective, and hence conclude that *Y* has cardinality greater than or equal to *X*. The element d has no element mapping to it, but this is permitted as we only require an injective mapping, and not necessarily a bijective mapping. The advantage of this notion is that it can be extended to infinite sets.
We can then extend this to an equality-style relation. Two sets *X* and *Y* are said to have the same *cardinality* if there exists a bijection between *X* and *Y*. By the Schroeder--Bernstein theorem, this is equivalent to there being *both* an injective mapping from *X* to *Y*, *and* an injective mapping from *Y* to *X*. We then write \|*X*\| = \|*Y*\|. The cardinal number of *X* itself is often defined as the least ordinal *a* with \|*a*\| = \|*X*\|. This is called the von Neumann cardinal assignment; for this definition to make sense, it must be proved that every set has the same cardinality as *some* ordinal; this statement is the well-ordering principle. It is however possible to discuss the relative cardinality of sets without explicitly assigning names to objects.
The classic example used is that of the infinite hotel paradox, also called Hilbert\'s paradox of the Grand Hotel. Supposing there is an innkeeper at a hotel with an infinite number of rooms. The hotel is full, and then a new guest arrives. It is possible to fit the extra guest in by asking the guest who was in room 1 to move to room 2, the guest in room 2 to move to room 3, and so on, leaving room 1 vacant. We can explicitly write a segment of this mapping:
: 1 → 2
: 2 → 3
: 3 → 4
: \...
: *n* → *n* + 1
: \...
With this assignment, we can see that the set {1,2,3,\...} has the same cardinality as the set {2,3,4,\...}, since a bijection between the first and the second has been shown. This motivates the definition of an infinite set being any set that has a proper subset of the same cardinality (i.e., a Dedekind-infinite set); in this case {2,3,4,\...} is a proper subset of {1,2,3,\...}.
When considering these large objects, one might also want to see if the notion of counting order coincides with that of cardinal defined above for these infinite sets. It happens that it does not; by considering the above example we can see that if some object \"one greater than infinity\" exists, then it must have the same cardinality as the infinite set we started out with. It is possible to use a different formal notion for number, called ordinals, based on the ideas of counting and considering each number in turn, and we discover that the notions of cardinality and ordinality are divergent once we move out of the finite numbers.
It can be proved that the cardinality of the real numbers is greater than that of the natural numbers just described. This can be visualized using Cantor\'s diagonal argument; classic questions of cardinality (for instance the continuum hypothesis) are concerned with discovering whether there is some cardinal between some pair of other infinite cardinals. In more recent times, mathematicians have been describing the properties of larger and larger cardinals.
Since cardinality is such a common concept in mathematics, a variety of names are in use. Sameness of cardinality is sometimes referred to as *equipotence*, *equipollence*, or *equinumerosity*. It is thus said that two sets with the same cardinality are, respectively, *equipotent*, *equipollent*, or *equinumerous*.
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# Cardinal number
## Formal definition {#formal_definition}
Formally, assuming the axiom of choice, the cardinality of a set *X* is the least ordinal number α such that there is a bijection between *X* and α. This definition is known as the von Neumann cardinal assignment. If the axiom of choice is not assumed, then a different approach is needed. The oldest definition of the cardinality of a set *X* (implicit in Cantor and explicit in Frege and *Principia Mathematica*) is as the class \[*X*\] of all sets that are equinumerous with *X*. This does not work in ZFC or other related systems of axiomatic set theory because if *X* is non-empty, this collection is too large to be a set. In fact, for *X* ≠ ∅ there is an injection from the universe into \[*X*\] by mapping a set *m* to {*m*} × *X*, and so by the axiom of limitation of size, \[*X*\] is a proper class. The definition does work however in type theory and in New Foundations and related systems. However, if we restrict from this class to those equinumerous with *X* that have the least rank, then it will work (this is a trick due to Dana Scott: it works because the collection of objects with any given rank is a set).
Von Neumann cardinal assignment implies that the cardinal number of a finite set is the common ordinal number of all possible well-orderings of that set, and cardinal and ordinal arithmetic (addition, multiplication, power, proper subtraction) then give the same answers for finite numbers. However, they differ for infinite numbers. For example, $2^\omega=\omega<\omega^2$ in ordinal arithmetic while $2^{\aleph_0}>\aleph_0=\aleph_0^2$ in cardinal arithmetic, although the von Neumann assignment puts $\aleph_0=\omega$. On the other hand, Scott\'s trick implies that the cardinal number 0 is $\{\emptyset\}$, which is also the ordinal number 1, and this may be confusing. A possible compromise (to take advantage of the alignment in finite arithmetic while avoiding reliance on the axiom of choice and confusion in infinite arithmetic) is to apply von Neumann assignment to the cardinal numbers of finite sets (those which can be well ordered and are not equipotent to proper subsets) and to use Scott\'s trick for the cardinal numbers of other sets.
Formally, the order among cardinal numbers is defined as follows: \|*X*\| ≤ \|*Y*\| means that there exists an injective function from *X* to *Y*. The Cantor--Bernstein--Schroeder theorem states that if \|*X*\| ≤ \|*Y*\| and \|*Y*\| ≤ \|*X*\| then \|*X*\| = \|*Y*\|. The axiom of choice is equivalent to the statement that given two sets *X* and *Y*, either \|*X*\| ≤ \|*Y*\| or \|*Y*\| ≤ \|*X*\|.
A set *X* is Dedekind-infinite if there exists a proper subset *Y* of *X* with \|*X*\| = \|*Y*\|, and Dedekind-finite if such a subset does not exist. The finite cardinals are just the natural numbers, in the sense that a set *X* is finite if and only if \|*X*\| = \|*n*\| = *n* for some natural number *n*. Any other set is infinite.
Assuming the axiom of choice, it can be proved that the Dedekind notions correspond to the standard ones. It can also be proved that the cardinal $\aleph_0$ (aleph null or aleph-0, where aleph is the first letter in the Hebrew alphabet, represented $\aleph$) of the set of natural numbers is the smallest infinite cardinal (i.e., any infinite set has a subset of cardinality $\aleph_0$). The next larger cardinal is denoted by $\aleph_1$, and so on. For every ordinal α, there is a cardinal number $\aleph_{\alpha},$ and this list exhausts all infinite cardinal numbers.
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# Cardinal number
## Cardinal arithmetic {#cardinal_arithmetic}
We can define arithmetic operations on cardinal numbers that generalize the ordinary operations for natural numbers. It can be shown that for finite cardinals, these operations coincide with the usual operations for natural numbers. Furthermore, these operations share many properties with ordinary arithmetic.
### Successor cardinal {#successor_cardinal}
If the axiom of choice holds, then every cardinal κ has a successor, denoted κ^+^, where κ^+^ \> κ and there are no cardinals between κ and its successor. (Without the axiom of choice, using Hartogs\' theorem, it can be shown that for any cardinal number κ, there is a minimal cardinal κ^+^ such that $\kappa^+\nleq\kappa.$) For finite cardinals, the successor is simply κ + 1. For infinite cardinals, the successor cardinal differs from the successor ordinal.
### Cardinal addition {#cardinal_addition}
If *X* and *Y* are disjoint, addition is given by the union of *X* and *Y*. If the two sets are not already disjoint, then they can be replaced by disjoint sets of the same cardinality (e.g., replace *X* by *X*×{0} and *Y* by *Y*×{1}).
$$|X| + |Y| = | X \cup Y|.$$
Zero is an additive identity *κ* + 0 = 0 + *κ* = *κ*.
Addition is associative (*κ* + *μ*) + *ν* = *κ* + (*μ* + *ν*).
Addition is commutative *κ* + *μ* = *μ* + *κ*.
Addition is non-decreasing in both arguments:
$$(\kappa \le \mu) \rightarrow ((\kappa + \nu \le \mu + \nu) \mbox{ and } (\nu + \kappa \le \nu + \mu)).$$
Assuming the axiom of choice, addition of infinite cardinal numbers is easy. If either *κ* or *μ* is infinite, then
$$\kappa + \mu = \max\{\kappa, \mu\}\,.$$
#### Subtraction
Assuming the axiom of choice and, given an infinite cardinal *σ* and a cardinal *μ*, there exists a cardinal *κ* such that *μ* + *κ* = *σ* if and only if *μ* ≤ *σ*. It will be unique (and equal to *σ*) if and only if *μ* \< *σ*.
### Cardinal multiplication {#cardinal_multiplication}
The product of cardinals comes from the Cartesian product.
$$|X|\cdot|Y| = |X \times Y|$$
Zero is a multiplicative absorbing element: *κ*·0 = 0·*κ* = 0.
There are no nontrivial zero divisors: *κ*·*μ* = 0 → (*κ* = 0 or *μ* = 0).
One is a multiplicative identity: *κ*·1 = 1·*κ* = *κ*.
Multiplication is associative: (*κ*·*μ*)·*ν* = *κ*·(*μ*·*ν*).
Multiplication is commutative: *κ*·*μ* = *μ*·*κ*.
Multiplication is non-decreasing in both arguments: *κ* ≤ *μ* → (*κ*·*ν* ≤ *μ*·*ν* and *ν*·*κ* ≤ *ν*·*μ*).
Multiplication distributes over addition: *κ*·(*μ* + *ν*) = *κ*·*μ* + *κ*·*ν* and (*μ* + *ν*)·*κ* = *μ*·*κ* + *ν*·*κ*.
Assuming the axiom of choice, multiplication of infinite cardinal numbers is also easy. If either *κ* or *μ* is infinite and both are non-zero, then
$$\kappa\cdot\mu = \max\{\kappa, \mu\}.$$ Thus the product of two infinite cardinal numbers is equal to their sum.
#### Division
Assuming the axiom of choice and given an infinite cardinal *π* and a non-zero cardinal *μ*, there exists a cardinal *κ* such that *μ* · *κ* = *π* if and only if *μ* ≤ *π*. It will be unique (and equal to *π*) if and only if *μ* \< *π*.
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# Cardinal number
## Cardinal arithmetic {#cardinal_arithmetic}
### Cardinal exponentiation {#cardinal_exponentiation}
Exponentiation is given by
$$|X|^{|Y|} = \left|X^Y\right|,$$ where *X^Y^* is the set of all functions from *Y* to *X*. It is easy to check that the right-hand side depends only on ${|X|}$ and ${|Y|}$.
: κ^0^ = 1 (in particular 0^0^ = 1), see empty function.
: If *μ* ≥ 1, then 0^*μ*^ = 0.
: 1^*μ*^ = 1.
: *κ*^1^ = *κ*.
: *κ*^*μ*\ +\ *ν*^ = *κ*^*μ*^·*κ*^*ν*^.
: κ^*μ*\ ·\ *ν*^ = (*κ*^*μ*^)^*ν*^.
: (*κ*·*μ*)^*ν*^ = *κ*^*ν*^·*μ*^*ν*^.
Exponentiation is non-decreasing in both arguments:
: (1 ≤ *ν* and *κ* ≤ *μ*) → (*ν*^*κ*^ ≤ *ν*^*μ*^) and
: (*κ* ≤ *μ*) → (*κ*^*ν*^ ≤ *μ*^*ν*^).
2^\|*X*\|^ is the cardinality of the power set of the set *X* and Cantor\'s diagonal argument shows that 2^\|*X*\|^ \> \|*X*\| for any set *X*. This proves that no largest cardinal exists (because for any cardinal *κ*, we can always find a larger cardinal 2^*κ*^). In fact, the class of cardinals is a proper class. (This proof fails in some set theories, notably New Foundations.)
All the remaining propositions in this section assume the axiom of choice:
: If *κ* and *μ* are both finite and greater than 1, and *ν* is infinite, then *κ*^*ν*^ = *μ*^*ν*^.
: If *κ* is infinite and *μ* is finite and non-zero, then *κ*^*μ*^ = *κ*.
If 2 ≤ *κ* and 1 ≤ *μ* and at least one of them is infinite, then:
: Max (*κ*, 2^*μ*^) ≤ *κ*^*μ*^ ≤ Max (2^*κ*^, 2^*μ*^).
Using König\'s theorem, one can prove *κ* \< *κ*^cf(*κ*)^ and *κ* \< cf(2^*κ*^) for any infinite cardinal *κ*, where cf(*κ*) is the cofinality of *κ*.
#### Roots
Assuming the axiom of choice and, given an infinite cardinal *κ* and a finite cardinal *μ* greater than 0, the cardinal *ν* satisfying $\nu^\mu = \kappa$ will be $\kappa$.
#### Logarithms
Assuming the axiom of choice and, given an infinite cardinal *κ* and a finite cardinal *μ* greater than 1, there may or may not be a cardinal *λ* satisfying $\mu^\lambda = \kappa$. However, if such a cardinal exists, it is infinite and less than *κ*, and any finite cardinality *ν* greater than 1 will also satisfy $\nu^\lambda = \kappa$.
The logarithm of an infinite cardinal number *κ* is defined as the least cardinal number *μ* such that *κ* ≤ 2^*μ*^. Logarithms of infinite cardinals are useful in some fields of mathematics, for example in the study of cardinal invariants of topological spaces, though they lack some of the properties that logarithms of positive real numbers possess.
## The continuum hypothesis {#the_continuum_hypothesis}
The continuum hypothesis (CH) states that there are no cardinals strictly between $\aleph_0$ and $2^{\aleph_0}.$ The latter cardinal number is also often denoted by $\mathfrak{c}$; it is the cardinality of the continuum (the set of real numbers). In this case $2^{\aleph_0} = \aleph_1.$
Similarly, the generalized continuum hypothesis (GCH) states that for every infinite cardinal $\kappa$, there are no cardinals strictly between $\kappa$ and $2^\kappa$. Both the continuum hypothesis and the generalized continuum hypothesis have been proved to be independent of the usual axioms of set theory, the Zermelo--Fraenkel axioms together with the axiom of choice (ZFC).
Indeed, Easton\'s theorem shows that, for regular cardinals $\kappa$, the only restrictions ZFC places on the cardinality of $2^\kappa$ are that $\kappa < \operatorname{cf}(2^\kappa)$, and that the exponential function is non-decreasing
| 563 |
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# Cecil B. DeMille
**Cecil Blount DeMille** (`{{IPAc-en|'|s|ɛ|s|əl|_|d|ə|ˈ|m|ɪ|l}}`{=mediawiki}; August 12, 1881`{{spnd}}`{=mediawiki}January 21, 1959) was an American filmmaker and actor. Between 1914 and 1958, he made 70 features, both silent and sound films. He is acknowledged as a founding father of American cinema and the most commercially successful producer-director in film history, with many films dominating the box office three or four at a time. His films were distinguished by their epic scale and by his cinematic showmanship. His silent films included social dramas, comedies, Westerns, farces, morality plays, and historical pageants. He was an active Freemason and member of Prince of Orange Lodge #16 in New York City.
DeMille was born in Ashfield, Massachusetts, where his parents were vacationing for the summer. He grew up in New York City. He began his career as a stage actor in 1900. He later began to write and direct stage plays, a few with his older brother William de Mille, and some with Jesse L. Lasky, who was then a vaudeville producer.
DeMille\'s first film, *The Squaw Man* (1914), was the first full-length feature film shot in Hollywood. Its interracial love story was commercially successful, and the film marked Hollywood as the new home of the U.S. film industry. It had previously been based in New York and New Jersey. Based on continued film successes, DeMille founded Famous Players Lasky which was later reverse merged into Paramount Pictures with Lasky and Adolph Zukor. His first biblical epic, *The Ten Commandments* (1923), was both a critical and commercial success; it held the Paramount revenue record for 25 years.
DeMille directed *The King of Kings* (1927), a biography of Jesus, which gained approval for its sensitivity and reached more than 800 million viewers. *The Sign of the Cross* (1932) is said to be the first sound film to integrate all aspects of cinematic technique. *Cleopatra* (1934) was his first film to be nominated for the Academy Award for Best Picture.
After more than 30 years in film production, DeMille reached a pinnacle in his career with *Samson and Delilah* (1949), a biblical epic that became the highest-grossing film of 1950. Along with biblical and historical narratives, he also directed films oriented toward \"neo-naturalism\", which tried to portray the laws of man fighting the forces of nature.
DeMille received his first nomination for the Academy Award for Best Director for his circus drama *The Greatest Show on Earth* (1952), which won both the Academy Award for Best Picture and the Golden Globe Award for Best Motion Picture -- Drama. His last and best-known film, *The Ten Commandments* (1956), also a Best Picture Academy Award nominee, and it is the eighth-highest-grossing film of all time, adjusted for inflation.
In addition to his Best Picture Awards, DeMille received an Academy Honorary Award for his film contributions, the Palme d\'Or (posthumously) for *Union Pacific* (1939), a DGA Award for Lifetime Achievement, and the Irving G. Thalberg Memorial Award. He was the first recipient of the Golden Globe Cecil B. DeMille Award, which was named in his honor. DeMille\'s reputation had a renaissance in the 2010s, and his work has influenced numerous other films and directors.
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# Cecil B. DeMille
## Biography
### 1881--1899: early years {#early_years}
Cecil Blount DeMille was of paternal Dutch ancestry. His surname was spelled de Mil`{{refn|group=note|There are several variants of DeMille's surname. His family's [[Dutch people|Dutch]] surname, originally spelled '' de Mil''.}}`{=mediawiki} before his grandfather William added an \"le\" for \"visual symmetry\".
As an adult, Cecil De Mille adopted the spelling *DeMille* because he believed it would look better on a marquee, but continued to use *de Mille* in private life. The family name *de Mille* was used by his children Cecilia, John, Richard, and Katherine. Cecil\'s brother, William, and his daughters, Margaret and Agnes, as well as DeMille\'s granddaughter, Cecilia de Mille Presley, also used the *de Mille* spelling.
DeMille was born on August 12, 1881, in a boarding house on Main Street in Ashfield, Massachusetts, where his parents had been vacationing for the summer. On September 1, 1881, the family returned with the newborn DeMille to their flat in New York. DeMille was named after his grandmothers Cecelia Wolff and Margarete Blount. He was the second of three children of Henry Churchill de Mille (September 4, 1853 -- February 10, 1893) and his wife, Matilda Beatrice deMille (née Samuel; January 30, 1853 -- October 8, 1923), known as Beatrice. His older brother, William C. deMille, was born on July 25, 1878.
Henry de Mille, whose ancestors were of English and Dutch-Belgian descent, was a North Carolina-born dramatist, actor, and lay reader in the Episcopal Church. In New York, Henry also taught English at Columbia College (now Columbia University). He worked as a playwright, administrator, and faculty member during the early years of the American Academy of Dramatic Arts, established in New York City in 1884. Henry de Mille frequently collaborated with David Belasco in playwriting; their best-known collaborations included \"The Wife\", \"Lord Chumley\", \"The Charity Ball\", and \"Men and Women\".
Cecil B. DeMille\'s mother, Beatrice, a literary agent and scriptwriter, was the daughter of German Jews. She had emigrated from England with her parents in 1871 when she was 18; the newly arrived family settled in Brooklyn, New York, where they maintained a middle-class, English-speaking household.
DeMille\'s parents met as members of a music and literary society in New York. Henry was a tall, red-headed student. Beatrice was intelligent, educated, forthright, and strong-willed. They married on July 1, 1876, despite Beatrice\'s parents\' objections because of the young couple\'s differing religions; Beatrice converted to Episcopalianism.
DeMille was a brave and confident child. He gained his love of theater while watching his father and Belasco rehearse their plays. A lasting memory for DeMille was a lunch with his father and actor Edwin Booth. As a child, DeMille created an alter ego, Champion Driver, a Robin Hood-like character, evidence of his creativity and imagination.
His father and his family had lived in Washington, North Carolina, until Henry built a three-story Victorian-style house for his family in Pompton Lakes, New Jersey ; they named this estate \"Pamlico\". John Philip Sousa was a friend of the family, and DeMille recalled throwing mud balls in the air so neighbor Annie Oakley could practice her shooting. DeMille\'s sister, Agnes, was born on April 23, 1891; his mother nearly did not survive the birth. Agnes died on February 11, 1894, from spinal meningitis.`{{refn|group=note|DeMille's niece and William deMille's daughter [[Agnes de Mille]] was a famed dancer-choreographer.<ref>{{cite magazine |last= Acocella |first=Joan |title=Agnes DeMille's Artistic Justice |url=https://www.newyorker.com/books/page-turner/agnes-de-milles-artistic-justice |access-date=May 23, 2019 |magazine=The New Yorker |date=November 5, 2015}}</ref>}}`{=mediawiki}
DeMille\'s parents operated a private school in Pompton Lakes and attended Christ Episcopal Church. DeMille recalled that this church was the place where he visualized the story of his 1923 version of *The Ten Commandments*.
On January 8, 1893, at age 40, Henry de Mille died suddenly from typhoid fever, leaving Beatrice with three children. To provide for her family, she opened the Henry C. de Mille School for Girls in her home in February 1893. The aim of the school was to teach young women to properly understand and fulfill the women\'s duty to themselves, their home, and their country. Beatrice had \"enthusiastically supported\" Henry\'s theatrical aspirations. She later became the second female play broker on Broadway. On Henry\'s deathbed, he told his wife that he did not want his sons to become playwrights. DeMille\'s mother sent him to Pennsylvania Military College (now Widener University) in Chester, Pennsylvania, at age 15. He fled the school to join the Spanish--American War, but failed to meet the age requirement. At the military college, even though his grades were average, he reportedly excelled in personal conduct.
DeMille attended the American Academy of Dramatic Arts (tuition-free due to his father\'s service to the academy). He graduated in 1900, and for graduation, his performance was the play *The Arcady Trail*. In the audience was Charles Frohman, who cast DeMille in his play *Hearts are Trumps*, DeMille\'s Broadway debut.
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# Cecil B. DeMille
## Biography
### 1900--1912: theater
#### Charles Frohman, Constance Adams, and David Belasco {#charles_frohman_constance_adams_and_david_belasco}
Cecil B. DeMille began his career as an actor on stage in 1900 in the theatrical company of Charles Frohman. He debuted on February 21, 1900, in the play *Hearts Are Trumps* at New York\'s Garden Theater. In 1901, DeMille starred in productions of *A Repentance*, *To Have and to Hold*, and *Are You a Mason?* At age 21, he married Constance Adams on August 16, 1902, at Adams\'s father\'s home in East Orange, New Jersey. The wedding party was small. Beatrice DeMille\'s family did not attend. Simon Louvish suggests that this was to conceal DeMille\'s partial Jewish heritage. Adams was 29 years old at the time of the marriage. They had met in a theater in Washington D.C. while they were both acting in *Hearts Are Trumps*.
They were sexually incompatible; according to DeMille, Adams was too \"pure\" to \"feel such violent and evil passions\" as he. DeMille had more violent sexual preferences and fetishes than his wife. Adams allowed DeMille to have several long-term mistresses during their marriage as an outlet while maintaining an appearance of a faithful marriage. One of DeMille\'s affairs was with his screenwriter Jeanie MacPherson. Despite his reputation for extramarital affairs, DeMille did not like to have affairs with his stars, as he believed it would cause him to lose control as a director. He once said he maintained his self-control when Gloria Swanson sat on his lap, and refused to touch her.
In 1902, he played a small part in *Hamlet*. Publicists wrote that he became an actor in order to learn how to direct and produce, but DeMille admitted that he became an actor in order to pay the bills. From 1904 to 1905, he attempted to make a living as a stock theater actor with his wife, Constance. DeMille made a 1905 reprise in *Hamlet* as Osric. In the summer of 1905, DeMille joined the stock cast at the Elitch Theatre in Denver, Colorado. He appeared in 11 of the 15 plays presented that season, all in minor roles. Maude Fealy was the featured actress in several productions that summer and developed a lasting friendship with DeMille. (He later cast her in *The Ten Commandments*.)
His brother, William, was establishing himself as a playwright and sometimes invited DeMille to collaborate. DeMille and William collaborated on *The Genius*, *The Royal Mounted*, and *After Five*. None of these was very successful. William de Mille was most successful when he worked alone.
DeMille and his brother at times worked with the legendary impresario David Belasco, who had been a friend and collaborator of their father. DeMille later adapted Belasco\'s *The Girl of the Golden West*, *Rose of the Rancho*, and *The Warrens of Virginia* into films. He was credited with the conception of Belasco\'s *The Return of Peter Grimm*. *The Return of Peter Grimm* sparked controversy, because Belasco had taken DeMille\'s unnamed screenplay, changed the characters, and named it *The Return of Peter Grimm*, producing and presenting it as his own work. DeMille was credited in small print as \"based on an idea by Cecil DeMille\". The play was successful, and DeMille was distraught that his childhood idol had plagiarized his work.
#### Losing interest in theater {#losing_interest_in_theater}
DeMille performed on stage with actors he later directed in films: Charlotte Walker, Mary Pickford, and Pedro de Cordoba. He also produced and directed plays. His 1905 performance in *The Prince Chap* as the Earl of Huntington was well received by audiences.
DeMille wrote a few of his own plays in between stage performances, but his playwriting was less successful. His first play was *The Pretender-A Play in a Prologue and 4 Acts* set in 17th-century Russia. Another unperformed play he wrote was *Son of the Winds*, a mythological Native American story. Life was difficult for DeMille and his wife as traveling actors, but travel allowed him to experience parts of the United States he had not yet seen. DeMille sometimes worked with the director E. H. Sothern, who influenced DeMille\'s later perfectionism. In 1907, due to a scandal with one of Beatrice\'s students, Evelyn Nesbit, the Henry de Mille School lost students. The school closed, and Beatrice filed for bankruptcy. DeMille wrote another play originally called *Sergeant Devil May Care* and renamed *The Royal Mounted*. He also toured with the Standard Opera Company, but there are few records of his singing ability.
On November 5, 1908, Constance and DeMille had a daughter, Cecilia, their only biological child. In the 1910s, DeMille began directing and producing other writers\' plays.
DeMille was poor and struggled to find work. Consequently, his mother hired him for her agency, The DeMille Play Company, and taught him how to be an agent and a playwright. He became the agency\'s manager and later a junior partner with his mother. In 1911, DeMille became acquainted with vaudeville producer Jesse Lasky when Lasky was searching for a writer for his new musical. He initially sought out William deMille. William had been a successful playwright, but DeMille was suffering from the failure of his plays *The Royal Mounted* and *The Genius*.
Beatrice introduced Lasky to Cecil DeMille instead. The collaboration of DeMille and Lasky produced a successful musical, *California*, which opened in New York in January 1912. Another DeMille-Lasky production that opened in January 1912 was *The Antique Girl*. In the spring of 1913, DeMille found success producing *Reckless Age* by Lee Wilson, a play about a high-society girl wrongly accused of manslaughter, starring Frederick Burton and Sydney Shields. But changes in the theater rendered DeMille\'s melodramas obsolete before they were produced, and true theatrical success eluded him. He produced many flops. Having become uninterested in working in theater, DeMille became ignited by passion for film when he watched the 1912 French film *Les Amours de la reine Élisabeth*.
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# Cecil B. DeMille
## Biography
### 1913--1914: entering films {#entering_films}
Desiring a change of scene, DeMille, Lasky, Sam Goldfish (later Samuel Goldwyn), and a group of East Coast businessmen created the Jesse L. Lasky Feature Play Company in 1913, of which DeMille became director-general. Lasky and DeMille were said to have sketched out the organization of the company on the back of a restaurant menu. As director-general, DeMille\'s job was to make the films. In addition to directing, he was the supervisor and consultant for the first year of films the company made. Sometimes, he directed scenes for other directors at the company in order to release films on time. Moreover, he co-authored other Lasky Company scripts and created screen adaptations that others directed.
The Lasky Play Company tried to recruit William de Mille, but he rejected the offer because he did not believe there was any promise in a film career. When William found out that DeMille had begun working in the motion picture industry, he wrote his brother a letter, saying that he was disappointed that Cecil was willing \"to throw away \[his\] future\" when he was \"born and raised in the finest traditions of the theater\".
The Lasky Company wanted to attract high-class audiences to their films, so it began producing films from literary works. The company bought the rights to Edwin Milton Royle\'s play *The Squaw Man* and cast Dustin Farnum in the lead role. It offered Farnum a choice between a quarter stock in the company or \$250 in weekly salary. Farnum chose the salary. Already \$15,000 in debt to Royle for the screenplay of *The Squaw Man*, Lasky\'s relatives bought the \$5,000 stock to save the Lasky Company from bankruptcy. With no knowledge of filmmaking, DeMille was introduced to observe the process at film studios. He was eventually introduced to Oscar Apfel, a stage director who had been a director with the Edison Company.
On December 12, 1913, DeMille, his cast, and crew boarded a Southern Pacific train bound for Flagstaff via New Orleans. His tentative plan was to shoot a film in Arizona, but he felt that Arizona lacked the Western look they were searching for. They also learned that other filmmakers were successfully shooting in Los Angeles, even in winter. He continued to Los Angeles. Once there, he chose not to shoot in Edendale, where many studios were, but in Hollywood. DeMille rented a barn to function as their film studio. Filming began on December 29, 1913, and lasted three weeks. Apfel filmed most of *The Squaw Man* due to DeMille\'s inexperience, but DeMille learned quickly and was particularly adept at impromptu screenwriting as necessary. He made his first film run 60 minutes, as long as a short play. *The Squaw Man* (1914), co-directed by Apfel, was a sensation, and it established the Lasky Company. It was the first feature-length film made in Hollywood. There were problems with the perforation of the film stock, and it was discovered the DeMille had brought a cheap British film perforator that had punched in 65 holes per foot instead of the industry standard of 64. Lasky and DeMille convinced film pioneer Siegmund Lubin of the Lubin Manufacturing Company to have his experienced technicians reperforate the film.
This was the first American feature film, according to its release date. D. W. Griffith\'s *Judith of Bethulia* was filmed earlier than *The Squaw Man*, but released later. This as the only film in which DeMille shared director\'s credit with Apfel.
*The Squaw Man* was a success, which led to the eventual founding of Paramount Pictures and Hollywood becoming the \"film capital of the world\". The film grossed more than ten times its budget after its New York premiere in February 1914. DeMille\'s next project was to aid Apfel in directing *Brewster\'s Millions*, which was wildly successful. In December 1914, Constance Adams brought home John DeMille, a 15-month-old boy, whom the couple legally adopted three years later. Biographer Scott Eyman suggested that she may have decided to adopt after recently having had a miscarriage.
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# Cecil B. DeMille
## Biography
### 1915--1928: silent era {#silent_era}
#### Westerns, Paradise, and World War I {#westerns_paradise_and_world_war_i}
Cecil B. DeMille\'s second film, credited exclusively to him, was *The Virginian*. It is the earliest of DeMille\'s films available in a quality, color-tinted video format, but that version is actually a 1918 rerelease. The Lasky Company\'s first few years were spent making films nonstop. DeMille directed 20 films by 1915. The most successful films during this period were *Brewster\'s Millions* (co-directed by DeMille), *Rose of the Rancho*, and *The Ghost Breaker*. DeMille adapted Belasco\'s dramatic lighting techniques to film technology, mimicking moonlight with U.S. cinema\'s first attempts at \"motivated lighting\" in *The Warrens of Virginia*. This was the first of a few film collaborations with his brother William. They struggled to adapt the play from the stage to the set. After the film was shown, viewers complained that the shadows and lighting prevented the audience from seeing the actors\' full faces and said they would pay only half price. Sam Goldwyn suggested that if they called it \"Rembrandt\" lighting, the audience would pay double the price. Additionally, because of DeMille\'s cordiality after the *Peter Grimm* incident, DeMille was able to rekindle his partnership with Belasco. He adapted several of Belasco\'s screenplays into film.
DeMille\'s most successful film was *The Cheat*; his direction in the film was acclaimed. In 1916, exhausted from three years of nonstop filmmaking, DeMille purchased land in the Angeles National Forest for a ranch that would become his getaway. He called this place \"Paradise\", declaring it a wildlife sanctuary; no shooting of animals besides snakes was allowed. His wife did not like Paradise, so DeMille often brought his mistresses there with him, including actress Julia Faye. In 1921, DeMille purchased a yacht he called *The Seaward*.
While filming *The Captive* in 1915, an extra, Charles Chandler, died on set when another extra failed to heed DeMille\'s orders to unload all guns for rehearsal. DeMille instructed the guilty man to leave town and never revealed his name. Lasky and DeMille maintained Chandler\'s widow on the payroll and, according to leading actor House Peters Sr., DeMille refused to stop production for Chandler\'s funeral. Peters said that he encouraged the cast to attend the funeral with him anyway since DeMille would not be able to shoot the film without him. On July 19, 1916, the Jesse Lasky Feature Play Company merged with Adolph Zukor\'s Famous Players Film Company, becoming Famous Players--Lasky. Zukor became president, Lasky vice president, DeMille director-general, and Goldwyn chairman of the board. Famous Players--Lasky later fired Goldwyn for frequent clashes with Lasky, DeMille, and Zukor. While on a European vacation in 1921, DeMille contracted rheumatic fever in Paris. He was confined to bed and unable to eat. His poor physical condition upon his return home affected the production of his 1922 film *Manslaughter*. According to Richard Birchard, DeMille\'s weakened state during production may have led to the film being received as uncharacteristically substandard.
During World War I, the Famous Players--Lasky organized a military company underneath the National Guard, the Home Guard, made up of film studio employees, with DeMille as captain. Eventually, the Guard was enlarged to a battalion and recruited soldiers from other film studios. They took time off weekly to practice military drills. Additionally, during the war, DeMille volunteered for the Justice Department\'s Intelligence Office, investigating friends, neighbors, and others he came in contact with in connection with the Famous Players--Lasky. He also volunteered for the Intelligence Office during World War II. DeMille considered enlisting in World War I, but stayed in the U.S. and made films. He did take a few months to set up a movie theater for the French front. Famous Players--Lasky donated the films. DeMille and Adams adopted Katherine Lester in 1920, whom Adams had found in the orphanage she directed.`{{Refn|group=note|Katherine's father had been killed in [[World War I]] and her mother had died of [[tuberculosis]].<ref>{{harvnb|Louvish|2007|p=185}}; {{harvnb|Eyman|2010|p=162}}</ref> To DeMille's dismay, Katherine became an actress; however, she ultimately gained his approval. In 1936 she married actor Anthony Quinn.<ref>{{cite news |last=Bergan |first=Ronald |title=Anthony Quinn: Colourful Hollywood star who built a career playing ethnic heroes and villains |url=https://www.theguardian.com/news/2001/jun/05/guardianobituaries.filmnews |work=The Guardian |date=June 5, 2001 |access-date=May 24, 2019}}</ref>}}`{=mediawiki} In 1922, the couple adopted Richard deMille.
#### Scandalous dramas, Biblical epics, and departure from Paramount {#scandalous_dramas_biblical_epics_and_departure_from_paramount}
Film started becoming more sophisticated and the Lasky company\'s subsequent films were criticized for primitive and unrealistic set design. Consequently, Beatrice deMille introduced the Famous Players--Lasky to Wilfred Buckland, whom DeMille knew from his time at the American Academy of Dramatic Arts, and he became DeMille\'s art director. William deMille reluctantly became a story editor. William later converted from theater to Hollywood and spent the rest of his career as a film director. DeMille frequently remade his own films. In 1917, he remade *The Squaw Man* (1918), only four years after the original. Despite its quick turnaround, the film was fairly successful. DeMille\'s second remake at MGM in 1931 was a failure.
After five years and 30 hit films, DeMille became the American film industry\'s most successful director. In the silent era, he was renowned for *Male and Female* (1919), *Manslaughter* (1922), *The Volga Boatman* (1926), and *The Godless Girl* (1928). His trademark scenes included bathtubs, lion attacks, and Roman orgies. Many of his films featured scenes in two-color Technicolor. In 1923, DeMille released the modern melodrama *The Ten Commandments*, a significant change from his previous irreligious films. The film was produced on a budget of \$600,000, Paramount\'s most expensive production. This concerned Paramount executives, but the film was the studio\'s highest-grossing film. It held the Paramount record for 25 years until DeMille broke the record again.
In the early 1920s, scandal surrounded Paramount; religious groups and the media opposed portrayals of immorality in films. A censorship board called the Hays Code was established. DeMille\'s film *The Affairs of Anatol* came under fire. Furthermore, DeMille argued with Zukor over his extravagant and over-budget production costs. Consequently, DeMille left Paramount in 1924 despite having helped establish it. He joined the Producers Distributing Corporation. His first film in the new production company, DeMille Pictures Corporation, was *The Road to Yesterday* in 1925. He directed and produced four films on his own, working with Producers Distributing Corporation because he found front office supervision too restricting. Aside from *The King of Kings,* none of DeMille\'s films away from Paramount were successful. *The King of Kings* established DeMille as \"master of the grandiose and of biblical sagas\". Considered at the time the most successful Christian film of the silent era, DeMille calculated that it had been viewed over 800 million times around the world. After the release of DeMille\'s *The Godless Girl*, silent films in America became obsolete, and DeMille was forced to shoot a shoddy final reel with the new sound production technique. Although this final reel looked so different from the first 11 reels that it appeared to be from another movie, according to Simon Louvish, the film is one of DeMille\'s strangest and most \"DeMillean\" film.
The immense popularity of DeMille\'s silent films enabled him to branch out into other areas. The Roaring Twenties were the boom years and DeMille took full advantage, opening the Mercury Aviation Company, one of America\'s first commercial airlines. He was also a real estate speculator, an underwriter of political campaigns, vice president of Bank of America, and vice president of the Commercial National Trust and Savings Bank in Los Angeles, where he approved loans for other filmmakers. In 1916, DeMille purchased a mansion in Hollywood. Charlie Chaplin lived next door for a time, and after he moved, DeMille purchased the other house and combined the estates.
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# Cecil B. DeMille
## Biography
### 1929--1956: sound era {#sound_era}
#### MGM and return to Paramount {#mgm_and_return_to_paramount}
When \"talking pictures\" were invented in 1928, DeMille made a successful transition, offering his own innovations to the painful process; he devised a microphone boom and a soundproof camera blimp. He also popularized the camera crane. His first three sound films, *Dynamite*, *Madame Satan*, and his 1931 remake of *The Squaw Man*, were produced at Metro-Goldwyn-Mayer. These films were critically and financially unsuccessful. He had completely adapted to the production of sound film despite the film\'s poor dialogue. After his contract ended at MGM, he left, but no production studios would hire him. He attempted to create a guild of a half a dozen directors with the same creative desires called the Director\'s Guild, but the idea failed due to lack of funding and commitment. Moreover, the Internal Revenue Service audited DeMille due to issues with his production company. This was, according to DeMille, the lowest point of his career. He traveled abroad to find employment until he was offered a deal at Paramount.
In 1932, DeMille returned to Paramount at Lasky\'s request, bringing with him his own production unit. His first film back at Paramount, *The Sign of the Cross*, was also his first success since leaving Paramount besides *The King of Kings*. Zukor approved DeMille\'s return on the condition that DeMille not exceed his production budget of \$650,000 for *The Sign of the Cross*. Produced in eight weeks without exceeding budget, the film was financially successful. *The Sign of the Cross* was the first film to integrate all cinematic techniques. The film was considered a \"masterpiece\" and surpassed the quality of other sound films of the time. DeMille followed this epic with two dramas released in 1933 and 1934, *This Day and Age* and *Four Frightened People*. These were box-office disappointments, though *Four Frightened People* received good reviews. DeMille stuck to large-budget spectaculars for the rest of his career.
#### Politics and *Lux Radio Theatre* {#politics_and_lux_radio_theatre}
DeMille was outspoken about his Episcopalian integrity, but his private life included mistresses and adultery. He was a conservative Republican activist, becoming more conservative as he aged. He was known as anti-union and worked to prevent the unionization of film production studios. But according to DeMille himself, he was not anti-union and belonged to a few unions. He said he was rather against union leaders such as Walter Reuther and Harry Bridges, whom he compared to dictators. He supported Herbert Hoover and in 1928 made his largest campaign donation to Hoover. But DeMille also liked Franklin D. Roosevelt, finding him charismatic, tenacious, and intelligent, and agreeing with Roosevelt\'s abhorrence of Prohibition. DeMille lent Roosevelt a car for his 1932 United States presidential election campaign and voted for him. He never again voted for a Democratic candidate in a presidential election.
From June 1, 1936, until January 22, 1945, DeMille hosted and directed *Lux Radio Theatre*, a weekly digest of current feature films. Broadcast on the Columbia Broadcasting System (CBS) from 1935 to 1954, *Lux Radio* was one of the most popular weekly shows in radio history. While DeMille was host, the show had 40 million weekly listeners and DeMille had an annual salary of \$100,000. From 1936 to 1945, he produced, hosted, and directed every show, with the occasional exception of a guest director. He resigned from *Lux Radio* because he refused to pay a dollar to the American Federation of Radio Artists (AFRA), on the principle that no organization had the right to \"levy a compulsory assessment upon any member\".
DeMille sued the union for reinstatement but lost. He appealed to the California Supreme Court and lost again. When the AFRA expanded to television, DeMille was banned from television appearances. Consequently, he formed the DeMille Foundation for Political Freedom to campaign for the right to work. He gave speeches across the nation for the next few years. DeMille\'s primary criticism was of closed shops, but later included criticism of communism and unions in general. The U.S. Supreme Court declined to review his case, but DeMille lobbied for the Taft--Hartley Act, which passed. It prohibited denying anyone the right to work if they refuse to pay a political assessment. But the law did not apply retroactively, so DeMille\'s television and radio appearance ban lasted the rest of his life, though he was permitted to appear on radio or television to publicize a movie. William Keighley replaced him. DeMille never worked in radio again.
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# Cecil B. DeMille
## Biography
### 1929--1956: sound era {#sound_era}
#### Adventure films and dramatic spectacles {#adventure_films_and_dramatic_spectacles}
In 1939, DeMille\'s *Union Pacific* was successful through DeMille\'s collaboration with the Union Pacific Railroad. The Union Pacific gave DeMille access to historical data, early period trains, and expert crews, adding to the film\'s authenticity. During pre-production, DeMille was dealing with his first serious health issue. In March 1938, he underwent a major emergency prostatectomy. He had a post-surgery infection from which he nearly did not recover, citing streptomycin as his saving grace. The surgery caused him to suffer from sexual dysfunction for the rest of his life, according to some family members. After his surgery and the success of *Union Pacific*, DeMille first used three-strip Technicolor in 1940, in *North West Mounted Police*. DeMille wanted to film in Canada, but due to budget constraints, the film was instead shot in Oregon and Hollywood. Critics were impressed with the visuals but found the scripts dull, calling it DeMille\'s \"poorest Western\". Despite the criticism, it was Paramount\'s highest-grossing film of the year. Audiences liked its highly saturated color, so DeMille made no further black-and-white features. DeMille was anti-communist and abandoned a project in 1940 to film Ernest Hemingway\'s *For Whom the Bell Tolls* due to its communist themes, even though he had already paid \$100,000 for the rights to the novel. He was so eager to produce the film that he hadn\'t yet read it. He claimed he abandoned the project in order to complete a different project, but it was actually to preserve his reputation and avoid appearing reactionary. While concurrently filmmaking, he served during World War II at age 60 as his neighborhood air-raid warden.
In 1942, DeMille worked with Jeanie MacPherson and William deMille to produce a film, *Queen of Queens*, that was intended to be about Mary, mother of Jesus. After reading the screenplay, Daniel A. Lord warned DeMille that Catholics would find the film too irreverent while non-Catholics would consider it Catholic propaganda. Consequently, the film was never made. MacPherson worked as a scriptwriter on many of DeMille\'s films. In 1938, DeMille supervised the film compilation *Land of Liberty* as the American film industry\'s contribution to the 1939 New York World\'s Fair. He used clips from his own films in it. *Land of Liberty* was not high-grossing, but it was well-received, and DeMille was asked to shorten its running time to allow for more showings per day. MGM distributed the film in 1941 and donated profits to World War II relief charities. In 1942, DeMille released Paramount\'s most successful film, *Reap the Wild Wind*. It had a large budget and many special effects, including an electronically operated giant squid. After working on it, DeMille was the master of ceremonies at a rally organized by David O. Selznick in the Los Angeles Coliseum in support of the Dewey--Bricker presidential ticket as well as Governor Earl Warren of California.`{{refn|group=note| The gathering drew 93,000, with short speeches by [[Hedda Hopper]] and [[Walt Disney]]. Among those in attendance were [[Ann Sothern]], [[Ginger Rogers]], [[Randolph Scott]], [[Adolphe Menjou]], [[Gary Cooper]], and [[Walter Pidgeon]]. Though the rally drew a good response, most Hollywood celebrities who took a public position sided with the [[Franklin Roosevelt|Roosevelt]]-[[Harry Truman|Truman]] ticket.<ref name="David M. Jordan 2011 pp. 231-232">David M. Jordan, ''FDR, Dewey, and the Election of 1944'' (Bloomington and Indianapolis: Indiana University Press, 2011), pp. 231–232.</ref>}}`{=mediawiki} DeMille\'s 1947 film *Unconquered* had the longest running time (146 minutes), longest filming schedule (102 days), and largest budget (\$5 million). Its sets and effects were so realistic that 30 extras needed to be hospitalized due to a scene with fireballs and flaming arrows. It was commercially very successful.
DeMille\'s next film, *Samson and Delilah* (1949), was Paramount\'s highest-grossing film up to that time. A Biblical epic with sex, it was a characteristically DeMille film. 1952\'s *The Greatest Show on Earth* became Paramount\'s highest-grossing film to that point and won the Academy Award for Best Picture and the Academy Award for Best Story. It began production in 1949. Ringling Brothers-Barnum and Bailey were paid \$250,000 for use of the title and facilities. DeMille toured with the circus while helping write the script. Noisy and bright, the film was not well-liked by critics but was an audience favorite. In 1953, DeMille signed a contract with Prentice Hall to publish an autobiography. He reminisced into a voice recorder, the recording was transcribed, and the information was organized by topic. Art Arthur also interviewed people for the autobiography. DeMille did not like the biography\'s first draft, saying he thought the person portrayed in it was an egotistical \"SOB\". In the early 1950s, Allen Dulles and Frank Wisner recruited DeMille to serve on the board of the anti-communist National Committee for a Free Europe, the public face of the organization that oversaw Radio Free Europe. In 1954, Secretary of the Air Force Harold E. Talbott asked DeMille for help designing the cadet uniforms at the newly established United States Air Force Academy. DeMille\'s designs, most notably that of the cadet parade uniform, were praised by Air Force and Academy leadership, adopted, and still worn.
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# Cecil B. DeMille
## Biography
### 1929--1956: sound era {#sound_era}
#### Final works and unrealized projects {#final_works_and_unrealized_projects}
In 1952, DeMille sought approval for a lavish remake of his 1923 silent film *The Ten Commandments*. He went before the Paramount board of directors, which was mostly Jewish-American. The board rejected his proposal, even though his last two films, *Samson and Delilah* and *The Greatest Show on Earth*, had been record-breaking hits. Adolph Zukor convinced the board to change its mind on the grounds of morality. DeMille did not have an exact budget proposal for the project, and it promised to be the most costly in U.S. film history. Still, the board unanimously approved it. *The Ten Commandments*, released in 1956, was DeMille\'s final film. It was the longest (3 hours, 39 minutes) and most expensive (\$13 million) film in Paramount history. Production began in October 1954. The Exodus scene was filmed on-site in Egypt with four Technicolor-VistaVision cameras filming 12,000 people. Filming continued in 1955 in Paris and Hollywood on 30 different sound stages. They even expanded to RKO sound studios for filming. Post-production lasted a year, and the film premiered in Salt Lake City. Nominated for an Academy Award for Best Picture, it grossed over \$80 million, which surpassed the gross of *The Greatest Show on Earth* and every other film in history except *Gone with the Wind*. DeMille offered ten percent of his profit to the crew, a unique practice at the time.
On November 7, 1954, while in Egypt filming the Exodus sequence for *The Ten Commandments*, DeMille (who was 73) climbed a 107 ft ladder to the top of the set and had a serious heart attack. Despite the urging of his associate producer, DeMille wanted to return to the set right away. He developed a plan with his doctor to allow him to continue directing while reducing his physical stress. DeMille completed the film, but his health was diminished by several more heart attacks. His daughter Cecilia took over as director as DeMille sat behind the camera with Loyal Griggs as the cinematographer. This film was his last.
Due to his frequent heart attacks, DeMille asked his son-in-law, actor Anthony Quinn, to direct a remake of his 1938 film *The Buccaneer*. DeMille served as executive producer, overseeing producer Henry Wilcoxon. Despite a cast led by Charlton Heston and Yul Brynner, the 1958 film *The Buccaneer* was a disappointment. DeMille attended its Santa Barbara premiere in December 1958. He was unable to attend its Los Angeles premiere. In the months before his death, DeMille was researching a film biography of Robert Baden-Powell, the founder of the Scout Movement. DeMille asked David Niven to star in the film, but it was never made. DeMille also was planning a film about the space race and a biblical epic based on the Book of Revelation. His autobiography was mostly complete when he died, and was published in November 1959.
#### Death
DeMille suffered a series of heart attacks from June 1958 to January 1959, and died on January 21, 1959, following an attack. His funeral was held on January 23 at St. Stephen\'s Episcopal Church. He was entombed at the Hollywood Memorial Cemetery (now known as Hollywood Forever). After his death, news outlets such as *The New York Times*, the *Los Angeles Times*, and *The Guardian* called DeMille a \"pioneer of movies\", \"the greatest creator and showman of our industry\", and \"the founder of Hollywood\". DeMille left his multi-million dollar estate in Los Feliz, Los Angeles, in Laughlin Park to his daughter Cecilia because his wife had dementia and was unable to care for an estate. She died a year later. His personal will drew a line between Cecilia and his three adopted children, with Cecilia receiving a majority of DeMille\'s inheritance and estate. The other three children were surprised by this, as DeMille had not treated them differently in life. Cecilia lived in the house until her death in 1984. The house was auctioned by his granddaughter Cecilia DeMille Presley, who also lived there in the late 1980s.`{{refn|group=note|The estate cycled through several different homeowners for the next 30 years until it was bought by American actress [[Angelina Jolie]] in 2017 for nearly $25 million.<ref name="jolie">{{cite news |last=David |first=Mark |title=Angelina Jolie Buys Cecil B. DeMille's Estate at Record-Shattering Price |url=https://variety.com/2017/dirt/real-estalker/angelina-jolie-cecil-b-demille-estate-laughlin-park-1202451889/ |access-date=June 26, 2019 |work=Variety |date=June 2, 2017}}</ref>}}`{=mediawiki}
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# Cecil B. DeMille
## Filmmaking
### Influences
DeMille believed his first influences to be his parents, Henry and Beatrice DeMille. His playwright father introduced him to the theater at a young age. Henry was heavily influenced by the work of Charles Kingsley, whose ideas trickled down to DeMille. DeMille noted that his mother had a \"high sense of the dramatic\" and was determined to continue the artistic legacy of her husband after he died. Beatrice became a play broker and author\'s agent, influencing DeMille\'s early life and career. DeMille\'s father worked with David Belasco who was a theatrical producer, impresario, and playwright. Belasco was known for adding realistic elements in his plays such as real flowers, food, and aromas that could transport his audiences into the scenes. While working in theatre, DeMille used real fruit trees in his play *California*, as influenced by Belasco. Similar to Belasco, DeMille\'s theatre revolved around entertainment rather than artistry. Generally, Belasco\'s influence of DeMille\'s career can be seen in DeMille\'s showmanship and narration. E. H. Sothern\'s early influence on DeMille\'s work can be seen in DeMille\'s perfectionism. DeMille recalled that one of the most influential plays he saw was *Hamlet*, directed by Sothern.
### Method
DeMille\'s filmmaking process always began with extensive research. Next, he would work with writers to develop the story that he was envisioning. Then, he would help writers construct a script. Finally, he would leave the script with artists and allow them to create artistic depictions and renderings of each scene. Plot and dialogue were not a strong point of DeMille\'s films. Consequently, he focused his efforts on his films\' visuals. He worked with visual technicians, editors, art directors, costume designers, cinematographers, and set carpenters in order to perfect the visual aspects of his films. With his editor, Anne Bauchens, DeMille used editing techniques to allow the visual images to bring the plot to climax rather than dialogue. DeMille had large and frequent office conferences to discuss and examine all aspects of the working film including story-boards, props, and special effects.
DeMille rarely gave direction to actors; he preferred to \"office-direct\", where he would work with actors in his office, going over characters and reading through scripts. Any problems on the set were often fixed by writers in the office rather than on the set. DeMille did not believe a large movie set was the place to discuss minor character or line issues. DeMille was particularly adept at directing and managing large crowds in his films. Martin Scorsese recalled that DeMille had the skill to maintain control of not only the lead actors in a frame but the many extras in the frame as well. DeMille was adept at directing \"thousands of extras\", and many of his pictures include spectacular set pieces: the toppling of the pagan temple in *Samson and Delilah*; train wrecks in *The Road to Yesterday*, *Union Pacific* and *The Greatest Show on Earth*; the destruction of an airship in *Madam Satan*; and the parting of the Red Sea in both versions of *The Ten Commandments*. In his early films, DeMille experimented with photographic light and shade, which created dramatic shadows instead of glare. His specific use of lighting, influenced by his mentor David Belasco, was for the purpose of creating \"striking images\" and heightening \"dramatic situations\". DeMille was unique in using this technique. In addition to his use of volatile and abrupt film editing, his lighting and composition were innovative for the time period as filmmakers were primarily concerned with a clear, realistic image. Another important aspect of DeMille\'s editing technique was to put the film away for a week or two after an initial edit in order to re-edit the picture with a fresh mind. This allowed for the rapid production of his films in the early years of the Lasky Company. The cuts were sometimes rough, but the movies were always interesting.
DeMille often edited in a manner that favored psychological space rather than physical space through his cuts. In this way, the characters\' thoughts and desires are the visual focus rather than the circumstances regarding the physical scene. As DeMille\'s career progressed, he increasingly relied on artist Dan Sayre Groesbeck\'s concept, costume, and storyboard art. Groesbeck\'s art was circulated on set to give actors and crew members a better understanding of DeMille\'s vision. His art was even shown at Paramount meetings when pitching new films. DeMille adored the art of Groesbeck, even hanging it above his fireplace, but film staff found it difficult to convert his art into three-dimensional sets. As DeMille continued to rely on Groesbeck, the nervous energy of his early films transformed into more steady compositions of his later films. While visually appealing, this made the films appear more old-fashioned.
Composer Elmer Bernstein described DeMille as \"sparing no effort\" when filmmaking. Bernstein recalled that DeMille would scream, yell, or flatter---whatever it took to achieve the perfection he required in his films. DeMille was painstakingly attentive to details on set and was as critical of himself as he was of his crew. Costume designer Dorothy Jeakins, who worked with DeMille on *The Ten Commandments* (1956), said that he was skilled in humiliating people. Jeakins admitted that she received quality training from him, but that it was necessary to become a perfectionist on a DeMille set to avoid being fired. DeMille had an authoritarian persona on set; he required absolute attention from the cast and crew. He had a band of assistants who catered to his needs. He would speak to the entire set, sometimes enormous with countless numbers of crew members and extras, via a microphone to maintain control of the set. He was disliked by many inside and outside of the film industry for his cold and controlling reputation.
DeMille was known for autocratic behavior on the set, singling out and berating extras who were not paying attention. Many of these displays were thought to be staged, however, as an exercise in discipline. He despised actors who were unwilling to take physical risks, especially when he had first demonstrated that the required stunt would not harm them. This occurred with Victor Mature in *Samson and Delilah*. Mature refused to wrestle Jackie the Lion, even though DeMille had just tussled with the lion, proving that he was tame. DeMille told the actor that he was \"one hundred percent yellow\". Paulette Goddard\'s refusal to risk personal injury in a scene involving fire in *Unconquered* cost her DeMille\'s favor and a role in *The Greatest Show on Earth*. DeMille did receive help in his films, notably from Alvin Wyckoff, who shot forty-three of DeMille\'s films; brother William deMille who would occasionally serve as his screenwriter; and Jeanie Macpherson, who served as DeMille\'s exclusive screenwriter for fifteen years; and Eddie Salven, DeMille\'s favorite assistant director.
DeMille made stars of unknown actors: Gloria Swanson, Bebe Daniels, Rod La Rocque, William Boyd, Claudette Colbert, and Charlton Heston. He also cast established stars such as Gary Cooper, Robert Preston, Paulette Goddard and Fredric March in multiple pictures. DeMille cast some of his performers repeatedly, including Henry Wilcoxon, Julia Faye, Joseph Schildkraut, Ian Keith, Charles Bickford, Theodore Roberts, Akim Tamiroff, and William Boyd. DeMille was credited by actor Edward G. Robinson with saving his career following his eclipse in the Hollywood blacklist.
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# Cecil B. DeMille
## Filmmaking
### Style and themes {#style_and_themes}
Cecil B. DeMille\'s film production career evolved from critically significant silent films to financially significant sound films. He began his career with reserved yet brilliant melodramas; from there, his style developed into marital comedies with outrageously melodramatic plots. In order to attract a high-class audience, DeMille based many of his early films on stage melodramas, novels, and short stories. He began the production of epics earlier in his career until they began to solidify his career in the 1920s. By 1930, DeMille had perfected his film style of mass-interest spectacle films with Western, Roman, or Biblical themes. DeMille was often criticized for making his spectacles too colorful and for being too occupied with entertaining the audience rather than accessing the artistic and auteur possibilities that film could provide. However, others interpreted DeMille\'s work as visually impressive, thrilling, and nostalgic. Along the same lines, critics of DeMille often qualify him by his later spectacles and fail to consider several decades of ingenuity and energy that defined him during his generation. Throughout his career, he did not alter his films to better adhere to contemporary or popular styles. Actor Charlton Heston admitted DeMille was, \"terribly unfashionable\" and Sidney Lumet called DeMille, \"the cheap version of D. W. Griffith\", adding that DeMille, \"\[didn\'t have\]\...an original thought in his head\", though Heston added that DeMille was much more than that. According to Scott Eyman, DeMille\'s films were at the same time masculine and feminine due to his thematic adventurousness and his eye for the extravagant. DeMille\'s distinctive style can be seen through camera and lighting effects as early as *The Squaw Man* with the use of daydream images; moonlight and sunset on a mountain; and side-lighting through a tent flap. In the early age of cinema, DeMille differentiated the Lasky Company from other production companies due to the use of dramatic, low-key lighting they called \"Lasky lighting\" and marketed as \"Rembrandt lighting\" to appeal to the public. DeMille achieved international recognition for his unique use of lighting and color tint in his film *The Cheat*. DeMille\'s 1956 version of *The Ten Commandments*, according to director Martin Scorsese, is renowned for its level of production and the care and detail that went into creating the film. He stated that *The Ten Commandments* was the final culmination of DeMille\'s style.
DeMille was interested in art and his favorite artist was Gustave Doré; DeMille based some of his most well-known scenes on the work of Doré. DeMille was the first director to connect art to filmmaking; he created the title of \"art director\" on the film set. DeMille was also known for his use of special effects without the use of digital technology. Notably, DeMille had cinematographer John P. Fulton create the parting of the Red Sea scene in his 1956 film *The Ten Commandments*, which was one of the most expensive special effects in film history, and has been called by Steven Spielberg \"the greatest special effect in film history\". The actual parting of the sea was created by releasing 360,000 gallons of water into a huge water tank split by a U-shaped trough, overlaying it with a film of a giant waterfall that was built on the Paramount backlot, and playing the clip backward.
Aside from his Biblical and historical epics, which are concerned with how man relates to God, some of DeMille\'s films contained themes of \"neo-naturalism\", which portray the conflict between the laws of man and the laws of nature. Although he is known for his later \"spectacular\" films, his early films are held in high regard by critics and film historians. DeMille discovered the possibilities of the \"bathroom\" or \"boudoir\" in the film without being \"vulgar\" or \"cheap\". DeMille\'s films *Male and Female*, *Why Change Your Wife?*, and *The Affairs of Anatol* can be retrospectively described as high camp and are categorized as \"early DeMille films\" due to their particular style of production and costume and set design. However, his earlier films *The Captive*, *Kindling*, *Carmen*, and *The Whispering Chorus* are more serious films. It is difficult to typify DeMille\'s films into one specific genre. His first three films were Westerns, and he filmed many Westerns throughout his career. However, throughout his career, he filmed comedies, periodic and contemporary romances, dramas, fantasies, propaganda, Biblical spectacles, musical comedies, suspense, and war films. At least one DeMille film can represent each film genre. DeMille produced the majority of his films before the 1930s, and by the time sound films were invented, film critics saw DeMille as antiquated, with his best filmmaking years behind him.
DeMille\'s films contained many similar themes throughout his career. However, the films of his silent era were often thematically different from the films of his sound era. His silent-era films often included the \"battle of the sexes\" theme due to the era of women\'s suffrage and the enlarging role of women in society. Moreover, before his religious-themed films, many of his silent era films revolved around \"husband-and-wife-divorce-and-remarry satires\", considerably more adult-themed. According to Simon Louvish, these films reflected DeMille\'s inner thoughts and opinions about marriage and human sexuality. Religion was a theme that DeMille returned to throughout his career. Of his seventy films, five revolved around stories of the Bible and the New Testament; however many others, while not direct retellings of Biblical stories, had themes of faith and religious fanaticism in films such as *The Crusades* and *The Road to Yesterday*. Western and frontier American were also themes that DeMille returned to throughout his career. His first several films were Westerns, and he produced a chain of westerns during the sound era. Instead of portraying the danger and anarchy of the West, he portrayed the opportunity and redemption found in Western America. Another common theme in DeMille\'s films is the reversal of fortune and the portrayal of the rich and the poor, including the war of the classes and man versus society conflicts such as in *The Golden Chance* and *The Cheat*. In relation to his own interests and sexual preferences, sadomasochism was a minor theme present in some of his films. Another minor characteristic of DeMille\'s films include train crashes, which can be found in several of his films.
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# Cecil B. DeMille
## Legacy
Known as the father of the Hollywood motion picture industry, Cecil B. DeMille made 70 films including several box-office hits. DeMille is one of the more commercially successful film directors in history, with his films before the release of *The Ten Commandments* estimated to have grossed \$650 million worldwide. Adjusted for inflation, DeMille\'s remake of *The Ten Commandments* is the eighth highest-grossing film in the world.
According to Sam Goldwyn, critics did not like DeMille\'s films, but the audiences did, and \"they have the final word\". Similarly, scholar David Blanke, argued that DeMille had lost the respect of his colleagues and film critics by his late film career. However, his final films maintained that DeMille was still respected by his audiences. Five of DeMille\'s films were the highest-grossing films at the year of their release, with only Spielberg topping him with six of his films as the highest-grossing films of the year. DeMille\'s highest-grossing films include: *The Sign of the Cross* (1932), *Unconquered* (1947), *Samson and Delilah* (1949), *The Greatest Show on Earth* (1952), and *The Ten Commandments* (1956). Director Ridley Scott has been called \"the Cecil B. DeMille of the digital era\" due to his classical and medieval epics.
Despite his box-office success, awards, and artistic achievements, DeMille has been dismissed and ignored by critics both during his life and posthumously. He was consistently criticized for producing shallow films without talent or artistic care. Compared to other directors, few film scholars have taken the time to academically analyze his films and style. During the French New Wave, critics began to categorize certain filmmakers as auteurs such as Howard Hawks, John Ford, and Raoul Walsh. DeMille was omitted from the list, thought to be too unsophisticated and antiquated to be considered an auteur. However, Simon Louvish wrote \"he was the complete master and auteur of his films\", and Anton Kozlovic called him the \"unsung American auteur\". Andrew Sarris, a leading proponent of the auteur theory, ranked DeMille highly as an auteur in the \"Far Side of Paradise\", just below the \"Pantheon\". Sarris added that despite the influence of the styles of contemporary directors throughout his career, DeMille\'s style remained unchanged. Robert Birchard wrote that one could argue the auteurship of DeMille on the basis that DeMille\'s thematic and visual style remained consistent throughout his career. However, Birchard acknowledged that Sarris\'s point was more likely that DeMille\'s style was behind the development of film as an art form. Meanwhile, Sumiko Higashi sees DeMille as \"not only a figure who was shaped and influenced by the forces of his era but as a filmmaker who left his own signature on the culture industry.\" The critic Camille Paglia has called *The Ten Commandments* one of the ten greatest films of all time.
DeMille was one of the first directors to become a celebrity in his own right. He cultivated the image of the omnipotent director, complete with megaphone, riding crop, and jodhpurs. He was known for his unique working wardrobe, which included riding boots, riding pants, and soft, open necked shirts. Joseph Henabery recalled that DeMille looked like \"a king on a throne surrounded by his court\" while directing films on a camera platform.
DeMille was liked by some of his fellow directors and disliked by others, though his actual films were usually dismissed by his peers as a vapid spectacle. Director John Huston intensely disliked both DeMille and his films. \"He was a thoroughly bad director\", Huston said. \"A dreadful showoff. Terrible. To diseased proportions.\" Said fellow director William Wellman: \"Directorially, I think his pictures were the most horrible things I\'ve ever seen in my life. But he put on pictures that made a fortune. In that respect, he was better than any of us.\" Producer David O. Selznick wrote: \"There has appeared only one Cecil B. DeMille. He is one of the most extraordinarily able showmen of modern times. However much I may dislike some of his pictures, it would be very silly of me, as a producer of commercial motion pictures, to demean for an instant his unparalleled skill as a maker of mass entertainment.\" Salvador Dalí wrote that DeMille, Walt Disney, and the Marx Brothers were \"the three great American Surrealists\". DeMille appeared as himself in numerous films, including the MGM comedy *Free and Easy*. He often appeared in his coming-attraction trailers and narrated many of his later films, even stepping on screen to introduce *The Ten Commandments*. DeMille was immortalized in Billy Wilder\'s *Sunset Boulevard* when Gloria Swanson spoke the line: \"All right, Mr. DeMille. I\'m ready for my close-up.\" DeMille plays himself in the film. DeMille\'s reputation had a renaissance in the 2010s.
As a filmmaker, DeMille was the aesthetic inspiration of many directors and films due to his early influence during the crucial development of the film industry. DeMille\'s early silent comedies influenced the comedies of Ernst Lubitsch and Charlie Chaplin\'s *A Woman of Paris*. Additionally, DeMille\'s epics such as *The Crusades* influenced Sergei Eisenstein\'s *Alexander Nevsky*. Moreover, DeMille\'s epics inspired directors such as Howard Hawks, Nicholas Ray, Joseph L. Mankiewicz, and George Stevens to try producing epics. Cecil B. DeMille has influenced the work of several well-known directors. Alfred Hitchcock cited DeMille\'s 1921 film *Forbidden Fruit* as an influence of his work and one of his top ten favorite films. DeMille has influenced the careers of many modern directors. Martin Scorsese cited *Unconquered*, *Samson and Delilah*, and *The Greatest Show on Earth* as DeMille films that have imparted lasting memories on him. Scorsese said he had viewed *The Ten Commandments* forty or fifty times. Famed director Steven Spielberg stated that DeMille\'s *The Greatest Show on Earth* was one of the films that influenced him to become a filmmaker. Furthermore, DeMille influenced about half of Spielberg\'s films, including *War of the Worlds*.`{{refn|group=note|DeMille had considered making the film himself. He bought the rights to the novel in 1925 but abandoned the project in pre-production.<ref>{{cite book |last=Flynn |first=John L. |title=War of the Worlds: From Wells to Spielberg |url=https://books.google.com/books?id=T0aCSs1-23sC&q=cecil+b+demille+%22war+of+the+worlds%22&pg=PA56 |publisher=Galactic Books |location=Owings Mills, MD |date=2005 |page=56 |isbn=0976940000 |access-date=July 1, 2019}}</ref>}}`{=mediawiki} *The Ten Commandments* inspired DreamWorks Animation\'s later film about Moses, *The Prince of Egypt*. As one of the establishing members of Paramount Pictures and co-founder of Hollywood, DeMille had a role in the development of the film industry. Consequently, the name \"DeMille\" has become synonymous with filmmaking.
Publicly Episcopalian, DeMille drew on his Christian and Jewish ancestors to convey a message of tolerance. DeMille received more than a dozen awards from Christian and Jewish religious and cultural groups, including B\'nai B\'rith. However, not everyone received DeMille\'s religious films favorably. DeMille was accused of antisemitism after the release of *The King of Kings*, and director John Ford despised DeMille for what he saw as \"hollow\" biblical epics meant to promote DeMille\'s reputation during the politically turbulent 1950s. In response to the claims, DeMille donated some of the profits from *The King of Kings* to charity. In the 2012 *Sight & Sound* poll, both DeMille\'s *Samson and Delilah* and 1923 version of *The Ten Commandments* received votes, but did not make the top 100 films. Although many of DeMille\'s films are available on DVD and Blu-ray release, only 20 of his silent films are commercially available on DVD.`{{refn|group=note|In the 1950s, Paramount sold its entire pre-1948 film library, including those of DeMille, to [[EMKA]]. Consequently, most of DeMille's pre-1948 films no longer belong to Paramount.<ref>{{cite journal |last=White |first=Timothy R. |title=Life After Divorce: The Corporate Strategy of Paramount Pictures Corporation in the 1950s |journal=Film History |date=1988 |volume=2 |issue=2 |page=114 |jstor=3815029}}</ref>}}`{=mediawiki}
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# Cecil B. DeMille
## Legacy
### Commemoration and tributes {#commemoration_and_tributes}
The original Lasky-DeMille Barn in which *The Squaw Man* was filmed was converted into a museum named the \"Hollywood Heritage Museum\". It opened on December 13, 1985, and features some of DeMille\'s personal artifacts. The Lasky-DeMille Barn was dedicated as a California historical landmark in a ceremony on December 27, 1956; DeMille was the keynote speaker. It was listed on the National Register of Historic Places in 2014. The Dunes Center in Guadalupe, California, contains an exhibition of artifacts uncovered in the desert near Guadalupe from DeMille\'s set of his 1923 version of *The Ten Commandments*, known as the \"Lost City of Cecil B. DeMille\".`{{refn|group=note|The set was discovered by Peter Brosnan after hearing a rumor in 1982 that DeMille had ordered the enormous set to be buried after filming rather than taken away. A documentary titled ''The Lost City of Cecil B. DeMille'' follows the story of Brosnan's 30-year journey to find and uncover the set.<ref>{{cite news |last=Linden |first=Sheri |title="The Lost City of Cecil B. DeMille": Film Review |url=https://www.hollywoodreporter.com/review/lost-city-cecil-b-demille-1011412 |work=The Hollywood Reporter |date=June 13, 2017 |access-date=July 10, 2019}}</ref>}}`{=mediawiki} Donated by the Cecil B. DeMille Foundation in 2004, the moving image collection of Cecil B. DeMille is held at the Academy Film Archive and includes home movies, outtakes, and never-before-seen test footage.
In summer 2019, The Friends of the Pompton Lakes Library hosted a Cecil B DeMille film festival to celebrate DeMille\'s achievements and connection to Pompton Lakes. They screened four of his films at Christ Church, where DeMille and his family attended church when they lived there. Two schools have been named after him: Cecil B. DeMille Middle School, in Long Beach, California, which was closed and demolished in 2010 to make way for a new high school; and Cecil B. DeMille Elementary School in Midway City, California. The former film building at Chapman University in Orange, California, is named in honor of DeMille. During the Apollo 11 mission, Buzz Aldrin referred to himself in one instance as \"Cecil B. DeAldrin\", as a humorous nod to DeMille. The title of the 2000 John Waters film *Cecil B. Demented* alludes to DeMille.
DeMille\'s legacy is maintained by his granddaughter Cecilia DeMille Presley who serves as the president of the Cecil B. DeMille Foundation, which strives to support higher education, child welfare, and film in Southern California. In 1963, the Cecil B. DeMille Foundation donated the \"Paradise\" ranch to the Hathaway Foundation, which cares for emotionally disturbed and abused children. A large collection of DeMille\'s materials including scripts, storyboards, and films resides at Brigham Young University in L. Tom Perry Special Collections.
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# Cecil B. DeMille
## Awards and recognition {#awards_and_recognition}
Cecil B. DeMille received many awards and honors, especially later in his career.
In August 1941, DeMille was honored with a block in the forecourt of Grauman\'s Chinese Theatre.
The American Academy of Dramatic Arts honored DeMille with an Alumni Achievement Award in 1958.
In 1957, DeMille gave the commencement address for the graduation ceremony of Brigham Young University, wherein he received an honorary Doctorate of Letter degree. Additionally, in 1958, he received an honorary Doctorate of Law degree from Temple University.
From the film industry, DeMille received the Irving G. Thalberg Memorial Award at the Academy Awards in 1953, and a Lifetime Achievement Award from the Directors Guild of America Award the same year. In the same ceremony, DeMille received a nomination from Directors Guild of America Award for Outstanding Directorial Achievement in Motion Pictures for *The Greatest Show on Earth*. In 1952, DeMille was awarded the first Cecil B. DeMille Award at the Golden Globes. An annual award, the Golden Globe\'s Cecil B. DeMille Award recognizes lifetime achievement in the film industry.`{{refn|group=note|Later recipients of the award include [[Kirk Douglas]], [[Robert Redford]], [[Lauren Bacall]].<ref>{{cite web |title=Academy Alum Cecil B. DeMille, The Founding Father of Hollywood Filmmaking |url=https://www.aada.edu/article/academy-alum-cecil-b-demille-the-founding-father-of-hollywood-filmmaking |website=The American Academy of Dramatic Arts |publisher=American Academy of Dramatic Arts |access-date=May 29, 2019}}</ref> [[Jeff Bridges]] was the 2019 Cecil B. DeMille Award winner.<ref>{{cite news |title=Jeff Bridges to Receive Cecil B. DeMille Award at 2019 Golden Globes |url=https://variety.com/2018/film/news/jeff-bridges-cecil-b-demille-award-golden-globes-2019-1203090682/ |access-date=May 29, 2019 |work=Variety |publisher=Variety Media |date=December 17, 2018}}</ref>}}`{=mediawiki} For his contribution to the motion picture and radio industry, DeMille has two stars on the Hollywood Walk of Fame. The first, for radio contributions, is located at 6240 Hollywood Blvd. The second star is located at 1725 Vine Street.
DeMille received two Academy Awards: an Honorary Award for \"37 years of brilliant showmanship\" in 1950 and a Best Picture award in 1953 for *The Greatest Show on Earth*. DeMille received a Golden Globe Award for Best Director and was additionally nominated for the Best Director category at the 1953 Academy Awards for the same film. He was further nominated in the Best Picture category for *The Ten Commandments* at the 1957 Academy Awards. DeMille\'s *Union Pacific* received a Palme d\'Or in retrospect at the 2002 Cannes Film Festival.
Two of DeMille\'s films have been selected for preservation in the National Film Registry by the United States Library of Congress: *The Cheat* (1915) and *The Ten Commandments* (1956).
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# Cecil B. DeMille
## Filmography
DeMille made 70 features, 52 of which are silent. The first 24 of his silents were produced during the first three years of his career (1913--1916). Eight of his films were \"epics\" with five classified as \"Biblical\". Six of DeMille\'s films --- *The Arab*, *The Wild Goose Chase*, *The Dream Girl*, *The Devil-Stone*, *We Can\'t Have Everything*, and *The Squaw Man* (1918) --- were destroyed by nitrate decomposition, and are considered lost. *The Ten Commandments* is broadcast every Saturday at Passover in the United States on the ABC Television Network.
### Directed features {#directed_features}
Filmography obtained from *Fifty Hollywood Directors*.
**Silent films** **Sound films** `{{div col|colwidth=22em|content=
* ''[[Dynamite (1929 film)|Dynamite]]'' (1929)
* ''[[Madam Satan]]'' (1930)
* ''[[The Squaw Man (1931 film)|The Squaw Man]]'' (1931)
* ''[[The Sign of the Cross (1932 film)|The Sign of the Cross]]'' (1932)
* ''[[This Day and Age (film)|This Day and Age]]'' (1933)
* ''[[Four Frightened People]]'' (1934)
* ''[[Cleopatra (1934 film)|Cleopatra]]'' (1934)
* ''[[The Crusades (1935 film)|The Crusades]]'' (1935)
* ''[[The Plainsman]]'' (1936)
* ''[[The Buccaneer (1938 film)|The Buccaneer]]'' (1938)
* ''[[Union Pacific (film)|Union Pacific]]'' (1939)
* ''[[North West Mounted Police (film)|North West Mounted Police]]'' (1940)
* ''[[Reap the Wild Wind]]'' (1942)
* ''[[The Story of Dr. Wassell]]'' (1944)
* ''[[Unconquered (1947 film)|Unconquered]]'' (1947)
* ''[[Samson and Delilah (1949 film)|Samson and Delilah]]'' (1949)
* ''[[The Greatest Show on Earth (film)|The Greatest Show on Earth]]'' (1952)
* ''[[The Ten Commandments (1956 film)|The Ten Commandments]]'' (1956)
}}`{=mediawiki}
### Directing or producing credit {#directing_or_producing_credit}
These are films which DeMille produced or assisted in directing, credited or uncredited.
- *Brewster\'s Millions* (1914, lost)
- *The Master Mind* (1914)
- *The Only Son* (1914, lost)
- *The Man on the Box* (1914)
- *The Ghost Breaker* (1914, lost)
- *After Five* (1915)
- *Nan of Music Mountain* (1917)
- *Chicago* (1927, Producer, uncredited)
- *When Worlds Collide* (1951, executive producer)
- *The War of the Worlds* (1953, executive producer)
- *The Buccaneer* (1958, producer)
### Acting and cameos {#acting_and_cameos}
DeMille frequently made cameos as himself in other Paramount films. Additionally, he often starred in prologues and special trailers that he created for his films, having an opportunity to personally address the audience
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# Chinese Islamic cuisine
**Chinese Islamic cuisine** consists of variations of regionally popular foods that are typical of Han Chinese cuisine, in particular to make them halal. Dishes borrow ingredients from Middle Eastern, Turkic, Iranian and South Asian cuisines, notably mutton and spices. Much like other northern Chinese cuisines, Chinese Islamic cuisine uses wheat noodles as the staple, rather than rice. Chinese Islamic dishes include clear-broth beef noodle soup and *chuanr*.
The Hui (ethnic Chinese Muslims), Bonan, Dongxiang, Salar and Uyghurs of China, as well as the Dungans of Central Asia and the Panthays of Burma, collectively contribute to Chinese Islamic cuisine.
## History
Due to the large Muslim population in Western China, many Chinese restaurants cater to or are run by Muslims. Northern Chinese Islamic cuisine originated in China proper. It is heavily influenced by Beijing cuisine, with nearly all cooking methods identical and differs only in material due to religious restrictions. As a result, northern Islamic cuisine is often included in home Beijing cuisine though seldom in east coast restaurants.
During the Yuan dynasty, halal and kosher methods of slaughtering animals and preparing food was banned and forbidden by the Mongol emperors, starting with Genghis Khan who banned Muslims and Jews from slaughtering their animals their own way and made them follow the Mongol method.
> Among all the \[subject\] alien peoples only the Hui-hui say \"we do not eat Mongol food.\" \[Cinggis Qa\'an replied:\] \"By the aid of heaven we have pacified you; you are our slaves. Yet you do not eat our food or drink. How can this be right?\" He thereupon made them eat. \"If you slaughter sheep, you will be considered guilty of a crime.\" He issued a regulation to that effect \... \[In 1279/1280 under Qubilai\] all the Muslims say: "if someone else slaughters \[the animal\] we do not eat.\" Because the poor people are upset by this, from now on, Musuluman \[Muslim\] Huihui and Zhuhu \[Jewish\] Huihui, no matter who kills \[the animal\] will eat \[it\] and must cease slaughtering sheep themselves, and cease the rite of circumcision.
Traditionally, there is a distinction between Northern and Southern Chinese Islamic cuisine despite both using lamb and mutton. Northern Chinese Islamic cuisine relies heavily on beef, but rarely ducks, geese, shrimp or seafood, while southern Islamic cuisine is the reverse. The reason for this difference is due to availability of the ingredients. Oxen have been long used for farming and Chinese governments have frequently strictly prohibited the slaughter of oxen for food. However, due to the geographic proximity of the northern part of China to minority-dominated regions that were not subjected to such restrictions, beef could be easily purchased and transported to Northern China. At the same time, ducks, geese and shrimp are rare in comparison to Southern China due to the arid climate of Northern China.
A Chinese Islamic restaurant (`{{zh|t=淸眞菜館|p=qīngzhēn càiguǎn}}`{=mediawiki}) can be similar to a Mandarin restaurant with the exception that there is no pork on the menu and the dishes are primarily noodle/soup based.
In most major eastern cities in China, there are very limited Islamic/Halal restaurants, which are typically run by migrants from Western China (e.g., Uyghurs). They primarily offer inexpensive noodle soups only. These restaurants are typically decorated with Islamic motifs such as Islamic writing.
Another difference is that lamb and mutton dishes are more commonly available than in other Chinese restaurants, due to the greater prevalence of these meats in the cuisine of Western Chinese regions. (Refer to image 1.)
Other Muslim ethnic minorities like the Bonan, Dongxiang, Salar and Tibetan Muslims have their own cuisines as well. Dongxiang people operate their own restaurants serving their cuisine.
Many cafeterias (canteens) at Chinese universities have separate sections or dining areas for Muslim students (Hui or Western Chinese minorities), typically labeled \"qingzhen\". Student ID cards sometimes indicate whether a student is Muslim and will allow access to these dining areas or will allow access on special occasions such as the Eid feast following Ramadan.
Several Hui restaurants serving Chinese Islamic cuisine exist in Los Angeles. San Francisco, despite its huge number of Chinese restaurants, appears to have only one whose cuisine would qualify as halal.
Many Chinese Hui Muslims who moved from Yunnan to Burma (Myanmar) are known as Panthays operate restaurants and stalls serving Chinese Islamic cuisine such as noodles. Chinese Hui Muslims from Yunnan who moved to Thailand are known as Chin Haw and they also own restaurants and stalls serving Chinese Islamic food.
In Central Asia, Dungan people, descendants of Hui, operate restaurants serving Chinese Islamic cuisine, which is respectively referred to as *Dungan cuisine* there. They cater to Chinese businessmen. Chopsticks are used by Dungans. The cuisine of the Dungan resembles northwestern Chinese cuisine.
Most Chinese regard Hui halal food as cleaner than food made by non-Muslims so their restaurants are popular in China. Hui who migrated to Northeast China (Manchuria) after the Chuang Guandong opened many new inns and restaurants to cater to travelers, which were regarded as clean.
The Hui who migrated to Taiwan operate Qingzhen restaurants and stalls serving Chinese Islamic cuisine in Taipei and other big cities.
The Thai Department of Export Promotion claims that \"China\'s halal food producers are small-scale entrepreneurs whose products have little value added and lack branding and technology to push their goods to international standards\" to encourage Thai private sector halal producers to market their products in China.
A 1903-started franchise serving Muslim food is Dong Lai Shun in Hankou.
400 meters have to be kept as a distance from each restaurant serving beef noodles to another of its type if they belong to Hui Muslims, since Hui have a pact between each other in Ningxia, Gansu and Shaanxi.
Halal restaurants are checked up upon by clerics from mosques.
Halal food manufacture has been sanctioned by the government of the Ningxia Autonomous Region.
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# Chinese Islamic cuisine
## Famous dishes {#famous_dishes}
### Lamian
**Lamian** (`{{zh|s=拉面|t=拉麪|p=lāmiàn}}`{=mediawiki}, Dungan: Ламян) is a Chinese dish of hand-made noodles, usually served in a beef or mutton-flavored soup (湯麪, даңмян, tāngmiàn), but sometimes stir-fried (炒麪, Чаомян, chǎomiàn) and served with a tomato-based sauce. Literally, 拉, ла (lā) means to pull or stretch, while 麪, мян (miàn) means noodle. The hand-making process involves taking a lump of dough and repeatedly stretching it to produce a single very long noodle. There exists a local variant in Lanzhou, the Lanzhou beef noodles, also known as Lanzhou lamian.
Words that begin with L are not native to Turkic --- läghmän is a loanword as stated by Uyghur linguist Abdlikim: It is of Chinese derivation and not originally Uyghur.
### Beef noodle soup {#beef_noodle_soup}
**Beef noodle soup** is a noodle soup dish composed of stewed beef, beef broth, vegetables and wheat noodles. It exists in various forms throughout East and Southeast Asia. It was created by the Hui people during the Qing dynasty of China.
In the west, this food may be served in a small portion as a soup. In China, a large bowl of it is often taken as a whole meal with or without any side dish.
### Chuanr
**Chuanr** (Chinese: 串儿, Dungan: Чўанр, Pinyin: chuànr (shortened from \"chuan er\"), \"*kebab*\"), originating in the Xinjiang (新疆) province of China and in recent years has been disseminated throughout the rest of that country, most notably in Beijing. It is a product of the Chinese Islamic cuisine of the Uyghur (维吾尔) people and other Chinese Muslims. Yang rou chuan or lamb kebabs, is particularly popular.
### Suan cai {#suan_cai}
**Suan cai** is a traditional fermented vegetable dish, similar to Korean kimchi and German sauerkraut, used in a variety of ways. It consists of pickled Chinese cabbage. Suan cai is a unique form of pao cai due to the material used and the method of production. Although *suan cai* is not exclusive to Chinese Islamic cuisine, it is used in Chinese Islamic cuisine to top off noodle soups, especially beef noodle soup.
### Nang
*Nang* (Chinese: 馕, Dungan: Нәң) is a type of round unleavened bread, topped with sesame. It is similar to South and Central Asia naan.
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# Chinese Islamic cuisine
## Image gallery {#image_gallery}
<File:Beef> noodle.JPG\|Beef noodle served <File:Peking> Duck.jpg\|Peking duck served at a halal restaurant in Beijing <File:5658-Linxia-City-niang-pi
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# Teochew cuisine
**Teochew cuisine**, also known as **Chiuchow cuisine**, **Chaozhou cuisine** or **Teo-swa cuisine**, originated from the Chaoshan region in the eastern part of China\'s Guangdong Province, which includes the cities of Chaozhou, Shantou and Jieyang. Teochew cuisine bears more similarities to that of Fujian cuisine, particularly Southern Min cuisine, due to the similarity of Teochew\'s and Fujian\'s culture, language, and their geographic proximity to each other. However, Teochew cuisine is also influenced by Cantonese cuisine in its style and technique.
## Background
Teochew cuisine is well known for its seafood and vegetarian dishes. Its use of flavouring is much less heavy-handed than most other Chinese cuisines and depends much on the freshness and quality of the ingredients for taste and flavour. As a delicate cuisine, oil is not often used in large quantities and there is a relatively heavy emphasis on poaching, steaming and braising, as well as the common Chinese method of stir-frying. Teochew cuisine is also known for serving congee (`{{zh|c=糜|p=mí|labels=no}}`{=mediawiki}; or *mue*), in addition to steamed rice or noodles with meals. The Teochew **mue** is rather different from the Cantonese counterpart, being very watery with the rice sitting loosely at the bottom of the bowl, while the Cantonese dish is more a thin gruel.
Authentic Teochew restaurants serve very strong oolong tea called Tieguanyin in very tiny cups before and after the meal. Presented as *gongfu* tea, the tea has a thickly bittersweet taste, colloquially known as *gam gam* (`{{zh|c=甘甘|p=gān gān|labels=no}}`{=mediawiki}).
A condiment that is popular in Fujian and Taiwanese cuisine and commonly associated with cuisine of certain Teochew groups is shacha sauce (`{{zh|s=沙茶酱|t=沙茶醬|p=shāchá jiàng|labels=no}}`{=mediawiki}). It is made from soybean oil, garlic, shallots, chilies, brill fish and dried shrimp. The paste has a savoury and slightly spicy taste. As an ingredient, it has multiple uses: as a base for soups, as a rub for barbecued meats, as a seasoning for stir-fried dishes, or as a component for dipping sauces.
In addition to soy sauce (widely used in all Chinese cuisines), Teochew people also use fish sauce in their cooking.
Teochew chefs often use a special stock called siang teng (`{{zh|s=上汤|t=上湯|p=shàngtāng|labels=no}}`{=mediawiki}), literally translates from the Teochew dialect as \"superior broth\". This stock remains on the stove and is continuously replenished. Portrayed in popular media, some Hong Kong chefs allegedly use the same superior broth that is preserved for decades. This stock can as well be seen on Chaozhou TV\'s cooking programmes.
There is a notable feast in Teochew cuisine called **jiat dot** (`{{zh|c=食桌|p=shízhuō|l=food table|labels=no}}`{=mediawiki}). A myriad of dishes are often served, which include shark fin soup, bird\'s nest soup, lobster, steamed fish, roasted suckling pig and braised goose.
Teochew chefs take pride in their skills of vegetable carving, and carved vegetables are used as garnishes on cold dishes and on the banquet table.
Teochew cuisine is also known for a late night meal known as *meh siao* (`{{zh|c=夜宵|p=yèxiāo|labels=no}}`{=mediawiki}) or *daa laang* (`{{zh|c=打冷|p=dǎléng|labels=no}}`{=mediawiki}) among the Cantonese. Teochew people enjoy eating out close to midnight in restaurants or at roadside food stalls. Some dai pai dong-like eateries stay open till dawn.
Unlike the typical menu selections of many other Chinese cuisines, Teochew restaurant menus often have a dessert section.
Many people of Teochew origin, also known as Teochiu or Teochew people, have settled in Hong Kong and places in Southeast Asia like Malaysia, Singapore, Cambodia and Thailand. Influences they bring can be noted in Singaporean cuisine and that of other settlements. A large number of Teochew people have also settled in Taiwan, evident in Taiwanese cuisine. Other notable Teochew diaspora communities are in Vietnam, Cambodia and France. A popular noodle soup in both Vietnam and Cambodia, known as hu tieu, originated from the Teochew . There is also a large diaspora of Teochew people (most were from Southeast Asia) in the United States - particularly in California. There is a Teochew Chinese Association in Paris called L\'Amicale des Teochews en France.
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# Teochew cuisine
## Notable dishes {#notable_dishes}
English Traditional Chinese Simplified Chinese Pinyin Peng\'im Description
------------------------------------------------- --------------------- -------------------- ----------------- ----------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Bak chor mee / *bhah4 co3 mi7* Boiled noodles, dried and mixed with variety sauce such as soy sauce, chilli sauce and lard topped with vegetables, sliced onion, minced pork, mushrooms and fish balls or fishcakes.
Bak kut teh / *nêg8 gug4 dê5* A hearty soup that, at its simplest, consists of meaty pork ribs in a complex broth of herbs and spices (including star anise, cinnamon, cloves, danggui, fennel seeds and garlic), boiled together with pork bones for hours. Dark and light soy sauce may also be added to the soup during the cooking stages. Some Teochew families like to add extra Chinese herbs such as yuzhu (rhizome of Solomon\'s seal) and juzhi (buckthorn fruit) for a sweeter, slightly stronger flavoured soup. The dish is usually eaten with rice or noodles (sometimes as a noodle soup), and often served with fried dough fritters. Garnish includes chopped coriander or green onions and a sprinkling of fried shallots. A variation of bak kut `{{not a typo|teh}}`{=mediawiki} uses chicken instead of pork, which then becomes chik kut teh. Bak kut `{{not a typo|teh}}`{=mediawiki} is particularly popular in Southeast Asian countries such as Singapore and Malaysia.
Braised varieties Teochew cuisine is noted for its variety of braised dishes, which includes geese, duck, pork, bean curd and offal.
Chai tau kueh A savoury fried cake, made of white radish and rice flour. It is commonly stir-fried with soy sauce, eggs, garlic, spring onion and occasionally dried shrimp.
Chwee kueh Cup-shaped steamed rice cakes topped with chopped preserved/salted radish.
Crystal balls A steamed dessert with a variety of fillings such as yellow milk (`{{zh|s=奶黄|t=奶黃|p=nǎihuáng|labels=no}}`{=mediawiki}; *ni ng*, ni7 ng5), yam paste (`{{zh|c=芋泥|p=yùní|labels=no}}`{=mediawiki}; *or ni*, ou7 ni5) or bean paste made from mung beans or azuki beans (red beans). They are similar to mochi.
Deep-Fried tofu A simple deep fried tofu dish, and was later adopted by Guangzhou\'s residents. First, deep-fry slices of fresh firm tofu until they are golden, and then serve with salted water dip (ingredients are boiling water, salt, and chopped Chinese chives). In modern times, some Teochew people now use the air fryer to prepare them for convenience and reduction of the amount of fat and calories in the food.
Fish balls / fishcakes / fish dumplings (*her ee*) / *he7 guê2* (*her kueh*) / *he7 gieu2* (*her kiaw*) This fish paste made into balls, cakes and dumplings can be cooked in many ways but are often served in Teochew-style noodle and soups.
Fish ball noodle soup (*her ee mee*) Any of several kinds of egg and rice noodles may be served either in a light fish-flavoured broth or dry, along with fishballs, fishcakes, beansprouts and lettuce.
Flavored-potted goose A well-known braised goose dish, often accompanised by tofu.
Fried beef balls (*za ghu bak ee*) A simple deep-fired beef ball dish serves with dipping sauce such as shacha sauce or salted water dip (ingredients are boiling water, salt, and chopped Chinese chives). In modern times, some Teochew people now use the air fryer to prepare them for convenience and reduction of the amount of fat and calories in the food.
Fun guo A type of steamed dumplings. This is usually filled with dried radish, garlic chives, ground pork, dried shrimp, shiitake mushrooms and peanuts. The dumpling wrapper is made from a mixture of flour or plant starches mixed together with water. In Cantonese, these are called *chiu chow fun guo* (`{{zh|c=潮州粉果|p=Cháozhōu fěnguǒ|labels=no}}`{=mediawiki}), in which the Chinese character *粿* is replaced by *果*.
Head of mustard greens with mushrooms A dish of *Brassica juncea* (Chinese mustard) and shiitake (Chinese black mushrooms) in a soup. Originally a vegetarian soup, it often added with diced pork belly and other ingredients.
Kway chap (*kueh chap*) A dish of flat, broad rice sheets in a soup made from dark soy sauce served with pig offal, braised duck meat, various kinds of bean curd, preserved salted vegetables and braised hard-boiled eggs.
Marinating pork head / Braised pig head Clean and braise pork head in soy sauce and rock sugar. Cilantro, garlic, ginger, chilies, star anise and other spices may also added.
Mee pok (*mee pok*) A popular noodle dish served with minced pork, braised mushrooms, fishballs, dumplings, sauce and other garnish.
Oolong tea (*Ou-leeng `{{not a typo|teh}}`{=mediawiki}*) Tieguanyin is one of the most popular Teochew teas. However, the Teochew people prefer their own brand of Oolong tea, which is the *hong wang dan cong teh* (`{{zh|s=凤凰单丛茶|t=鳳凰單丛茶|p=fènghuáng dāncóng chá|labels=no}}`{=mediawiki}).
Oyster omelette (*or lua*) A dish of omelette cooked with fresh raw oysters, tapioca starch and eggs. Teochew-style oyster omelette is usually deep fried and very crisp. Dip condiments are fish sauce and pepper or chili sauce.
Pan-fried marinated fish A pan-fried dish of marinated fish, typically using Larimichthys crocea as the main ingredient but can use other alternatives such as a white croaker, Japanese sea bass or other types of bass, or tilefish.
Patriotic soup (Protect the Country Dish) Developed during the Mongol conquest of the Song dynasty and named by Song\'s last emperor Zhao Bing. A simple soup boiled with stir-fried leaf vegetable (commonly sweet potato leaves since the Ming dynasty but also can use amaranth, spinach, Ipomoea aquatica or other leafy greens as alternatives) and edible mushrooms (preferably straw mushrooms) and broth (vegetable, chicken, or beef).
Pig\'s organ soup (Pork offal soup) (*ter zap terng*)
Popiah (薄饼) (*po piah*) A fresh (non-fried) spring roll usually eaten during the Qingming Festival. The skin is a soft, thin paper-like crepe made from wheat flour. The filling is mainly finely grated and steamed or stir-fried turnip, yam bean (jicama), which has been cooked with a combination of other ingredients such as bean sprouts, French beans, and lettuce leaves, depending on the individual vendor, along with grated carrots, slices of Chinese sausage, thinly sliced fried tofu, chopped peanuts or peanut powder, fried shallots and shredded omelette. Other common variations of popiah include pork (lightly seasoned and stir-fried), shrimp or crab meat. It is eaten in accompaniment with a sweet sauce (often a bean sauce, a blended soy sauce or hoisin sauce or a shrimp paste sauce).
Pork jelly (*ter ka dang*) Braised pig\'s leg made into jelly form, sliced and served cold.
Prawns sautéed with olive vegetables A dish of deep-fried prawns
Raw Pickled Seafood There are various kinds of Chaoshan fresh seafoods pickles, such as raw pickled crab, raw pickled blood clams, raw pickled shrimp, raw pickled prawns, raw pickled mantis shrimp. Seafoods are steeped in a pickling bath made of vinegar, salt, soy sauce, wine, cilantro, garlic, ginger, chilies and other spices.
Red peach cake (*ang tao kueh*, *ung toh kway*) Pink hue rice flour skin wrapped with flavorful glutinous rice. Pressed on a nicely designed peach shaped wooden mould, and then steam the dumpling to perfection. You can eat it freshly steamed, or pan-fried.
Salted vegetable duck soup (*kiam cai ak terng*) A soup boiled with duck, preserved salted vegetable, tomatoes and preserved sour plum.
Scalding (hot water dipping) blood clams Wash the blood clams and then soak them in cold salted water to let them release sands inside their body. Boil a pot of water, add some coriander, carefully pour the blood clams into the boiling water, dip them in hot water for 10 seconds and they are ready to eat.
Sichuan pepper chicken A traditionally deep-fried chicken dish, usually accompanied with leafy green from *Lysimachia clethroides*, known as pearl vegetable (*珍珠菜*). However, *Lysimachia clethroides*\'s leaves are unavailable to use in culinary outside of China, but basil, spinach, or other leafy green vegetables can be substitutes to them in preparation of the dish.
Sliced Cuttlefish on Ice with Wasabi Sauce Clean the cuttlefish, remove the skin, internal organs and head and boil it in 80^o^C salty water for 10 minutes. Soak it in ice water for 5 minutes after cook. Pat dry with kitchen towel and slice it. Place the slices on top of a dish with a thick layer of ice. When eating, pick up the cuttlefish slices with chopsticks and dip them in mustard and soy sauce.
Spring rolls with prawn or minced meat fillings (heh gerng) / *siê1 geng2*, *sio1 geng2* (sio gerng) / *ngou6 hiang1* (ngo hiang) Mixed pork and prawn paste (sometimes fish), seasoned with five-spice powder, wrapped and rolled in a bean curd skin and deep-fried or pan-fried. It is sometimes referred to as Teochew-style spring roll in restaurant menus.
Steamed chives dumplings They are sometimes sautéed to give them a crispy texture.
Steamed goose
Taro paste (orh ni / orh nee) A traditional Teochew dessert made primarily from taro. The taro is steamed and then mashed into a thick paste, which forms the base of the dessert. Pumpkin is also added for sweetness and to create a smoother consistency. Lard or fried onion oil is then added for fragrance. The dessert is traditionally sweetened with water chestnut syrup, and served with ginkgo nuts. Modern versions of the dessert include the addition of coconut cream and sweet corn. The dessert is commonly served at traditional Teochew wedding banquet dinners as the last course, marking the end of the banquet.
Teochew chicken *Cháozhōu jī* *dio7/diê7 ziu1 goi1* (Teochew koi) A dish of sliced chicken
Teochew cold crab (Teochew ngang hoi) The whole crab is first steamed then served chilled. The species of crab most commonly used is *Charybdis cruciata*.
Teochew cold fish (Teochew he bung) Steam fish with ginger slices, let it cool down to room temperature, then remove the ginger slices and keep it in refrigerator for at least 2 hours.
Teochew hot pot / Teochew steamboat (Teochew zuang lou) A dish where fresh, thinly sliced ingredients are placed into a simmering flavourful broth to cook and then dipped into various mixed sauces, usually with Shacha and soy sauce as its main components. Ingredients often include leafy vegetables, yam, tofu, pomfret and other seafood, beef balls, fish balls, pork balls, mushrooms and Chinese noodles, among others. Teochew hot pot, like other Chinese hot pots, is served in a large communal metal pot at the center of the dining table.
Teochew Oyster Congee Teochew congee with oysters and minced pork
Teochew rice noodle soup (Teochew kuay teow) A quintessential Teochew-style noodle soup that is also particularly popular in Vietnam and Cambodia (known respectively as *hủ tiếu /hủ tíu * and គុយទាវ *kuyteav*), through the influx of Teochew immigrants. It is a dish of yellow egg noodles and thin rice noodles served in a delicate, fragrant soup with meatballs, other various meats, seafood (such as shrimp), fried fishcake slices, quail eggs, blanched Chinese cabbage and sometimes offal. The soup base is typically made of pork or chicken bones and dried squid. Just before serving, the noodle soup is garnished with fried minced garlic, fried shallots, thinly sliced scallions and fresh cilantro (coriander) sprigs. For those who enjoy their noodle soup with added depth, the solid ingredients may be dipped into Shacha sauce or Teochew chilli oil.
Teochew-style congee (Teochew mue) A rice soup that has a more watery texture as compared to the Cantonese congee. It is commonly served with various salty accompaniments such as salted vegetables (*kiam chai*), preserved radish (*chai por*), black Chinese olives (*烏橄欖*), olive grits (*橄欖糝*), boiled salted duck eggs, fried salted fish and fried peanuts.
Teochew-style steamed pomfret (Teochew chue chioh her) Silvery pomfret steamed with preserved salted vegetables, lard and sour plums.
Yusheng (her sae) A raw fish salad (similar to ceviche or sashimi) whose typical ingredients include fresh salmon, white radish, carrot, red pepper (capsicum), ginger, kaffir lime leaves, Chinese parsley, chopped peanuts, toasted sesame seeds, Chinese shrimp crackers or fried dried shrimp, and five-spice powder, with the dressing primarily made from plum sauce. It is customarily served as an appetiser to bring good luck for the new year and is usually eaten on the seventh day of the Lunar New Year.
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# Teochew cuisine
## Gallery
<File:HK> Wan Chai 春園街 Spring Garden Lane night Chiu Chow food shop window.jpg\|\"Flavor potted\" goose (*滷水鵝*) <File:Teochew> Sweet Yam Paste - After Stirring.jpg\|Taro paste (*芋泥*) <File:Shui> jing bao zz.JPG\|Crystal balls (*水晶包*) <File:Teochew> pomfret.jpg\|Steamed fish (*炊魚*) <File:Oyster> omelette.jpg\|Oyster omelette (*蚝烙*) <File:Khanom> kuichai.jpg\|Fried chive dumplings (*韭菜粿*) <File:Song> dynasty\'s \'patriotic soup\' (prepared in Clovis California) 宋朝的"護國菜"（在加利福尼亞克洛維斯市製備）。.jpg\|Patriotic Soup (Protect the Country Dish (*護國菜*)) <File:Fried> Tofu (炸豆腐).jpg\|A dish of fried tofu (*炸豆腐*) with dipping sauce. <File:Teochew> rice noodle soup (潮州粿條).jpg\|Teochew rice noodle soup (*潮州粿條*). <File:Sautéed> Prawns with Olive Vegetables (欖菜焗蝦).jpg\|Sautéed prawns with olive vegetables (*欖菜焗蝦*) . <File:Teochew> Hotpot (prepared in Clovis California) 潮州火鍋（在加利福尼亞克洛維斯市製備）.jpg\|Teochew hotpot (*潮州火鍋*) <File:Sichuan> pepper chicken - air-fried version (川椒雞 - 氣炸版).jpg\|Sichuan pepper chicken (*川椒雞*) <File:Mixed> Bak Kut Teh - Teochew Bak Kut Teh (4590434658)
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# Co-NP
In computational complexity theory, **co-NP** is a complexity class. A decision problem X is a member of co-NP if and only if its complement `{{overline|X}}`{=mediawiki} is in the complexity class NP. The class can be defined as follows: a decision problem is in co-NP if and only if for every *no*-instance we have a polynomial-length \"certificate\" and there is a polynomial-time algorithm that can be used to verify any purported certificate.
That is, **co-NP** is the set of decision problems where there exists a polynomial `{{tmath|p(n)}}`{=mediawiki} and a polynomial-time bounded Turing machine *M* such that for every instance *x*, *x* is a *no*-instance if and only if: for some possible certificate *c* of length bounded by `{{tmath|p(n)}}`{=mediawiki}, the Turing machine *M* accepts the pair `{{math|(''x'', ''c'')}}`{=mediawiki}.
## Complementary problems {#complementary_problems}
While an NP problem asks whether a given instance is a *yes*-instance, its *complement* asks whether an instance is a *no*-instance, which means the complement is in co-NP. Any *yes*-instance for the original NP problem becomes a *no*-instance for its complement, and vice versa.
### Unsatisfiability
An example of an NP-complete problem is the Boolean satisfiability problem: given a Boolean formula, is it *satisfiable* (is there a possible input for which the formula outputs true)? The complementary problem asks: \"given a Boolean formula, is it *unsatisfiable* (do all possible inputs to the formula output false)?\". Since this is the *complement* of the satisfiability problem, a certificate for a *no*-instance is the same as for a *yes*-instance from the original NP problem: a set of Boolean variable assignments which make the formula true. On the other hand, a certificate of a *yes*-instance for the complementary problem (whatever form it might take) would be equally as complex as for the *no*-instance of the original NP satisfiability problem.
## co-NP-completeness {#co_np_completeness}
A problem *L* is co-NP-complete if and only if *L* is in co-NP and for any problem in co-NP, there exists a polynomial-time reduction from that problem to *L*.
### Tautology reduction {#tautology_reduction}
Determining if a formula in propositional logic is a tautology is co-NP-complete: that is, if the formula evaluates to true under every possible assignment to its variables.
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# Co-NP
## Relationship to other classes {#relationship_to_other_classes}
P, the class of polynomial time solvable problems, is a subset of both NP and co-NP. P is thought to be a strict subset in both cases. Because P is closed under complementation, and NP and co-NP are complementary, it cannot be strict in one case and not strict in the other: if P equals NP, it must also equal co-NP, and vice versa.
NP and co-NP are also thought to be unequal, and their equality would imply the collapse of the polynomial hierarchy PH to NP. If they are unequal, then no NP-complete problem can be in co-NP and no co-NP-complete problem can be in NP. This can be shown as follows. Suppose for the sake of contradiction there exists an NP-complete problem `{{mathcal|X}}`{=mediawiki} that is in co-NP. Since all problems in NP can be reduced to `{{mathcal|X}}`{=mediawiki}, it follows that for every problem in NP, we can construct a non-deterministic Turing machine that decides its complement in polynomial time; i.e., `{{tmath|\textsf{NP} \subseteq \textsf{co-NP} }}`{=mediawiki}. From this, it follows that the set of complements of the problems in NP is a subset of the set of complements of the problems in co-NP; i.e., `{{tmath|\textsf{co-NP} \subseteq \textsf{NP} }}`{=mediawiki}. Thus `{{tmath|1=\textsf{co-NP} = \textsf{NP} }}`{=mediawiki}. The proof that no co-NP-complete problem can be in NP if `{{tmath|\textsf{NP} \neq \textsf{co-NP} }}`{=mediawiki} is symmetrical.
co-NP is a subset of PH, which itself is a subset of PSPACE.
### Integer factorization {#integer_factorization}
An example of a problem that is known to belong to both NP and co-NP (but not known to be in P) is Integer factorization: given positive integers *m* and *n*, determine if *m* has a factor less than *n* and greater than one. Membership in NP is clear; if *m* does have such a factor, then the factor itself is a certificate. Membership in co-NP is also straightforward: one can just list the prime factors of *m*, all greater or equal to *n*, which the verifier can confirm to be valid by multiplication and the AKS primality test. It is presently not known whether there is a polynomial-time algorithm for factorization, equivalently that integer factorization is in P, and hence this example is interesting as one of the most natural problems known to be in NP and co-NP but not known to be in P
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# Convention on Fishing and Conservation of the Living Resources of the High Seas
The **Convention on Fishing and Conservation of Living Resources of the High Seas** is an agreement that was designed to solve through international cooperation the problems involved in the conservation of living resources of the high seas, considering that because of the development of modern technology some of these resources are in danger of being overexploited. The convention opened for signature on 29 April 1958 and entered into force on 20 March 1966.
## Participation
*Parties* -- (39): Australia, Belgium, Bosnia and Herzegovina, Burkina Faso, Cambodia, Colombia, Republic of the Congo, Denmark, Dominican Republic, Fiji, Finland, France, Haiti, Jamaica, Kenya, Lesotho, Madagascar, Malawi, Malaysia, Mauritius, Mexico, Montenegro, Netherlands, Nigeria, Portugal, Senegal, Serbia, Sierra Leone, Solomon Islands, South Africa, Spain, Switzerland, Thailand, Tonga, Trinidad and Tobago, Uganda, United Kingdom, United States, Venezuela.
*Countries that have signed, but not yet ratified* -- (21): Afghanistan, Argentina, Bolivia, Canada, Costa Rica, Cuba, Ghana, Iceland, Indonesia, Iran, Ireland, Israel, Lebanon, Liberia, Nepal, New Zealand, Pakistan, Panama, Sri Lanka, Tunisia, Uruguay
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# Convention on Long-Range Transboundary Air Pollution
`{{Pollution sidebar}}`{=mediawiki}
The **Convention on Long-Range Transboundary Air Pollution**, often abbreviated as **Air Convention** or **CLRTAP**, is intended to protect the human environment against air pollution and to gradually reduce and prevent air pollution, including long-range transboundary air pollution. It is implemented by the European Monitoring and Evaluation Programme (EMEP), directed by the United Nations Economic Commission for Europe (UNECE).
The convention opened for signature on `{{Format date|1979|Nov|13}}`{=mediawiki}, and entered into force on `{{Format date|1983|3|16}}`{=mediawiki}.
## Secretariat
The Convention, which now has 51 Parties, identifies the Executive Secretary of the United Nations Economic Commission for Europe (UNECE) as its secretariat. The current parties to the Convention are shown on the map.
The Convention is implemented by the European Monitoring and Evaluation Programme (EMEP) (short for *Co-operative Programme for Monitoring and Evaluation of the Long-range Transmission of Air Pollutants in Europe*). Results of the EMEP programme are published on the EMEP website, [www.emep.int](http://www.emep.int/).
## Procedure
The aim of the Convention is that Parties shall endeavour to limit and, as far as possible, gradually reduce and prevent air pollution including long-range transboundary air pollution. Parties develop policies and strategies to combat the discharge of air pollutants through exchanges of information, consultation, research and monitoring.
The Parties meet annually at sessions of the Executive Body to review ongoing work and plan future activities including a workplan for the coming year. The three main subsidiary bodies -- the Working Group on Effects, the Steering Body to EMEP and the Working Group on Strategies and Review -- as well as the Convention\'s Implementation Committee, report to the Executive Body each year.
Currently, the Convention\'s priority activities include review and possible revision of its most recent protocols, implementation of the Convention and its protocols across the entire UNECE region (with special focus on Eastern Europe, the Caucasus and Central Asia and South-East Europe) and sharing its knowledge and information with other regions of the world.
## Protocols
Since 1979 the Convention on Long-range Transboundary Air Pollution has addressed some of the major environmental problems of the UNECE region through scientific collaboration and policy negotiation
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# Environmental Modification Convention
The **Environmental Modification Convention** (**ENMOD**), formally the **Convention on the Prohibition of Military or Any Other Hostile Use of Environmental Modification Techniques**, is an international treaty prohibiting the military or other hostile use of environmental modification techniques having widespread, long-lasting or severe effects. It opened for signature on 18 May 1977 in Geneva and entered into force on 5 October 1978.
The Convention bans weather warfare, which is the use of weather modification techniques for the purposes of inducing damage or destruction. The Convention on Biological Diversity of 2010 would also ban some forms of weather modification or geoengineering.
Many states do not regard this as a complete ban on the use of herbicides in warfare, such as Agent Orange, but it does require case-by-case consideration.
## Parties
The convention was signed by 48 states; 16 of the signatories have not ratified. As of 2022 the convention has 78 state parties.
## History
The problem of artificial modification of the environment for military or other hostile purposes was brought to the international agenda in the early 1970s. Following the US decision of July 1972 to renounce the use of climate modification techniques for hostile purposes, the 1973 resolution by the US Senate calling for an international agreement \"prohibiting the use of any environmental or geophysical modification activity as a weapon of war\", and an in-depth review by the Department of Defense of the military aspects of weather and other environmental modification techniques, US decided to seek agreement with the Soviet Union to explore the possibilities of an international agreement.
In July 1974, US and USSR agreed to hold bilateral discussions on measures to overcome the danger of the use of environmental modification techniques for military purposes and three subsequent rounds of discussions in 1974 and 1975. In August 1975, US and USSR tabled identical draft texts of a convention at the Conference of the Committee on Disarmament (CCD), Conference on Disarmament, where intensive negotiations resulted in a modified text and understandings regarding four articles of this Convention in 1976.
The convention was approved by Resolution 31/72 of the General Assembly of the United Nations on 10 December 1976, by 96 to 8 votes with 30 abstentions.
## Environmental Modification Technique {#environmental_modification_technique}
Environmental Modification Technique includes any technique for changing -- through the deliberate manipulation of natural processes -- the dynamics, composition or structure of the earth, including its biota, lithosphere, hydrosphere and atmosphere, or of outer space.
## Structure of ENMOD {#structure_of_enmod}
The Convention contains ten articles and one Annex on the Consultative Committee of Experts. Integral part of the convention are also the Understandings relating to articles I, II, III and VIII. These Understandings are not incorporated into the convention but are part of the negotiating record and were included in the report transmitted by the Conference of the Committee on Disarmament to the United Nations General Assembly in September 1976 Report of the Conference of the Committee on Disarmament, Volume I, General Assembly Official records: Thirty-first session, Supplement No. 27 (A/31/27), New York, United Nations, 1976, pp. 91--92.
## Anthropogenic climate change {#anthropogenic_climate_change}
ENMOD treaty members are responsible for 83% of carbon dioxide emissions since the treaty entered into force in 1978. The ENMOD treaty could potentially be used by ENMOD member states seeking climate-change loss and damage compensation from other ENMOD member states at the International Court of Justice. With the knowledge that carbon dioxide emissions can enhance extreme weather events, the continued unmitigated greenhouse gas emissions from some ENMOD member states could be viewed as 'reckless' in the context of deliberately declining emissions from other ENMOD member states. It is unclear whether the International Court of Justice will consider the ENMOD treaty when it issues a legal opinion on international climate change obligations requested by the United Nations General Assembly on 29 March 2023
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# Charles Ancillon
**Charles Ancillon** (28 July 1659`{{snd}}`{=mediawiki}5 July 1715) was a French jurist and diplomat.
## Life
Ancillon was born in Metz into a distinguished family of Huguenots. His father, David Ancillon (1617--1692), was obliged to leave France on the revocation of the Edict of Nantes, and became pastor of the French Protestant community in Berlin.
Ancillon studied law at Marburg, Geneva and Paris, where he was called to the bar. At the request of the Huguenots at Metz, he pleaded its cause at the court of King Louis XIV, urging that it should be excepted in the revocation of the Edict of Nantes, but his efforts were unsuccessful, and he joined his father in Berlin. He was at once appointed by Elector Frederick III \"*juge et directeur de colonie de Berlin*.\" He also became the first headmaster of Französisches Gymnasium Berlin. Before this, he had published several works on the revocation of the Edict of Nantes and its consequences, but his literary capacity was mediocre, his style stiff and cold, and it was his personal character rather than his reputation as a writer that earned him the confidence of the elector.
In 1687 Ancillon was appointed head of the so-called *Academie des nobles,* the principal educational establishment of the state; later on, as councillor of embassy, he took part in the negotiations which led to the assumption of the title of \"King in Prussia\" by the elector. In 1699 he succeeded Samuel Pufendorf as historiographer to the elector, and the same year replaced his uncle Joseph Ancillon as judge of all the French refugees in the Margraviate of Brandenburg.
Ancillon is mainly remembered for what he did for education in Brandenburg-Prussia, and the share he took, in co-operation with Gottfried Leibniz, in founding the Academy of Berlin. Of his fairly numerous works the most valued is the \"*Histoire de l\'etablissement des Francais refugies dans les etats de Brandebourg*\" published in Berlin in 1690
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# Context-sensitive grammar
A **context-sensitive grammar** (**CSG**) is a formal grammar in which the left-hand sides and right-hand sides of any production rules may be surrounded by a context of terminal and nonterminal symbols. Context-sensitive grammars are more general than context-free grammars, in the sense that there are languages that can be described by a CSG but not by a context-free grammar. Context-sensitive grammars are less general (in the same sense) than unrestricted grammars. Thus, CSGs are positioned between context-free and unrestricted grammars in the Chomsky hierarchy.
A formal language that can be described by a context-sensitive grammar, or, equivalently, by a noncontracting grammar or a linear bounded automaton, is called a context-sensitive language. Some textbooks actually define CSGs as non-contracting, although this is not how Noam Chomsky defined them in 1959. This choice of definition makes no difference in terms of the languages generated (i.e. the two definitions are weakly equivalent), but it does make a difference in terms of what grammars are structurally considered context-sensitive; the latter issue was analyzed by Chomsky in 1963.
Chomsky introduced context-sensitive grammars as a way to describe the syntax of natural language where it is often the case that a word may or may not be appropriate in a certain place depending on the context. Walter Savitch has criticized the terminology \"context-sensitive\" as misleading and proposed \"non-erasing\" as better explaining the distinction between a CSG and an unrestricted grammar.
Although it is well known that certain features of languages (e.g. cross-serial dependency) are not context-free, it is an open question how much of CSGs\' expressive power is needed to capture the context sensitivity found in natural languages. Subsequent research in this area has focused on the more computationally tractable mildly context-sensitive languages. The syntaxes of some visual programming languages can be described by context-sensitive graph grammars.
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