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# Computational complexity
## Problem complexity (lower bounds) {#problem_complexity_lower_bounds}
The complexity of a problem is the infimum of the complexities of the algorithms that may solve the problem, including unknown algorithms. Thus the complexity of a problem is not greater than the complexity of any algorithm that solves the problems.
It follows that every complexity of an algorithm, that is expressed with big O notation, is also an upper bound on the complexity of the corresponding problem.
On the other hand, it is generally hard to obtain nontrivial lower bounds for problem complexity, and there are few methods for obtaining such lower bounds.
For solving most problems, it is required to read all input data, which, normally, needs a time proportional to the size of the data. Thus, such problems have a complexity that is at least linear, that is, using big omega notation, a complexity $\Omega(n).$
The solution of some problems, typically in computer algebra and computational algebraic geometry, may be very large. In such a case, the complexity is lower bounded by the maximal size of the output, since the output must be written. For example, a system of `{{mvar|n}}`{=mediawiki} polynomial equations of degree `{{mvar|d}}`{=mediawiki} in `{{mvar|n}}`{=mediawiki} indeterminates may have up to $d^n$ complex solutions, if the number of solutions is finite (this is Bézout\'s theorem). As these solutions must be written down, the complexity of this problem is $\Omega(d^n).$ For this problem, an algorithm of complexity $d^{O(n)}$ is known, which may thus be considered as asymptotically quasi-optimal.
A nonlinear lower bound of $\Omega(n\log n)$ is known for the number of comparisons needed for a sorting algorithm. Thus the best sorting algorithms are optimal, as their complexity is $O(n\log n).$ This lower bound results from the fact that there are `{{math|''n''!}}`{=mediawiki} ways of ordering `{{mvar|n}}`{=mediawiki} objects. As each comparison splits in two parts this set of `{{math|''n''!}}`{=mediawiki} orders, the number of `{{mvar|N}}`{=mediawiki} of comparisons that are needed for distinguishing all orders must verify $2^N>n!,$ which implies $N =\Omega(n\log n),$ by Stirling\'s formula.
A standard method for getting lower bounds of complexity consists of *reducing* a problem to another problem. More precisely, suppose that one may encode a problem `{{mvar|A}}`{=mediawiki} of size `{{mvar|n}}`{=mediawiki} into a subproblem of size `{{math|''f''(''n'')}}`{=mediawiki} of a problem `{{mvar|B}}`{=mediawiki}, and that the complexity of `{{mvar|A}}`{=mediawiki} is $\Omega(g(n)).$ Without loss of generality, one may suppose that the function `{{mvar|f}}`{=mediawiki} increases with `{{mvar|n}}`{=mediawiki} and has an inverse function `{{mvar|h}}`{=mediawiki}. Then the complexity of the problem `{{mvar|B}}`{=mediawiki} is $\Omega(g(h(n))).$ This is the method that is used to prove that, if P ≠ NP (an unsolved conjecture), the complexity of every NP-complete problem is $\Omega(n^k),$ for every positive integer `{{mvar|k}}`{=mediawiki}.
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# Computational complexity
## Use in algorithm design {#use_in_algorithm_design}
Evaluating the complexity of an algorithm is an important part of algorithm design, as this gives useful information on the performance that may be expected.
It is a common misconception that the evaluation of the complexity of algorithms will become less important as a result of Moore\'s law, which posits the exponential growth of the power of modern computers. This is wrong because this power increase allows working with large input data (big data). For example, when one wants to sort alphabetically a list of a few hundreds of entries, such as the bibliography of a book, any algorithm should work well in less than a second. On the other hand, for a list of a million of entries (the phone numbers of a large town, for example), the elementary algorithms that require $O(n^2)$ comparisons would have to do a trillion of comparisons, which would need around three hours at the speed of 10 million of comparisons per second. On the other hand, the quicksort and merge sort require only $n\log_2 n$ comparisons (as average-case complexity for the former, as worst-case complexity for the latter). For `{{math|1=''n'' = 1,000,000}}`{=mediawiki}, this gives approximately 30,000,000 comparisons, which would only take 3 seconds at 10 million comparisons per second.
Thus the evaluation of the complexity may allow eliminating many inefficient algorithms before any implementation. This may also be used for tuning complex algorithms without testing all variants. By determining the most costly steps of a complex algorithm, the study of complexity allows also focusing on these steps the effort for improving the efficiency of an implementation
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# Cosmological argument
In the philosophy of religion, a **cosmological argument** is an argument for the existence of God based upon observational and factual statements concerning the universe (or some general category of its natural contents) typically in the context of causation, change, contingency or finitude. In referring to reason and observation alone for its premises, and precluding revelation, this category of argument falls within the domain of natural theology. A cosmological argument can also sometimes be referred to as an **argument from universal causation**, an **argument from first cause**, the **causal argument** or the **prime mover argument**.
The concept of causation is a principal underpinning idea in all cosmological arguments, particularly in affirming the necessity for a First Cause. The latter is typically determined in philosophical analysis to be God, as identified within classical conceptions of theism.
The origins of the argument date back to at least Aristotle, developed subsequently within the scholarly traditions of Neoplatonism and early Christianity, and later under medieval Islamic scholasticism through the 9th to 12th centuries. It would eventually be re-introduced to Christian theology in the 13th century by Thomas Aquinas. In the 18th century, it would become associated with the principle of sufficient reason formulated by Gottfried Leibniz and Samuel Clarke, itself an exposition of the Parmenidean causal principle that \"nothing comes from nothing\".
Contemporary defenders of cosmological arguments include William Lane Craig, Robert Koons, John Lennox, Stephen Meyer, and Alexander Pruss.
## History
### Classical philosophy {#classical_philosophy}
Plato (c. 427--347 BC) and Aristotle (c. 384--322 BC) both posited first cause arguments, though each had certain notable caveats. In *The Laws* (Book X), Plato posited that all movement in the world and the Cosmos was \"imparted motion\". This required a \"self-originated motion\" to set it in motion and to maintain it. In *Timaeus*, Plato posited a \"demiurge\" of supreme wisdom and intelligence as the creator of the Cosmos.
Aristotle argued *against* the idea of a first cause, often confused with the idea of a \"prime mover\" or \"unmoved mover\" (*πρῶτον κινοῦν ἀκίνητον* or *primus motor*) in his *Physics* and *Metaphysics*. Aristotle argued in *favor* of the idea of several unmoved movers, one powering each celestial sphere, which he believed lived beyond the sphere of the fixed stars, and explained why motion in the universe (which he believed was eternal) had continued for an infinite period of time. Aristotle argued the atomist\'s assertion of a non-eternal universe would require a first uncaused cause -- in his terminology, an efficient first cause -- an idea he considered a nonsensical flaw in the reasoning of the atomists.
Like Plato, Aristotle believed in an eternal cosmos with no beginning and no end (which in turn follows Parmenides\' famous statement that \"nothing comes from nothing\"). In what he called \"first philosophy\" or metaphysics, Aristotle *did* intend a theological correspondence between the prime mover and a deity; functionally, however, he provided an explanation for the apparent motion of the \"fixed stars\" (now understood as the daily rotation of the Earth). According to his theses, immaterial unmoved movers are eternal unchangeable beings that constantly think about thinking, but being immaterial, they are incapable of interacting with the cosmos and have no knowledge of what transpires therein. From an \"aspiration or desire\", the celestial spheres, *imitate* that purely intellectual activity as best they can, by uniform circular motion. The unmoved movers *inspiring* the planetary spheres are no different in kind from the prime mover, they merely suffer a dependency of relation to the prime mover. Correspondingly, the motions of the planets are subordinate to the motion inspired by the prime mover in the sphere of fixed stars. Aristotle\'s natural theology admitted no creation or capriciousness from the immortal pantheon, but maintained a defense against dangerous charges of impiety.
### Late antiquity to the Islamic Golden Age {#late_antiquity_to_the_islamic_golden_age}
Plotinus, a third-century Platonist, taught that the One transcendent absolute caused the universe to exist simply as a consequence of its existence (*creatio ex deo*). His disciple Proclus stated, \"The One is God\". In the 6th century, Syriac Christian neo-Platonist John Philoponus (c. 490 -- c. 570) examined the contradiction between Greek pagan adherences to the concept of a past-eternal world and Aristotelian rejection of the existence of actual infinities. Thereupon, he formulated arguments in defense of temporal finitism, which underpinned his arguments for the existence of God. Philosopher Steven M. Duncan notes that Philoponus\'s ideas eventually received their fullest articulation \"at the hands of Muslim and Jewish exponents of *kalam*\", or medieval Islamic scholasticism.
In the 11th century, Islamic philosopher Avicenna (c. 980 -- 1037) inquired into the question of being, in which he distinguished between essence (*māhiyya*) and existence (*wuǧūd*). He argued that the fact of existence could not be inferred from or accounted for by the essence of existing things, and that form and matter by themselves could not originate and interact with the movement of the universe or the progressive actualization of existing things. Thus, he reasoned that existence must be due to an agent cause that necessitates, imparts, gives, or adds existence to an essence. To do so, the cause must coexist with its effect and be an existing thing.
### Medieval Christian theology {#medieval_christian_theology}
Thomas Aquinas (c. 1225 -- 1274) adapted and enhanced the argument he found in his reading of Aristotle, Avicenna (the Proof of the Truthful) and Maimonides to formulate one of the most influential versions of the cosmological argument. His conception of the first cause was the idea that the universe must be caused by something that is itself uncaused, which he claimed is \'that which we call God\':
Importantly, Aquinas\'s Five Ways, given the second question of his *Summa Theologica*, are not the entirety of Aquinas\'s demonstration that the Christian God exists. The Five Ways form only the beginning of Aquinas\'s Treatise on the Divine Nature.
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# Cosmological argument
## General principles {#general_principles}
### The infinite regress {#the_infinite_regress}
A *regress* is a series of related elements, arranged in some type of sequence of succession, examined in backwards succession (regression) from a fixed point of reference. Depending on the type of regress, this retrograde examination may take the form of recursive analysis, in which the elements in a series are studied as products of prior, often simpler, elements. If there is no \'last member\' in a regress (i.e. no \'first member\' in the series) it becomes an infinite regress, continuing in perpetuity. In the context of the cosmological argument the term \'regress\' usually refers to *causal regress*, in which the series is a chain of cause and effect, with each element in the series arising from causal activity of the prior member. Some variants of the argument may also refer to *temporal regress*, wherein the elements are past events (discrete units of time) arranged in a temporal sequence.
An infinite regress argument attempts to establish the falsity of a proposition by showing that it entails an infinite regress that is vicious. The cosmological argument is a type of *positive* infinite regress argument given that it defends a proposition (in this case, the existence of a first cause) by arguing that its negation would lead to a vicious regress. An infinite regress may be vicious due to various reasons:
- Impossibility: Thought experiments such as Hilbert\'s Hotel are cited to demonstrate the metaphysical impossibility of actual infinities existing in reality. Accordingly, it may be argued that an infinite causal or temporal regress cannot occur in the real world.
- Implausibility: The regress contradicts empirical evidence (e.g. for the finitude of the past) or basic principles such as Occam\'s razor.
- Explanatory failure: A failure of explanatory goals resulting in an infinite regress of explanations. This may arise in the case of logical fallacies such as begging the question or from an attempt to investigate causes concerning origins or fundamental principles.
### Accidental and essential ordering of causes {#accidental_and_essential_ordering_of_causes}
Aquinas refers to the distinction found in Aristotle\'s *Physics* (8.5) that a series of causes may either be accidental or essential, though the designation of this terminology would follow later under John Duns Scotus at the turn of the 14th century.
In an accidentally ordered series of causes, earlier members need not continue exerting causal activity (having done so to propagate the chain) for the series to continue. For example, in a generational line, ancestors need no longer exist for their offspring to continue the sequence of descent. In an essential series, prior members must maintain causal interrelationship for the series to continue: If a hand grips a stick that moves a rock along the ground, the rock would stop motion once the hand or stick ceases to exist.
Based upon this distinction Frederick Copleston (1907--1994) characterises two types of causation: Causes *in fieri*, which cause an effect\'s *becoming*, or coming into existence, and causes *in esse*, which causally sustain an effect, in *being*, once it exists.
Two specific properties of an essentially ordered series have significance in the context of the cosmological argument:
- A first cause is essential: Later members exercise no independent causal power in continuing the series. In the example illustrated above, the rock derives its causal power essentially from the stick, which derives its causal power essentially from the hand.
- All members in the causal series must exist simultaneously in time, or timelessly.
Thomistic philosopher, R. P. Phillips comments on the characteristics of essential ordering:
: \"Each member of the series of causes possesses being solely by virtue of the actual present operation of a superior cause \... Life is dependent *inter alia* on a certain atmospheric pressure, this again on the continual operation of physical forces, whose being and operation depends on the position of the earth in the solar system, which itself must endure relatively unchanged, a state of being which can only be continuously produced by a definite---if unknown---constitution of the material universe. This constitution, however, cannot be its own cause \... We are thus irresistibly led to posit a first efficient cause which, while itself uncaused, shall impart causality to a whole series.\"
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# Cosmological argument
## Versions of the argument {#versions_of_the_argument}
### Aquinas\'s argument from contingency {#aquinass_argument_from_contingency}
In the scholastic era, Aquinas formulated the \"argument from contingency\", following Aristotle, in claiming that there must be something to explain the existence of the universe. Since the universe could, under different circumstances, conceivably *not* exist (i.e. it is contingent) its existence must have a cause. This cause cannot be embodied in another contingent thing, but something that exists by necessity (i.e. that *must* exist in order for anything else to exist). It is a form of argument from universal causation, therefore compatible with the conception of a universe that has no beginning in time. In other words, according to Aquinas, even if the universe has always existed, it still owes its continuing existence to an uncaused cause, he states: \"\... and this we understand to be God.\"
Aquinas\'s argument from contingency is formulated as the Third Way (Q2, A3) in the *Summa Theologica*. It may be expressed as follows:
1. There exist contingent things, for which non-existence is possible.
2. It is impossible for contingent things to always exist, so at some time they did not exist.
3. Therefore, if all things are contingent, then nothing would exist now.
4. There exists something rather than nothing.
He concludes thereupon that contingent beings are an insufficient explanation for the existence of other contingent beings. Furthermore, that there must exist a *necessary* being, whose non-existence is impossible, to explain the origination of all contingent beings.
5. Therefore, there exists a necessary being.
6. It is possible that a necessary being has a cause of its necessity in another necessary being.
7. The derivation of necessity between beings cannot regress to infinity (being an essentially ordered causal series).
8. Therefore, there exists a being that is necessary of itself, from which all necessity derives.
9. That being is whom everyone calls God.
### Leibnizian cosmological argument {#leibnizian_cosmological_argument}
In 1714, German philosopher Gottfried Leibniz presented a variation of the cosmological argument based upon the principle of sufficient reason. He writes: \"There can be found no fact that is true or existent, or any true proposition, without there being a sufficient reason for its being so and not otherwise, although we cannot know these reasons in most cases.\" Stating his argument succinctly:
: \"Why is there something rather than nothing? The sufficient reason \... is found in a substance which \... is a necessary being bearing the reason for its existence within itself.\"
Alexander Pruss formulates the argument as follows:
1. Every contingent fact has an explanation.
2. There is a contingent fact that includes all other contingent facts.
3. Therefore, there is an explanation of this fact.
4. This explanation must involve a necessary being.
5. This necessary being is God.
Premise 1 expresses the principle of sufficient reason. In premise 2, Leibniz proposes the existence of a logical conjunction of all contingent facts, referred to in later literature as the *Big Conjunctive Contingent Fact* (BCCF), representing the sum total of contingent reality. Premise 3 applies the principle of sufficient reason to the BCCF, given that it too, as a contingency, has a sufficient explanation. It follows, in statement 4, that the explanation of the BCCF must be necessary, not contingent, given that the BCCF incorporates all contingent facts. Statement 5 proposes that the necessary being explaining the totality of contingent facts is God.
Philosophers Joshua Rasmussen and T. Ryan Byerly have argued in defence of the inference from statement 4 to statement 5.
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# Cosmological argument
## Versions of the argument {#versions_of_the_argument}
### Duns Scotus\'s metaphysical argument {#duns_scotuss_metaphysical_argument}
At the turn of the 14th century, medieval Christian theologian John Duns Scotus (1265/66--1308) formulated a metaphysical argument for the existence of God inspired by Aquinas\'s argument of the unmoved mover. Like other philosophers and theologians, Scotus believed that his statement for God\'s existence could be considered distinct to that of Aquinas. The form of the argument can be summarised as follows:
1. An effect cannot be produced by itself.
2. An effect cannot be produced by nothing.
3. A circle of causes is impossible.
4. Therefore, an effect must be produced by something else.
5. An accidentally ordered causal series cannot exist without an essentially ordered series.
```{=html}
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1. Each member in an accidentally ordered series (except a possible first) exists via causal activity of a prior member.
2. That causal activity is exercised by virtue of a certain form.
3. Therefore, that form is required by each member to effect causation.
4. The form itself is not a member of the series.
5. Therefore \[c,d\], accidentally ordered causes cannot exist without higher-order (essentially ordered) causes.
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```
6. An essentially ordered causal series cannot regress to infinity.
7. Therefore \[4,5,6\], there exists a first agent.
Scotus affirms, in premise 5, that an accidentally ordered series of causes is impossible without higher-order laws and processes that govern the basic principles of accidental causation, which he characterises as essentially ordered causes.
Premise 6 continues, in accordance with Aquinas\'s discourses on the Second Way and Third Way, that an essentially ordered series of causes cannot be an infinite regress. On this, Scotus posits that, if it is merely possible that a first agent exists, then it is necessarily true that a first agent exists, given that the non-existence of a first agent entails the impossibility of its own existence (by virtue of being a first cause in the chain). He argues further that it is *not impossible* for a being to exist that is causeless by virtue of ontological perfection.
With the formulation of this argument, Scotus establishes the first component of his \'triple primacy\': The characterisation of a being that is first in efficient causality, final causality and pre-eminence, or maximal excellence, which he ascribes to God.
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# Cosmological argument
## Versions of the argument {#versions_of_the_argument}
### Kalam cosmological argument {#kalam_cosmological_argument}
The Kalam cosmological argument\'s central thesis is the impossibility of an infinite temporal regress of events (or past-infinite universe). Though a modern formulation that defends the finitude of the past through philosophical and scientific arguments, many of the argument\'s ideas originate in the writings of early Christian theologian John Philoponus (490--570 AD), developed within the proceedings of medieval Islamic scholasticism through the 9th to 12th centuries, eventually returning to Christian theological scholarship in the 13th century.
These ideas were revitalised for modern discourse by philosopher and theologian William Lane Craig through publications such as *The Kalām Cosmological Argument* (1979) and the *Blackwell Companion to Natural Theology* (2009). The form of the argument popularised by Craig is expressed in two parts, as an initial deductive syllogism followed by further philosophical analysis.
#### Initial syllogism {#initial_syllogism}
1. Everything that begins to exist has a cause.
2. The universe began to exist.
3. Therefore, the universe has a cause.
#### Conceptual analysis of the conclusion {#conceptual_analysis_of_the_conclusion}
Craig argues that the cause of the universe necessarily embodies specific properties in creating the universe *ex nihilo* and in effecting creation from a timeless state (implying free agency). Based upon this analysis, he appends a further premise and conclusion:
4. If the universe has a cause, then an uncaused, personal Creator of the universe exists who *sans (without)* the universe is beginningless, changeless, immaterial, timeless, spaceless and enormously powerful.
5. Therefore, an uncaused, personal Creator of the universe exists, who *sans* the universe is beginningless, changeless, immaterial, timeless, spaceless and enormously powerful.
For scientific evidence of the finitude of the past, Craig refers to the Borde-Guth-Vilenkin theorem, which posits a past boundary to cosmic inflation, and the general consensus on the standard model of cosmology, which refers to the origin of the universe in the Big Bang.
For philosophical evidence, he cites Hilbert\'s paradox of the grand hotel and Bertrand Russell\'s Tristram Shandy paradox to prove (respectively) the impossibility of actual infinites existing in reality and of forming an actual infinite by successive addition. He concludes that past events, in comprising a series of events that are instantiated in reality and formed by successive addition, cannot extend to an infinite past.
Craig remarks upon the theological implications that follow from the conclusion of the argument:
: \"\... our whole universe was caused to exist by something beyond it and greater than it. For it is no secret that one of the most important conceptions of what theists mean by \'God\' is Creator of heaven and earth.\"
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# Cosmological argument
## Criticism and discourse {#criticism_and_discourse}
### \"What caused the first cause?\" {#what_caused_the_first_cause}
Objections to the cosmological argument may question why a first cause is unique in that it does not require any causes. Critics contend that the concept of a first cause qualifies as special pleading, or that arguing for the first cause\'s exemption raises the question of why there should be a first cause at all. Defenders maintain that this question is addressed by various formulations of the cosmological argument, emphasizing that none of its major iterations rests on the premise that everything requires a cause.
Andrew Loke refers to the Kalam cosmological argument, in which the causal premise (\"whatever begins to exist has a cause\") stipulates that only things which *begin to exist* require a cause. William Lane Craig asserts that---even if one posits a plurality of causes for the existence of the universe---a first uncaused cause is necessary, otherwise an infinite regress of causes would arise, which he argues is impossible. Similarly, Edward Feser proposes, in accordance with Aquinas\'s discourses on the Second Way, that an essentially ordered series of causes cannot regress to infinity, even if it may be theoretically possible for accidentally ordered causes to do so.
Various arguments have been presented to demonstrate the metaphysical impossibility of an actually infinite regress occurring in the real world, referring to thought experiments such as Hilbert\'s Hotel, the tale of Tristram Shandy, and variations.
### \"Does the universe need a cause?\" {#does_the_universe_need_a_cause}
Craig maintains that the causal principle is predicated in the metaphysical intuition that *nothing comes from nothing.* If such intuitions are false, he argues it would be inexplicable why anything and everything does not randomly come into existence without a cause. Yet, not all philosophers subscribe to the view of causality as *a priori* in justification. David Hume contends that the principle is rooted in experience, therefore within the category of *a posteriori* knowledge and subject to the problem of induction.
Whereas J. L. Mackie argues that cause and effect cannot be extrapolated to the origins of the universe based upon our inductive experiences and intellectual preferences, Craig proposes that causal laws are unrestricted metaphysical truths that are \"not contingent upon the properties, causal powers, and dispositions of the natural kinds of substances which happen to exist\".
### Identifying the first cause {#identifying_the_first_cause}
Secular philosophers such as Michael Martin argue that a cosmological argument may establish the existence of a first cause, but falls short of identifying that cause as personal, or as God as defined within classical or other specific conceptions of theism.
Defenders of the argument note that most formulations, such as by Aquinas, Duns Scotus and Craig, employ conceptual analysis to establish the identity of the cause. In Aquinas\'s *Summa Theologica*, the *Prima Pars* (First Part) is devoted predominantly to establishing the attributes of the cause, such as uniqueness, perfection and intelligence. In Scotus\'s *Ordinatio*, his metaphysical argument is the first component of the \'triple primacy\' through which he characterises the first cause as a being with the attributes of maximal excellence.
### Timeless origin of the universe {#timeless_origin_of_the_universe}
In the topic of cosmic origins and the standard model of cosmology, the initial singularity of the Big Bang is postulated to be the point at which space and time, as well as all matter and energy, came into existence. J. Richard Gott and James E. Gunn assert that the question of \"What was there before the Universe?\" makes no sense and that the concept of *before* becomes meaningless when considering a timeless state. They add that questioning what occurred before the Big Bang is akin to questioning what is north of the North Pole.
Craig refers to Kant\'s postulate that a cause can be simultaneous with its effect, denoting that this is true of the moment of creation when time itself came into being. He affirms that the history of 20th century cosmology belies the proposition that researchers have no strong intuition to pursue a causal explanation of the origin of time and the universe. Accordingly, physicists have sought to examine the causal origins of the Big Bang by conjecturing such scenarios as the collision of membranes. Feser also notes that versions of the cosmological argument presented by classical philosophers do not require a commitment to the Big Bang, or even to a cosmic origin.
### The Hume-Edwards principle {#the_hume_edwards_principle}
William L. Rowe characterises the Hume-Edwards principle, referring to arguments presented by David Hume, and later Paul Edwards, in their criticisms of the cosmological argument:
The principle stipulates that a causal series---even one that regresses to infinity---requires no explanatory causes beyond those that are members within that series. If every member of a series has a causal explanation within the sequence, the series in itself is explanatorily complete. Thus, it rejects arguments, such as by Duns Scotus, for the existence of higher-order, efficient causes that govern the basic principles of material causation. Notably, it contradicts Hume\'s own *Dialogues Concerning Natural Religion*, in which the character Demea reflects that, even if a succession of causes is infinite, the very existence of the chain still requires a cause.
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# Cosmological argument
## Criticism and discourse {#criticism_and_discourse}
### Causal loop arguments {#causal_loop_arguments}
Some objections to the cosmological argument refer to the possibility of loops in the structure of cause and effect that would avoid the need for a first cause. Gott and Li refer to the curvature of spacetime and closed timelike curves as possible mechanisms by which the universe may bring about its own existence. Richard Hanley contends that causal loops are neither logically nor physically impossible, remarking: \"\[In timed systems\] the only possibly objectionable feature that all causal loops share is that coincidence is required to explain them.\"
Andrew Loke argues that there is insufficient evidence to postulate a causal loop of the type that would avoid a first cause. He proposes that such a mechanism would suffer from the problem of vicious circularity, rendering it metaphysically impossible
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# Cassandra
**Cassandra** or **Kassandra** (`{{IPAc-en|k|ə|'|s|æ|n|d|r|ə}}`{=mediawiki}; *Κασσάνδρα*, `{{IPA|el|kas:ándra|pron}}`{=mediawiki}, sometimes referred to as **Alexandra**; *Ἀλεξάνδρα*) in Greek mythology was a Trojan priestess dedicated to the god Apollo and fated by him to utter true prophecies but never to be believed. In modern usage her name is employed as a rhetorical device to indicate a person whose accurate prophecies, generally of impending disaster, are not believed.
Cassandra was a daughter of King Priam and Queen Hecuba of Troy. Her elder brother was Hector, the hero of the Greek-Trojan War. The older and most common versions of the myth state that she was admired by the god Apollo, who sought to win her love by means of the gift of seeing the future. According to Aeschylus, she promised him her favours, but after receiving the gift, she went back on her word. As the enraged Apollo could not revoke a divine power, he added to it the curse that nobody would believe her prophecies. In other sources, such as Hyginus and Pseudo-Apollodorus, Cassandra broke no promise to Apollo, but rather the power of foresight was given to her as an enticement to enter into a romantic engagement, the curse being added only when it failed to produce the result desired by the god.
Later versions on the contrary describe her falling asleep in a temple, where snakes licked (or whispered into) her ears which enabled her to hear the future.
## Etymology
Hjalmar Frisk (*Griechisches Etymologisches Wörterbuch*, Heidelberg, 1960--1970) notes \"unexplained etymology\", citing \"various hypotheses\" found in Wilhelm Schulze, Edgar Howard Sturtevant, J. Davreux, and Albert Carnoy. R. S. P. Beekes cites García Ramón\'s derivation of the name from the Proto-Indo-European root \**(s)kend-* \"raise\". The Online Etymology Dictionary states \"though the second element looks like a fem. form of Greek *andros* \"of man, male human being.\" Watkins suggests PIE *\*(s)kand-* \"to shine\" as source of second element. The name also has been connected to *kekasmai* \"to surpass, excel.\"
## Description
Cassandra was described by the chronicler Malalas in his account of the *Chronography* as \"shortish, round-faced, white, mannish figure, good nose, good eyes, dark pupils, blondish, curly, good neck, bulky breasts, small feet, calm, noble, priestly, an accurate prophet foreseeing everything, practicing hard, virgin\". Meanwhile, in the account of Dares the Phrygian, she was illustrated as \". . .of moderate stature, round-mouthed, and auburn-haired. Her eyes flashed. She knew the future.\"
## Biography
Cassandra was one of the many children born to the king and queen of Troy, Priam and Hecuba. She is the fraternal twin sister of Helenus, as well as the sister to Hector and Paris. One of the oldest and most common versions of her myth states that Cassandra was admired for her beauty and intelligence by the god Apollo, who sought to win her with the gift to see the future. According to Aeschylus, Cassandra promised Apollo favors, but, after receiving the gift, went back on her word and refused Apollo. Since the enraged Apollo could not revoke a divine power, he added a curse that nobody would believe Cassandra\'s prophecies.
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# Cassandra
## Mythology
Cassandra appears in texts written by Homer, Virgil, Aeschylus and Euripides. Each author depicts her prophetic powers differently.
In Homer\'s work, Cassandra is mentioned a total of four times \"as a virgin daughter of Priam, as bewailing Hector\'s death, as chosen by Agamemnon as his slave mistress after the sack of Troy, and is killed by Clytemnestra over Agamemnon\'s corpse after Clytemnestra murders him on his return home.\"
In Virgil\'s work, Cassandra appears in book two of his epic poem titled *Aeneid*, with her powers of prophecy restored. In Book 2 of the Aeneid, unlike Homer, Virgil presents Cassandra as having fallen into a mantic state and her prophecies reflect it. Likewise Seneca the Younger, in his play *Agamemnon*, has her prophesy why Agamemnon deserves his recorded death:
> *Quid me vocatis sospitem solam e meis, umbrae meorum? te sequor, tota pater Troia sepulte; frater, auxilium Phrygum terrorque Danaum, non ego antiquum decus video aut calentes ratibus ambustis manus, sed lacera membra et saucios vinclo gravi illos lacertos. te sequor... (Ag. 741--747)*\
> \
> *Why do you call me, the lone survivor of my family, My shades? I follow you, father buried with all of Troy; Brother, bulwark of Trojans, terrorizer of Greeks, I do not see your beauty of old or hands warmed by burnt ships, But your lacerated limbs and those famous shoulders savaged By heavy chains. I follow you\...*
Later on in Seneca\'s work, this behavior is reflected in acts 4 and 5 as \"Her mantic vision in act 4 will be supplemented by a further (in)sight into what is going on inside the palace in act 5 when she becomes a quasi-messenger and provides a meticulous account of Agamemnon\'s murder in the bath: \'I see and I am there and I enjoy it, no false vision deceives my eyes: let\'s watch\' (*video et intersum et fruor, / imago visus dubia non fallit meos: / spectemus*.)\"
### Gift of prophecy {#gift_of_prophecy}
Cassandra was given the gift of prophecy, but was also cursed by the god Apollo so that her true prophecies would not be believed. Many versions of the myth relate that she incurred the god\'s wrath by refusing him sexual favours after promising herself to him in exchange for the power of prophecy. In Aeschylus\' *Agamemnon*, she bemoans her relationship with Apollo:
> Apollo, Apollo! God of all ways, but only Death\'s to me, Once and again, O thou, Destroyer named, Thou hast destroyed me, thou, my love of old!
And she acknowledges her fault:
> I consented \[marriage\] to Loxias \[Apollo\] but broke my word. \... Ever since that fault I could persuade no one of anything.
Latin author Hyginus in Fabulae says: `{{blockquote|Cassandra, daughter of the king and queen, in the temple of Apollo, exhausted from practising, is said to have fallen asleep; whom, when Apollo wished to embrace her, she did not afford the opportunity of her body. On account of which thing, when she prophesied true things, she was not believed.}}`{=mediawiki}
Louise Bogan, an American poet, writes that another way Cassandra, as well as her twin brother Helenus, had earned their prophetic powers: \"*she and her brother Helenus were left overnight in the temple of the Thymbraean Apollo. No reason has been advanced for this night in the temple; perhaps it was a ritual routinely performed by everyone. When their parents looked in on them the next morning, the children were entwined with serpents, which flicked their tongues into the children\'s ears. This enabled Cassandra and Helenus to divine the future.*\" It would not be until Cassandra is much older that Apollo appears in the same temple and tried to seduce Cassandra, who rejects his advances, and curses her by making her prophecies not be believed.
Her cursed gift from Apollo became an endless pain and frustration to her. She was seen as a liar and a madwoman by her family and by the Trojan people. Because of this, her father, Priam, had locked her away in a chamber and guarded her like the madwoman she was believed to be. Though Cassandra made many predictions that went unbelieved, the one prophecy that was believed was that of Paris being her abandoned brother.
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# Cassandra
## Mythology
### Cassandra and the Fall of Troy {#cassandra_and_the_fall_of_troy}
#### Before the fall of Troy {#before_the_fall_of_troy}
Before the fall of Troy took place, Cassandra foresaw that if Paris went to Sparta and brought Helen back as his wife, the arrival of Helen would spark the downfall and destruction of Troy during the Trojan War. Despite the prophecy and ignoring Cassandra\'s warning, Paris still went to Sparta and returned with Helen. While the people of Troy rejoiced, Cassandra, angry with Helen\'s arrival, furiously snatched away Helen\'s golden veil and tore at her hair.
In Virgil\'s epic poem, the Aeneid, Cassandra warned the Trojans about the Greeks hiding inside the Trojan Horse, Agamemnon\'s death, her own demise at the hands of Aegisthus and Clytemnestra, her mother Hecuba\'s fate, Odysseus\'s ten-year wanderings before returning to his home, and the murder of Aegisthus and Clytemnestra by the latter\'s children Electra and Orestes. Cassandra predicted that her cousin Aeneas would escape during the fall of Troy and found a new nation in Rome.
#### During the fall of Troy {#during_the_fall_of_troy}
Coroebus and Othronus came to the aid of Troy during the Trojan War out of love for Cassandra and in exchange for her hand in marriage, but both were killed. According to one account, Priam offered Cassandra to Telephus\'s son Eurypylus, in order to induce Eurypylus to fight on the side of the Trojans. Cassandra was also the first to see the body of her brother Hector being brought back to the city.In *The Fall of Troy*, told by Quintus Smyrnaeus, Cassandra attempted to warn the Trojan people that Greek warriors were hiding in the Trojan Horse while they were celebrating their victory over the Greeks with feasting. Disbelieving Cassandra, the Trojans resorted to calling her names and hurling insults at her. Attempting to prove herself right, Cassandra took an axe in one hand and a burning torch in the other, and ran towards the Trojan Horse, intent on destroying the Greeks herself, but the Trojans stopped her. The Greeks hiding inside the Horse were relieved, but alarmed by how clearly she had divined their plan. At the fall of Troy, Cassandra sought shelter in the temple of Athena. There she embraced the wooden statue of Athena in supplication for her protection, but was abducted and brutally raped by Ajax the Lesser. Cassandra clung so tightly to the statue of the goddess that Ajax knocked it from its stand as he dragged her away. The actions of Ajax were a sacrilege because Cassandra was a supplicant at the sanctuary under the protection of the goddess Athena, and Ajax further defiled the temple by raping Cassandra.
In Apollodorus chapter 6, section 6, Ajax\'s death comes at the hands of both Athena and Poseidon: \"Athena threw a thunderbolt at the ship of Ajax; and when the ship went to pieces he made his way safe to a rock, and declared that he was saved in spite of the intention of Athena. But Poseidon smote the rock with his trident and split it, and Ajax fell into the sea and perished; and his body, being washed up, was buried by Thetis in Myconos\".
In some versions, Cassandra intentionally left a chest behind in Troy, with a curse on whichever Greek opened it first. Inside the chest was an image of Dionysus, made by Hephaestus and presented to the Trojans by Zeus. It was given to the Greek leader Eurypylus as a part of his share of the victory spoils of Troy. When he opened the chest and saw the image of the god, he went mad.
#### The aftermath of Troy and Cassandra\'s death {#the_aftermath_of_troy_and_cassandras_death}
Once Troy had fallen, Cassandra was taken as a *pallake* (concubine) by King Agamemnon of Mycenae. While he was away at war, Agamemnon\'s wife, Clytemnestra, had taken Aegisthus as her lover. Cassandra and Agamemnon were later killed by either Clytemnestra or Aegisthus. Various sources state that Cassandra and Agamemnon had twin boys, Teledamus and Pelops, who were murdered by Aegisthus.
The final resting place of Cassandra is either in Amyclae or Mycenae. Statues of Cassandra exist both in Amyclae and across the Peloponnese peninsula from Mycenae to Leuctra. In Mycenae, German business man and pioneer archeologist Heinrich Schliemann discovered in Grave Circle A the graves of Cassandra and Agamemnon and telegraphed back to King George I of Greece:
> *With great joy I announce to Your Majesty that I have discovered the tombs which the tradition proclaimed by Pausanias indicates to be the graves of Agamemnon, Cassandra, Eurymedon and their companions, all slain at a banquet by Clytemnestra and her lover Aegisthos.*
However, it was later discovered that the graves predated the Trojan War by at least 300 years.
## *Agamemnon* by Aeschylus {#agamemnon_by_aeschylus}
The play *Agamemnon* from Aeschylus\'s trilogy *Oresteia* depicts the king treading the scarlet cloth laid down for him, and walking offstage to his death. After the chorus\'s ode of foreboding, time is suspended in Cassandra\'s \"mad scene\". She has been onstage, silent and ignored. Her madness that is unleashed now is not the physical torment of other characters in Greek tragedy, such as in Euripides\' *Heracles* or Sophocles\' *Ajax*.
According to author Seth Schein, two further familiar descriptions of her madness are that of Heracles in *The Women of Trachis* or Io in *Prometheus Bound*. He specifies that her madness is not the type that uses language to descriptive physical agony or other physical symptoms. Instead, she speaks, disconnectedly and transcendent, in the grip of her psychic possession by Apollo, witnessing past and future events. Schein says, \"She evokes the same awe, horror and pity as do schizophrenics\". Cassandra is one of those \"who often combine deep, true insight with utter helplessness, and who retreat into madness.\"
Eduard Fraenkel remarked on the powerful contrasts between declaimed and sung dialogue in this scene. The frightened and respectful chorus are unable to comprehend her. She goes to her inevitable offstage murder by Clytemnestra with full knowledge of what is to befall her
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# Couplet
In poetry, a **couplet** (`{{IPAc-en|ˈ|k|ʌ|p|l|ə|t}}`{=mediawiki} `{{respell|CUP|lət}}`{=mediawiki}) or **distich** (`{{IPAc-en|ˈ|d|ɪ|s|t|ɪ|k}}`{=mediawiki} `{{respell|DISS|tick}}`{=mediawiki}) is a pair of successive lines that rhyme and have the same metre. A couplet may be formal (closed) or run-on (open). In a formal (closed) couplet, each of the two lines is end-stopped, implying that there is a grammatical pause at the end of a line of verse. In a run-on (open) couplet, the meaning of the first line continues to the second.
## Background
The word \"couplet\" comes from the French word meaning \"two pieces of iron riveted or hinged together\". The term \"couplet\" was first used to describe successive lines of verse in Sir P. Sidney\'s *Arcadia*in 1590: \"In singing some short coplets, whereto the one halfe beginning, the other halfe should answere.\"
While couplets traditionally rhyme, not all do. Poems may use white space to mark out couplets if they do not rhyme. Couplets in iambic pentameter are called *heroic couplets*. John Dryden in the 17th century and Alexander Pope in the 18th century were both well known for their writing in heroic couplets. The Poetic epigram is also in the couplet form. Couplets can also appear as part of more complex rhyme schemes, such as sonnets.
Rhyming couplets are one of the simplest rhyme schemes in poetry. Because the rhyme comes so quickly, it tends to call attention to itself. Good rhyming couplets tend to \"explode\" as both the rhyme and the idea come to a quick close in two lines. Here are some examples of rhyming couplets where the sense as well as the sound \"rhymes\":
:
: True wit is nature to advantage dress\'d;
: What oft was thought, but ne\'er so well express\'d.
: --- Alexander Pope
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:
: Whether or not we find what we are seeking
: Is idle, biologically speaking.
: --- Edna St. Vincent Millay (at the end of a sonnet)
On the other hand, because rhyming couplets have such a predictable rhyme scheme, they can feel artificial and plodding. Here is a Pope parody of the predictable rhymes of his era:
:
: Where-e\'er you find \"the cooling western breeze,\"
: In the next line, it \"whispers through the trees;\"
: If crystal streams \"with pleasing murmurs creep,\"
: The reader\'s threatened (not in vain) with \"sleep.\"
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# Couplet
## In English poetry {#in_english_poetry}
Regular rhyme was not originally a feature of English poetry: Old English verse came in metrically paired units somewhat analogous to couplets, but constructed according to alliterative verse principles. The rhyming couplet entered English verse in the early Middle English period through the imitation of medieval Latin and Old French models. The earliest surviving examples are a metrical paraphrase of the Lord\'s Prayer in short-line couplets, and the *Poema Morale* in septenary (or \"heptameter\") couplets, both dating from the twelfth century.
Rhyming couplets were often used in Middle English and early modern English poetry. Chaucer\'s *Canterbury Tales*, for instance, is predominantly written in rhyming couplets, and Chaucer also incorporated a concluding couplet into his rhyme royal stanza. Similarly, Shakespearean sonnets often employ rhyming couplets at the end to emphasize the theme. Take one of Shakespeare\'s most famous sonnets, Sonnet 18, for example (the rhyming couplet is shown in italics):
:
: Shall I compare thee to a summer\'s day?
: Thou art more lovely and more temperate:
: Rough winds do shake the darling buds of May,
: And summer\'s lease hath all too short a date:
: Sometimes too hot the eye of heaven shines,
: And often is his gold complexion dimm\'d;
: And every fair from fair sometime declines,
: By chance or nature\'s changing course untrimm\'d;
: But thy eternal summer shall not fade
: Nor lose possession of that fair thou owest;
: Nor shall Death brag thou wander\'st in his shade,
: When in eternal lines to time thou growest:
: *So long as men can breathe or eyes can see,*
: *So long lives this and this gives life to thee.*
In the late seventeenth century and early eighteenth-century English rhyming couplets achieved the zenith of their prestige in English verse, in the popularity of heroic couplets. The heroic couplet was used by famous poets for ambitious translations of revered Classical texts, for instance, in John Dryden\'s translation of the *Aeneid* and in Alexander Pope\'s translation of the *Iliad*.
Though poets still sometimes write in couplets, the form fell somewhat from favour in English in the twentieth century; contemporary poets writing in English sometimes prefer unrhymed couplets, distinguished by layout rather than by matching sounds.
## In Chinese poetry {#in_chinese_poetry}
Couplets called duilian may be seen on doorways in Chinese communities worldwide. Duilian displayed as part of the Chinese New Year festival, on the first morning of the New Year, are called chunlian (春聯; 春联). These are usually purchased at a market a few days before and glued to the doorframe. The text of the couplets is often traditional and contains hopes for prosperity. Other chunlian reflect more recent concerns. For example, the CCTV New Year\'s Gala usually promotes couplets reflecting current political themes in mainland China.
Some duilian may consist of two lines of four characters each. Duilian are read from top to bottom where the first line starts from the right.
## In Tamil poetry {#in_tamil_poetry}
Tamil literature contains some of the notable examples of ancient couplet poetry. The Tamil language has a rich and refined grammar for couplet poetry, and distichs in Tamil poetry follow the venpa metre. One of the most notable examples of Tamil couplet poetry is the ancient Tamil moral text of the Tirukkural, which contains a total of 1330 couplets written in the kural venpa metre from which the title of the work was derived centuries later. Each Kural couplet is made of exactly 7 words---4 in the first line and 3 in the second. The first word may rhyme with the fourth or the fifth word. Below is an example of a couplet:
:
: . (Tirukkural, verse 205)
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:
: *Transliteration*: Ilan endru theeyavai seyyarkka seyyin
: Ilanaagum matrum peyartthu
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```
:
: *Translation*: Make not thy poverty a plea for ill;
: Thine evil deeds will make thee poorer still. (Pope, 1886)
## In Hindustani poetry {#in_hindustani_poetry}
In Hindi, a couplet is called a *doha*, while in Urdu, it is called a *sher*.
Couplets were the most common form of poetry between the 12th and 18th Centuries, in Hidustani. Famous poets include Kabir, Tulsidas and Rahim Khan-i-Khanan.
Kabir (also known as Kabirdas) is thought to be one of the greatest composers of Hindustani couplets.
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# Couplet
## Distich
The American poet J. V. Cunningham was noted for many distichs included in the various forms of epigrams included in his poetry collections, as exampled here:
Deep summer, and time passes. Sorrow wastes\
To a new sorrow
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# Charles Williams (British writer)
**Charles Walter Stansby Williams** (20 September 1886 -- 15 May 1945) was an English poet, novelist, playwright, theologian and literary critic. Most of his life was spent in London, where he was born, but in 1939 he moved to Oxford with the university press for which he worked until his death.
## Early life and education {#early_life_and_education}
Charles Williams was born in London in 1886, the only son of (Richard) Walter Stansby Williams (1848--1929) and Mary (née Wall). His father Walter was a journalist and foreign business correspondent for an importing firm, writing in French and German, who was a \'regular and valued\' contributor of verse, stories and articles to many popular magazines. His mother Mary, the sister of the ecclesiologist and historian J. Charles Wall, was a former milliner (hatmaker), of Islington. He had one sister, Edith, born in 1889. The Williams family lived in \'shabby-genteel\' circumstances, owing to Walter\'s increasing blindness and the decline of the firm by which he was employed, in Holloway. In 1894 the family moved to St Albans in Hertfordshire, where Williams lived until his marriage in 1917.
Educated at St Albans School, Williams was awarded a scholarship to University College London, but he left in 1904 without attempting to gain a degree due to an inability to pay tuition fees.
Williams began work in 1904 in a Methodist bookroom. He was employed by the Oxford University Press (OUP) as a proofreading assistant in 1908 and quickly climbed to the position of editor. He continued to work at the OUP in various positions of increasing responsibility until his death in 1945. One of his greatest editorial achievements was the publication of the first major English-language edition of the works of Søren Kierkegaard. His work was part of the literature event in the art competition at the 1924 Summer Olympics.
Although chiefly remembered as a novelist, Williams also published poetry, works of literary criticism, theology, drama, history, biography, and a voluminous number of book reviews. Some of his best-known novels are *War in Heaven* (1930), *Descent into Hell* (1937), and *All Hallows\' Eve* (1945). T. S. Eliot, who wrote an introduction for the last of these, described Williams\'s novels as \"supernatural thrillers\" because they explore the sacramental intersection of the physical with the spiritual while also examining the ways in which power, even spiritual power, can corrupt as well as sanctify.
All of Williams\'s fantasies, unlike those of J. R. R. Tolkien and most of those of C. S. Lewis, are set in the contemporary world. Williams has been described by Colin Manlove as one of the three main writers of \"Christian fantasy\" in the twentieth century (the other two being C. S. Lewis and T. F. Powys). Some writers of fantasy novels with contemporary settings, notably Tim Powers, cite Williams as their inspiration.
W. H. Auden, one of Williams\'s greatest admirers, reportedly re-read Williams\'s extraordinary and highly unconventional history of the church, *The Descent of the Dove* (1939), every year. Williams\'s study of Dante entitled *The Figure of Beatrice* (1944) was very highly regarded at its time of publication and continues to be consulted by Dante scholars today. His work inspired Dorothy L. Sayers to undertake her translation of *The Divine Comedy*. Williams, however, regarded his most important work to be his extremely dense and complex Arthurian poetry, of which two books were published, *Taliessin through Logres* (1938) and *The Region of the Summer Stars* (1944), and more remained unfinished at his death. Some of Williams\'s essays were collected and published posthumously in *Image of the City and Other Essays* (1958), edited by Anne Ridler.
Williams gathered many followers and disciples during his lifetime. He was, for a period, a member of the Salvator Mundi Temple of the Fellowship of the Rosy Cross. He met fellow Anglican Evelyn Underhill in 1937 and later wrote the introduction to her published *Letters* in 1943.
When World War II broke out in 1939, Oxford University Press moved its offices from London to Oxford. Williams was reluctant to leave his beloved city, and his wife Florence refused to go. From the nearly 700 letters he wrote to his wife during the war years, a generous selection has been published -- \"primarily... love letters,\" the editor calls them.
The move to Oxford did allow him to participate regularly in Lewis\'s literary society, the Inklings. In this setting Williams read (and improved) his final published novel, *All Hallows\' Eve.* He heard J. R. R. Tolkien read aloud to the group some of his early drafts of *The Lord of the Rings*. In addition to meeting in Lewis\'s rooms at Oxford, they regularly met at The Eagle and Child pub in Oxford. During this time Williams gave lectures at Oxford on John Milton, William Wordsworth, and other authors, and received an honorary M.A. degree.
Williams is buried in Holywell Cemetery in Oxford. His headstone bears the word \"poet\" followed by the words \"Under the Mercy\", a phrase often used by Williams himself.
## Personal life {#personal_life}
In 1917 Williams married his first sweetheart, Florence Conway, following a long courtship during which he presented her with a sonnet sequence that would later become his first published book of poetry, *The Silver Stair*. Their son Michael was born in 1922.
Williams was an unswerving and devoted member of the Church of England, reputedly with a tolerance of the scepticism of others and a firm belief in the necessity of a \"doubting Thomas\" in any apostolic body.
Although Williams attracted the attention and admiration of some of the most notable writers of his day, including T. S. Eliot and W. H. Auden, his greatest admirer was probably C. S. Lewis, whose novel *That Hideous Strength* (1945) has been regarded as partially inspired by his acquaintance with both the man and his novels and poems. Williams came to know Lewis after reading Lewis\'s then-recently published study *The Allegory of Love*; he was so impressed he jotted down a letter of congratulation and dropped it in the mail. Coincidentally, Lewis had just finished reading Williams\'s novel *The Place of the Lion* and had written a similar note of congratulation. The letters crossed in the mail and led to an enduring and fruitful friendship.
Lewis wrote the Preface to *Essays presented to Charles Williams*, originally intended as a festschrift for Williams, but published after his death. Essays were contributed by Lewis, Sayers, Tolkien, Owen Barfield, Gervase Mathew and Warren Lewis.
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# Charles Williams (British writer)
## Theology
Williams developed the concept of co-inherence and gave rare consideration to the theology of romantic love. Falling in love for Williams was a form of mystical envisioning in which one saw the beloved as he or she was seen through the eyes of God. Co-inherence was a term used in Patristic theology to describe the relationship between the human and divine natures of Jesus Christ and the relationship between the persons of the blessed Trinity. Williams extended the term to include the ideal relationship between the individual parts of God\'s creation, including human beings. It is our mutual indwelling: Christ in us and we in Christ, interdependent. It is also the web of interrelationships, social and economic and ecological, by which the social fabric and the natural world function. But especially for Williams, co-inherence is a way of talking about the Body of Christ and the communion of saints. He proposed founding an order, to be called the Companions of the Co-inherence, who would practice substitution and exchange, living in love-in-God, truly bearing one another\'s burdens, being willing to sacrifice and to forgive, living from and for one another in Christ. According to Gunnar Urang, co-inherence is the focus of all Williams\'s novels.
## Works
### Fiction
- 1930: *War in Heaven* (London: Victor Gollancz) -- The Holy Grail surfaces in an obscure country parish and becomes variously a sacramental object to protect or a vessel of power to exploit.
- 1930: *Many Dimensions* (London: Victor Gollancz) -- An evil antiquarian illegally purchases the fabled Stone of Suleiman (Williams uses this Muslim form rather than the more familiar King Solomon) from its Islamic guardian and returns to England to discover not only that the Stone can multiply itself infinitely without diminishing the original, but that it also allows its possessor to transcend the barriers of space and time.
- \"Et in Sempiternum Pereant,\" a short story first published in *The London Mercury*, December 1935, in which Lord Arglay (protagonist in *Many Dimensions*) has his life put at risk encountering a ghost on the path to damnation. Later included in *The Oxford Book of English Ghost Stories* (London: Oxford University Press, 1986)
- 1931: *The Place of the Lion* (London: Mundanus) -- Platonic archetypes begin to appear around an English country town, wreaking havoc and drawing to the surface the spiritual strengths and flaws of individual characters.
- 1932: *The Greater Trumps* (London: Victor Gollancz) -- The original Tarot deck is used to unlock enormous metaphysical powers by allowing the possessors to see across space and time, create matter, and raise powerful natural storms.
- 1933: *Shadows of Ecstasy* (London: Victor Gollancz) -- A humanistic adept has discovered that by focusing his energies inward he can extend his life almost indefinitely. He undertakes an experiment using African lore to die and resurrect his own body thereby assuring his immortality. His followers begin a revolutionary movement to supplant European civilisation. The first of Williams\'s novels to be written, though not the first published.
- 1937: *Descent into Hell* (London: Faber & Faber) -- Generally thought to be Williams\'s best novel, *Descent* deals with various forms of selfishness, and how the cycle of sin brings about the necessity for redemptive acts. In it, an academic becomes so far removed from the world that he fetishises a woman to the extent that his perversion takes the form of a succubus. Other characters include a doppelgänger, the ghost of a suicidal Victorian labourer, and a playwright modelled in some ways on the author. Illustrates Williams\'s belief in the replacement of sin and substitutional love.
- 1945: *All Hallows\' Eve* (London: Faber & Faber) -- Follows the fortunes of two women after death and their interactions with those they knew before, contrasting the results of action based either on selfishness or an accepting love.
- 1970--72: *The Noises That Weren\'t There*. Unfinished. First three chapters published in *Mythlore* 6 (Autumn 1970), 7 (Winter 1971) and 8 (Winter 1972).
### Plays
- c\. 1912: *The Chapel of the Thorn* (edited by Sørina Higgins; Berkeley: Apocryphile Press, 2014)
- 1930: *A Myth of Shakespeare* (London: Oxford University Press)
- 1930: *A Myth of Francis Bacon* (Published in the *Charles Williams Society Newsletter*, 11, 12, and 14)
- 1929--31: *Three Plays* (London: Oxford University Press)
- *The Rite of the Passion* (1929)
- *The Chaste Wanton* (1930)
- *The Witch* (1931)
- 1963: *Collected Plays by Charles Williams* (edited by John Heath-Stubbs; London: Oxford University Press)
- *Thomas Cranmer of Canterbury* (1936). Canterbury Festival play, following T. S. Eliot\'s *Murder in the Cathedral* in the preceding (inaugural) year.
- *Seed of Adam* (1937)
- *Judgement at Chelmsford* (1939)
- *The Death of Good Fortune* (1939)
- *The House by the Stable* (1939)
- *Terror of Light* (1940)
- *Grab and Grace* (1941)
- *The Three Temptations* (1942)
- *House of the Octopus* (1945)
- 2000: *The Masques of Amen House* (edited by David Bratman. Mythopoeic Press).
- *The Masque of the Manuscript* (1927)
- *The Masque of Perusal* (1929)
- *The Masque of the Termination of Copyright* (1930)
### Poetry
- 1912: *The Silver Stair* (London: Herbert and Daniel)
- 1917: *Poems of Conformity* (London: Oxford University Press)
- 1920: *Divorce* (London: Oxford University Press)
- 1924: *Windows of Night* (London: Oxford University Press)
- 1930: *Heroes and Kings* (London: Sylvan Press)
- 1954: *Taliessin through Logres* (1938) and *The Region of the Summer Stars* (1944) (London: Oxford University Press)
- 1991: *Charles Williams*, ed. David Llewellyn Dodds (Woodbridge and Cambridge, UK: Boydell & Brewer: Arthurian Poets series). Part II, Uncollected and unpublished poems (pp. 149--281).
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# Charles Williams (British writer)
## Works
### Theology {#theology_1}
- 1938: *He Came Down from Heaven* (London: Heinemann).
- 1939: *The Descent of the Dove: A Short History of the Holy Spirit in the Church* (London: Longmans, Green)
- 1941: *Witchcraft* (London: Faber & Faber)
- 1942: *The Forgiveness of Sins* (London: G. Bles)
- 1958: *The Image of the City and Other Essays* (edited by Anne Ridler; London: Oxford University Press). Parts II through V
- 1990: *Outlines of Romantic Theology* (Grand Rapids, Mich.: Eerdmans)
### Literary criticism {#literary_criticism}
- 1930: *Poetry at Present* (Oxford: Clarendon Press).
- 1932: *The English Poetic Mind* (Oxford: Clarendon Press).
- 1933: *Reason and Beauty in the Poetic Mind* (Oxford: Clarendon Press)
- 1940: *Introduction to Milton* (based on a lecture at Oxford University), in *The English Poems of John Milton* (Oxford University Press)
- 1941: *Religion and Love in Dante: The Theology of Romantic Love* (Dacre Press, Westminster).
- 1943: *The Figure of Beatrice* (London: Faber & Faber)
- 1948: *The Figure of Arthur* (unfinished), in *Arthurian Torso*, ed. C. S. Lewis (London: Oxford University Press)
- 1958: *The Image of the City and Other Essays* (edited by Anne Ridler; London: Oxford University Press). Parts I and VI
- 2003: *The Detective Fiction Reviews of Charles Williams* (edited by Jared C. Lobdell; McFarland)
- 2017: *The Celian Moment and Other Essays* (edited by Stephen Barber; Oxford: The Greystones Press)
### Biography
- 1933: *Bacon* (London: Arthur Barker)
- 1933: *A Short Life of Shakespeare* (Oxford: Clarendon Press). Abridgment of the 2-volume work by Sir Edmund Chambers
- 1934: *James I* (London: Arthur Barker)
- 1935: *Rochester* (London: Arthur Barker)
- 1936: *Queen Elizabeth* (London: Duckworth)
- 1937: *Henry VII* (London: Arthur Barker)
- 1937: *Stories of Great Names* (London: Oxford University Press). Alexander, Julius Caesar, Charlemagne, Joan of Arc, Shakespeare, Voltaire, John Wesley
- 1946: *Flecker of Dean Close* (London: Canterbury Press)
### Other works {#other_works}
- 1931: Introduction, *Poems of Gerard Manley Hopkins* (Ed. Robert Bridges; 2nd ed.; London: Oxford University Press; `{{OCLC|162569501}}`{=mediawiki})
- 1936: *The Story of the Aeneid* (London: Oxford University Press; `{{OCLC|221046736}}`{=mediawiki})
- 1939: *The Passion of Christ* (Oxford University Press, New York, `{{oclc|5655518}}`{=mediawiki} London `{{oclc|752602153}}`{=mediawiki})
- 1940: Introduction, Søren Kierkegaard\'s *The Present Age* (trans. Dru and Lowrie; Oxford University Press; `{{OCLC|2193267}}`{=mediawiki})
- 1943: Introduction, *The Letters of Evelyn Underhill* (Longmans, Green and Co.)
- 1958: *The New Christian Year* (Oxford University Press `{{OCLC|7003710}}`{=mediawiki})
- 1989: *Letters to Lalage: The Letters of Charles Williams to Lois Lang-Sims* (Kent State University Press)
- 2002: *To Michal from Serge: Letters from Charles Williams to His Wife, Florence, 1939--1945* (edited by Roma King Jr
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# Cessna
**Cessna** (`{{IPAc-en|ˈ|s|ɛ|s|n|ə|}}`{=mediawiki}) is an American brand of general aviation aircraft owned by Textron Aviation since 2014, headquartered in Wichita, Kansas. Originally, it was a brand of the **Cessna Aircraft Company**, an American general aviation aircraft manufacturing corporation also headquartered in Wichita. The company produced small, piston-powered aircraft, as well as business jets. For much of the mid-to-late 20th century, Cessna was one of the highest-volume and most diverse producers of general aviation aircraft in the world. It was founded in 1927 by Clyde Cessna and Victor Roos and was purchased by General Dynamics in 1985, then by Textron in 1992. In March 2014, when Textron purchased the Beechcraft and Hawker Aircraft corporations, Cessna ceased operations as a subsidiary company, and joined the others as one of the three distinct brands produced by Textron Aviation.
Throughout its history, and especially in the years following World War II, Cessna became best known for producing small, high-wing, piston aircraft. Its most popular and iconic aircraft is the Cessna 172, delivered since 1956 (with a break from 1986 to 1996), with more sold than any other aircraft in history. Since the first model was delivered in 1972, the brand has also been well known for its Citation family of low-wing business jets which vary in size.
## History
### Origins
Clyde Cessna, a farmer in Rago, Kansas, built his own aircraft and flew it in June 1911. He was the first person to do so between the Mississippi River and the Rocky Mountains. Cessna started his wood-and-fabric aircraft ventures in Enid, Oklahoma, testing many of his early planes on the salt flats. When bankers in Enid refused to lend him more money to build his planes, he moved to Wichita.
Cessna Aircraft was formed when Clyde Cessna and Victor Roos became partners in the Cessna-Roos Aircraft Company in 1927. Roos resigned just one month into the partnership, selling back his interest to Cessna. Shortly afterward, Roos\'s name was dropped from the company name.
The Cessna DC-6 earned certification on the same day as the stock market crash of 1929, October 29, 1929.
In 1932, the Cessna Aircraft Company closed due to the Great Depression.
However, the Cessna CR-3 custom racer made its first flight in 1933. The plane won the 1933 American Air Race in Chicago and later set a new world speed record for engines smaller than 500 cubic inches by averaging 237 mph.
Cessna\'s nephews, brothers Dwane and Dwight Wallace, bought the company from Cessna in 1934. They reopened it and began the process of building it into what would become a global success.
The Cessna C-37 was introduced in 1937 as Cessna\'s first seaplane when equipped with Edo floats. In 1940, Cessna received their largest order to date, when they signed a contract with the U.S. Army for 33 specially equipped Cessna T-50s, their first twin engine plane. Later in 1940, the Royal Canadian Air Force placed an order for 180 T-50s.
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# Cessna
## History
### Postwar boom {#postwar_boom}
Cessna returned to commercial production in 1946, after the revocation of wartime production restrictions (L-48), with the release of the Model 120 and Model 140. The approach was to introduce a new line of all-metal aircraft that used production tools, dies and jigs, rather than the hand-built tube-and-fabric construction process used before the war.
The Model 140 was named by the US Flight Instructors Association as the \"Outstanding Plane of the Year\" in 1948.
Cessna\'s first helicopter, the Cessna CH-1, received FAA type certification in 1955.
Cessna introduced the Cessna 172 in 1956. It became the most produced airplane in history. During the post-World War II era, Cessna was known as one of the \"Big Three\" in general aviation aircraft manufacturing, along with Piper and Beechcraft.
In 1959, Cessna acquired Aircraft Radio Corporation (ARC), of Boonton, New Jersey, a leading manufacturer of aircraft radios. During these years, Cessna expanded the ARC product line, and rebranded ARC radios as \"Cessna\" radios, making them the \"factory option\" for avionics in new Cessnas. However, during this time, ARC radios suffered a severe decline in quality and popularity. Cessna kept ARC as a subsidiary until 1983, selling it to avionics-maker Sperry.
In 1960, Cessna acquired McCauley Industrial Corporation, of Ohio, a leading manufacturer of propellers for light aircraft. McCauley became the world\'s leading producer of general aviation aircraft propellers, largely through their installation on Cessna airplanes.
In 1960, Cessna affiliated itself with Reims Aviation of Reims, France. In 1963, Cessna produced its 50,000th airplane, a Cessna 172.
Cessna\'s first business jet, the Cessna Citation I, performed its maiden flight on September 15, 1969.
Cessna produced its 100,000th single-engine airplane in 1975.
In 1985, Cessna ceased to be an independent company. It was purchased by General Dynamics. Production of the Cessna Caravan began. General Dynamics in turn sold Cessna to Textron in 1992.
Late in 2007, Cessna purchased the bankrupt Columbia Aircraft company for US\$26.4M and would continue production of the Columbia 350 and 400 as the Cessna 350 and Cessna 400 at the Columbia factory in Bend, Oregon. However, production of both aircraft had ended by 2018.
### Chinese production controversy {#chinese_production_controversy}
On November 27, 2007, Cessna announced the then-new Cessna 162 would be built in China by Shenyang Aircraft Corporation, which is a subsidiary of the China Aviation Industry Corporation I (AVIC I), a Chinese government-owned consortium of aircraft manufacturers. Cessna reported that the decision was made to save money and because the company had no more plant capacity in the United States at the time. Cessna received much negative feedback for this decision, with complaints centering on the recent quality problems with Chinese production of other consumer products, China\'s human rights record, exporting of jobs and China\'s less than friendly political relationship with the United States. The customer backlash surprised Cessna and resulted in a company public relations campaign. In early 2009, the company attracted further criticism for continuing plans to build the 162 in China while laying off large numbers of workers in the United States. In the end, the Cessna 162 was not a commercial success and only a small number were delivered before production was cancelled.
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# Cessna
## History
### 2008--2010 economic crisis {#economic_crisis}
The company\'s business suffered notably during the late-2000s recession, laying off more than half its workforce between January 2009 and September 2010.
On November 4, 2008, Cessna\'s parent company, Textron, indicated that Citation production would be reduced from the original 2009 target of 535 \"due to continued softening in the global economic environment\" and that this would result in an undetermined number of lay-offs at Cessna.
On November 8, 2008, at the Aircraft Owners and Pilots Association (AOPA) Expo, CEO Jack Pelton indicated that sales of Cessna aircraft to individual buyers had fallen, but piston and turboprop sales to businesses had not. \"While the economic slowdown has created a difficult business environment, we are encouraged by brisk activity from new and existing propeller fleet operators placing almost 200 orders for 2009 production aircraft,\" Pelton stated.
Beginning in January 2009, a total of 665 jobs were cut at Cessna\'s Wichita and Bend, Oregon, plants. The Cessna factory at Independence, Kansas, which builds the Cessna piston-engined aircraft and the Cessna Mustang, did not see any layoffs, but one third of the workforce at the former Columbia Aircraft facility in Bend was laid off. This included 165 of the 460 employees who built the Cessna 350 and 400. The remaining 500 jobs were eliminated at the main Cessna Wichita plant.
In January 2009, the company laid off an additional 2,000 employees, bringing the total to 4,600. The job cuts included 120 at the Bend, Oregon, facility reducing the plant that built the Cessna 350 and 400 to fewer than half the number of workers that it had when Cessna bought it. Other cuts included 200 at the Independence, Kansas, plant that builds the single-engined Cessnas and the Mustang, reducing that facility to 1,300 workers.
On April 29, 2009, the company suspended the Citation Columbus program and closed the Bend, Oregon, facility. The Columbus program was finally cancelled in early July 2009. The company reported, \"Upon additional analysis of the business jet market related to this product offering, we decided to formally cancel further development of the Citation Columbus\". With the 350 and 400 production moving to Kansas, the company indicated that it would lay off 1,600 more workers, including the remaining 150 employees at the Bend plant and up to 700 workers from the Columbus program.
In early June 2009, Cessna laid off an additional 700 salaried employees, bringing the total number of lay-offs to 7,600, which was more than half the company\'s workers at the time.
The company closed its three Columbus, Georgia, manufacturing facilities between June 2010 and December 2011. The closures included the new 100000 sqft facility that was opened in August 2008 at a cost of US\$25M, plus the McCauley Propeller Systems plant. These closures resulted in total job losses of 600 in Georgia. Some of the work was relocated to Cessna\'s Independence, Kansas, or Mexican facilities.
Cessna\'s parent company, Textron, posted a loss of US\$8M in the first quarter of 2010, largely driven by continuing low sales at Cessna, which were down 44%. Half of Cessna\'s workforce remained laid-off and CEO Jack Pelton stated that he expected the recovery to be long and slow.
In September 2010, a further 700 employees were laid off, bringing the total to 8,000 jobs lost. CEO Jack Pelton indicated this round of layoffs was due to a \"stalled \[and\] lackluster economy\" and noted that while the number of orders cancelled for jets had been decreasing, new orders had not met expectations. Pelton added, \"our strategy is to defend and protect our current markets while investing in products and services to secure our future, but we can do this only if we succeed in restructuring our processes and reducing our costs.\"
### 2010s
On May 2, 2011, CEO Jack J. Pelton retired. The new CEO, Scott A. Ernest, started on May 31, 2011. Ernest joined Textron after 29 years at General Electric, where he had most recently served as vice president and general manager, global supply chain for GE Aviation. Ernest previously worked for Textron CEO Scott Donnelly when both worked at General Electric.
In September 2011, the Federal Aviation Administration (FAA) proposed a US\$2.4 million fine against the company for its failure to follow quality assurance requirements while producing fiberglass components at its plant in Chihuahua, Mexico. Excess humidity meant that the parts did not cure correctly and quality assurance did not detect the problems. The failure to follow procedures resulted in the delamination in flight of a 7 ft section of one Cessna 400\'s wing skin from the spar while the aircraft was being flown by an FAA test pilot. The aircraft was landed safely. The FAA also discovered 82 other aircraft parts that had been incorrectly made and not detected by the company\'s quality assurance. The investigation resulted in an emergency Airworthiness Directive that affected 13 Cessna 400s.
Since March 2012, Cessna has been pursuing building business jets in China as part of a joint venture with Aviation Industry Corporation of China (AVIC). The company stated that it intends to eventually build all aircraft models in China, saying \"The agreements together pave the way for a range of business jets, utility single-engine turboprops and single-engine piston aircraft to be manufactured and certified in China.\"
In late April 2012, the company added 150 workers in Wichita as a result of anticipated increased demand for aircraft production. Overall, they have cut more than 6000 jobs in the Wichita plant since 2009.
In March 2014, Cessna ceased operations as a company and instead became a brand of Textron Aviation.
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# Cessna
## Marketing initiatives {#marketing_initiatives}
During the 1950s and 1960s, Cessna\'s marketing department followed the lead of Detroit automakers and came up with many unique marketing terms in an effort to differentiate its product line from their competitors.
Other manufacturers and the aviation press widely ridiculed and spoofed many of the marketing terms, but Cessna built and sold more aircraft than any other manufacturer during the boom years of the 1960s and 1970s.
Generally, the names of Cessna models do not follow a theme, but there is usually logic to the numbering: the 100 series are the light singles, the 200s are the heftier, the 300s are light to medium twins, the 400s have \"wide oval\" cabin-class accommodation and the 500s are jets. Many Cessna models have names starting with C for the sake of alliteration (e.g. Citation, Crusader, Chancellor).
### Company terminology {#company_terminology}
Cessna marketing terminology includes:
- **Para-Lift Flaps** -- Large Fowler flaps Cessna introduced on the 170B in 1952, replacing the narrow chord plain flaps then in use.
- **Land-O-Matic** -- In 1956, Cessna introduced sprung-steel tricycle landing gear on the 172. The marketing department chose \"Land-O-Matic\" to imply that these aircraft were much easier to land and take off than the preceding conventional landing gear equipped Cessna 170. They even went as far as to say pilots could do \"drive-up take-offs and drive-in landings\", implying that flying these aircraft was as easy as driving a car. In later years, some Cessna models had their steel sprung landing gear replaced with steel tube gear legs. The 206 retains the original spring steel landing gear today.
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- **Omni-Vision** -- The rear windows on some Cessna singles, starting with the 182 and 210 in 1962 and followed by the 172 and 150 in 1963 and 1964 respectively. The term was intended to make the pilot feel visibility was improved on the notably poor-visibility Cessna line. The introduction of the rear window caused in most models a loss of cruise speed due to the extra drag, while not adding any useful visibility.
- **Cushioned Power** -- The rubber mounts on the cowling of the 1967 model 150, in addition to the rubber mounts isolating the engine from the cabin.
- **Omni-Flash** -- The flashing beacon on the tip of the fin that could be seen all around.
- **Open-View** -- This referred to the removal of the top section of the control wheel in 1967 models. These had been rectangular, they now became \"ram\'s horn\" shaped, thus not blocking the instrument panel as much.
- **Quick-Scan** -- Cessna introduced a new instrument panel layout in the 1960s and this buzzword was to indicate Cessna\'s panels were ahead of the competition.
- **Nav-O-Matic** -- The name of the Cessna autopilot system, which implied the system was relatively simple.
- **Camber-Lift** -- A marketing name used to describe Cessna aircraft wings starting in 1972 when the aerodynamics designers at Cessna added a slightly drooped leading edge to the standard NACA 2412 airfoil used on most of the light aircraft fleet. Writer Joe Christy described the name as \"stupid\" and added \"Is there any other kind \[of lift\]?\"
- **Stabila-Tip** -- Cessna started commonly using wingtip fuel tanks, carefully shaped for aerodynamic effect rather than being tubular-shaped. Tip tanks do have an advantage of reducing free surface effect of fuel affecting the balance of the aircraft in rolling maneuvers
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# Cello
The **violoncello** (`{{IPAc-en|ˌ|v|aɪ|ə|l|ə|n|ˈ|tʃ|ɛ|l|oʊ|audio=LL-Q1860 (eng)-Flame, not lame-Cello.wav}}`{=mediawiki} `{{respell|VY|ə|lən|CHEL|oh}}`{=mediawiki}, `{{IPA|it|vjolonˈtʃɛllo}}`{=mediawiki}), commonly abbreviated as **cello** (`{{IPAc-en|ˈ|tʃ|ɛ|l|oʊ}}`{=mediawiki} `{{respell|CHEL|oh}}`{=mediawiki}), is a middle pitched bowed (sometimes plucked and occasionally hit) string instrument of the violin family. Its four strings are usually tuned in perfect fifths: from low to high, C~2~, G~2~, D~3~ and A~3~. The viola\'s four strings are each an octave higher. Music for the cello is generally written in the bass clef; the tenor clef and treble clef are used for higher-range passages.
Played by a *cellist* or *violoncellist*, it enjoys a large solo repertoire with and without accompaniment, as well as numerous concerti. As a solo instrument, the cello uses its whole range, from bass to soprano, and in chamber music, such as string quartets and the orchestra\'s string section, it often plays the bass part, where it may be reinforced an octave lower by the double basses. Figured bass music of the Baroque era typically assumes a cello, viola da gamba or bassoon as part of the basso continuo group alongside chordal instruments such as organ, harpsichord, lute, or theorbo. Cellos are found in many other ensembles, from modern Chinese orchestras to cello rock bands.
## Etymology
The name *cello* is derived from the ending of the Italian *violoncello*, which means \"little violone\". Violone (\"big viola\") was a large-sized member of viol (viola da gamba) family or the violin (viola da braccio) family. The term \"violone\" today usually refers to the lowest-pitched instrument of the viols, a family of stringed instruments that went out of fashion around the end of the 17th century in most countries except England and, especially, France, where they survived another half-century before the louder violin family came into greater favour in that country as well.
In modern symphony orchestras, it is the second largest stringed instrument (the double bass is the largest). Thus, the name \"violoncello\" contained both the augmentative \"*-one*\" (\"big\") and the diminutive \"*-cello*\" (\"little\"). By the turn of the 20th century, it had become common to shorten the name to \'cello, with the apostrophe indicating the missing stem. It is now customary to use \"cello\" without apostrophe as the full designation. *Viol* is derived from the root *viola*, which was derived from Medieval Latin *vitula*, meaning stringed instrument.
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# Cello
## General description {#general_description}
### Tuning
Cellos are tuned in fifths, starting with C~2~ (two octaves below middle C), followed by G~2~, D~3~, and then A~3~. It is tuned in the exact same intervals and strings as the viola, but an octave lower. Similar to the double bass, the cello has an endpin that rests on the floor to support the instrument\'s weight. The cello is most closely associated with European classical music. The instrument is a part of the standard orchestra, as part of the string section, and is the bass voice of the string quartet (although many composers give it a melodic role as well), as well as being part of many other chamber groups.
### Works
Among the most well-known Baroque works for the cello are Johann Sebastian Bach\'s six unaccompanied Suites. Other significant works include Sonatas and Concertos by Antonio Vivaldi, and solo sonatas by Francesco Geminiani and Giovanni Bononcini. Domenico Gabrielli was one of the first composers to treat the cello as a solo instrument. As a basso continuo instrument the cello may have been used in works by Francesca Caccini (1587--1641), Barbara Strozzi (1619--1677) with pieces such as *Il primo libro di madrigali, per 2--5 voci e basso continuo, op. 1* and Elisabeth Jacquet de La Guerre (1665--1729), who wrote six sonatas for violin and basso continuo. Francesco Supriani\'s *Principij da imparare a suonare il violoncello e con 12 Toccate a solo* (before 1753), an early manual for learning the cello, dates from this era. As the title of the work suggests, it contains 12 toccatas for solo cello, which along with Johann Sebastian Bach\'s Cello Suites, are some of the first works of that type.
From the Classical era, the two concertos by Joseph Haydn in C major and D major stand out, as do the five sonatas for cello and pianoforte of Ludwig van Beethoven, which span the important three periods of his compositional evolution. Other outstanding examples include the three Concerti by Carl Philipp Emanuel Bach, Capricci by dall\'Abaco, and Sonatas by Flackton, Boismortier, and Luigi Boccherini. A *Divertimento for Piano, Clarinet, Viola and Cello* is among the surviving works by Duchess Anna Amalia of Brunswick-Wolfenbüttel (1739--1807). Wolfgang Amadeus Mozart supposedly wrote a Cello Concerto in F major, K. 206a in 1775, but this has since been lost. His Sinfonia Concertante in A major, K. 320e includes a solo part for cello, along with the violin and viola, although this work is incomplete and only exists in fragments, therefore it is given an Anhang number (Anh. 104).
Well-known works of the Romantic era include the Robert Schumann Concerto, the Antonín Dvořák Concerto, the first Camille Saint-Saëns Concerto, as well as the two sonatas and the Double Concerto by Johannes Brahms. A review of compositions for cello in the Romantic era must include the German composer Fanny Mendelssohn (1805--1847), who wrote Fantasia in G Minor for cello and piano and a Capriccio in A-flat for cello.
Compositions from the late 19th and early 20th century include three cello sonatas (including the Cello Sonata in C Minor written in 1880) by Dame Ethel Smyth (1858--1944), Edward Elgar\'s Cello Concerto in E minor, Claude Debussy\'s Sonata for Cello and Piano, and unaccompanied cello sonatas by Zoltán Kodály and Paul Hindemith. Pieces including cello were written by American Music Center founder Marion Bauer (1882--1955) (two trio sonatas for flute, cello, and piano) and Ruth Crawford Seeger (1901--1953) (Diaphonic suite No. 2 for bassoon and cello).
The cello\'s versatility made it popular with many composers in this era, such as Sergei Prokofiev, Dmitri Shostakovich, Benjamin Britten, György Ligeti, Witold Lutoslawski and Henri Dutilleux. Polish composer Grażyna Bacewicz (1909--1969) was writing for cello in the mid 20th century with Concerto No. 1 for Cello and Orchestra (1951), Concerto No. 2 for Cello and Orchestra (1963) and in 1964 composed her Quartet for four cellos.
Today it is sometimes featured in pop and rock recordings, examples of which are noted later in this article. The cello has also appeared in major hip-hop and R & B performances, such as singers Rihanna and Ne-Yo\'s 2007 performance at the American Music Awards. The instrument has also been modified for Indian classical music by Nancy Lesh and Saskia Rao-de Haas.^\[5\]^
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# Cello
## History
The violin family, including cello-sized instruments, emerged c. 1500 as a family of instruments distinct from the viola da gamba family. The earliest depictions of the violin family, from Italy c. 1530, show three sizes of instruments, roughly corresponding to what we now call violins, violas, and cellos. Contrary to a popular misconception, the cello did not evolve from the viola da gamba, but existed alongside it for about two and a half centuries. The violin family is also known as the viola da braccio (meaning viola for the arm) family, a reference to the primary way the members of the family are held. This is to distinguish it from the viola da gamba (meaning viola for the leg) family, in which all the members are all held with the legs. The likely predecessors of the violin family include the lira da braccio and the rebec. The earliest surviving cellos are made by Andrea Amati, the first known member of the celebrated Amati family of luthiers.
The direct ancestor to the violoncello was the bass violin.^\[*unt.\ library*\]^ Monteverdi referred to the instrument as \"basso de viola da braccio\" in *Orfeo* (1607). Although the first bass violin, possibly invented as early as 1538, was most likely inspired by the viol, it was created to be used in consort with the violin. The bass violin was actually often referred to as a \"*violone*\", or \"large viola\", as were the viols of the same period. Instruments that share features with both the bass violin and the *viola da gamba* appear in Italian art of the early 16th century.
The invention of wire-wound strings (fine wire around a thin gut core), c. 1660 in Bologna, allowed for a finer bass sound than was possible with purely gut strings on such a short body. Bolognese makers exploited this new technology to create the cello, a somewhat smaller instrument suitable for solo repertoire due to both the timbre of the instrument and the fact that the smaller size made it easier to play virtuosic passages. This instrument had disadvantages as well, however. The cello\'s light sound was not as suitable for church and ensemble playing, so it had to be doubled by organ, theorbo, or violone.
Around 1700, Italian players popularized the cello in northern Europe, although the bass violin (basse de violon) continued to be used for another two decades in France. Many existing bass violins were literally cut down in size to convert them into cellos according to the smaller pattern developed by Stradivarius, who also made a number of old pattern large cellos (the \'Servais\'). The sizes, names, and tunings of the cello varied widely by geography and time. The size was not standardized until c. 1750.
Despite similarities to the viola da gamba, the cello is actually part of the viola da braccio family, meaning \"viol of the arm\", which includes, among others, the violin and viola. Though paintings like Bruegel\'s \"The Rustic Wedding\", and Jambe de Fer in his *Epitome Musical* suggest that the bass violin had alternate playing positions, these were short-lived and the more practical and ergonomic *a gamba* position eventually replaced them entirely.
Baroque-era cellos differed from the modern instrument in several ways. The neck has a different form and angle, which matches the baroque bass-bar and stringing. The fingerboard is usually shorter than that of the modern cello, as the highest notes are not often called for in baroque music. Modern cellos have an endpin at the bottom to support the instrument (and transmit some of the sound through the floor), while Baroque cellos are held only by the calves of the player. Modern bows curve in and are held at the frog; Baroque bows curve out and are held closer to the bow\'s point of balance. Modern strings are normally flatwound with a metal (or synthetic) core; Baroque strings are made of gut, with the G and C strings wire-wound. Modern cellos often have fine tuners connecting the strings to the tailpiece, which makes it much easier to tune the instrument, but such pins are rendered ineffective by the flexibility of the gut strings used on Baroque cellos. Overall, the modern instrument has much higher string tension than the Baroque cello, resulting in a louder, more projecting tone, with fewer overtones. In addition, the instrument was less standardized in size and number of strings; a smaller, five-string variant (the violoncello piccolo) was commonly used as a solo instrument and five-string instruments are occasionally specified in the Baroque repertoire. BWV 1012 (Bach\'s 6th Cello Suite) was written for 5-string cello. The additional high E string on the five-string cello is an octave below the same string on the Violin, so anything written for the violin can be played on the 5 string cello, sounding an octave lower than written.
Few educational works specifically devoted to the cello existed before the 18th century and those that do exist contain little value to the performer beyond simple accounts of instrumental technique. One of the earliest cello manuals is Michel Corrette\'s *Méthode, thèorique et pratique pour apprendre en peu de temps le violoncelle dans sa perfection* (Paris, 1741).
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# Cello
## Modern use {#modern_use}
### Orchestral
thumb\|left\|upright=0.9\|The cello section of the orchestra of the Munich University of Applied Sciences is shown here. Cellos are part of the standard symphony orchestra, which usually includes eight to twelve cellists. The cello section, in standard orchestral seating, is located on stage left (the audience\'s right) in the front, opposite the first violin section. However, some orchestras and conductors prefer switching the positioning of the viola and cello sections. The *principal* cellist is the section leader, determining bowings for the section in conjunction with other string principals, playing solos, and leading entrances (when the section begins to play its part). Principal players always sit closest to the audience.
The cellos are a critical part of orchestral music; all symphonic works involve the cello section, and many pieces require cello soli or solos. Much of the time, cellos provide part of the low-register harmony for the orchestra. Often, the cello section plays the melody for a brief period, before returning to the harmony role. There are also cello concertos, which are orchestral pieces that feature a solo cellist accompanied by an entire orchestra.
### Solo
There are numerous cello concertos -- where a solo cello is accompanied by an orchestra -- notably 25 by Vivaldi, 12 by Boccherini, at least three by Haydn, three by C. P. E. Bach, two by Saint-Saëns, two by Dvořák, and one each by Robert Schumann, Lalo, and Elgar. There were also some composers who, while not otherwise cellists,`{{Clarify|date=February 2020|reason=Does this mean that Vivaldi, Haydn, CPE Bach, Sait-Saëns, Dvořák, Schumann, Lalo, and Elgar were all, like Boccherini, cellists?}}`{=mediawiki} did write cello-specific repertoire, such as Nikolaus Kraft, who wrote six cello concertos. Beethoven\'s Triple Concerto for Cello, Violin and Piano and Brahms\' Double Concerto for Cello and Violin are also part of the concertante repertoire, although in both cases the cello shares solo duties with at least one other instrument. Moreover, several composers wrote large-scale pieces for cello and orchestra, which are concertos in all but name. Some familiar \"concertos\" are Richard Strauss\' tone poem *Don Quixote*, Tchaikovsky\'s *Variations on a Rococo Theme*, Bloch\'s *Schelomo* and Bruch\'s *Kol Nidrei*.
In the 20th century, the cello repertoire grew immensely. This was partly due to the influence of virtuoso cellist Mstislav Rostropovich, who inspired, commissioned, and premiered dozens of new works. Among these, Prokofiev\'s *Symphony-Concerto*, Britten\'s *Cello Symphony*, the concertos of Shostakovich and Lutosławski as well as Dutilleux\'s *Tout un monde lointain\...* have already become part of the standard repertoire. Other major composers who wrote concertante works for him include Messiaen, Jolivet, Berio, and Penderecki. In addition, Arnold, Barber, Glass, Hindemith, Honegger, Ligeti, Myaskovsky, Penderecki, Rodrigo, Villa-Lobos and Walton wrote major concertos for other cellists, notably for Gaspar Cassadó, Aldo Parisot, Gregor Piatigorsky, Siegfried Palm and Julian Lloyd Webber.
There are also many sonatas for cello and piano. Those written by Beethoven, Mendelssohn, Chopin, Brahms, Grieg, Rachmaninoff, Debussy, Fauré, Shostakovich, Prokofiev, Poulenc, Carter, and Britten are particularly well known.
Other important pieces for cello and piano include Schumann\'s five *Stücke im Volkston* and transcriptions like Schubert\'s *Arpeggione Sonata* (originally for arpeggione and piano), César Franck\'s Cello Sonata (originally a violin sonata, transcribed by Jules Delsart with the composer\'s approval), Stravinsky\'s *Suite italienne* (transcribed by the composer -- with Gregor Piatigorsky -- from his ballet *Pulcinella*) and Bartók\'s first rhapsody (also transcribed by the composer, originally for violin and piano).
There are pieces for cello solo, Johann Sebastian Bach\'s six Suites for Cello (which are among the best-known solo cello pieces), Kodály\'s Sonata for Solo Cello and Britten\'s three Cello Suites. Other notable examples include Hindemith\'s and Ysaÿe\'s Sonatas for Solo Cello, Dutilleux\'s *Trois Strophes sur le Nom de Sacher*, Berio\'s *Les Mots Sont Allés*, Cassadó\'s Suite for Solo Cello, Ligeti\'s Solo Sonata, Carter\'s two *Figment*s and Xenakis\' *Nomos Alpha* and *Kottos*.
There are also modern solo pieces written for cello, such as Julie-O by Mark Summer.
### Quartets and other ensembles {#quartets_and_other_ensembles}
The cello is a member of the traditional string quartet as well as string quintets, sextet or trios and other mixed ensembles. There are also pieces written for two, three, four, or more cellos; this type of ensemble is also called a \"cello choir\" and its sound is familiar from the introduction to Rossini\'s William Tell Overture as well as Zaccharia\'s prayer scene in Verdi\'s Nabucco. Tchaikovsky\'s 1812 Overture also starts with a cello ensemble, with four cellos playing the top lines and two violas playing the bass lines. As a self-sufficient ensemble, its most famous repertoire is Heitor Villa-Lobos\' first of his Bachianas Brasileiras for cello ensemble (the fifth is for soprano and 8 cellos). Other examples are Offenbach\'s cello duets, quartet, and sextet, Pärt\'s Fratres for eight cellos and Boulez\' *Messagesquisse* for seven cellos, or even Villa-Lobos\' rarely played *Fantasia Concertante* (1958) for 32 cellos. The 12 cellists of the Berlin Philharmonic Orchestra (or \"the Twelve\" as they have since taken to being called) specialize in this repertoire and have commissioned many works, including arrangements of well-known popular songs.
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# Cello
## Modern use {#modern_use}
### Popular music, jazz, world music and neoclassical {#popular_music_jazz_world_music_and_neoclassical}
The cello is less common in popular music than in classical music. Several bands feature a cello in their standard line-up, including Hoppy Jones of the Ink Spots and Joe Kwon of the Avett Brothers. The more common use in pop and rock is to bring the instrument in for a particular song. In the 1960s, artists such as the Beatles and Cher used the cello in popular music, in songs such as The Beatles\' \"Yesterday\", \"Eleanor Rigby\" and \"Strawberry Fields Forever\", and Cher\'s \"Bang Bang (My Baby Shot Me Down)\". \"Good Vibrations\" by the Beach Boys includes the cello in its instrumental ensemble, which includes a number of instruments unusual for this sort of music. Bass guitarist Jack Bruce, who had originally studied music on a performance scholarship for cello, played a prominent cello part in \"As You Said\" on Cream\'s *Wheels of Fire* studio album (1968).
In the 1970s, the Electric Light Orchestra enjoyed great commercial success taking inspiration from so-called \"Beatlesque\" arrangements, adding the cello (and violin) to the standard rock combo line-up and in 1978 the UK-based rock band Colosseum II collaborated with cellist Julian Lloyd Webber on the recording *Variations*. Most notably, Pink Floyd included a cello solo in their 1970 epic instrumental \"Atom Heart Mother\". Bass guitarist Mike Rutherford of Genesis was originally a cellist and included some cello parts in their *Foxtrot* album.
Established non-traditional cello groups include Apocalyptica, a group of Finnish cellists best known for their versions of Metallica songs; Rasputina, a group of cellists committed to an intricate cello style intermingled with Gothic music; the Massive Violins, an ensemble of seven singing cellists known for their arrangements of rock, pop and classical hits; Von Cello, a cello-fronted rock power trio; Break of Reality, who mix elements of classical music with the more modern rock and metal genre; Cello Fury, a cello rock band that performs original rock/classical crossover music; and Jelloslave, a Minneapolis-based cello duo with two percussionists. These groups are examples of a style that has become known as cello rock. The crossover string quartet Bond also includes a cellist. Silenzium and Cellissimo Quartet are Russian (Novosibirsk) groups playing rock and metal and having more and more popularity in Siberia. Cold Fairyland from Shanghai, China is using a cello along with a pipa as the main solo instrument to create East meets West progressive (folk) rock.
More recent bands who have used the cello include Clean Bandit, Aerosmith, The Auteurs, Nirvana, Oasis, Ra Ra Riot, Smashing Pumpkins, James, Talk Talk, Phillip Phillips, OneRepublic, Electric Light Orchestra and the baroque rock band Arcade Fire. An Atlanta-based trio, King Richard\'s Sunday Best, also uses a cellist in their lineup. So-called \"chamber pop\" artists like Kronos Quartet, The Vitamin String Quartet and Margot and the Nuclear So and So\'s have also recently made cello common in modern alternative rock. Heavy metal band System of a Down has also made use of the cello\'s rich sound. The indie rock band The Stiletto Formal are known for using a cello as a major staple of their sound; similarly, the indie rock band Canada employs two cello players in their lineup. The orch-rock group The Polyphonic Spree, which has pioneered the use of stringed and symphonic instruments, employs the cello in creative ways for many of their \"psychedelic-esque\" melodies. The first-wave screamo band I Would Set Myself On Fire For You featured a cello as well as a viola to create a more folk-oriented sound. The band Panic! at the Disco uses a cello in their song \"Build God, Then We\'ll Talk\", with lead vocalist Brendon Urie recording the cello solo himself. The Lumineers added cellist Nela Pekarek to the band in 2010. Radiohead makes frequent use of cello in their music, notably for the songs \"Burn The Witch\" and \"Glass Eyes\" in 2016.
In jazz, bassists Oscar Pettiford and Harry Babasin were among the first to use the cello as a solo instrument; both tuned their instruments in fourths, an octave above the double bass. Fred Katz (who was not a bassist) was one of the first notable jazz cellists to use the instrument\'s standard tuning and arco technique. Contemporary jazz cellists include Abdul Wadud, Diedre Murray, Ron Carter, Dave Holland, David Darling, Lucio Amanti, Akua Dixon, Ernst Reijseger, Fred Lonberg-Holm, Tom Cora and Erik Friedlander. Modern musical theatre pieces like Jason Robert Brown\'s *The Last Five Years*, Duncan Sheik\'s *Spring Awakening*, Adam Guettel\'s *Floyd Collins*, and Ricky Ian Gordon\'s *My Life with Albertine* use small string ensembles (including solo cellos) to a prominent extent.
In Indian classical music, Saskia Rao-de Haas is a well-established soloist as well as playing duets with her sitarist husband, Pt. Shubhendra Rao. Other cellists performing Indian classical music are Nancy Lesh (Dhrupad) and Anup Biswas. Both Rao and Lesh play the cello sitting cross-legged on the floor.
The cello can also be used in bluegrass and folk music, with notable players including Ben Sollee of the Sparrow Quartet and the \"Cajun cellist\" Sean Grissom, as well as Vyvienne Long, who, in addition to her own projects, has played for those of Damien Rice. Cellists such as Natalie Haas, Abby Newton, and Liz Davis Maxfield have contributed significantly to the use of cello playing in Celtic folk music, often with the cello featured as a primary melodic instrument and employing the skills and techniques of traditional fiddle playing. Lindsay Mac is becoming well known for playing the cello like a guitar, with her cover of The Beatles\' \"Blackbird\".
Canadian electronic music producer Aaron Funk (Venetian Snares), in the piece Szamár Madár (on his 2005 album Rossz Csillag Alatt Született), extensively samples Edward Elgar\'s Cello Concerto in E minor, Op. 85.
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# Cello
## Construction
The cello is typically made from carved wood, although other materials such as carbon fiber or aluminum may be used. A traditional cello has a spruce top, with maple for the back, sides, and neck. Other woods, such as poplar or willow, are sometimes used for the back and sides. Less expensive cellos frequently have tops and backs made of laminated wood. Laminated cellos are widely used in elementary and secondary school orchestras and youth orchestras, because they are much more durable than carved wood cellos (i.e., they are less likely to crack if bumped or dropped) and they are much less expensive.
The top and back are traditionally hand-carved, though less expensive cellos are often machine-produced. The sides, or ribs, are made by heating the wood and bending it around forms. The cello body has a wide top bout, narrow middle formed by two C-bouts, and wide bottom bout, with the bridge and F holes just below the middle. The top and back of the cello have a decorative border inlay known as purfling. While purfling is attractive, it is also functional: if the instrument is struck, the purfling can prevent cracking of the wood. A crack may form at the rim of the instrument but spreads no further. Without purfling, cracks can spread up or down the top or back. Playing, traveling and the weather all affect the cello and can increase a crack if purfling is not in place.
The fingerboard and pegs on a cello are generally made from ebony, as it is strong and does not wear out easily.
### Alternative materials {#alternative_materials}
In the late 1920s and early 1930s, the Aluminum Company of America (Alcoa) as well as German luthier G.A. Pfretzschner produced an unknown number of aluminum cellos (in addition to aluminum double basses and violins). Cello manufacturer Luis & Clark constructs cellos from carbon fibre. Carbon fibre instruments are particularly suitable for outdoor playing because of the strength of the material and its resistance to humidity and temperature fluctuations. Luis & Clark has produced over 1000 cellos, some of which are owned by cellists such as Yo-Yo Ma and Josephine van Lier.
### Neck, fingerboard, pegbox, and scroll {#neck_fingerboard_pegbox_and_scroll}
Above the main body is the carved neck. The neck has a curved cross-section on its underside, which is where the player\'s thumb runs along the neck during playing. The neck leads to a pegbox and the scroll, which are all normally carved out of a single piece of wood, usually maple. The fingerboard is glued to the neck and extends over the body of the instrument. The fingerboard is given a curved shape, matching the curve on the bridge. Both the fingerboard and bridge need to be curved so that the performer can bow individual strings. If the cello were to have a flat fingerboard and bridge, as with a typical guitar, the performer would only be able to bow the leftmost and rightmost two strings or bow all the strings. The performer would not be able to play the inner two strings alone.
The nut is a raised piece of wood, fitted where the fingerboard meets the pegbox, in which the strings rest in shallow slots or grooves to keep them the correct distance apart. The pegbox houses four tapered tuning pegs, one for each string. The pegs are used to tune the cello by either tightening or loosening the string. The pegs are called \"friction pegs\", because they maintain their position by friction. The scroll is a traditional ornamental part of the cello and a feature of all other members of the violin family. Ebony is usually used for the tuning pegs, fingerboard, and nut, but other hardwoods, such as boxwood or rosewood, can be used. Black fittings on low-cost instruments are often made from inexpensive wood that has been blackened or \"ebonized\" to look like ebony, which is much harder and more expensive. Ebonized parts such as tuning pegs may crack or split, and the black surface of the fingerboard will eventually wear down to reveal the lighter wood underneath.
### Strings
Historically, cello strings had cores made out of catgut, which, despite its name, is made from sheep or goat intestines. Most modern strings used in the 2010s are wound with metallic materials like aluminum, titanium and chromium. Cellists may mix different types of strings on their instruments. The pitches of the open strings are C, G, D, and A (black note heads in the playing range figure above), unless alternative tuning (scordatura) is specified by the composer. Some composers (e.g. Ottorino Respighi in the final movement of *The Pines of Rome*) ask that the low C be tuned down to a B-flat so that the performer can play a different low note on the lowest open string.
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## Construction
### Tailpiece and endpin {#tailpiece_and_endpin}
The tailpiece and endpin are found in the lower part of the cello. The tailpiece is the part of the cello to which the \"ball ends\" of the strings are attached by passing them through holes. The tailpiece is attached to the bottom of the cello. The tailpiece is traditionally made of ebony or another hardwood, but can also be made of plastic or steel on lower-cost instruments. It attaches the strings to the lower end of the cello and can have one or more fine tuners. The fine tuners are used to make smaller adjustments to the pitch of the string. The fine tuners can increase the tension of each string (raising the pitch) or decrease the tension of the string (lowering the pitch). When the performer is putting on a new string, the fine tuner for that string is normally reset to a middle position, and then the peg is turned to bring the string up to pitch. The fine turners are used for subtle, minor adjustments to pitch, such as tuning a cello to the oboe\'s 440 Hz A note or tuning the cello to a piano.
The endpin or spike is made of wood, metal, or rigid carbon fiber and supports the cello in playing position. The endpin can be retracted into the hollow body of the instrument when the cello is being transported in its case. This makes the cello easier to move about. When the performer wishes to play the cello, the endpin is pulled out to lengthen it. The endpin is locked into the player\'s preferred length with a screw mechanism. The adjustable nature of endpins enables performers of different ages and body sizes to adjust the endpin length to suit them. In the Baroque period, the cello was held between the calves, as there was no endpin at that time. The endpin was \"introduced by Adrien Servais c. 1845 to give the instrument greater stability\". Modern endpins are retractable and adjustable; older ones were removed when not in use. (The word \"endpin\" sometimes also refers to the button of wood located at this place in all instruments in the violin family, but this is usually called \"tailpin\".) The sharp tip of the cello\'s endpin is sometimes capped with a rubber tip that protects the tip from dulling and prevents the cello from slipping on the floor. Many cellists use a rubber pad with a metal cup to keep the tip from slipping on the floor. A number of accessories exist to keep the endpin from slipping; these include ropes that attach to the chair leg and other devices.
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# Cello
## Construction
### Bridge and f-holes {#bridge_and_f_holes}
The bridge holds the strings above the cello and transfers their vibrations to the top of the instrument and the soundpost inside (see below). The bridge is not glued but rather held in place by the tension of the strings. The bridge is usually positioned by the cross point of the \"f-hole\" (i.e., where the horizontal line occurs in the \"f\"). The f-holes, named for their shape, are located on either side of the bridge and allow air to move in and out of the instrument as part of the sound-production process. The f-holes also act as access points to the interior of the cello for repairs or maintenance. Sometimes a small length of rubber hose containing a water-soaked sponge, called a Dampit, is inserted through the f-holes and serves as a humidifier. This keeps the wood components of the cello from drying out.
### Internal features {#internal_features}
Internally, the cello has two important features: a bass bar, which is glued to the underside of the top of the instrument, and a round wooden sound post, a solid wooden cylinder which is wedged between the top and bottom plates. The bass bar, found under the bass foot of the bridge, serves to support the cello\'s top and distribute the vibrations from the strings to the body of the instrument. The soundpost, found under the treble side of the bridge, connects the back and front of the cello. Like the bridge, the soundpost is not glued but is kept in place by the tensions of the bridge and strings. Together, the bass bar and sound post transfer the strings\' vibrations to the top (front) of the instrument (and to a lesser extent the back), acting as a diaphragm to produce the instrument\'s sound.
### Glue
Cellos are constructed and repaired using hide glue, which is strong but reversible, allowing for disassembly when needed. Tops may be glued on with diluted glue since some repairs call for the removal of the top. Theoretically, hide glue is weaker than the body\'s wood, so as the top or back shrinks side-to-side, the glue holding it lets go and the plate does not crack. Cellists repairing cracks in their cello do not use regular wood glue, because it cannot be steamed open when a repair has to be made by a luthier.
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## Construction
### Bow
thumb\|right\|upright=0.7\|A cello French bow *sul ponticello* Traditionally, bows are made from pernambuco or brazilwood. Both come from the same species of tree (*Caesalpinia echinata*), but Pernambuco, used for higher-quality bows, is the heartwood of the tree and is darker in color than brazilwood (which is sometimes stained to compensate). Pernambuco is a heavy, resinous wood with great elasticity, which makes it an ideal wood for instrument bows. Horsehair is stretched out between the two ends of the bow. The taut horsehair is drawn over the strings, while being held roughly parallel to the bridge and perpendicular to the strings, to produce sound. A small knob is twisted to increase or decrease the tension of the horsehair. The tension on the bow is released when the instrument is not being used. The amount of tension a cellist puts on the bow hair depends on the preferences of the player, the style of music being played, and for students, the preferences of their teacher.
Bows are also made from other materials, such as carbon fibre---stronger than wood---and fiberglass (often used to make inexpensive, lower-quality student bows). An average cello bow is 73 cm long (shorter than a violin or viola bow) 3 cm high (from the frog to the stick) and 1.5 cm wide. The frog of a cello bow typically has a rounded corner like that of a viola bow, but is wider. A cello bow is roughly 10 g heavier than a viola bow, which in turn is roughly 10 g heavier than a violin bow.
Bow hair is traditionally horsehair, though synthetic hair, in varying colors, is also used. Prior to playing, the musician tightens the bow by turning a screw to pull the frog (the part of the bow under the hand) back and increase the tension of the hair. Rosin is applied by the player to make the hair sticky. Bows need to be re-haired periodically. Baroque-style (1600--1750) cello bows were much thicker and were formed with a larger outward arch than modern cello bows. The inward arch of a modern cello bow produces greater tension, which in turn produces a louder sound.
The cello bow has also been used to play electric guitars. Jimmy Page pioneered its application on tracks such as \"Dazed and Confused\". The post-rock Icelandic band Sigur Rós\'s lead singer often plays guitar using a cello bow.
In 1989, the German cellist Michael Bach began developing a curved bow, encouraged by John Cage, Dieter Schnebel, Mstislav Rostropovich and Luigi Colani: and since then many pieces have been composed especially for it. This curved bow (*BACH.Bow*) is a convex curved bow which, unlike the ordinary bow, renders possible polyphonic playing on the various strings of the instrument. The BACH.Bow is particularly well-suited to the solo repertoire for violin and cello by J. S. Bach; which requires both polyphonic and monophonic playing.
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## Physics
### Physical aspects {#physical_aspects}
When a string is bowed or plucked, it vibrates and moves the air around it, producing sound waves. Because the string is quite thin, not much air is moved by the string itself, and consequently, if the string was not mounted on a hollow body, the sound would be weak. In acoustic stringed instruments such as the cello, this lack of volume is solved by mounting the vibrating string on a larger hollow wooden body. The vibrations are transmitted to the larger body, which can move more air and produce a louder sound. Different designs of the instrument produce variations in the instrument\'s vibrational patterns and thus change the character of the sound produced. A string\'s fundamental pitch can be adjusted by changing its stiffness, which depends on tension and length. Tightening a string stiffens it by increasing both the outward forces along its length and the net forces it experiences during a distortion. A cello can be tuned by adjusting the tension of its strings, by turning the tuning pegs mounted on its pegbox and tension adjusters (fine tuners) on the tailpiece.
A string\'s length also affects its fundamental pitch. Shortening a string stiffens it by increasing its curvature during a distortion and subjecting it to larger net forces. Shortening the string also reduces its mass, but does not alter the mass per unit length, and it is the latter ratio rather than the total mass which governs the frequency. The string vibrates in a standing wave whose speed of propagation is given by $\sqrt{\frac{T}{m}}$, where `{{mvar|T}}`{=mediawiki} is the tension and `{{mvar|m}}`{=mediawiki} is the mass per unit length; there is a node at either end of the vibrating length, and thus the vibrating length `{{mvar|l}}`{=mediawiki} is half a wavelength. Since the frequency of any wave is equal to the speed divided by the wavelength, we have $\mathrm{frequency} = \frac{1}{2l} \cdot \sqrt{\frac{T}{m}}$. (Some writers, including Muncaster (cited below), use the Greek letter `{{mvar|μ}}`{=mediawiki} in place of `{{mvar|m}}`{=mediawiki}.) Thus shortening a string increases the frequency, and thus the pitch. Because of this effect, you can raise and change the pitch of a string by pressing it against the fingerboard in the cello\'s neck and effectively shortening it. Likewise strings with less mass per unit length, if under the same tension, will have a higher frequency and thus higher pitch than more massive strings. This is a prime reason the different strings on all string instruments have different fundamental pitches, with the lightest strings having the highest pitches.
thumb\|upright=0.45\|Spectrogram of a D chord arpeggiated on the cello. Yellow bands at the same level indicate the same harmonics excited by the bowing of different notes. Notes played from left to right: D--F`{{music|#}}`{=mediawiki}--A--F`{{music|#}}`{=mediawiki}--D.
A played note of E or F`{{sharp}}`{=mediawiki} has a frequency that is often very close to the natural resonating frequency of the body of the instrument, and if the problem is not addressed this can set the body into near resonance. This may cause an unpleasant sudden amplification of this pitch, and additionally a loud beating sound results from the interference produced between these nearby frequencies; this is known as the \"wolf tone\" because it is an unpleasant growling sound. The wood resonance appears to be split into two frequencies by the driving force of the sounding string. These two periodic resonances beat with each other. This wolf tone must be eliminated or significantly reduced for the cello to play the nearby notes with a pleasant tone. This can be accomplished by modifying the cello front plate, attaching a wolf eliminator (a metal cylinder or a rubber cylinder encased in metal), or moving the soundpost.
When a string is bowed or plucked to produce a note, the fundamental note is accompanied by higher frequency overtones. Each sound has a particular recipe of frequencies that combine to make the total sound.
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# Cello
## Playing technique {#playing_technique}
Playing the cello is done while seated with the instrument supported on the floor by the endpin. The right hand bows (or sometimes plucks) the strings to sound the notes. The left-hand fingertips stop the strings along their length, determining the pitch of each fingered note. Stopping the string closer to the bridge results in a higher-pitched sound because the vibrating string length has been shortened. On the contrary, a string stopped closer to the tuning pegs produces a lower sound. In the *neck* positions (which use just less than half of the fingerboard, nearest the top of the instrument), the thumb rests on the back of the neck, some people use their thumb as a marker of their position; in *thumb position* (a general name for notes on the remainder of the fingerboard) the thumb usually rests alongside the fingers on the string. Then, the side of the thumb is used to play notes. The fingers are normally held curved with each knuckle bent, with the fingertips in contact with the string. If a finger is required on two (or more) strings at once to play perfect fifths (in double stops or chords), it is used flat. The contact point can move slightly away from the nail to the finger\'s pad in slower or more expressive playing, allowing a fuller vibrato.
Vibrato is a small oscillation in the pitch of a note, usually considered an expressive technique. The closer towards the bridge the note is, the smaller the oscillation needed to create the effect. Harmonics played on the cello fall into two classes; natural and artificial. Natural harmonics are produced by lightly touching (but not depressing) the string at certain places and then bowing (or, rarely, plucking) the string. For example, the halfway point of the string will produce a harmonic that is one octave above the unfingered (open) string. Natural harmonics only produce notes that are part of the harmonic series on a particular string. Artificial harmonics (also called false harmonics or stopped harmonics), in which the player depresses the string fully with one finger while touching the same string lightly with another finger, can produce any note above middle C. Glissando (Italian for \"sliding\") is an effect achieved by sliding the finger up or down the fingerboard without releasing the string. This causes the pitch to rise and fall smoothly, without separate, discernible steps.
In cello playing, the bow is much like the breath of a wind instrument player. Arguably, it is a major factor in the expressiveness of the playing. The right hand holds the bow and controls the duration and character of the notes. In general, the bow is drawn across the strings roughly halfway between the end of the fingerboard and the bridge, in a direction perpendicular to the strings; however, the player may wish to move the bow\'s point of contact higher or lower depending on the desired sound. The bow is held and manipulated with all five fingers of the right hand, with the thumb opposite the fingers and closer to the cellist\'s body. Tone production and volume of sound depend on a combination of several factors. The four most important ones are *weight* applied to the string, the *angle* of the bow on the string, bow *speed*, and the *point of contact* of the bow hair with the string (sometimes abbreviated WASP).
Double stops involve the playing of two notes simultaneously. Two strings are fingered at once, and the bow is drawn to sound them both. Often, in pizzicato playing, the string is plucked directly with the fingers or thumb of the right hand. However, the strings may be plucked with a finger of the left hand in certain advanced pieces, either so that the cellist can play bowed notes on another string along with pizzicato notes or because the speed of the piece would not allow the player sufficient time to pluck with the right hand. In musical notation, pizzicato is often abbreviated as \"pizz.\" The position of the hand in pizzicato is commonly slightly over the fingerboard and away from the bridge.
A player using the col legno technique strikes or rubs the strings with the wood of the bow rather than the hair. In spiccato playing, the bow still moves in a horizontal motion on the string but is allowed to bounce, generating a lighter, somewhat more percussive sound. In staccato, the player moves the bow a small distance and stops it on the string, making a short sound, the rest of the written duration being taken up by silence. Legato is a technique in which notes are smoothly connected without breaks. It is indicated by a slur (curved line) above or below -- depending on their position on the staff -- the notes of the passage that is to be played legato.
*Sul ponticello* (\"on the bridge\") refers to bowing closer to (or nearly on) the bridge, while *sul tasto* (\"on the fingerboard\") calls for bowing nearer to (or over) the end of the fingerboard. At its extreme, sul ponticello produces a harsh, shrill sound with emphasis on overtones and high harmonics. In contrast, sul tasto produces a more flute-like sound that emphasizes the note\'s fundamental frequency and produces softened overtones. Composers have used both techniques, particularly in an orchestral setting, for special sounds and effects.
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# Cello
## Sizes
Standard-sized cellos are referred to as \"full-size\" or \"`{{frac|4|4}}`{=mediawiki}\" but are also made in smaller (fractional) sizes, including `{{frac|15|16}}`{=mediawiki}, `{{frac|7|8}}`{=mediawiki}, `{{frac|3|4}}`{=mediawiki}, `{{frac|1|2}}`{=mediawiki}, `{{frac|1|4}}`{=mediawiki}, `{{frac|1|8}}`{=mediawiki}, `{{frac|1|10}}`{=mediawiki}, and `{{frac|1|16}}`{=mediawiki}. The fractions refer to volume rather than length, so a `{{frac|1|2}}`{=mediawiki} size cello is much longer than half the length of a full size. The smaller cellos are identical to standard cellos in construction, range, and usage, but are simply scaled-down for the benefit of children and shorter adults.
Cellos in sizes larger than `{{frac|4|4}}`{=mediawiki} do exist, and cellists with unusually large hands may require such a non-standard instrument. Cellos made before c. 1700 tended to be considerably larger than those made and commonly played today. Around 1680, changes in string-making technology made it possible to play lower-pitched notes on shorter strings. The cellos of Stradivari, for example, can be clearly divided into two models: the style made before 1702, characterized by larger instruments (of which only three exist in their original size and configuration), and the style made during and after 1707, when Stradivari began making smaller cellos. This later model is the design most commonly used by modern luthiers. The scale length of a `{{frac|4|4}}`{=mediawiki} cello is about 27+1/2 in. The new size offered fuller tonal projection and a greater range of expression. The instrument in this form was able to contribute to more pieces musically and offered the possibility of greater physical dexterity for the player to develop technique.
Approximate dimensions for `{{frac|4|4}}`{=mediawiki} size cello{{cite web url=<http://www.stevensoncases.co.uk/chart.htm> title=Table of \'cello measurements access-date=2007-10-26 last=Stevenson archive-url = <https://web.archive.org/web/20080104141444/http://www.stevensoncases.co.uk/chart.htm> \|archive-date = 2008-01-04}} Average size
---------------------------------------------------------------------------- ------------------------------------------------- ------------------------------------- ------------------------ ---------------- ------------------------------------------------------------------------------------------------------------------------------------ --------------
Approximate width horizontally from A peg to C peg ends
Back length excluding half-round where neck joins
Upper bouts (shoulders)
Lower bouts (hips)
Bridge height
Rib depth at shoulders including edges of front and back
Rib depth at hips including edges
Distance beneath fingerboard to surface of belly at neck join
Bridge to back total depth
Overall height excluding end pin
End pin unit and spike
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# Cello
## Accessories
thumb\|right\|upright=0.9\|Rosin is applied to bow hair to increase the friction of the bow on the strings. thumb\|upright=0.7\|A brass wolf tone eliminator typically placed on the G string (second string from the left) of a cello, between the bridge and the tailpiece. (The black rubber piece on the D string (third from the left) is a mute.)
There are many accessories for the cello.
- Cases are used to protect the cello and bow (or multiple bows).
- Rosin, made from resins tapped from conifers, is applied to the bow hair to increase the effectiveness of the friction, grip or bite, and allow proper sound production. Rosin may have additives to modify the friction such as beeswax, gold, silver or tin. Commonly, rosins are classified as either dark or light, referring to color.
- Endpin stops or straps (tradenames include Rock stop and Black Hole) keep the cello from sliding if the endpin does not have a rubber piece on the end, or if a floor is particularly slippery.
- Wolf tone eliminators are placed on cello strings between the tailpiece and the bridge to eliminate acoustic anomalies known as wolf tones or \"wolfs\".
- Mutes are used to change the sound of the cello by adding mass and stiffness to the bridge. They alter the overtone structure, modifying the timbre and reducing the overall volume of sound produced by the instrument.
- Metronomes provide a steady tempo by sounding out a certain number of beats per minute. This tool is often used to instill a sense of rhythm into a musician. It acts as a mirror for rhythmic stability, allowing the musician to analyze where they rush or drag a tempo.
- Fine tuners, located on the tailpiece, allow the cello to be tuned easily and with greater accuracy.
## Instrument makers {#instrument_makers}
Cellos are made by luthiers, specialists in building and repairing stringed instruments, ranging from guitars to violins. The following luthiers are notable for the cellos they have produced:
- Nicolò Amati and others in the Amati family
- Nicolò Gagliano
- Matteo Goffriller
- Giovanni Battista Guadagnini
- Andrea Guarneri
- Pietro Guarneri
- Charles Mennégand
- Domenico Montagnana
- Giovanni Battista Rogeri
- Francesco Ruggieri
- Stefano Scarampella
- Antonio Stradivari
- David Tecchler
- Carlo Giuseppe Testore
- Jean Baptiste Vuillaume
## Cellists
A person who plays the cello is called a *cellist*. For a list of notable cellists, see the list of cellists and :Category:Cellists.
## Famous instruments {#famous_instruments}
right\|thumbnail\|upright=0.7\|The Servais Stradivarius is preserved in the Smithsonian Institution\'s National Museum of American History
Specific instruments are famous (or become famous) for a variety of reasons. An instrument\'s notability may arise from its age, the fame of its maker, its physical appearance, its acoustic properties, and its use by notable performers. The most famous instruments are generally known for all of these things. The most highly prized instruments are now collector\'s items and are priced beyond the reach of most musicians. These instruments are typically owned by some kind of organization or investment group, which may loan the instrument to a notable performer. For example, the Davidov Stradivarius, which is currently in the possession of one of the most widely known living cellists, Yo-Yo Ma, is actually owned by the Vuitton Foundation.
Some notable cellos:
- the \"King\", by Andrea Amati, is one of the oldest known cellos, built between 1538 and 1560---it is in the collection of the National Music Museum in South Dakota.
- Servais Stradivarius is in the collection of the Smithsonian Institution, Washington DC.
- Batta-Piatigorsky Stradivarius, played by Gregor Piatigorsky.
- Davidov Stradivarius, played by Jacqueline du Pré, currently played by Yo-Yo Ma.
- Barjansky Stradivarius, played by Julian Lloyd Webber.
- Bonjour Stradivarius, played by Soo Bae.
- Paganini-Ladenburg Stradivarius, played by Clive Greensmith of the Tokyo String Quartet.
- Duport Stradivarius, formerly played by Mstislav Rostropovich
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# Conditional proof
A **conditional proof** is a proof that takes the form of asserting a conditional, and proving that the antecedent of the conditional necessarily leads to the consequent.
## Overview
The assumed antecedent of a conditional proof is called the **conditional proof assumption** (**CPA**). Thus, the goal of a conditional proof is to demonstrate that if the CPA were true, then the desired conclusion necessarily follows. The validity of a conditional proof does not require that the CPA be true, only that *if it were true* it would lead to the consequent.
Conditional proofs are of great importance in mathematics. Conditional proofs exist linking several otherwise unproven conjectures, so that a proof of one conjecture may immediately imply the validity of several others. It can be much easier to show a proposition\'s truth to follow from another proposition than to prove it independently.
A famous network of conditional proofs is the NP-complete class of complexity theory. There is a large number of interesting tasks (see *List of NP-complete problems*), and while it is not known if a polynomial-time solution exists for any of them, it is known that if such a solution exists for some of them, one exists for all of them. Similarly, the Riemann hypothesis has many consequences already proven.
## Symbolic logic {#symbolic_logic}
As an example of a conditional proof in symbolic logic, suppose we want to prove A → C (if A, then C) from the first two premises below:
----- ---------- -----------------------------------------------------------------------------
1\. A → B (\"If A, then B\")
2\. B → C (\"If B, then C\")
3\. A (conditional proof assumption, \"Suppose A is true\")
4\. B (follows from lines 1 and 3, modus ponens; \"If A then B; A, therefore B\")
5\. C (follows from lines 2 and 4, modus ponens; \"If B then C; B, therefore C\")
6\
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# Conjunction introduction
**Conjunction introduction** (often abbreviated simply as **conjunction** and also called **and introduction** or **adjunction**) is a valid rule of inference of propositional logic. The rule makes it possible to introduce a conjunction into a logical proof. It is the inference that if the proposition $P$ is true, and the proposition $Q$ is true, then the logical conjunction of the two propositions $P$ and $Q$ is true. For example, if it is true that \"it is raining\", and it is true that \"the cat is inside\", then it is true that \"it is raining and the cat is inside\". The rule can be stated:
$$\frac{P,Q}{\therefore P \land Q}$$
where the rule is that wherever an instance of \"$P$\" and \"$Q$\" appear on lines of a proof, a \"$P \land Q$\" can be placed on a subsequent line
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# English in the Commonwealth of Nations
The use of the English language in current and former countries of the Commonwealth was largely inherited from British colonisation, with some exceptions. English forms part of the Commonwealth\'s common culture and serves as the medium of inter-Commonwealth relations.
***Commonwealth English*** refers to English as practised in the Commonwealth; the term is most often interchangeable with *British English*, but is also used to distinguish between British English and that in the rest of the Commonwealth. English in the Commonwealth is diverse, and many regions have developed their own local varieties of the language. The official status of English varies; in Bangladesh, it lacks any but is widely used, and likewise in Cyprus, it is not official but is used as the *\[\[lingua franca\]\]*.
Written English in current and former Commonwealth countries generally favours British English spelling as opposed to that of American English, with some exceptions, particularly in Canada, where there are strong influences from neighbouring American English.
## Native varieties {#native_varieties}
Southern Hemisphere native varieties of English began to develop during the 18th century, with the colonisation of Australasia and South Africa. Australian English and New Zealand English are closely related to each other and share some similarities with South African English. Nonetheless, South African English has unique influences from indigenous African languages, and Dutch influences inherited alongside the evolution of Afrikaans, while New Zealand English has a lot of influences from the Māori language.
Canadian English contains elements of British English and American English, as well as many Canadianisms and some French influences. It is the product of several waves of immigration and settlement, from Britain, Ireland, France, the United States, and around the world, over a period of more than two centuries. In many Commonwealth countries, there exists a relatively small native Anglophone minority amongst a larger population who speak English as a second language; Anglo-Indians speak English as their mother tongue, but it is not the first language of most Indians.
### Africa
In addition to South Africa, a number of Commonwealth countries in Africa have native varieties of English. A community of native English speakers exists in Zimbabwe; the country\'s dialect bears features of British English, South African English and other Southern Hemisphere varieties of Commonwealth English. Also in Southern Africa and with historical influence from South Africa, Namibia and Botswana have their own dialects, with smaller native English-speaking populations. The same is true of Kenya and Uganda in East Africa.
### Caribbean
Caribbean English is drawn from British English and West African languages. It is influenced by constant contact with English-based Creoles. There is considerable influence from Hindustani and other South Asian languages in countries with language Indian populations, including Trinidad and Tobago, and Guyana. Jamaican English and Barbadian English bear influences of Irish English.
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# English in the Commonwealth of Nations
## Non-native varieties {#non_native_varieties}
Second-language varieties of English in Africa and Asia have often undergone \"indigenisation\"; that is, each English-speaking community has developed (or is in the process of developing) its own standards of usage, often under the influence of local languages. These dialects are sometimes referred to as *New Englishes* (McArthur, p. 36); most of them inherited non-rhoticity from Southern British English.
### Africa {#africa_1}
Several dialects of West African English exist, with considerable regional variation, though there is a set of common tendencies of pronunciation. Nigerian and Ghanaian English are the varieties with the largest number of speakers; English also holds official or national status in Sierra Leone, Cameroon's Anglophone provinces, the Gambia, and Saint Helena, a British territory. It also holds official status in Liberia, which is not a Commonwealth country but rather has a history connected to the United States of America.
National varieties of English are also spoken in Kenya, Uganda, and Tanzania.
Prior to Togo\'s admission at the 2022 Commonwealth Heads of Government Meeting, Togolese Foreign Minister Robert Dussey said that he expected Commonwealth membership to provide opportunities for Togolese citizens to learn English, and remarked that the country sought closer ties with the Anglophone world.
### Asia
#### Hong Kong {#hong_kong}
Hong Kong ceased to be part of the Commonwealth by virtue of being a British territory in 1997. Nonetheless, the English language there still enjoys official status.
#### Indian subcontinent {#indian_subcontinent}
English was introduced to the subcontinent by the British Raj. India has the largest English-speaking population in the Commonwealth, although comparatively very few speakers of Indian English are first-language speakers. The same is true of English spoken in other parts of South Asia, including Pakistani English, Sri Lankan English, Bangladeshi English and Myanmar English; though Myanmar is not a Commonwealth country, English is the mother tongue of the Anglo-Burmese population. South Asian English is fairly homogeneous across the subcontinent, though there are some differences based on various regional factors.
#### Malay Archipelago {#malay_archipelago}
Southeast Asian English includes Singapore English, Malaysian English, and Brunei English as well as other varieties in non-Commonwealth countries; it is not only the result of British colonisation but also American colonisation (as in the case of the Philippines) and globalisation. It has interacted with diverse local ecologies, shaping its form, function and status in the region
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# Charles McCarry
**Charles McCarry** (June 14, 1930 -- February 26, 2019) was an American writer, primarily of spy fiction, and a former undercover operative for the Central Intelligence Agency.
## Biography
McCarry\'s family came from The Berkshires area of western Massachusetts. He was born in Pittsfield, and lived in Virginia. He graduated from Dalton High School.
McCarry began his writing career in the United States Army as a correspondent for *Stars and Stripes*. He served from 1948 to 1951 and achieved the rank of sergeant. He received initial training at Fort Benning, Georgia, and was stationed in Germany for almost two years and at Camp Pickett, Virginia for about a year.
After his army service, he was a speechwriter in the early Administration of President Dwight D. Eisenhower. In 1958, at the invitation of Cord Meyer, he accepted a post with the CIA, for whom he traveled the globe as a deep cover operative. He took a leave of absence to work for the 1960 Nixon campaign, writing for vice-presidential candidate Henry Cabot Lodge. He left the CIA for the last time in 1967, becoming a writer of spy novels.
McCarry was also an editor-at-large for *National Geographic* and contributed pieces to *The New York Times*, *The Wall Street Journal*, *The Washington Post*, the *Saturday Evening Post*, and other national publications.
## Approach to writing {#approach_to_writing}
McCarry believed that \"the best novels are about ordinary things: love, betrayal, death, trust, loneliness, marriage, fatherhood.\" In 1988 McCarry described the themes of his novels to date as \"ordinary things -- love, death, betrayal and the American dream.\"
McCarry wrote that: \"After I resigned \[from the CIA\], intending to spend the rest of my life writing fiction and knowing what tricks the mind can play when the gates are thrown wide open, as they are by the act of writing, between the imagination and that part of the brain in which information is stored, I took the precaution of writing a closely remembered narrative of my clandestine experiences. After correcting the manuscript, I burned it. What I kept for my own use was the atmosphere of secret life: How it worked on the five senses and what it did to the heart and mind. All the rest went up in flames, setting me free henceforth to make it all up. In all important matters, such as the creation of characters and the invention of plots, with rare and minor exceptions, that is what I have done. And, as might be expected, when I have been weak enough to use something that really happened as an episode in a novel, it is that piece of scrap, buried in a landfill of the imaginary, readers invariably refuse to believe.\"
McCarry was an admirer of the work of Eric Ambler and W. Somerset Maugham, especially the latter\'s Ashenden stories. He was also an admirer of Richard Condon, author of *The Manchurian Candidate* (1959).
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# Charles McCarry
## Paul Christopher series {#paul_christopher_series}
Ten of McCarry\'s novels involve the life story of a fictional character named Paul Christopher, who grew up in pre-Nazi Germany, and later served in the Marines and became an operative for a U.S. government entity known as \"the Outfit\", meant to represent the Central Intelligence Agency.
These books are, in order of publication:
1. *The Miernik Dossier* (1973): Christopher investigates a possible Soviet spy in Geneva
2. *The Tears of Autumn* (1974): Christopher investigates the Kennedy Assassination
3. *The Secret Lovers* (1977): Christopher discovers a secret plot within the CIA
4. *The Better Angels* (1979): Christopher\'s cousins steal a Presidential election
5. *The Last Supper* (1983): introduction to Christopher\'s parents in pre-World War II Germany; Christopher is imprisoned in China
6. *The Bride of the Wilderness* (1988): historical novel concerning 17th-century Christopher ancestors
7. *Second Sight* (1991): released from a Chinese prison, Christopher meets a daughter he did not know he had
8. *Shelley\'s Heart* (1995): sequel to *The Better Angels*: Christopher\'s cousins cause a Presidential impeachment
9. *Old Boys* (2004): Christopher\'s old associates discover a plot involving terrorists and the fate of Christopher\'s mother
10. *Christopher\'s Ghosts* (2007): the story of Christopher\'s first love in pre-World War II Germany
Alternately, in chronological order of events depicted:
1. *Bride of the Wilderness* (Christopher\'s ancestors)
2. *Last Supper* \[in part\] (Christopher\'s parents)
3. *Christopher\'s Ghosts*
4. *The Miernik Dossier*
5. *Secret Lovers*
6. *The Tears of Autumn*
7. *Last Supper* \[in part\]
8. *The Better Angels*
9. *Second Sight* (Christopher is a peripheral character)
10. *Shelley\'s Heart*
11. *Old Boys* (Christopher is a peripheral character)
## Reception
*The Wall Street Journal* described McCarry in 2013 as \"the dean of American spy writers\". *The New Republic* magazine called him \"poet laureate of the CIA\"; and Otto Penzler described him as \"the greatest espionage writer that America has ever produced.\" Jonathan Yardley, Pulitzer Prize-winning critic for the *Washington Post*, calls him a \"\'serious\' novelist\" whose work may include \"the best novel ever written about life in high-stakes Washington, D.C.\" In 2004 P. J. O\'Rourke called him \"the best modern writer on the subject of intrigue.\"
## Adaptations
The film *Wrong is Right* (1982), starring Sean Connery, was loosely based on McCarry\'s novel, *The Better Angels* (1979).
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# Charles McCarry
## Other books and publications {#other_books_and_publications}
### Non-Paul Christopher novels {#non_paul_christopher_novels}
- *Lucky Bastard* (1999). A comic novel in which a likeable but amoral, devious, and oversexed politician (thought by many to evoke Bill Clinton, when in fact McCarry himself said he was thinking about John F Kennedy.) is controlled by a female eastern-bloc subversive.
- *Ark* (2011). Earth\'s wealthiest man attempts to save humanity from a coming apocalypse.
- *The Shanghai Factor* (2013). A rookie spy in China is drawn into the lonely, compartmentalized world of counterintelligence, and misunderstands everything that he and those around him are doing.
- *The Mulberry Bush* (2015). Explores the world of South America\'s elites and militant revolutionaries, and the role of lifelong personal passions and agendas in their work and that of intelligence operatives.
### Non-fiction {#non_fiction}
- *Citizen Nader* (1972)
- *Double Eagle: Ben Abruzzo, Maxie Anderson, Larry Newman* (1979)
- *The Great Southwest* (1980)
- *Isles of the Caribbean* (National Geographic Society, Washington, DC, 1980, co-author)
- *For the Record: From Wall Street to Washington* (1988, by Donald Regan with Charles McCarry)
- *Paths of Resistance: The Art and Craft of the Political Novel* (1989, with Isabel Allende, Marge Piercy, Robert Stone and Gore Vidal)
- *Inner Circles: How America Changed the World: a Memoir* (1992, by Alexander Haig with Charles McCarry)
- *Caveat: Realism, Reagan, and Foreign Policy* (1984, by Alexander Haig with Charles McCarry). Stories include: In March 1981, shortly after taking office, Ronald Reagan was shot; Secretary of State Haig appeared in the White House press room and announced, \"I am in charge here!\"
- *From the Field: A Collection of Writings from National Geographic* (1997, editor)
### Collections including McCarry\'s work {#collections_including_mccarrys_work}
- Harlan Coben, ed. *The Best American Mystery Stories: 2011* − includes \"The End of the String.\"
- Alan Furst, editor *The Book of Spies −* includes excerpt from *The Tears of Autumn*.
Otto Penzler, editor:
- *Agents of Treachery* − includes \"The End of the Sting.\"
- *The 50 Greatest Mysteries of All Time* − includes \"The Hand of Carlos\"
- *The Big Book of Espionage* − includes \"The Hand of Carlos\"
### Short stories (fiction) {#short_stories_fiction}
- \"The Saint Who Said No\", *Saturday Evening Post*, December 9, 1961
- \"The Hand of Carlos\", *Armchair Detective* (1992)
- \"The End of the String\"
### Magazine articles (non-fiction) {#magazine_articles_non_fiction}
- \"A \..
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# Claus Sluter
thumb\|upright=1.4\|David and Jeremiah from the *Well of Moses* **Claus Sluter** (1340s in Haarlem -- 1405 or 1406 in Dijon) was a Dutch sculptor, living in the Duchy of Burgundy from about 1380. He was the most important northern European sculptor of his age and is considered a pioneer of the \"northern realism\" of the Early Netherlandish painting that came into full flower with the work of Jan van Eyck and others in the next generation.
## Life
The name \"Claes de Slutere van Herlam\" is inscribed in the Register of the Corporation of Stonemasons and Sculptors of Brussels around the years 1379/1380. He then moved to the Burgundian capital of Dijon, where from 1385 to 1389 he was the assistant of Jean de Marville, court sculptor to Philip the Bold, Duke of Burgundy. From 1389 to his death he was court sculptor himself, with the rank of *valet de chambre*. He was succeeded by his nephew Claus de Werve.
## Work
Sluter\'s most significant work is the so-called *Well of Moses* (1395--1403), or the Great Cross. It was created for the Carthusian monastery of Champmol, which was founded by Philip the Bold right outside Dijon in 1383. For many years, the top portion was thought to have included (along with Christ on a cross), sculptures of the Virgin and John the Evangelist. However it was more likely just Christ, with Mary Magdalene kneeling at the foot of the cross. The cross, and whatever was on the terrace below, was destroyed at some point after 1736 and before 1789, probable because the roof of the building protecting the monument collapsed. Some fragments from the original Cross are preserved in the Musée Archéologique de Dijon. Life-sized figures representing Old Testament prophets and kings (Moses, David, Daniel, Jeremiah, Zachariah, and Isaiah) stand around the base, holding phylacteries and books inscribed with verses from their respective texts, which were interpreted in the Middle Ages as typological prefigurations of the sacrifice of Christ. The work\'s physical structure, in which the Old Testament figures support those of the New Dispensation, literalizes the typological iconography. The pedestal surmounts a hexagonal fountain. The entire monument is executed in limestone quarried from Tonnerre and Asnières.
upright=1.4\|thumb\|Monumental portal of the Chartreuse of Champmol at Dijon by Claus Sluter The portal of the former mortuary chapel of Champmol is positioned a few feet away from the Well of Moses. It consists of three sculptural groups by Sluter: a standing Madonna and Child at the trumeau; the duke and St. John, his patron saint, at the left jamb and the duchess and her patron saint, Catherine, at the right one. Sluter was also responsible for the main part of the work on Philip\'s tomb, which (restored and partly reconstructed) has been moved to the Museum of Fine Arts which is housed in the former ducal palace in Dijon.
Sluter was one of the sculptors of the pleurants, or mourners, which occupy niches below the tombs of Philip the Bold, his wife Margaret, and John the Fearless
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# Cotangent space
In differential geometry, the **cotangent space** is a vector space associated with a point $x$ on a smooth (or differentiable) manifold $\mathcal M$; one can define a cotangent space for every point on a smooth manifold. Typically, the cotangent space, $T^*_x\!\mathcal M$ is defined as the dual space of the tangent space at *$x$*, $T_x\mathcal M$, although there are more direct definitions (see below). The elements of the cotangent space are called **cotangent vectors** or **tangent covectors**.
## Properties
All cotangent spaces at points on a connected manifold have the same dimension, equal to the dimension of the manifold. All the cotangent spaces of a manifold can be \"glued together\" (i.e. unioned and endowed with a topology) to form a new differentiable manifold of twice the dimension, the cotangent bundle of the manifold.
The tangent space and the cotangent space at a point are both real vector spaces of the same dimension and therefore isomorphic to each other via many possible isomorphisms. The introduction of a Riemannian metric or a symplectic form gives rise to a natural isomorphism between the tangent space and the cotangent space at a point, associating to any tangent covector a canonical tangent vector.
## Formal definitions {#formal_definitions}
### Definition as linear functionals {#definition_as_linear_functionals}
Let $\mathcal M$ be a smooth manifold and let $x$ be a point in $\mathcal M$. Let $T_x\mathcal M$ be the tangent space at $x$. Then the cotangent space at $x$ is defined as the dual space of `{{nowrap|<math>T_x\mathcal M</math>:}}`{=mediawiki}
$$T^*_x\!\mathcal M = (T_x \mathcal M)^*$$
Concretely, elements of the cotangent space are linear functionals on $T_x\mathcal M$. That is, every element $\alpha\in T^*_x\mathcal M$ is a linear map
$$\alpha:T_x\mathcal M \to F$$
where $F$ is the underlying field of the vector space being considered, for example, the field of real numbers. The elements of $T^*_x\!\mathcal M$ are called cotangent vectors.
### Alternative definition {#alternative_definition}
In some cases, one might like to have a direct definition of the cotangent space without reference to the tangent space. Such a definition can be formulated in terms of equivalence classes of smooth functions on $\mathcal M$. Informally, we will say that two smooth functions *f* and *g* are equivalent at a point $x$ if they have the same first-order behavior near $x$, analogous to their linear Taylor polynomials; two functions *f* and *g* have the same first order behavior near $x$ if and only if the derivative of the function *f* − *g* vanishes at $x$. The cotangent space will then consist of all the possible first-order behaviors of a function near $x$.
Let $\mathcal M$ be a smooth manifold and let $x$ be a point in $\mathcal M$. Let $I_x$be the ideal of all functions in $C^\infty\! (\mathcal M)$ vanishing at $x$, and let $I_x^2$ be the set of functions of the form $\sum_i f_i g_i$, where $f_i, g_i \in I_x$. Then $I_x$ and $I_x^2$ are both real vector spaces and the cotangent space can be defined as the quotient space $T^*_x\!\mathcal M = I_x/I^2_x$ by showing that the two spaces are isomorphic to each other.
This formulation is analogous to the construction of the cotangent space to define the Zariski tangent space in algebraic geometry. The construction also generalizes to locally ringed spaces.
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# Cotangent space
## The differential of a function {#the_differential_of_a_function}
Let $M$ be a smooth manifold and let $f\in C^\infty(M)$ be a smooth function. The differential of $f$ at a point $x$ is the map
$$\mathrm d f_x(X_x) = X_x(f)$$ where $X_x$ is a tangent vector at $x$, thought of as a derivation. That is $X(f)=\mathcal{L}_Xf$ is the Lie derivative of $f$ in the direction $X$, and one has $\mathrm df(X)=X(f)$. Equivalently, we can think of tangent vectors as tangents to curves, and write
$$\mathrm d f_x(\gamma'(0))=(f\circ\gamma)'(0)$$ In either case, $\mathrm df_x$ is a linear map on $T_xM$ and hence it is a tangent covector at $x$.
We can then define the differential map $\mathrm d:C^\infty(M)\to T_x^*(M)$ at a point $x$ as the map which sends $f$ to $\mathrm df_x$. Properties of the differential map include:
1. $\mathrm d$ is a linear map: $\mathrm d(af+bg)=a\mathrm df + b\mathrm dg$ for constants $a$ and $b$,
2. $\mathrm d(fg)_x=f(x)\mathrm dg_x+g(x)\mathrm df_x$
The differential map provides the link between the two alternate definitions of the cotangent space given above. Since for all $f \in I^2_x$ there exist $g_i, h_i \in I_x$ such that $f=\sum_i g_i h_i$, we have,
$\begin{array}{rcl}
\mathrm d f_x & = & \sum_i \mathrm d (g_i h_i)_x \\
& = & \sum_i (g_i(x)\mathrm d(h_i)_x+\mathrm d(g_i)_x h_{i}(x)) \\
& = & \sum_i (0\mathrm d(h_i)_x+\mathrm d(g_i)_x 0) \\
& = & 0
\end{array}$
So that all function in $I^2_x$ have differential zero, it follows that for every two functions $f \in I^2_x$, $g \in I_x$, we have $\mathrm d (f+g)=\mathrm d (g)$. We can now construct an isomorphism between $T^*_x\!\mathcal M$ and $I_x/I^2_x$ by sending linear maps $\alpha$ to the corresponding cosets $\alpha + I^2_x$. Since there is a unique linear map for a given kernel and slope, this is an isomorphism, establishing the equivalence of the two definitions.
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# Cotangent space
## The pullback of a smooth map {#the_pullback_of_a_smooth_map}
Just as every differentiable map $f:M\to N$ between manifolds induces a linear map (called the *pushforward* or *derivative*) between the tangent spaces
$$f_{*}^{}\colon T_x M \to T_{f(x)} N$$ every such map induces a linear map (called the *pullback*) between the cotangent spaces, only this time in the reverse direction:
$$f^{*}\colon T_{f(x)}^{*} N \to T_{x}^{*} M .$$ The pullback is naturally defined as the dual (or transpose) of the pushforward. Unraveling the definition, this means the following:
$$(f^{*}\theta)(X_x) = \theta(f_{*}^{}X_x) ,$$ where $\theta\in T_{f(x)}^*N$ and $X_x\in T_xM$. Note carefully where everything lives.
If we define tangent covectors in terms of equivalence classes of smooth maps vanishing at a point then the definition of the pullback is even more straightforward. Let $g$ be a smooth function on $N$ vanishing at $f(x)$. Then the pullback of the covector determined by $g$ (denoted $\mathrm d g$) is given by
$$f^{*}\mathrm dg = \mathrm d(g \circ f).$$ That is, it is the equivalence class of functions on $M$ vanishing at $x$ determined by $g\circ f$.
## Exterior powers {#exterior_powers}
The $k$-th exterior power of the cotangent space, denoted $\Lambda^k(T_x^*\mathcal{M})$, is another important object in differential and algebraic geometry. Vectors in the $k$-th exterior power, or more precisely sections of the $k$-th exterior power of the cotangent bundle, are called differential $k$-forms. They can be thought of as alternating, multilinear maps on $k$ tangent vectors. For this reason, tangent covectors are frequently called *one-forms*
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# Cnidaria
**Cnidaria** (`{{IPAc-en|n|ᵻ|ˈ|d|ɛər|i|ə|,_|n|aɪ|-}}`{=mediawiki} `{{respell|nih|DAIR|ee|ə|,_|ny|-}}`{=mediawiki}) is a phylum under kingdom Animalia containing over 11,000 species of aquatic invertebrates found both in freshwater and marine environments (predominantly the latter), including jellyfish, hydroids, sea anemones, corals and some of the smallest marine parasites. Their distinguishing features are an uncentralized nervous system distributed throughout a gelatinous body and the presence of cnidocytes or cnidoblasts, specialized cells with ejectable flagella used mainly for envenomation and capturing prey. Their bodies consist of mesoglea, a non-living, jelly-like substance, sandwiched between two layers of epithelium that are mostly one cell thick. Cnidarians are also some of the few animals that can reproduce both sexually and asexually.
Cnidarians mostly have two basic body forms: swimming medusae and sessile polyps, both of which are radially symmetrical with mouths surrounded by tentacles that bear cnidocytes, which are specialized stinging cells used to capture prey. Both forms have a single orifice and body cavity that are used for digestion and respiration. Many cnidarian species produce colonies that are single organisms composed of medusa-like or polyp-like zooids, or both (hence they are trimorphic). Cnidarians\' activities are coordinated by a decentralized nerve net and simple receptors. Cnidarians also have rhopalia, which are involved in gravity sensing and sometimes chemoreception. Several free-swimming species of Cubozoa and Scyphozoa possess balance-sensing statocysts, and some have simple eyes. Not all cnidarians reproduce sexually, but many species have complex life cycles of asexual polyp stages and sexual medusae stages. Some, however, omit either the polyp or the medusa stage, and the parasitic classes evolved to have neither form.
Cnidarians were formerly grouped with ctenophores, also known as comb jellies, in the phylum Coelenterata, but increasing awareness of their differences caused them to be placed in separate phyla. Most cnidarians are classified into four main groups: the almost wholly sessile Anthozoa (sea anemones, corals, sea pens); swimming Scyphozoa (jellyfish); Cubozoa (box jellies); and Hydrozoa (a diverse group that includes all the freshwater cnidarians as well as many marine forms, and which has both sessile members, such as *Hydra*, and colonial swimmers (such as the Portuguese man o\' war)). Staurozoa have recently been recognised as a class in their own right rather than a sub-group of Scyphozoa, and the highly derived parasitic Myxozoa and Polypodiozoa were firmly recognized as cnidarians only in 2007.
Most cnidarians prey on organisms ranging in size from plankton to animals several times larger than themselves, but many obtain much of their nutrition from symbiotic dinoflagellates, and a few are parasites. Many are preyed on by other animals including starfish, sea slugs, fish, turtles, and even other cnidarians. Many scleractinian corals---which form the structural foundation for coral reefs---possess polyps that are filled with symbiotic photo-synthetic zooxanthellae. While reef-forming corals are almost entirely restricted to warm and shallow marine waters, other cnidarians can be found at great depths, in polar regions, and in freshwater.
Cnidarians are a very ancient phylum, with fossils having been found in rocks formed about `{{ma|580}}`{=mediawiki} during the Ediacaran period, preceding the Cambrian Explosion. Other fossils show that corals may have been present shortly before `{{ma|490}}`{=mediawiki} and diversified a few million years later. Molecular clock analysis of mitochondrial genes suggests an even older age for the crown group of cnidarians, estimated around `{{ma|741}}`{=mediawiki}, almost 200 million years before the Cambrian period, as well as before any fossils. Recent phylogenetic analyses support monophyly of cnidarians, as well as the position of cnidarians as the sister group of bilaterians.
## Etymology
The term *cnidaria* derives from the Ancient Greek word *knídē* (κνίδη "nettle"), signifying the coiled thread reminiscent of cnidocytes.
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# Cnidaria
## Distinguishing features {#distinguishing_features}
Cnidarians form a phylum of animals that are more complex than sponges, about as complex as ctenophores (comb jellies), and less complex than bilaterians, which include almost all other animals. Both cnidarians and ctenophores are more complex than sponges as they have: cells bound by inter-cell connections and carpet-like basement membranes; muscles; nervous systems; and **some** have sensory organs. Cnidarians are distinguished from all other animals by having cnidocytes that fire harpoon-like structures that are mainly used to capture prey. In some species, cnidocytes can also be used as anchors. Cnidarians are also distinguished by the fact that they have only one opening in their body for ingestion and excretion i.e. they do not have a separate mouth and anus.
Like sponges and ctenophores, cnidarians have two main layers of cells that sandwich a middle layer of jelly-like material, which is called the mesoglea in cnidarians; more complex animals have three main cell layers and no intermediate jelly-like layer. Hence, cnidarians and ctenophores have traditionally been labelled diploblastic, along with sponges. However, both cnidarians and ctenophores have a type of muscle that, in more complex animals, arises from the middle cell layer. As a result, some recent text books classify ctenophores as triploblastic, and it has been suggested that cnidarians evolved from triploblastic ancestors.
Sponges Cnidarians Ctenophores Bilateria
------------------------------------------------------------- ----------------------------------------------------------------------------- -------------------------------------------- ---------------------- -------------------
Cnidocytes No Yes No
Colloblasts No Yes No
Digestive and circulatory organs No Yes
Number of main cell layers Two, with jelly-like layer between them Two Two Three
Cells in each layer bound together cell-adhesion molecules, but no basement membranes except Homoscleromorpha. inter-cell connections; basement membranes
Sensory organs No Yes
Number of cells in middle \"jelly\" layer Many Few (Not applicable)
Cells in outer layers can move inwards and change functions Yes No (Not applicable)
Nervous system No Yes, simple Simple to complex
Muscles None Mostly epitheliomuscular Mostly myoepithelial Mostly myocytes
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# Cnidaria
## Description
### Basic body forms {#basic_body_forms}
Most adult cnidarians appear as either free-swimming medusae or sessile polyps, and many hydrozoans species are known to alternate between the two forms.
Both are radially symmetrical, like a wheel and a tube respectively. Since these animals have no heads, their ends are described as \"oral\" (nearest the mouth) and \"aboral\" (furthest from the mouth).
Most have fringes of tentacles equipped with cnidocytes around their edges, and medusae generally have an inner ring of tentacles around the mouth. Some hydroids may consist of colonies of zooids that serve different purposes, such as defence, reproduction and catching prey. The mesoglea of polyps is usually thin and often soft, but that of medusae is usually thick and springy, so that it returns to its original shape after muscles around the edge have contracted to squeeze water out, enabling medusae to swim by a sort of jet propulsion.
### Skeletons
In medusae, the only supporting structure is the mesoglea. *Hydra* and most sea anemones close their mouths when they are not feeding, and the water in the digestive cavity then acts as a hydrostatic skeleton, rather like a water-filled balloon. Other polyps such as *Tubularia* use columns of water-filled cells for support. Sea pens stiffen the mesoglea with calcium carbonate spicules and tough fibrous proteins, rather like sponges.
In some colonial polyps, a chitinous epidermis gives support and some protection to the connecting sections and to the lower parts of individual polyps. A few polyps collect materials such as sand grains and shell fragments, which they attach to their outsides. Some colonial sea anemones stiffen the mesoglea with sediment particles.
A mineralized exoskeleton made of calcium carbonate is found in subphylum Anthozoa in the order Scleractinia (stony corals; class Hexacorallia) and the class Octocorallia, and in subphylum Medusozoa in three hydrozoan families in order Anthoathecata; Milleporidae, Stylasteridae and Hydractiniidae (the latter with a mix of calcified and uncalcified species).
### Main cell layers {#main_cell_layers}
Cnidaria are diploblastic animals; in other words, they have two main cell layers, while more complex animals are triploblasts having three main layers. The two main cell layers of cnidarians form epithelia that are mostly one cell thick, and are attached to a fibrous basement membrane, which they secrete. They also secrete the jelly-like mesoglea that separates the layers. The layer that faces outwards, known as the ectoderm (\"outside skin\"), generally contains the following types of cells:
- Epitheliomuscular cells whose bodies form part of the epithelium but whose bases extend to form muscle fibers in parallel rows. The fibers of the outward-facing cell layer generally run at right angles to the fibers of the inward-facing one. In Anthozoa (anemones, corals, etc.) and Scyphozoa (jellyfish), the mesoglea also contains some muscle cells.
- Cnidocytes, the harpoon-like \"nettle cells\" that give the phylum Cnidaria its name. These appear between or sometimes on top of the muscle cells.
- Nerve cells. Sensory cells appear between or sometimes on top of the muscle cells, and communicate via synapses (gaps across which chemical signals flow) with motor nerve cells, which lie mostly between the bases of the muscle cells. Some form a simple nerve net.
- Interstitial cells, which are unspecialized and can replace lost or damaged cells by transforming into the appropriate types. These are found between the bases of muscle cells.
In addition to epitheliomuscular, nerve and interstitial cells, the inward-facing gastroderm (\"stomach skin\") contains gland cells that secrete digestive enzymes. In some species it also contains low concentrations of cnidocytes, which are used to subdue prey that is still struggling.
The mesoglea contains small numbers of amoeba-like cells, and muscle cells in some species. However, the number of middle-layer cells and types are much lower than in sponges.
### Polymorphism
Polymorphism refers to the occurrence of structurally and functionally more than two different types of individuals within the same organism. It is a characteristic feature of cnidarians, particularly the polyp and medusa forms, or of zooids within colonial organisms like those in Hydrozoa. In Hydrozoans, colonial individuals arising from individual zooids will take on separate tasks. For example, in *Obelia* there are feeding individuals, the gastrozooids; the individuals capable of asexual reproduction only, the gonozooids, blastostyles and free-living or sexually reproducing individuals, the medusae.
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# Cnidaria
## Description
### Cnidocytes
These \"nettle cells\" function as harpoons, since their payloads remain connected to the bodies of the cells by threads. Three types of cnidocytes are known:
- Nematocysts inject venom into prey, and usually have barbs to keep them embedded in the victims. Most species have nematocysts.
- Spirocysts do not penetrate the victim or inject venom, but entangle it by means of small sticky hairs on the thread.
- Ptychocysts are not used for prey capture --- instead the threads of discharged ptychocysts are used for building protective tubes in which their owners live. Ptychocysts are found only in the order Ceriantharia, tube anemones.
The main components of a cnidocyte are:
- A cilium (fine hair) which projects above the surface and acts as a trigger. Spirocysts do not have cilia.
- A tough capsule, the cnida, which houses the thread, its payload and a mixture of chemicals that may include venom or adhesives or both. (\"cnida\" is derived from the Greek word κνίδη, which means \"nettle\")
- A tube-like extension of the wall of the cnida that points into the cnida, like the finger of a rubber glove pushed inwards. When a cnidocyte fires, the finger pops out. If the cell is a venomous nematocyte, the \"finger\"\'s tip reveals a set of barbs that anchor it in the prey.
- The thread, which is an extension of the \"finger\" and coils round it until the cnidocyte fires. The thread is usually hollow and delivers chemicals from the cnida to the target.
- An operculum (lid) over the end of the cnida. The lid may be a single hinged flap or three flaps arranged like slices of pie.
- The cell body, which produces all the other parts.
It is difficult to study the firing mechanisms of cnidocytes as these structures are small but very complex. At least four hypotheses have been proposed:
- Rapid contraction of fibers round the cnida may increase its internal pressure.
- The thread may be like a coiled spring that extends rapidly when released.
- In the case of *Chironex* (the \"sea wasp\"), chemical changes in the cnida\'s contents may cause them to expand rapidly by polymerization.
- Chemical changes in the liquid in the cnida make it a much more concentrated solution, so that osmotic pressure forces water in very rapidly to dilute it. This mechanism has been observed in nematocysts of the class Hydrozoa, sometimes producing pressures as high as 140 atmospheres, similar to that of scuba air tanks, and fully extending the thread in as little as 2 milliseconds (0.002 second).
Cnidocytes can only fire once, and about 25% of a hydra\'s nematocysts are lost from its tentacles when capturing a brine shrimp. Used cnidocytes have to be replaced, which takes about 48 hours. To minimise wasteful firing, two types of stimulus are generally required to trigger cnidocytes: nearby sensory cells detect chemicals in the water, and their cilia respond to contact. This combination prevents them from firing at distant or non-living objects. Groups of cnidocytes are usually connected by nerves and, if one fires, the rest of the group requires a weaker minimum stimulus than the cells that fire first.
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# Cnidaria
## Description
### Locomotion
Medusae swim by a form of jet propulsion: muscles, especially inside the rim of the bell, squeeze water out of the cavity inside the bell, and the springiness of the mesoglea powers the recovery stroke. Since the tissue layers are very thin, they provide too little power to swim against currents and just enough to control movement within currents.
Hydras and some sea anemones can move slowly over rocks and sea or stream beds by various means: creeping like snails, crawling like inchworms, or by somersaulting. A few can swim clumsily by waggling their bases.
### Nervous system and senses {#nervous_system_and_senses}
Cnidarians are generally thought to have no brains or even central nervous systems. However, they do have integrative areas of neural tissue that could be considered some form of centralization. Most of their bodies are innervated by decentralized nerve nets that control their swimming musculature and connect with sensory structures, though each clade has slightly different structures. These sensory structures, usually called rhopalia, can generate signals in response to various types of stimuli such as light, pressure, chemical changes, and much more. Medusa usually have several of them around the margin of the bell that work together to control the motor nerve net, that directly innervates the swimming muscles. Most cnidarians also have a parallel system. In scyphozoans, this takes the form of a diffuse nerve net, which has modulatory effects on the nervous system. As well as forming the \"signal cables\" between sensory neurons and motoneurons, intermediate neurons in the nerve net can also form ganglia that act as local coordination centers. Communication between nerve cells can occur by chemical synapses or gap junctions in hydrozoans, though gap junctions are not present in all groups. Cnidarians have many of the same neurotransmitters as bilaterians, including chemicals such as glutamate, GABA, and glycine. Serotonin, dopamine, noradrenaline, octopamine, histamine, and acetylcholine, on the other hand, are absent.
This structure ensures that the musculature is excited rapidly and simultaneously, and can be directly stimulated from any point on the body, and it also is better able to recover after injury.
Medusae and complex swimming colonies such as siphonophores and chondrophores sense tilt and acceleration by means of statocysts, chambers lined with hairs which detect the movements of internal mineral grains called statoliths. If the body tilts in the wrong direction, the animal rights itself by increasing the strength of the swimming movements on the side that is too low. Most species have ocelli (\"simple eyes\"), which can detect sources of light. However, the agile box jellyfish are unique among Medusae because they possess four kinds of true eyes that have retinas, corneas and lenses. Although the eyes probably do not form images, Cubozoa can clearly distinguish the direction from which light is coming as well as negotiate around solid-colored objects.
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# Cnidaria
## Description
### Feeding and excretion {#feeding_and_excretion}
Cnidarians feed in several ways: predation, absorbing dissolved organic chemicals, filtering food particles out of the water, obtaining nutrients from symbiotic algae within their cells, and parasitism. Most obtain the majority of their food from predation but some, including the corals *Hetroxenia* and *Leptogorgia*, depend almost completely on their endosymbionts and on absorbing dissolved nutrients. Cnidaria give their symbiotic algae carbon dioxide, some nutrients, and protection against predators.
Predatory species use their cnidocytes to poison or entangle prey, and those with venomous nematocysts may start digestion by injecting digestive enzymes. The \"smell\" of fluids from wounded prey makes the tentacles fold inwards and wipe the prey off into the mouth. In medusae, the tentacles around the edge of the bell are often short and most of the prey capture is done by \"oral arms\", which are extensions of the edge of the mouth and are often frilled and sometimes branched to increase their surface area. These \"oral arms\" aid in cnidarians\' ability to move prey towards their mouth once it has been poisoned and entangled. Medusae often trap prey or suspended food particles by swimming upwards, spreading their tentacles and oral arms and then sinking. In species for which suspended food particles are important, the tentacles and oral arms often have rows of cilia whose beating creates currents that flow towards the mouth, and some produce nets of mucus to trap particles. Their digestion is both intra and extracellular.
Once the food is in the digestive cavity, gland cells in the gastroderm release enzymes that reduce the prey to slurry, usually within a few hours. This circulates through the digestive cavity and, in colonial cnidarians, through the connecting tunnels, so that gastroderm cells can absorb the nutrients. Absorption may take a few hours, and digestion within the cells may take a few days. The circulation of nutrients is driven by water currents produced by cilia in the gastroderm or by muscular movements or both, so that nutrients reach all parts of the digestive cavity. Nutrients reach the outer cell layer by diffusion or, for animals or zooids such as medusae which have thick mesogleas, are transported by mobile cells in the mesoglea.
Indigestible remains of prey are expelled through the mouth. The main waste product of cells\' internal processes is ammonia, which is removed by the external and internal water currents.
### Respiration
There are no respiratory organs, and both cell layers absorb oxygen from and expel carbon dioxide into the surrounding water. When the water in the digestive cavity becomes stale it must be replaced, and nutrients that have not been absorbed will be expelled with it. Some Anthozoa have ciliated grooves on their tentacles, allowing them to pump water out of and into the digestive cavity without opening the mouth. This improves respiration after feeding and allows these animals, which use the cavity as a hydrostatic skeleton, to control the water pressure in the cavity without expelling undigested food.
Cnidaria that carry photosynthetic symbionts may have the opposite problem, an excess of oxygen, which may prove toxic. The animals produce large quantities of antioxidants to neutralize the excess oxygen.
### Regeneration
All cnidarians can regenerate, allowing them to recover from injury and to reproduce asexually. Medusae have limited ability to regenerate, but polyps can do so from small pieces or even collections of separated cells. This enables corals to recover even after apparently being destroyed by predators.
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# Cnidaria
## Reproduction
### Sexual
Cnidarian sexual reproduction often involves a complex life cycle with both polyp and medusa stages. For example, in Scyphozoa (jellyfish) and Cubozoa (box jellies), a larva swims until it finds a good site, and then becomes a polyp. This grows normally but then absorbs its tentacles and splits horizontally into a series of disks that become juvenile medusae, a process called strobilation. The juveniles swim off and slowly grow to maturity, while the polyp re-grows and may continue strobilating periodically. The adult medusae have gonads in the gastroderm, and these release ova and sperm into the water in the breeding season.
This phenomenon of succession of differently organized generations (one asexually reproducing, sessile polyp, followed by a free-swimming medusa or a sessile polyp that reproduces sexually) is sometimes called \"alternation of asexual and sexual phases\" or \"metagenesis\", but should not be confused with the alternation of generations as found in plants.
Shortened forms of this life cycle are common, for example some oceanic scyphozoans omit the polyp stage completely, and cubozoan polyps produce only one medusa. Hydrozoa have a variety of life cycles. Some have no polyp stages and some (e.g. *hydra*) have no medusae. In some species, the medusae remain attached to the polyp and are responsible for sexual reproduction; in extreme cases these reproductive zooids may not look much like medusae. Meanwhile, life cycle reversal, in which polyps are formed directly from medusae without the involvement of sexual reproduction process, was observed in both Hydrozoa (*Turritopsis dohrnii* and *Laodicea undulata*) and Scyphozoa (*Aurelia* sp.1). Anthozoa have no medusa stage at all and the polyps are responsible for sexual reproduction.
Spawning is generally driven by environmental factors such as changes in the water temperature, and their release is triggered by lighting conditions such as sunrise, sunset or the phase of the moon. Many species of Cnidaria may spawn simultaneously in the same location, so that there are too many ova and sperm for predators to eat more than a tiny percentage --- one famous example is the Great Barrier Reef, where at least 110 corals and a few non-cnidarian invertebrates produce enough gametes to turn the water cloudy. These mass spawnings may produce hybrids, some of which can settle and form polyps, but it is not known how long these can survive. In some species the ova release chemicals that attract sperm of the same species.
The fertilized eggs develop into larvae by dividing until there are enough cells to form a hollow sphere (blastula) and then a depression forms at one end (gastrulation) and eventually becomes the digestive cavity. However, in cnidarians the depression forms at the end further from the yolk (at the animal pole), while in bilaterians it forms at the other end (vegetal pole). The larvae, called planulae, swim or crawl by means of cilia. They are cigar-shaped but slightly broader at the \"front\" end, which is the aboral, vegetal-pole end and eventually attaches to a substrate if the species has a polyp stage.
Anthozoan larvae either have large yolks or are capable of feeding on plankton, and some already have endosymbiotic algae that help to feed them. Since the parents are immobile, these feeding capabilities extend the larvae\'s range and avoid overcrowding of sites. Scyphozoan and hydrozoan larvae have little yolk and most lack endosymbiotic algae, and therefore have to settle quickly and metamorphose into polyps. Instead, these species rely on their medusae to extend their ranges.
### Asexual
All known cnidarians can reproduce asexually by various means, in addition to regenerating after being fragmented. Hydrozoan polyps only bud, while the medusae of some hydrozoans can divide down the middle. Scyphozoan polyps can both bud and split down the middle. In addition to both of these methods, Anthozoa can split horizontally just above the base. Asexual reproduction makes the daughter cnidarian a clone of the adult. The ability of cnidarians to asexually reproduce ensures a greater number of mature medusa that can mature to reproduce sexually.
### DNA repair {#dna_repair}
Two classical DNA repair pathways, nucleotide excision repair and base excision repair, are present in hydra, and these repair pathways facilitate unhindered reproduction. The identification of these pathways in hydra is based, in part, on the presence in the hydra genome of genes homologous to genes in other genetically well studied species that have been demonstrated to play key roles in these DNA repair pathways.
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# Cnidaria
## Classification
Cnidarians were for a long time grouped with ctenophores in the phylum Coelenterata, but increasing awareness of their differences caused them to be placed in separate phyla. Modern cnidarians are generally classified into four main classes: sessile Anthozoa (sea anemones, corals, sea pens); swimming Scyphozoa (jellyfish) and Cubozoa (box jellies); and Hydrozoa, a diverse group that includes all the freshwater cnidarians as well as many marine forms, and has both sessile members such as *Hydra* and colonial swimmers such as the Portuguese Man o\' War. Staurozoa have recently been recognised as a class in their own right rather than a sub-group of Scyphozoa, and the parasitic Myxozoa and Polypodiozoa are now recognized as highly derived cnidarians rather than more closely related to the bilaterians.
Hydrozoa Scyphozoa Cubozoa Anthozoa Myxozoa
-------------------------------------- ------------------------ ----------- ------------- -------------------------------- ------------------------
Number of species 3,600 228 42 6,100 1300
Examples *Hydra*, siphonophores Jellyfish Box jellies Sea anemones, corals, sea pens *Myxobolus cerebralis*
Cells found in mesoglea No Yes Yes Yes
Nematocysts in exodermis No Yes Yes Yes
Medusa phase in life cycle In some species Yes Yes No
Number of medusae produced per polyp Many Many One (not applicable)
Stauromedusae, small sessile cnidarians with stalks and no medusa stage, have traditionally been classified as members of the Scyphozoa, but recent research suggests they should be regarded as a separate class, Staurozoa.
The Myxozoa, microscopic parasites, were first classified as protozoans. Research then found that *Polypodium hydriforme*, a non-myxozoan parasite *within* the egg cells of sturgeon, is closely related to the Myxozoa and suggested that both *Polypodium* and the Myxozoa were intermediate between cnidarians and bilaterian animals. More recent research demonstrates that the previous identification of bilaterian genes reflected contamination of the myxozoan samples by material from their host organism, and they are now firmly identified as heavily derived cnidarians, and more closely related to Hydrozoa and Scyphozoa than to Anthozoa.
Some researchers classify the extinct conulariids as cnidarians, while others propose that they form a completely separate phylum.
Current classification according to the World Register of Marine Species:
- class Anthozoa Ehrenberg, 1834
- subclass Ceriantharia Perrier, 1893 --- Tube-dwelling anemones
- subclass Hexacorallia Haeckel, 1896 --- stony corals
- subclass Octocorallia Haeckel, 1866 --- soft corals and sea fans
- class Cubozoa Werner, 1973 --- box jellies
- class Hydrozoa Owen, 1843 --- hydrozoans (fire corals, hydroids, hydroid jellyfishes, siphonophores\...)
- class Myxozoa Grassé, 1970 --- obligate parasites
- class Polypodiozoa Raikova, 1994 --- (uncertain status)
- class Scyphozoa Goette, 1887 --- \"true\" jellyfishes
- class Staurozoa Marques & Collins, 2004 --- stalked jellyfishes
Image:Cerianthus filiformis.jpg\|*Cerianthus filiformis* (Ceriantharia) Image:Haeckel Actiniae.jpg\|Sea anemones (Actiniaria, part of Hexacorallia) Image:Hertshoon.jpg\|Coral *Acropora muricata* (Scleractinia, part of Hexacorallia) Image:Gorgonia ventalina, Bahamas.jpg\|Sea fan *Gorgonia ventalina* (Alcyonacea, part of Octocorallia) Image:Carybdea branchi9.jpg\|Box jellyfish *Carybdea branchi* (Cubozoa) Image:Portuguese Man-O-War (Physalia physalis).jpg\|Siphonophore *Physalia physalis* (Hydrozoa) Image:Fdl17-9-grey.jpg\|*Myxobolus cerebralis* (Myxozoa) Image:Polypodium hydriforme.jpg\|*Polypodium hydriforme* (Polypodiozoa) Image:Phyllorhiza punctata macro II.jpg\|Jellyfish *Phyllorhiza punctata* (Scyphozoa) Image:Haliclystus antarcticus 1B.jpg\|Stalked jelly *Haliclystus antarcticus* (Staurozoa)
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# Cnidaria
## Ecology
Many cnidarians are limited to shallow waters because they depend on endosymbiotic algae for much of their nutrients. The life cycles of most have polyp stages, which are limited to locations that offer stable substrates. Nevertheless, major cnidarian groups contain species that have escaped these limitations. Hydrozoans have a worldwide range: some, such as *Hydra*, live in freshwater; *Obelia* appears in the coastal waters of all the oceans; and *Liriope* can form large shoals near the surface in mid-ocean. Among anthozoans, a few scleractinian corals, sea pens and sea fans live in deep, cold waters, and some sea anemones inhabit polar seabeds while others live near hydrothermal vents over 10 km below sea-level. Reef-building corals are limited to tropical seas between 30°N and 30°S with a maximum depth of 46 m, temperatures between 20 and, high salinity, and low carbon dioxide levels. Stauromedusae, although usually classified as jellyfish, are stalked, sessile animals that live in cool to Arctic waters. Cnidarians range in size from a mere handful of cells for the parasitic myxozoans through *Hydra*\'s length of 5 -, to the lion\'s mane jellyfish, which may exceed 2 m in diameter and 75 m in length.
Prey of cnidarians ranges from plankton to animals several times larger than themselves. Some cnidarians are parasites, mainly on jellyfish but a few are major pests of fish. Others obtain most of their nourishment from endosymbiotic algae or dissolved nutrients. Predators of cnidarians include: sea slugs, flatworms and comb jellies, which can incorporate nematocysts into their own bodies for self-defense (nematocysts used by cnidarian predators are referred to as kleptocnidae); starfish, notably the crown of thorns starfish, which can devastate corals; butterfly fish and parrot fish, which eat corals; and marine turtles, which eat jellyfish. Some sea anemones and jellyfish have a symbiotic relationship with some fish; for example clownfish live among the tentacles of sea anemones, and each partner protects the other against predators.
Coral reefs form some of the world\'s most productive ecosystems. Common coral reef cnidarians include both anthozoans (hard corals, octocorals, anemones) and hydrozoans (fire corals, lace corals). The endosymbiotic algae of many cnidarian species are very effective primary producers, in other words converters of inorganic chemicals into organic ones that other organisms can use, and their coral hosts use these organic chemicals very efficiently. In addition, reefs provide complex and varied habitats that support a wide range of other organisms. Fringing reefs just below low-tide level also have a mutually beneficial relationship with mangrove forests at high-tide level and seagrass meadows in between: the reefs protect the mangroves and seagrass from strong currents and waves that would damage them or erode the sediments in which they are rooted, while the mangroves and seagrass protect the coral from large influxes of silt, fresh water and pollutants. This additional level of variety in the environment is beneficial to many types of coral reef animals, which for example may feed in the sea grass and use the reefs for protection or breeding.
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# Cnidaria
## Evolutionary history {#evolutionary_history}
### Fossil record {#fossil_record}
The earliest widely accepted animal fossils are rather modern-looking cnidarians, possibly from around `{{ma|580}}`{=mediawiki}, although fossils from the Doushantuo Formation can only be dated approximately. The identification of some of these as embryos of animals has been contested, but other fossils from these rocks strongly resemble tubes and other mineralized structures made by corals. Their presence implies that the cnidarian and bilaterian lineages had already diverged. Although the Ediacaran fossil *Charnia* used to be classified as a jellyfish or sea pen, more recent study of growth patterns in *Charnia* and modern cnidarians has cast doubt on this hypothesis, leaving the Canadian polyp *Haootia* and the British *Auroralumina* as the only recognized cnidarian body fossils from the Ediacaran. *Auroralumina* is the earliest known animal predator. Few fossils of cnidarians without mineralized skeletons are known from more recent rocks, except in Lagerstätten that preserved soft-bodied animals.
A few mineralized fossils that resemble corals have been found in rocks from the Cambrian period, and corals diversified in the Early Ordovician. These corals, which were wiped out in the Permian--Triassic extinction event about `{{ma|252}}`{=mediawiki}, did not dominate reef construction since sponges and algae also played a major part. During the Mesozoic era, rudist bivalves were the main reef-builders, but they were wiped out in the Cretaceous--Paleogene extinction event `{{ma|66}}`{=mediawiki}, and since then the main reef-builders have been scleractinian corals.
Hydroconozoa is an extinct class of cnidarians, established by K.B. Korde in 1964 based on Lower Cambrian fossils from Tuva, USSR. These conical and cylindrical organisms, including genera like Hydroconus and Tuvaeconus, possessed external skeletons with features resembling both scyphozoans and tetracorals. Their unique skeletal structures suggest a distinct lineage within early cnidarian evolution.
### Phylogeny
It is difficult to reconstruct the early stages in the evolutionary \"family tree\" of animals using only morphology (their shapes and structures) because of the large differences between the major groups of animals. Hence, reconstructions now rely almost entirely on molecular phylogenetics, which groups organisms based on their biochemistry, most commonly by analyzing DNA or RNA sequences.
In 1866, it was proposed that Cnidaria and Ctenophora were more closely related to each other than to Bilateria and formed a group called Coelenterata (\"hollow guts\") because both rely on the flow of water in and out of a single cavity for feeding, excretion and respiration. In 1881, it was proposed that Ctenophora and Bilateria were more closely related to each other, since they shared features that Cnidaria lack, such as a middle layer of cells (mesoglea in Ctenophora, mesoderm in Bilateria) between the outer and inner layer found in other animals. However, more recent analyses indicate that these similarities were evolved independently in both lineages, instead of being present in their common ancestor. The current view is that Cnidaria and Bilateria are more closely related to each other than either is to Ctenophora. This grouping of Cnidaria and Bilateria has been labelled \"Planulozoa\", named so because the earliest Bilateria were probably similar to the planula larvae of Cnidaria.
In 2005, Katja Seipel and Volker Schmid suggested that cnidarians and ctenophores are simplified descendants of triploblastic animals, since ctenophores and the medusa stage of some cnidarians have striated muscle, which in bilaterians arises from the mesoderm. They did not commit themselves on whether bilaterians evolved from early cnidarians or from the hypothesized triploblastic ancestors of cnidarians.
Resolving the evolutionary relationships within Cnidaria has also been challenging, with almost every possible combination of clades being proposed. As time went on though, a semi-consensus has started to emerge. The enigmatic *Polypodium hydriforme* and subphylum Myxozoa have been firmly placed within the Cnidaria and have been shown to be closely related to the Medusozoa. In addition, these two groups have been found to likely be each other\'s closest relatives which, if true, would form the clade \"Endocnidozoa\". The relationships within the Medusozoa are currently probably the most contentious part of the tree. Traditionally, the class Scyphozoa also included Staurozoa and Cubozoa, but significant morphological differences eventually lead to the split of the three. The group containing them has since been named \"Acraspeda\". The relationships between these three and Hydrozoa have since and still are debated. A relationship between Scyphozoa and Cubozoa with Staurozoa as its sister has seen support in nearly all studies, but the position of the remaining class, Hydrozoa, is not understood. Several studies have found that Acraspeda is paraphyletic, with Hydrozoa being more closely related to Scyphozoa than to the other classes. At the same time, other studies have recovered Acraspeda as being monophyletic. The subphylum Anthozoa is argued to have either two or three classes, but the relationships between them is not disputed; the tube-dwelling anemones of the class Ceriantharia have consistently shown to be more closely related to the Hexacorallia than to the Octocorallia.
In molecular phylogenetics analyses from 2005 onwards, important groups of developmental genes show the same variety in cnidarians as in chordates. In fact cnidarians, and especially anthozoans (sea anemones and corals), retain some genes that are present in bacteria, protists, plants and fungi but not in bilaterians.
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# Cnidaria
## Interaction with humans {#interaction_with_humans}
Jellyfish stings killed about 1,500 people in the 20th century, and cubozoans are particularly dangerous. On the other hand, some large jellyfish are considered a delicacy in East and Southeast Asia. Coral reefs have long been economically important as providers of fishing grounds, protectors of shore buildings against currents and tides, and more recently as centers of tourism. However, they are vulnerable to over-fishing, mining for construction materials, pollution, and damage caused by tourism.
Beaches protected from tides and storms by coral reefs are often the best places for housing in tropical countries. Reefs are an important food source for low-technology fishing, both on the reefs themselves and in the adjacent seas. However, despite their great productivity, reefs are vulnerable to over-fishing, because much of the organic carbon they produce is exhaled as carbon dioxide by organisms at the middle levels of the food chain and never reaches the larger species that are of interest to fishermen. Tourism centered on reefs provides much of the income of some tropical islands, attracting photographers, divers and sports fishermen. However, human activities damage reefs in several ways: mining for construction materials; pollution, including large influxes of fresh water from storm drains; commercial fishing, including the use of dynamite to stun fish and the capture of young fish for aquariums; and tourist damage caused by boat anchors and the cumulative effect of walking on the reefs. Coral, mainly from the Pacific Ocean has long been used in jewellery, and demand rose sharply in the 1980s.
Some large jellyfish species of the Rhizostomeae order are commonly consumed in Japan, Korea and Southeast Asia. In parts of the range, fishing industry is restricted to daylight hours and calm conditions in two short seasons, from March to May and August to November. The commercial value of jellyfish food products depends on the skill with which they are prepared, and \"Jellyfish Masters\" guard their trade secrets carefully. Jellyfish is very low in cholesterol and sugars, but cheap preparation can introduce undesirable amounts of heavy metals.
The \"sea wasp\" *Chironex fleckeri* has been described as the world\'s most venomous jellyfish and is held responsible for 67 deaths, although it is difficult to identify the animal as it is almost transparent. Most stingings by *C. fleckeri* cause only mild symptoms. Seven other box jellies can cause a set of symptoms called Irukandji syndrome, which takes about 30 minutes to develop, and from a few hours to two weeks to disappear. Hospital treatment is usually required, and there have been a few deaths.
A number of the parasitic myxozoans are commercially important pathogens in salmonid aquaculture. A Scyphozoa species -- *Pelagia noctiluca* -- and a Hydrozoa -- *Muggiaea atlantica* -- have caused repeated mass mortality in salmon farms over the years around Ireland. A loss valued at £1 million struck in November 2007, 20,000 died off Clare Island in 2013 and four fish farms collectively lost tens of thousands of salmon in September 2017
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# Children of Dune
***Children of Dune*** is a 1976 science fiction novel by Frank Herbert, the third in his *Dune* series of six novels. Originally serialized in *Analog Science Fiction and Fact* in 1976, it was the last *Dune* novel to be serialized before book publication.
At the end of *Dune Messiah*, Paul Atreides walks into the desert, a blind man, leaving his sister Alia to rule the universe as regent for his twin children, Leto II and Ghanima. Awakened in the womb by the spice, the children are the heirs to Paul\'s prescient vision of the fate of the universe, a role that Alia desperately craves. House Corrino schemes to return to the throne, while the Bene Gesserit make common cause with the Tleilaxu and Spacing Guild to gain control of the spice and Paul\'s children.
Initially selling over 75,000 copies, it became the first hardcover best-seller in science fiction. The novel was critically well-received for its plot, action, and atmosphere and was nominated for the Hugo Award for Best Novel in 1977. *Dune Messiah* (1969) and *Children of Dune* were collectively adapted by the Sci-Fi Channel in 2003 into a miniseries titled *Frank Herbert\'s Children of Dune*.
## Plot
Nine years after Emperor Paul \"Muad\'Dib\" Atreides walked into the desert, the ecological transformation of Dune has reached the point where some Fremen are living without stillsuits in the less arid climate and have started to move out of the sietches and into villages and cities. As the old ways erode, more and more pilgrims arrive to experience the planet of Muad\'Dib. The imperial high council has lost its political might and is powerless to control the jihad.
Paul\'s young twin children, Leto II and Ghanima, have concluded that their aunt and guardian Alia has succumbed to Abomination---possession by her grandfather Baron Vladimir Harkonnen---and fear that a similar fate awaits them. They (and Alia) also realize that the terraforming of Dune will kill all the sandworms, thus destroying the source of the spice, but the Baron desires this outcome. Leto also fears that, like his father, he will become trapped by his prescience.
Meanwhile, a new religious figure called \"The Preacher\" has risen in the desert, rallying against the religious government\'s injustices and the changes among the Fremen. Some Fremen believe he is Paul Atreides. Princess Wensicia of the fallen House Corrino on Salusa Secundus plots to assassinate the twins and regain power for her House.
Lady Jessica returns to Arrakis and recognizes that her daughter is possessed, but finds no signs of Abomination in the twins. Leto arranges for Fremen leader Stilgar to protect Ghanima if there is an attempt on their lives. The Preacher journeys to Salusa Secundus to meet Wensicia\'s son Farad\'n, and in return pledges the Duncan Idaho ghola as an agent of House Corrino. Alia attempts to assassinate Jessica, who escapes into the desert with Duncan\'s help, precipitating a rebellion among the Fremen. The twins anticipate and survive the Corrino assassination plot, faking Leto\'s death.
Leto leaves to seek out Jacurutu, a mythical Fremen sietch and possible holdout of the Preacher, while Ghanima, changing her memory with self-hypnosis, reports (and believes) that her brother has been murdered. Duncan and Jessica flee to Salusa Secundus, where Jessica begins to mentor Farad\'n in the ways of the Bene Gesserit. He sidelines and publicly denounces his regent mother Wensicia over the assassination attempt, and allies with the Bene Gesserit, who promise to marry him to Ghanima and support his bid to become Emperor.
A band of Fremen outlaws capture Leto and force him to undergo the spice trance at the suggestion of Gurney Halleck, who has infiltrated the group on Jessica\'s orders. Leto\'s spice-induced visions show him a myriad of possible futures where humanity becomes extinct and only one where it survives. He names this future \"The Golden Path\" and resolves to bring it to fruition---something that his father, who had already glimpsed this future, refused to do. He escapes his captors and sacrifices his humanity in pursuit of the Golden Path by physically fusing with a school of sandtrout, the larval form of sandworms, in the process gaining superhuman strength and near-invulnerability. He travels across the desert destroying qanats to slow down the ecological transformation of Dune, and eventually confronts the Preacher, who is indeed Paul.
Duncan returns to Arrakis and provokes Stilgar into killing him so that Stilgar is forced to take Ghanima and go into hiding. Eventually though, Alia recaptures Ghanima and arranges her marriage to Farad\'n, planning to exploit the expected chaos when Ghanima kills him to avenge her brother\'s murder. Paul and Leto return to the capital, where Jessica and Farad\'n have arrived for his betrothal to Ghanima, to confront Alia. Upon arriving, Paul is publicly murdered by agents of Alia\'s government, to her horror. Leto reveals himself in a display of superhuman strength and triggers the return of Ghanima\'s genuine memories. He confronts Alia and offers to help her overcome her possession, but the Baron resists. Alia, while fighting the Baron\'s possession, manages to throw herself off a high balcony, killing both herself and the Baron.
Leto declares himself Emperor and asserts control over the Fremen. Farad\'n enlists in his service and delivers control of the Corrino armies and his Sardaukar. In describing the Golden Path to Farad\'n, Leto reveals that he will live for thousands of years due to the sandworm skin and genetics he is encased in. Leto marries Ghanima to consolidate power, but because his sandworm skin destroyed his ability to reproduce, he allows Farad\'n to be her true consort so the Atreides line can continue. Ghanima reflects that one twin had to follow the Path, but Leto was always the stronger.
## Publication history {#publication_history}
Parts of *Dune Messiah* and *Children of Dune* were written before *Dune* was completed. *Children of Dune* was originally serialized in *Analog Science Fiction and Fact* in 1976, and was the last *Dune* novel to be serialized before book publication. *Dune Messiah* and *Children of Dune* were published in one volume by the Science Fiction Book Club in 2002.
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# Children of Dune
## Analysis
Herbert likened the initial trilogy of novels (*Dune*, *Dune Messiah*, and *Children of Dune*) to a fugue -- *Dune* was a heroic melody, *Dune Messiah* was its inversion, while *Children of Dune* expands the number of interplaying themes. Paul rises to power in *Dune* by seizing control of the single critical resource in the universe, melange. His enemies are dead or overthrown, and he is set to take the reins of power and bring a hard but enlightened peace to the universe. Herbert chose in the books that followed to undermine Paul\'s triumph with a string of failures and philosophical paradoxes.
## Critical reception {#critical_reception}
Initially selling over 75,000 copies, *Children of Dune* became the first hardcover best-seller in the science fiction field. The novel was critically well-received for its gripping plot, action, and atmosphere, and was nominated for the Hugo Award for Best Novel in 1977.
The *Los Angeles Times* called *Children of Dune* \"a major event\", and *Challenging Destiny* noted that \"Herbert adds enough new twists and turns to the ongoing saga that familiarity with the recurring elements brings pleasure.\" *Publishers Weekly* wrote, \"Ranging from palace intrigue and desert chases to religious speculation and confrontations with the supreme intelligence of the universe, there is something here for all science fiction fans.\" In a 1976 review, Spider Robinson found *Children of Dune* unsatisfying, faulting the ending as unconvincing and thematically overfamiliar. The novel is referred to in *A Thousand Plateaus* (1980) by Gilles Deleuze and Félix Guattari. David Pringle gave the novel a rating of two stars out of four and described the novel as \"dark and convoluted stuff.\"
## Adaptation
*Dune Messiah* (1969) and *Children of Dune* were collectively adapted by the Sci-Fi Channel in 2003 into a miniseries titled *Frank Herbert\'s Children of Dune*. The three-part, six-hour miniseries covers the bulk of the plot of *Dune Messiah* in the first installment, and adapts *Children of Dune* in the second and third parts
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# Chapterhouse: Dune
***Chapterhouse: Dune*** is a 1985 science fiction novel by Frank Herbert, the last in his *Dune* series of six novels. It rose to No. 2 on *The New York Times* Best Seller list.
A direct follow-up to *Heretics of Dune*, the novel chronicles the continued struggles of the Bene Gesserit sisterhood against the violent Honored Matres, who are succeeding in their bid to seize control of the universe and destroy the factions and planets that oppose them.
*Chapterhouse: Dune* ends with a cliffhanger, and Herbert\'s subsequent death in 1986 left some overarching plotlines of the series unresolved. Two decades later, Herbert\'s son Brian Herbert, along with Kevin J. Anderson, published two sequels -- *Hunters of Dune* (2006) and *Sandworms of Dune* (2007) -- based in part on notes left behind by Frank Herbert for what he referred to as *Dune 7*, his own planned seventh novel in the *Dune* series.
## Plot
The Bene Gesserit find themselves the target of the Honored Matres, whose conquest of the Old Empire is almost complete. The Matres are seeking to assimilate the technology and superhuman skills of the Bene Gesserit, and exterminate the Sisterhood itself. Now in command of the Bene Gesserit, Mother Superior Darwi Odrade continues to develop her drastic, secret plan to overcome the Honored Matres. The Bene Gesserit are also terraforming the planet Chapterhouse to accommodate the all-important sandworms, as the planet Dune had been destroyed by the Matres.
Sheeana, in charge of the project, expects sandworms to appear soon. The Honored Matres have also destroyed the entire Bene Tleilax civilization, with Tleilaxu Master Scytale the only one of his kind left alive. In Bene Gesserit captivity, Scytale possesses the Tleilaxu secret of ghola production, which he has reluctantly traded for the Sisterhood\'s protection. The first ghola produced is that of their recently deceased military genius, Miles Teg. The Bene Gesserit have two other prisoners on Chapterhouse: the latest Duncan Idaho ghola, and his lover, former Honored Matre Murbella, whom they have accepted as a novice despite their suspicion that she intends to escape back to the Honored Matres.
Lampadas, a center for Bene Gesserit education, is destroyed by the Honored Matres. The planet\'s Chancellor, Reverend Mother Lucilla, manages to escape carrying the shared-minds of millions of Reverend Mothers. Lucilla is forced to land on Gammu where she seeks refuge with an underground group of Jews, known as \"Secret Israel\". The Rabbi gives Lucilla sanctuary, but to save his people from the Matres he must deliver her to them. Before doing so, he reveals Rebecca, a \"wild\" Reverend Mother who has gained her Other Memory without Bene Gesserit training.
Lucilla shares minds with Rebecca, who promises to take the memories of Lampadas safely back to the Sisterhood. Lucilla is then \"betrayed\", and taken before the Great Honored Matre Dama, who tries to persuade her to join the Honored Matres, preserving her life in exchange for Bene Gesserit secrets. The Honored Matres are particularly interested in learning to voluntarily modify their body chemistry, a skill that atrophied among the Bene Gesserit who went out into the Scattering and evolved into the Honored Matres. From this, Lucilla deduces that the greater enemy that the Matres are fleeing from is making extensive use of biological warfare. Lucilla refuses to share this knowledge with the Matres, and Dama ultimately kills her.
Back on Chapterhouse, Odrade confronts Duncan and forces him to admit that he is a Mentat, proving that he retains the memories of his many ghola lives. Meanwhile, Murbella collapses under the pressure of Bene Gesserit training, and realizes that she wants to be Bene Gesserit. Odrade believes that the Sisterhood made a mistake in fearing emotion, and that in order to evolve, they must learn to accept emotions. Murbella survives the spice agony and becomes a Reverend Mother. Odrade confronts Sheeana, discovering that Duncan and Sheeana have been allies for some time. Sheeana does not reveal that they have been considering the option of reawakening Teg\'s memory through imprinting, nor does Odrade discover that Sheeana has the keys to Duncan\'s no-ship prison.
Teg is awakened by Sheeana using imprinting techniques. Odrade appoints him again as Bashar of the military forces of the Sisterhood for the assault on the Honored Matres. Odrade announces to the Bene Gesserit that Teg will lead an attack against the Honored Matres. She also makes clear her intention to share her memories with Murbella and Sheeana, making them candidates to succeed her as Mother Superior if she dies. Odrade meets with the Great Honored Matre while the Bene Gesserit forces under Teg attack Gammu, and then Junction, with tremendous force. Teg uses his secret ability to see no-ships to secure control of the system, and victory for the Bene Gesserit seems inevitable. In the midst of this battle, Rebecca and the Jews take refuge with the Bene Gesserit fleet.
Dama\'s chief advisor Logno assassinates Dama with poison and assumes control of the Honored Matres. Too late, Odrade and Teg realize they have fallen into a trap, and the Honored Matres use a mysterious weapon, which kills without wounding, to turn defeat into victory, and capture Odrade. Murbella saves as much of the Bene Gesserit force as she can and they withdraw to Chapterhouse. Odrade, however, had planned for the possible failure of the Bene Gesserit attack and left Murbella instructions for a last desperate gamble. Murbella pilots a small craft down to the surface, announcing herself as an Honored Matre who, in the confusion, has managed to escape the Bene Gesserit with all their secrets. She arrives on the planet and is taken to the Great Honored Matre, and taunts her. Unable to control her anger, Logno attacks but is killed by Murbella.
Awed by her physical prowess, the remaining Honored Matres are forced to accept her as their new leader. Odrade is also killed in the melee and Murbella shares with Odrade to absorb her newest memories, as they had already shared prior to the battle. Murbella\'s ascension to leadership, and her bringing the Honored Matres to merge with the Bene Gesserit, is not accepted as victory by all the latter. Some flee Chapterhouse, notably Sheeana, who has a vision of her own, and arranges to have some of the new worms that have emerged in the Chapterhouse desert brought aboard the no-ship. Sheeana is joined by Duncan. The two escape in the giant no-ship, with Scytale, Teg and the Jews. Murbella recognizes their plan at the last minute, but is powerless to stop them. Two mysterious entities resembling an old married couple, Daniel and Marty, whom Duncan had seen in visions, wryly note the refugees\' escape.
## Reception
*Chapterhouse: Dune* debuted at No. 5 and rose to No. 2 on *The New York Times* Best Seller list. Gerald Jonas of *The New York Times* noted that \"Against all odds, the universe of *Dune* keeps getting richer in texture, more challenging in its moral dilemmas.\"
Dave Langford reviewed the novel for *White Dwarf* #65, and stated that \"The hyper-acute characters are impressive, the resolution thoughtful and humane. Though initially I gave up after *Children*, *Heretics* and *Chapter House* have partially Restored My Faith.\"
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# Chapterhouse: Dune
## Sequels
Two decades after Frank Herbert\'s death, his son Brian Herbert, along with Kevin J. Anderson, published two sequels -- *Hunters of Dune* (2006) and *Sandworms of Dune* (2007) -- based on notes left behind by Frank Herbert for what he referred to as *Dune 7*, his own planned seventh novel in the *Dune* series,`{{Herbert notes}}`{=mediawiki} while also continuing plot-lines from Brian Herbert\'s and Kevin J. Anderson\'s own *Dune* prequel novels
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# Cantor Fitzgerald
**Cantor Fitzgerald, L.P.** is an American financial services firm that was founded in 1945. It specializes in institutional equity, fixed-income sales and trading, and serving the middle market with investment banking services, prime brokerage, and commercial real estate financing. It is also active in new businesses, including advisory and asset management services, gaming technology, and e-commerce. It has more than 5,000 institutional clients.
Cantor Fitzgerald is one of 24 primary dealers that are authorized to trade US government securities with the Federal Reserve Bank of New York.
Cantor Fitzgerald\'s 1,600 employees work in more than 30 locations, including financial centers in the Americas, Europe, Asia-Pacific, and the Middle East. Together with its affiliates, Cantor Fitzgerald operates in more than 60 offices in 20 countries and has more than 12,500 employees.
Before 2001, the company\'s headquarters were located between the 101st and 105th floors of the North Tower of the World Trade Center in New York City, just above the impact site of American Airlines Flight 11 during the September 11 attacks. 658 Cantor Fitzgerald employees who were present that day were killed, representing the largest loss of life among any single organization in the attacks.
## Early history {#early_history}
Cantor Fitzgerald was formed in 1945 by Bernard Gerald Cantor and John Fitzgerald as an investment bank and brokerage business.
In 1965, Cantor Fitzgerald began \"large block\" sales/trading of equities for institutional customers. It became the world\'s first electronic marketplace for US government securities in 1972, and in 1983 it was the first to offer worldwide screen brokerage services in US government securities, becoming in time the market\'s premier government securities dealer. It also became known for `{{clarification needed span|text=the quality of its institutional distribution business model.|reason=What exactly does this mean, in layman's terms, linked as best as it can be to pertinent Wikipedia articles.|date=April 2025}}`{=mediawiki}
In 1991, Howard Lutnick was named president and CEO of Cantor Fitzgerald; he became chairman of Cantor Fitzgerald, L.P., in 1996.
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# Cantor Fitzgerald
## September 11 attacks {#september_11_attacks}
Cantor Fitzgerald\'s corporate headquarters and New York City office, on the 101st to the 105th floors of 1 World Trade Center in Lower Manhattan (2 to 6 floors above the impact zone of American Airlines Flight 11), were destroyed during the September 11 attacks. At 8:46:46 a.m., eighteen seconds after the plane struck the tower, a Goldman Sachs server issued an alert saying that its trading system had gone offline because it could not connect with the server. Since all stairwells leading past the impact zone were destroyed by the initial crash or blocked with smoke, fire, or debris, every employee who reported for work that morning was killed in the attacks; 658 of its 960 New York employees were killed or missing, or 68.5% of its total workforce, which was considerably more than any of the other World Trade Center tenants, the New York City Police Department, the Port Authority Police Department, the New York City Fire Department, or the Department of Defense. Forty-six contractors, food service workers, and visitors in the Cantor Fitzgerald offices at the time were also killed. CEO Howard Lutnick was not present that day, but his younger brother, Gary, was among those killed. Lutnick vowed to keep the company alive, and the company was able to bring its trading markets back online within a week.
On September 19, Cantor Fitzgerald made a pledge to distribute 25% of the firm\'s profits for the next five years (that would otherwise have been distributed to its partners), and committed to paying for ten years of health care for the benefit of the families of its 658 former Cantor Fitzgerald, eSpeed, and TradeSpark employees. In 2006, the company had completed its promise, having paid a total of \$180 million (and an additional \$17 million from a relief fund run by Lutnick\'s sister, Edie).
Until the attacks, Cantor had handled about a quarter of the daily transactions in the multi-trillion dollar treasury security market. Cantor Fitzgerald subsequently rebuilt its infrastructure, partly through the efforts of its London office, and relocated its headquarters to Midtown Manhattan. The company\'s effort to regain its footing was the subject of Tom Barbash\'s 2003 book *On Top of the World: Cantor Fitzgerald, Howard Lutnick, and 9/11: A Story of Loss and Renewal* as well as a 2012 documentary, *Out of the Clear Blue Sky*.
On September 2, 2004, Cantor and other organizations filed a civil lawsuit against Saudi Arabia for allegedly providing money to the hijackers and al-Qaeda. It was later joined in the suit by the Port Authority of New York and New Jersey. Most of the claims against Saudi Arabia were dismissed on January 18, 2005.
In December 2013, Cantor Fitzgerald settled its lawsuit against American Airlines for \$135 million. Cantor Fitzgerald had been suing for loss of property and interruption of business by alleging the airline to have been negligent by allowing hijackers to board Flight 11.
## Recent history {#recent_history}
In 2003, the firm launched its fixed-income sales and trading group. Three years later, the Federal Reserve added Cantor Fitzgerald & Co. to its list of primary dealers. The firm later launched Cantor Prime Services in 2009. It was meant to be a provider of multi-asset, perimeter brokerage prime brokerage platforms to exploit its clearing, financing, and execution capabilities. A year after, Cantor Fitzgerald began building its real estate business with the launch of CCRE. Cantor\'s affiliate, BGC Partners, expanded into commercial real estate services in 2011 by its purchase of Newmark Knight Frank and the assets of Grubb & Ellis, to form Newmark Grubb Knight Frank.
On December 5, 2014, two Cantor Fitzgerald analysts were said to be in the top 25 analysts on TipRanks. Cantor Fitzgerald has a prolific special-purpose acquisition company underwriting practice, having led all banks in SPAC underwriting activity in both 2018 and 2019.
In March 2016, Sage Kelly, formerly of Jefferies & Co., joined the firm as senior managing director and head of its investment-banking division.
## Philanthropy
Former chairman and CEO Howard Lutnick\'s sister Edie wrote *An Unbroken Bond: The Untold Story of How the 658 Cantor Fitzgerald Families Faced the Tragedy of 9/11 and Beyond*. All proceeds from the book\'s sale benefit the Cantor Fitzgerald Relief Fund and the charities it assists.
The Cantor Fitzgerald Relief Fund provided \$10 million to families affected by Hurricane Sandy. Howard Lutnick and the Relief Fund \"adopted\" 19 elementary schools in impacted areas by distributing \$1,000 prepaid debit cards to each family from the schools. A total of \$10 million in funds was given to families affected by the storm.
Two days after the 2013 Moore tornado struck Moore, Oklahoma, killing 24 people and injuring hundreds, Lutnick pledged to donate \$2 million to families affected by the tornado. The donation was given to families in the form of \$1,000 debit cards.
Each year, on September 11, Cantor Fitzgerald and its affiliate, BGC Partners, donate 100% of their revenue to charitable causes on their annual Charity Day, which was initially established to raise money to assist the families of the Cantor employees who died in the World Trade Center attacks. Since its inception, Charity Day has raised \$192 million for charities globally.
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# Cantor Fitzgerald
## Subsidiaries and affiliates {#subsidiaries_and_affiliates}
The firm has many subsidiaries and affiliates, including:
- BGC Partners, named after fixed-income trading innovator and founder B. Gerald Cantor, is a global brokerage company that services the wholesale financial markets and commercial real estate marketplace in New York, London, and other financial centers. BGC Partners includes Newmark Grubb Knight Frank, the fourth-largest real estate service provider in the US.
- Cantor Ventures is the company\'s corporate venture capital and enterprise development arm. Led by Henrique De Castro, the group\'s current investments include delivery.com, Ritani, TopLine Game Labs, AdFin, Lucera, NewsWhip, and XIX Entertainment.
- Hollywood Stock Exchange, founded in 1996, is the world\'s virtual entertainment stock market.
- TopLine Game Labs is a technology company to create short-duration fantasy sports and entertainment-based social gaming. Headquartered in Los Angeles, TopLine Game Labs was, in 2013, building a platform-agnostic architecture to power game experiences for sports.
## Senior management {#senior_management}
### List of chairpersons {#list_of_chairpersons}
1. Bernie Cantor (1945--1996)
2. Howard Lutnick (1996--2025)
3. Brandon Lutnick (2025--present)
### List of CEOs {#list_of_ceos}
1. Bernie Cantor (1945--1991)
2. Howard Lutnick (1991--2025)
3. Pascal Bandelier, Sage Kelly, and Christian Wall (co-CEOs) (since February 2025)
### List of presidents {#list_of_presidents}
1
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# Lists of composers
This is a list of lists of composers grouped by various criteria
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# Codec
A **codec** is a computer hardware or software component that encodes or decodes a data stream or signal. *Codec* is a portmanteau of **coder/decoder**.
In electronic communications, an **endec** is a device that acts as both an encoder and a decoder on a signal or data stream, and hence is a type of codec. *Endec* is a portmanteau of **encoder/decoder**.
A coder or encoder encodes a data stream or a signal for transmission or storage, possibly in encrypted form, and the decoder function reverses the encoding for playback or editing. Codecs are used in videoconferencing, streaming media, and video editing applications.
## History
Originally, in the mid-20th century, a codec was a hardware device that coded analog signals into digital form using pulse-code modulation (PCM). Later, the term was also applied to software for converting between digital signal formats, including companding functions.
## Examples
An audio codec converts analog audio signals into digital signals for transmission or encodes them for storage. A receiving device converts the digital signals back to analog form using an audio decoder for playback. An example of this is the codecs used in the sound cards of personal computers. A video codec accomplishes the same task for video signals.
When implementing the Infrared Data Association (IrDA) protocol, an endec may be used between the UART and the optoelectronic systems.
## Compression
In addition to encoding a signal, a codec may also compress the data to reduce transmission bandwidth or storage space. Compression codecs are classified primarily into lossy codecs and lossless codecs.
Lossless codecs are often used for archiving data in compressed form while retaining all information present in the original stream. If preserving the original quality of the stream is more important than eliminating the correspondingly larger data sizes, lossless codecs are preferred. This is especially true if the data is to undergo further processing (for example, editing) in which case the repeated application of processing (encoding and decoding) on lossy codecs will degrade the quality of the resulting data such that it is no longer identifiable (visually, audibly, or both). Using more than one codec or encoding scheme successively can also degrade quality significantly. The decreasing cost of storage capacity and network bandwidth has a tendency to reduce the need for lossy codecs for some media.
Many popular codecs are lossy. They reduce quality in order to maximize compression. Often, this type of compression is virtually indistinguishable from the original uncompressed sound or images, depending on the codec and the settings used. The most widely used lossy data compression technique in digital media is based on the discrete cosine transform (DCT), used in compression standards such as JPEG images, H.26x and MPEG video, and MP3 and AAC audio. Smaller data sets ease the strain on relatively expensive storage sub-systems such as non-volatile memory and hard disk, as well as write-once-read-many formats such as CD-ROM, DVD, and Blu-ray Disc. Lower data rates also reduce cost and improve performance when the data is transmitted, e.g., over the internet.
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# Codec
## Media codecs {#media_codecs}
Two principal techniques are used in codecs, pulse-code modulation and delta modulation. Codecs are often designed to emphasize certain aspects of the media to be encoded. For example, a digital video (using a DV codec) of a sports event needs to encode motion well but not necessarily exact colors, while a video of an art exhibit needs to encode color and surface texture well.
Audio codecs for cell phones need to have very low latency between source encoding and playback. In contrast, audio codecs for recording or broadcasting can use high-latency audio compression techniques to achieve higher fidelity at a lower bit rate.
There are thousands of audio and video codecs, ranging in cost from free to hundreds of dollars or more. This variety of codecs can create compatibility and obsolescence issues. The impact is lessened for older formats, for which free or nearly-free codecs have existed for a long time. The older formats are often ill-suited to modern applications, however, such as playback on small portable devices. For example, raw uncompressed PCM audio (44.1 kHz, 16-bit stereo, as represented on an audio CD or in a .wav or .aiff file) has long been a standard across multiple platforms, but its transmission over networks is slow and expensive compared with more modern compressed formats, such as Opus and MP3.
Many multimedia data streams contain both audio and video, and often some metadata that permits synchronization of audio and video. Each of these three streams may be handled by different programs, processes, or hardware; but for the multimedia data streams to be useful in stored or transmitted form, they must be encapsulated together in a container format.
Lower bitrate codecs allow more users, but they also have more distortion. Beyond the initial increase in distortion, lower bit rate codecs also achieve their lower bit rates by using more complex algorithms that make certain assumptions, such as those about the media and the packet loss rate. Other codecs may not make those same assumptions. When a user with a low bitrate codec talks to a user with another codec, additional distortion is introduced by each transcoding.
Audio Video Interleave (AVI) is sometimes erroneously described as a codec, but AVI is actually a container format, while a codec is a software or hardware tool that encodes or decodes audio or video into or from some audio or video format. Audio and video encoded with many codecs might be put into an AVI container, although AVI is not an ISO standard. There are also other well-known container formats, such as Ogg, ASF, QuickTime, RealMedia, Matroska, and DivX Media Format. MPEG transport stream, MPEG program stream, MP4, and ISO base media file format are examples of container formats that are ISO standardized.
## Malware
**`{{vanchor|Fake codec|text=Fake codecs}}`{=mediawiki}** are used when an online user takes a type of codec and installs viruses and other malware into whatever data is being compressed and uses it as a disguise. This disguise appears as a codec download through a pop-up alert or ad. When a user goes to click or download that codec, the malware is then installed on the computer. Once a fake codec is installed it is often used to access private data, corrupt an entire computer system or to keep spreading the malware. One of the previous most used ways to spread malware was fake AV pages and with the rise of codec technology, both have been used in combination to take advantage of online users. This combination allows fake codecs to be automatically downloaded to a device through a website linked in a pop-up ad, virus/codec alerts or articles as well
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# Christopher Báthory
**Christopher Báthory** (*Báthory Kristóf*; 1530 -- 27 May 1581) was voivode of Transylvania from 1576 to 1581. He was a younger son of Stephen Báthory of Somlyó. Christopher\'s career began during the reign of Queen Isabella Jagiellon, who administered the eastern territories of the Kingdom of Hungary on behalf of her son, John Sigismund Zápolya, from 1556 to 1559. He was one of the commanders of John Sigismund\'s army in the early 1560s.
Christopher\'s brother, Stephen Báthory, who succeeded John Sigismund in 1571, made Christopher captain of Várad (now Oradea in Romania). After being elected King of Poland, Stephen Báthory adopted the title of Prince of Transylvania and made Christopher voivode in 1576. Christopher cooperated with Márton Berzeviczy, whom his brother appointed to supervise the administration of the Principality of Transylvania as the head of the Transylvanian chancellery at Kraków. Christopher ordered the imprisonment of Ferenc Dávid, a leading theologian of the Unitarian Church of Transylvania, who started to condemn the adoration of Jesus. He supported his brother\'s efforts to settle the Jesuits in Transylvania.
## Early life {#early_life}
Christopher was the third of the four sons of Stephen Báthory of Somlyó and Catherine Telegdi. His father was a supporter of John Zápolya, King of Hungary, who made him voivode of Transylvania in February 1530. Christopher was born in Báthorys\' castle at Szilágysomlyó (now Șimleu Silvaniei in Romania) in the same year. His father died in 1534.
His brother, Andrew, and their kinsman, Tamás Nádasdy, took charge of Christopher\'s education. Christopher visited England, France, Italy, Spain, and the Holy Roman Empire in his youth. He also served as a page in Emperor Charles V\'s court.
## Career
Christopher entered the service of John Zápolya\'s widow, Isabella Jagiellon, in the late 1550s. At the time, Isabella administered the eastern territories of the Kingdom of Hungary on behalf of her son, John Sigismund Zápolya. She wanted to persuade Henry II of France to withdraw his troops from three fortresses that the Ottomans had captured in Banat, so she sent Christopher to France to start negotiations in 1557.
John Sigismund took charge of the administration of his realm after his mother died on 15 November 1559. He retained his mother\'s advisors, including Christopher who became one of his most influential officials. After the rebellion of Melchior Balassa, Christopher persuaded John Sigismund to fight for his realm instead of fleeing to Poland in 1562. Christopher was one of the commanders of John Sigismund\'s troops during the ensuing war against the Habsburg rulers of the western territories of the Kingdom of Hungary, Ferdinand and Maximilian, who tried to reunite the kingdom under their rule. Christopher defeated Maximilian\'s commander, Lazarus von Schwendi, forcing him to lift the siege of Huszt (now Khust in Ukraine) in 1565.
After the death of John Sigismund, the Diet of Transylvania elected Christopher\'s younger brother, Stephen Báthory, voivode (or ruler) on 25 May 1571. Stephen made Christopher captain of Várad (now Oradea in Romania). The following year, the Ottoman Sultan, Selim II (who was the overlord of Transylvania), acknowledged the hereditary right of the Báthory family to rule the province.
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# Christopher Báthory
## Reign
Stephen Báthory was elected King of Poland on 15 December 1575. He adopted the title of Prince of Transylvania and made Christopher voivode on 14 January 1576. An Ottoman delegation confirmed Christopher\'s appointment at the Diet in Gyulafehérvár (now Alba Iulia in Romania) in July. The sultan\'s charter (or *ahidnâme*) sent to Christopher emphasized that he should keep the peace along the frontiers. Stephen set up a separate chancellery in Kraków to keep an eye on the administration of Transylvania. The head of the new chancellery, Márton Berzeviczy, and Christopher cooperated closely.
Anti-Trinitarian preachers began to condemn the worshiping of Jesus in Partium and Székely Land in 1576, although the Diet had already forbade all doctrinal innovations. Ferenc Dávid, the most influential leader of the Unitarian Church of Transylvania, openly joined the dissenters in the autumn of 1578. Christopher invited Fausto Sozzini, a leading Anti-Trinitarian theologian, to Transylvania to convince Dávid that the new teaching was erroneous. Since Dávid refused to obey, Christopher held a Diet and the \"Three Nations\" (including the Unitarian delegates) ordered Dávid\'s imprisonment. Christopher also supported his brother\'s attempts to strengthen the position of the Roman Catholic Church in Transylvania. He granted estates to the Jesuits to promote the establishment of a college in Kolozsvár (now Cluj-Napoca in Romania) on 5 May 1579.
Christopher fell seriously ill after his second wife, Elisabeth Bocskai, died in early 1581. After a false rumor about Christopher\'s death reached Istanbul, Koca Sinan Pasha proposed Transylvania to Pál Márkházy whom Christopher had been forced into exile. Although Christopher\'s only surviving son Sigismund was still a minor, the Diet elected him as voivode before Christopher\'s death, because they wanted to prevent the appointment of Márkházy. Christopher died in Gyulafehérvár on 27 May 1581. He was buried in the Jesuits\' church in Gyulafehérvár, almost two years later, on 14 March 1583.
## Family
Christopher\'s first wife, Catherina Danicska, was a Polish noblewoman, but only the Hungarian form of her name is known. Their eldest son, Balthasar Báthory, moved to Kraków shortly after Stephen Báthory was crowned King of Poland; he drowned in the Vistula River in May 1577 at the age of 22. Christopher\'s and Catherina\'s second son, Nicholas, was born in 1567 and died in 1576.
Christopher\'s second wife, Elisabeth Bocskai, was a Calvinist noblewoman. Their first child, Cristina (or Griselda), was born in 1569. She was given in marriage to Jan Zamoyski, Chancellor of Poland, in 1583. Christopher\'s youngest son, Sigismund, was born in 1573
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# Caribbean cuisine
**Caribbean cuisine** is a fusion of West African, Creole, Amerindian, European, Latin American, Indian/South Asian, Chinese, Javanese/Indonesian, North American, and Middle Eastern cuisines. These traditions were brought from many countries when they moved to the Caribbean. In addition, the population has created styles that are unique to the region.
## History
As a result of the colonization, the Caribbean is a fusion of multiple sources; British, Spanish, Dutch and French colonized the area and brought their respective cuisines that mixed with West African as well as Amerindian, Indian/South Asian, East Asian, Portuguese, and Arab, influences from enslaved, indentured and other laborers brought to work on the plantations.
In 1493, during the voyages of Christopher Columbus, the Spaniards introduced a variety of ingredients, including coconut, chickpeas, cilantro, eggplants, onions and garlic.
## Caribbean dishes {#caribbean_dishes}
Ingredients that are common in most islands\' dishes are rice, plantains, beans, cassava, cilantro, bell peppers, chickpeas, tomatoes, sweet potatoes, coconut, and any of various meats that are locally available like beef, poultry, pork, goat or fish. A characteristic seasoning for the region is a green herb-and-oil-based marinade called sofrito, which imparts a flavor profile which is quintessentially Caribbean in character. Ingredients may include garlic, onions, Scotch bonnet peppers, celery, green onions, and herbs like cilantro, Mexican mint, chives, marjoram, rosemary, tarragon and thyme. This green seasoning is used for a variety of dishes like curries, stews and roasted meats.
Traditional dishes are so important to regional culture that, for example, the local version of Caribbean goat stew has been chosen as the official national dish of Montserrat and is also one of the signature dishes of St. Kitts and Nevis. Another popular dish in the Anglophone Caribbean is called \"cook-up\", or pelau. Ackee and saltfish is another popular dish that is unique to Jamaica. Callaloo is a dish containing leafy vegetables such as spinach and sometimes okra amongst others, widely distributed in the Caribbean, with a distinctively mixed African and indigenous character.
The variety of dessert dishes in the area also reflects the mixed origins of the recipes. In some areas, black cake, a derivative of English Christmas pudding, may be served, especially on special occasions.
Over time, food from the Caribbean has evolved into a narrative technique through which their culture has been accentuated and promoted. However, by studying Caribbean culture through a literary lens there then runs the risk of generalizing exoticist ideas about food practices from the tropics. Some food theorists argue that this depiction of Caribbean food in various forms of media contributes to the inaccurate conceptions revolving around their culinary practices, which are much more grounded in unpleasant historical events. Therefore, it can be argued that the connection between the idea of the Caribbean being the ultimate paradise and Caribbean food being exotic is based on inaccurate information
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# Communications in Afghanistan
**Communications in Afghanistan** is under the control of the Ministry of Communications and Information Technology (MCIT). It has rapidly expanded after the Karzai administration was formed in late 2001, and has embarked on wireless companies, internet, radio stations and television channels.
The Afghan government signed a \$64.5 million agreement in 2006 with China\'s ZTE on the establishment of a countrywide optical fiber telecommunications network. The project began to improve telephone, internet, television and radio services throughout Afghanistan. About 90% of the country\'s population had access to communication services by the end of 2013.
Afghanistan uses its own space satellite called Afghansat 1. There are about 18 million mobile phone users in the country. Telecom companies include Afghan Telecom, Afghan Wireless, Etisalat, MTN, Roshan, Salaam. Around 20% of the population has access to the Internet.
## Internet
Afghanistan was given legal control of the \".af\" domain in 2003, and the Afghanistan Network Information Center (AFGNIC) was established to administer domain names. The country has 327,000 IP addresses and around 6,000 .af domains. Internet in Afghanistan is accessed by over 9 million users today. According to a 2020 estimate, over 7 million residents, which is roughly 18% of the population, had access to the internet. There are over a dozen different internet service providers in Afghanistan.
## Postal service {#postal_service}
In 1870, a central post office was established at Bala Hissar in Kabul and a post office in the capital of each province. The service was slowly being expanded over the years as more postal offices were established in each large city by 1918. Afghanistan became a member of the Universal Postal Union in 1928, and the postal administration elevated to the Ministry of Communication in 1934. Civil war caused a disruption in issuing official stamps during the 1980s--90s war but in 1999 postal service was operating again. Postal services to/from Kabul worked remarkably well all throughout the war years. Postal services to/from Herat resumed in 1997. The Afghan government has reported to the UPU several times about illegal stamps being issued and sold in 2003 and 2007.
Afghanistan Post has been reorganizing the postal service in 2000s with assistance from Pakistan Post. The Afghanistan Postal commission was formed to prepare a written policy for the development of the postal sector, which will form the basis of a new postal services law governing licensing of postal services providers. The project was expected to finish by 2008.
## Radio
Radio broadcasting in Afghanistan began in 1925 with Radio Kabul being the first station. The country currently has over 200 AM, FM and shortwave radio stations. They broadcast in Dari, Pashto, English, Uzbeki and a number of other languages.
## Satellite
In January 2014 the Afghan Ministry of Communications and Information Technology signed an agreement with Eutelsat for the use of satellite resources to enhance deployment of Afghanistan\'s national broadcasting and telecommunications infrastructure as well as its international connectivity. Afghansat 1 was officially launched in May 2014, with expected service for at least seven years in Afghanistan. The Afghan government plans to launch Afghansat 2 after the lease of Afghansat 1 ends.
## Telephone
According to 2013 statistics, there were 20,521,585 GSM mobile phone subscribers and 177,705 CDMA subscribers in Afghanistan. Mobile communications have improved because of the introduction of wireless carriers. The first was Afghan Wireless and the second Roshan, which began providing services to all major cities within Afghanistan. There are also a number of VSAT stations in major cities such as Kabul, Kandahar, Herat, Mazari Sharif, and Jalalabad, providing international and domestic voice/data connectivity. The international calling code for Afghanistan is +93. The following is a partial list of mobile phone companies in the country:
- Afghan Telecom (provides 4G services)
- Afghan Wireless (provides 4G services)
- Etisalat (provides 4G services)
- MTN Group (provides 4G services)
- Roshan (provides 4G services)
- Salaam Network (provides 3G services)
All the companies providing communication services are obligated to deliver 2.5% of their income to the communication development fund annually. According to the Ministry of Communication and Information Technology there are 4760 active towers throughout the country which covers 85% of the population. The Ministry of Communication and Information Technology plans to expand its services in remote parts of the country where the remaining 15% of the population will be covered with the installation of 700 new towers. According to WikiLeaks, phone calls in Afghanistan have been monitored by the National Security Agency.
## Television
There are over 106 television operators in Afghanistan and 320 television transmitters, many of which are based Kabul, while others are broadcast from other provinces. Selected foreign channels are also shown to the public in Afghanistan, but with the use of the internet, over 3,500 international TV channels may be accessed in Afghanistan
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# Christian of Oliva
**Christian of Oliva** (*Chrystian z Oliwy*), also **Christian of Prussia** (*Christian von Preußen*) (died 4 December(?) 1245) was the first missionary bishop of Prussia.
## History
Christian was born about 1180 in the Duchy of Pomerania, possibly in the area of Chociwel (according to Johannes Voigt). Probably as a juvenile he joined the Cistercian Order at newly established Kołbacz (*Kolbatz*) Abbey and in 1209 entered Oliwa Abbey near Gdańsk, founded in 1178 by the Samboride dukes of Pomerelia. At this time the Piast duke Konrad I of Masovia with the consent of Pope Innocent III had started the first of several unsuccessful Prussian Crusades into the adjacent Chełmno Land and Christian acted as a missionary among the Prussians east of the Vistula River.
In 1209, Christian was commissioned by the Pope to be responsible for the Prussian missions between the Vistula and Neman Rivers and in 1212 he was appointed bishop. In 1215 he went to Rome in order to report to the Curia on the condition and prospects of his mission, and was consecrated first \"Bishop of Prussia\" at the Fourth Council of the Lateran. His seat as a bishop remained at Oliwa Abbey on the western side of the Vistula, whereas the pagan Prussian (later East Prussian) territory was on the eastern side of it.
The attempts by Konrad of Masovia to subdue the Prussian lands had picked long-term and intense border quarrels, whereby the Polish lands of Masovia, Cuyavia and even Greater Poland became subject to continuous Prussian raids. Bishop Christian asked the new Pope Honorius III for the consent to start another Crusade, however a first campaign in 1217 proved a failure and even the joint efforts by Duke Konrad with the Polish High Duke Leszek I the White and Duke Henry I the Bearded of Silesia in 1222/23 only led to the reconquest of Chełmno Land but did not stop the Prussian invasions. At least Christian was able to establish the Diocese of Chełmno east of the Vistula, adopting the episcopal rights from the Masovian Bishop of Płock, confirmed by both Duke Konrad and the Pope.
Duke Konrad of Masovia still was not capable to end the Prussian attacks on his territory and in 1226 began to conduct negotiations with the Teutonic Knights under Grand Master Hermann von Salza in order to strengthen his forces. As von Salza initially hesitated to offer his services, Christian created the military Order of Dobrzyń (*Fratres Milites Christi*) in 1228, however to little avail.
Meanwhile, von Salza had to abandon his hope to establish an Order\'s State in the Burzenland region of Transylvania, which had led to an éclat with King Andrew II of Hungary. He obtained a charter by Emperor Frederick II issued in the 1226 Golden Bull of Rimini, whereby Chełmno Land would be the unshared possession of the Teutonic Knights, which was confirmed by Duke Konrad of Masovia in the 1230 Treaty of Kruszwica. Christian ceded his possessions to the new State of the Teutonic Order and in turn was appointed Bishop of Chełmno the next year.
Bishop Christian continued his mission in Sambia (*Samland*), where from 1233 to 1239 he was held captive by pagan Prussians, and freed in trade for five other hostages who then in turn were released for a ransom of 800 Marks, granted to him by Pope Gregory IX. He had to deal with the constant cut-back of his autonomy by the Knights and asked the Roman Curia for mediation. In 1243, the Papal legate William of Modena divided the Prussian lands of the Order\'s State into four dioceses, whereby the bishops retained the secular rule over about on third of the diocesan territory:
- Bishopric of Chełmno (Chełmno Land, Ziemia Chełminska)
- Bishopric of Pomesania (Pomesania)
- Bishopric of Warmia (Ermland) (state)/ Diocese of Warmia (ecclesiastical ambit)
- Bishopric of Samland (Sambia)
all suffragan dioceses under the Archbishopric of Riga. Christian was supposed to choose one of them, but did not agree to the division. He possibly retired to the Cistercians Abbey in Sulejów, where he died before the conflict was solved
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# Cofinality
In mathematics, especially in order theory, the **cofinality** cf(*A*) of a partially ordered set *A* is the least of the cardinalities of the cofinal subsets of *A*. Formally,
$$\operatorname{cf}(A) = \inf \{|B| : B \subseteq A, (\forall x \in A) (\exists y \in B) (x \leq y)\}$$
This definition of cofinality relies on the axiom of choice, as it uses the fact that every non-empty set of cardinal numbers has a least member. The cofinality of a partially ordered set *A* can alternatively be defined as the least ordinal *x* such that there is a function from *x* to *A* with cofinal image. This second definition makes sense without the axiom of choice. If the axiom of choice is assumed, as will be the case in the rest of this article, then the two definitions are equivalent.
Cofinality can be similarly defined for a directed set and is used to generalize the notion of a subsequence in a net.
## Examples
- The cofinality of a partially ordered set with greatest element is 1 as the set consisting only of the greatest element is cofinal (and must be contained in every other cofinal subset).
- In particular, the cofinality of any nonzero finite ordinal, or indeed any finite directed set, is 1, since such sets have a greatest element.
- Every cofinal subset of a partially ordered set must contain all maximal elements of that set. Thus the cofinality of a finite partially ordered set is equal to the number of its maximal elements.
- In particular, let $A$ be a set of size $n,$ and consider the set of subsets of $A$ containing no more than $m$ elements. This is partially ordered under inclusion and the subsets with $m$ elements are maximal. Thus the cofinality of this poset is $n$ choose $m.$
- A subset of the natural numbers $\N$ is cofinal in $\N$ if and only if it is infinite, and therefore the cofinality of $\aleph_0$ is $\aleph_0.$ Thus $\aleph_0$ is a regular cardinal.
- The cofinality of the real numbers with their usual ordering is $\aleph_0,$ since $\N$ is cofinal in $\R.$ The usual ordering of $\R$ is not order isomorphic to $c,$ the cardinality of the real numbers, which has cofinality strictly greater than $\aleph_0.$ This demonstrates that the cofinality depends on the order; different orders on the same set may have different cofinality.
## Properties
If $A$ admits a totally ordered cofinal subset, then we can find a subset $B$ that is well-ordered and cofinal in $A.$ Any subset of $B$ is also well-ordered. Two cofinal subsets of $B$ with minimal cardinality (that is, their cardinality is the cofinality of $B$) need not be order isomorphic (for example if $B = \omega + \omega,$ then both $\omega + \omega$ and $\{\omega + n : n < \omega\}$ viewed as subsets of $B$ have the countable cardinality of the cofinality of $B$ but are not order isomorphic). But cofinal subsets of $B$ with minimal order type will be order isomorphic.
## Cofinality of ordinals and other well-ordered sets {#cofinality_of_ordinals_and_other_well_ordered_sets}
The **cofinality of an ordinal** $\alpha$ is the smallest ordinal $\delta$ that is the order type of a cofinal subset of $\alpha.$ The cofinality of a set of ordinals or any other well-ordered set is the cofinality of the order type of that set.
Thus for a limit ordinal $\alpha,$ there exists a $\delta$-indexed strictly increasing sequence with limit $\alpha.$ For example, the cofinality of $\omega^2$ is $\omega,$ because the sequence $\omega \cdot m$ (where $m$ ranges over the natural numbers) tends to $\omega^2;$ but, more generally, any countable limit ordinal has cofinality $\omega.$ An uncountable limit ordinal may have either cofinality $\omega$ as does $\omega_\omega$ or an uncountable cofinality.
The cofinality of 0 is 0. The cofinality of any successor ordinal is 1. The cofinality of any nonzero limit ordinal is an infinite regular cardinal.
## Regular and singular ordinals {#regular_and_singular_ordinals}
A **regular ordinal** is an ordinal that is equal to its cofinality. A **singular ordinal** is any ordinal that is not regular.
Every regular ordinal is the initial ordinal of a cardinal. Any limit of regular ordinals is a limit of initial ordinals and thus is also initial but need not be regular. Assuming the axiom of choice, $\omega_{\alpha+1}$ is regular for each $\alpha.$ In this case, the ordinals $0, 1, \omega, \omega_1,$ and $\omega_2$ are regular, whereas $2, 3, \omega_\omega,$ and $\omega_{\omega \cdot 2}$ are initial ordinals that are not regular.
The cofinality of any ordinal $\alpha$ is a regular ordinal, that is, the cofinality of the cofinality of $\alpha$ is the same as the cofinality of $\alpha.$ So the cofinality operation is idempotent.
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# Cofinality
## Cofinality of cardinals {#cofinality_of_cardinals}
If $\kappa$ is an infinite cardinal number, then $\operatorname{cf}(\kappa)$ is the least cardinal such that there is an unbounded function from $\operatorname{cf}(\kappa)$ to $\kappa;$ $\operatorname{cf}(\kappa)$ is also the cardinality of the smallest set of strictly smaller cardinals whose sum is $\kappa;$ more precisely $\operatorname{cf}(\kappa) = \min \left\{ |I|\ :\ \kappa = \sum_{i \in I} \lambda_i\ \land \forall i \in I \colon \lambda_i < \kappa\right\}.$
That the set above is nonempty comes from the fact that $\kappa = \bigcup_{i \in \kappa} \{i\}$ that is, the disjoint union of $\kappa$ singleton sets. This implies immediately that $\operatorname{cf}(\kappa) \leq \kappa.$ The cofinality of any totally ordered set is regular, so $\operatorname{cf}(\kappa) = \operatorname{cf}(\operatorname{cf}(\kappa)).$
Using König\'s theorem, one can prove $\kappa < \kappa^{\operatorname{cf}(\kappa)}$ and $\kappa < \operatorname{cf}\left(2^\kappa\right)$ for any infinite cardinal $\kappa.$
The last inequality implies that the cofinality of the cardinality of the continuum must be uncountable. On the other hand, $\aleph_\omega = \bigcup_{n < \omega} \aleph_n,$ the ordinal number ω being the first infinite ordinal, so that the cofinality of $\aleph_\omega$ is card(ω) = $\aleph_0.$ (In particular, $\aleph_\omega$ is singular.) Therefore, $2^{\aleph_0} \neq \aleph_\omega.$
(Compare to the continuum hypothesis, which states $2^{\aleph_0} = \aleph_1.$)
Generalizing this argument, one can prove that for a limit ordinal $\delta$ $\operatorname{cf} (\aleph_\delta) = \operatorname{cf} (\delta).$
On the other hand, if the axiom of choice holds, then for a successor or zero ordinal $\delta$ $\operatorname{cf} (\aleph_\delta) = \aleph_\delta
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# Citadel
A **citadel** is the most fortified area of a town or city. It may be a castle, fortress, or fortified center. The term is a diminutive of *city*, meaning \"little city\", because it is a smaller part of the city of which it is the defensive core.
In a fortification with bastions, the citadel is the strongest part of the system, sometimes well inside the outer walls and bastions, but often forming part of the outer wall for the sake of economy. It is positioned to be the last line of defence, should the enemy breach the other components of the fortification system.
## History
### 3300--1300 BC
Some of the oldest known structures which have served as citadels were built by the Indus Valley civilisation, where citadels represented a centralised authority. Citadels in Indus Valley were almost 12 meters tall. The purpose of these structures, however, remains debated. Though the structures found in the ruins of Mohenjo-daro were walled, it is far from clear that these structures were defensive against enemy attacks. Rather, they may have been built to divert flood waters.
Several settlements in Anatolia, including the Assyrian cities of Kaneš in modern-day Kültepe, featured citadels. Kaneš\' citadel contained the city\'s palace, temples, and official buildings. The citadel of the Greek city of Mycenae was built atop a highly-defensible rectangular hill and was later surrounded by walls in order to increase its defensive capabilities.
### 800 BC -- 400 AD {#bc_400_ad}
In Ancient Greece, the Acropolis, which literally means \"high city\", placed on a commanding eminence, was important in the life of the people, serving as a lookout, a refuge, and a stronghold in peril, as well as containing military and food supplies, the shrine of the god and a royal palace. The most well known is the Acropolis of Athens, but nearly every Greek city-state had one -- the Acrocorinth is famed as a particularly strong fortress. In a much later period, when Greece was ruled by the Latin Empire, the same strong points were used by the new feudal rulers for much the same purpose.
In the first millennium BC, the Castro culture emerged in northwestern Portugal and Spain in the region extending from the Douro river up to the Minho, but soon expanding north along the coast, and east following the river valleys. It was an autochthonous evolution of Atlantic Bronze Age communities. In 2008, the origins of the Celts were attributed to this period by John T. Koch and supported by Barry Cunliffe. The Ave River Valley in Portugal was the core region of this culture, with a large number of small settlements (the *castros*), but also settlements known as citadels or oppida by the Roman conquerors. These had several rings of walls and the Roman conquest of the citadels of Abobriga, Lambriaca and Cinania around 138 BC was possible only by prolonged siege. Ruins of notable citadels still exist, and are known by archaeologists as Citânia de Briteiros, Citânia de Sanfins, Cividade de Terroso and Cividade de Bagunte.
#### 167--160 BC {#bc_1}
Rebels who took power in a city, but with the citadel still held by the former rulers, could by no means regard their tenure of power as secure. One such incident played an important part in the history of the Maccabean Revolt against the Seleucid Empire. The Hellenistic garrison of Jerusalem and local supporters of the Seleucids held out for many years in the Acra citadel, making Maccabean rule in the rest of Jerusalem precarious. When finally gaining possession of the place, the Maccabeans pointedly destroyed and razed the Acra, though they constructed another citadel for their own use in a different part of Jerusalem.
### 400--1600
At various periods, and particularly during the Middle Ages and the Renaissance, the citadel -- having its own fortifications, independent of the city walls -- was the last defence of a besieged army, often held after the town had been conquered. Locals and defending armies have often held out citadels long after the city had fallen. For example, in the 1543 Siege of Nice the Ottoman forces led by Barbarossa conquered and pillaged the town and took many captives, but the citadel held out.
In the Philippines, the Ivatan people of the northern islands of Batanes often built fortifications to protect themselves during times of war. They built their so-called *idjangs* on hills and elevated areas. These fortifications were likened to European castles because of their purpose. Usually, the only entrance to the castles would be via a rope ladder that would only be lowered for the villagers and could be kept away when invaders arrived.
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# Citadel
## History
### 1600 to the present {#to_the_present}
In times of war, the citadel in many cases afforded retreat to the people living in the areas around the town. However, citadels were often used also to protect a garrison or political power from the inhabitants of the town where it was located, being designed to ensure loyalty from the town that they defended. This was used, for example, during the Dutch Wars of 1664--1667, King Charles II of England constructed a Royal Citadel at Plymouth, an important channel port which needed to be defended from a possible naval attack. However, due to Plymouth\'s support for the Parliamentarians, in the then-recent English Civil War, the Plymouth Citadel was so designed that its guns could fire on the town as well as on the sea approaches.
Barcelona had a great citadel built in 1714 to intimidate the Catalans against repeating their mid-17th- and early-18th-century rebellions against the Spanish central government. In the 19th century, when the political climate had liberalized enough to permit it, the people of Barcelona had the citadel torn down, and replaced it with the city\'s main central park, the Parc de la Ciutadella. A similar example is the Citadella in Budapest, Hungary.
The attack on the Bastille in the French Revolution -- though afterwards remembered mainly for the release of the handful of prisoners incarcerated there -- was to considerable degree motivated by the structure\'s being a Royal citadel in the midst of revolutionary Paris.
Similarly, after Garibaldi\'s overthrow of Bourbon rule in Palermo, during the 1860 Unification of Italy, Palermo\'s Castellamare Citadel -- a symbol of the hated and oppressive former rule -- was ceremoniously demolished.
Following Belgium gaining its independence in 1830, a Dutch garrison under General David Hendrik Chassé held out in Antwerp Citadel between 1830 and 1832, while the city had already become part of independent Belgium.
The Siege of the Alcázar in the Spanish Civil War, in which the Nationalists held out against a much larger Republican force for two months until relieved, shows that in some cases a citadel can be effective even in modern warfare; a similar case is the Battle of Huế during the Vietnam War, where a North Vietnamese Army division held the citadel of Huế for 26 days against roughly their own numbers of much better-equipped US and South Vietnamese troops.
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# Citadel
## History
### Modern usage {#modern_usage}
The Citadelle of Québec (the construction was started in 1673 and completed in 1820) still survives as the largest citadel still in official military operation in North America. It is home to the Royal 22nd Regiment of the Canadian Army and forms part of the Ramparts of Quebec City dating back to 1620s.
Since the mid 20th century, citadels have commonly enclosed military command and control centres, rather than cities or strategic points of defence on the boundaries of a country. These modern citadels are built to protect the command centre from heavy attacks, such as aerial or nuclear bombardment. The military citadels under London in the UK, including the massive underground complex Pindar beneath the Ministry of Defence, are examples, as is the Cheyenne Mountain nuclear bunker in the US.
## Naval term {#naval_term}
On armoured warships, the heavily armoured section of the ship that protects the ammunition and machinery spaces is called the armoured citadel.
A modern naval interpretation refers to the heaviest protected part of the hull as \"the vitals\", and the citadel is the semi-armoured freeboard above the vitals. Generally, Anglo-American and German languages follow this while Russian sources/language refer to \"the vitals\" as цитадель \"citadel\". Likewise, Russian literature often refers to the turret of a tank as the \'tower\'.
The safe room on a ship is also called a citadel
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# Cerberus
In Greek mythology, **Cerberus** (`{{IPAc-en|ˈ|s|ɜr|b|ər|ə|s|audio=LL-Q1860 (eng)-Naomi Persephone Amethyst (NaomiAmethyst)-Cerberus.wav}}`{=mediawiki} or `{{IPAc-en|ˈ|k|ɜr|b|ər|ə|s}}`{=mediawiki}; *Κέρβερος* *Kérberos* `{{IPA|el|ˈkerberos|}}`{=mediawiki}), often referred to as the **hound of Hades**, is a multi-headed dog that guards the gates of the underworld to prevent the dead from leaving. He was the offspring of the monsters Echidna and Typhon, and was usually described as having three heads, a serpent for a tail, and snakes protruding from his body. Cerberus is primarily known for his capture by Heracles, the last of Heracles\' twelve labours.
## Etymology
The etymology of Cerberus\' name is uncertain. Ogden refers to attempts to establish an Indo-European etymology as \"not yet successful\". It has been claimed to be related to the Sanskrit word सर्वरा *sarvarā*, used as an epithet of one of the dogs of Yama, from a Proto-Indo-European word \**k̑érberos*, meaning \"spotted\". Lincoln (1991), among others, critiques this etymology. This etymology was also rejected by Manfred Mayrhofer, who proposed an Austro-Asiatic origin for the word, and by Beekes. Lincoln notes a similarity between Cerberus and the Norse mythological dog Garmr, relating both names to a Proto-Indo-European root *\*ger-* \"to growl\" (perhaps with the suffixes *-\*m/\*b* and *-\*r*). However, as Ogden observes, this analysis actually requires *Kerberos* and *Garmr* to be derived from two *different* Indo-European roots (\**ker-* and \**gher-* respectively), and so does not actually establish a relationship between the two names.
Though probably not Greek, Greek etymologies for Cerberus have been offered. An etymology given by Servius (the late-fourth-century commentator on Virgil)---but rejected by Ogden---derives Cerberus from the Greek word *creoboros* meaning \"flesh-devouring\". Another suggested etymology derives Cerberus from \"Ker berethrou\", meaning \"evil of the pit\".
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# Cerberus
## Descriptions
Descriptions of Cerberus vary, including the number of his heads. Cerberus was usually three-headed, though not always. Cerberus had several multi-headed relatives. His father was the multi snake-footed Typhon, and Cerberus was the brother of three other multi-headed monsters, the multi-snake-headed Lernaean Hydra; Orthrus, the two-headed dog that guarded the Cattle of Geryon; and the Chimera, who had three heads: that of a lion, a goat, and a snake. And, like these close relatives, Cerberus was, with only the rare iconographic exception, multi-headed.
In the earliest description of Cerberus, Hesiod\'s *Theogony* (c. 8th -- 7th century BC), Cerberus has fifty heads, while Pindar (c. 522 -- c. 443 BC) gave him one hundred heads. However, later writers almost universally give Cerberus three heads. An exception is the Latin poet Horace\'s Cerberus which has a single dog head, and one hundred snake heads. Perhaps trying to reconcile these competing traditions, Apollodorus\'s Cerberus has three dog heads and the heads of \"all sorts of snakes\" along his back, while the Byzantine poet John Tzetzes (who probably based his account on Apollodorus) gives Cerberus fifty heads, three of which were dog heads, the rest being the \"heads of other beasts of all sorts\".
In art Cerberus is most commonly depicted with two dog heads (visible), never more than three, but occasionally with only one. On one of the two earliest depictions (c. 590--580 BC), a Corinthian cup from Argos (see below), now lost, Cerberus was shown as a normal single-headed dog. The first appearance of a three-headed Cerberus occurs on a mid-sixth-century BC Laconian cup (see below).
Horace\'s many snake-headed Cerberus followed a long tradition of Cerberus being part snake. This is perhaps already implied as early as in Hesiod\'s *Theogony*, where Cerberus\' mother is the half-snake Echidna, and his father the snake-headed Typhon. In art, Cerberus is often shown as being part snake, for example the lost Corinthian cup showed snakes protruding from Cerberus\' body, while the mid sixth-century BC Laconian cup gives Cerberus a snake for a tail. In the literary record, the first certain indication of Cerberus\' serpentine nature comes from the rationalized account of Hecataeus of Miletus (fl. 500--494 BC), who makes Cerberus a large poisonous snake. Plato refers to Cerberus\' composite nature, and Euphorion of Chalcis (3rd century BC) describes Cerberus as having multiple snake tails, and presumably in connection to his serpentine nature, associates Cerberus with the creation of the poisonous aconite plant. Virgil has snakes writhe around Cerberus\' neck, Ovid\'s Cerberus has a venomous mouth, necks \"vile with snakes\", and \"hair inwoven with the threatening snake\", while Seneca gives Cerberus a mane consisting of snakes, and a single snake tail.
Cerberus was given various other traits. According to Euripides, Cerberus not only had three heads but three bodies, and according to Virgil he had multiple backs. Cerberus ate raw flesh (according to Hesiod), had eyes which flashed fire (according to Euphorion), a three-tongued mouth (according to Horace), and acute hearing (according to Seneca).
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# Cerberus
## Twelfth Labour of Heracles {#twelfth_labour_of_heracles}
Cerberus\' only mythology concerns his capture by Heracles. As early as Homer we learn that Heracles was sent by Eurystheus, the king of Tiryns, to bring back Cerberus from Hades the king of the underworld. According to Apollodorus, this was the twelfth and final labour imposed on Heracles. In a fragment from a lost play *Pirithous*, (attributed to either Euripides or Critias) Heracles says that, although Eurystheus commanded him to bring back Cerberus, it was not from any desire to see Cerberus, but only because Eurystheus thought that the task was impossible.
Heracles was aided in his mission by his being an initiate of the Eleusinian Mysteries. Euripides has his initiation being \"lucky\" for Heracles in capturing Cerberus. And both Diodorus Siculus and Apollodorus say that Heracles was initiated into the Mysteries, in preparation for his descent into the underworld. According to Diodorus, Heracles went to Athens, where Musaeus, the son of Orpheus, was in charge of the initiation rites, while according to Apollodorus, he went to Eumolpus at Eleusis.
Heracles also had the help of Hermes, the usual guide of the underworld, as well as Athena. In the *Odyssey*, Homer has Hermes and Athena as his guides. And Hermes and Athena are often shown with Heracles on vase paintings depicting Cerberus\' capture. By most accounts, Heracles made his descent into the underworld through an entrance at Tainaron, the most famous of the various Greek entrances to the underworld. The place is first mentioned in connection with the Cerberus story in the rationalized account of Hecataeus of Miletus (fl. 500--494 BC), and Euripides, Seneca, and Apolodorus, all have Heracles descend into the underworld there. However Xenophon reports that Heracles was said to have descended at the Acherusian Chersonese near Heraclea Pontica, on the Black Sea, a place more usually associated with Heracles\' exit from the underworld (see below). Heraclea, founded c. 560 BC, perhaps took its name from the association of its site with Heracles\' Cerberian exploit.
### Theseus and Pirithous {#theseus_and_pirithous}
While in the underworld, Heracles met the heroes Theseus and Pirithous, where the two companions were being held prisoner by Hades for attempting to carry off Hades\'s wife Persephone. Along with bringing back Cerberus, Heracles also managed (usually) to rescue Theseus, and in some versions Pirithous as well. According to Apollodorus, Heracles found Theseus and Pirithous near the gates of Hades, bound to the \"Chair of Forgetfulness, to which they grew and were held fast by coils of serpents\", and when they saw Heracles, \"they stretched out their hands as if they should be raised from the dead by his might\", and Heracles was able to free Theseus, but when he tried to raise up Pirithous, \"the earth quaked and he let go.\"
The earliest evidence for the involvement of Theseus and Pirithous in the Cerberus story, is found on a shield-band relief (c. 560 BC) from Olympia, where Theseus and Pirithous (named) are seated together on a chair, arms held out in supplication, while Heracles approaches, about to draw his sword. The earliest literary mention of the rescue occurs in Euripides, where Heracles saves Theseus (with no mention of Pirithous). In the lost play *Pirithous*, both heroes are rescued, while in the rationalized account of Philochorus, Heracles was able to rescue Theseus, but not Pirithous. In one place Diodorus says Heracles brought back both Theseus and Pirithous, by the favor of Persephone, while in another he says that Pirithous remained in Hades, or according to \"some writers of myth\" that neither Theseus, nor Pirithous returned. Both are rescued in the *Fabulae* of Hyginus.
### Capture
There are various versions of how Heracles accomplished Cerberus\' capture. According to Apollodorus, Heracles asked Hades for Cerberus, and Hades told Heracles he would allow him to take Cerberus only if he \"mastered him without the use of the weapons which he carried\", and so, using his lion-skin as a shield, Heracles squeezed Cerberus around the head until he submitted.
In some early sources Cerberus\' capture seems to involve Heracles fighting Hades. Homer (*Iliad* 5.395--397) has Hades injured by an arrow shot by Heracles. A scholium to the *Iliad* passage, explains that Hades had commanded that Heracles \"master Cerberus without shield or Iron\". Heracles did this, by (as in Apollodorus) using his lion-skin instead of his shield, and making stone points for his arrows, but when Hades still opposed him, Heracles shot Hades in anger. Consistent with the no iron requirement, on an early-sixth-century BC lost Corinthian cup, Heracles is shown attacking Hades with a stone, while the iconographic tradition, from c. 560 BC, often shows Heracles using his wooden club against Cerberus.
Euripides has Amphitryon ask Heracles: \"Did you conquer him in fight, or receive him from the goddess \[i.e. Persephone\]? To which Heracles answers: \"In fight\", and the *Pirithous* fragment says that Heracles \"overcame the beast by force\". However, according to Diodorus, Persephone welcomed Heracles \"like a brother\" and gave Cerberus \"in chains\" to Heracles. Aristophanes has Heracles seize Cerberus in a stranglehold and run off, while Seneca has Heracles again use his lion-skin as shield, and his wooden club, to subdue Cerberus, after which a quailing Hades and Persephone allow Heracles to lead a chained and submissive Cerberus away. Cerberus is often shown being chained, and Ovid tells that Heracles dragged the three headed Cerberus with chains of adamant.
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# Cerberus
## Twelfth Labour of Heracles {#twelfth_labour_of_heracles}
### Exit from the underworld {#exit_from_the_underworld}
There were several locations which were said to be the place where Heracles brought up Cerberus from the underworld. The geographer Strabo (63/64 BC -- c. AD 24) reports that \"according to the myth writers\" Cerberus was brought up at Tainaron, the same place where Euripides has Heracles enter the underworld. Seneca has Heracles enter and exit at Tainaron. Apollodorus, although he has Heracles enter at Tainaron, has him exit at Troezen. The geographer Pausanias tells us that there was a temple at Troezen with \"altars to the gods said to rule under the earth\", where it was said that, in addition to Cerberus being \"dragged\" up by Heracles, Semele was supposed to have been brought up out of the underworld by Dionysus.
Another tradition had Cerberus brought up at Heraclea Pontica (the same place which Xenophon had earlier associated with Heracles\' descent) and the cause of the poisonous plant aconite which grew there in abundance. Herodorus of Heraclea and Euphorion said that when Heracles brought Cerberus up from the underworld at Heraclea, Cerberus \"vomited bile\" from which the aconite plant grew up. Ovid, also makes Cerberus the cause of the poisonous aconite, saying that on the \"shores of Scythia\", upon leaving the underworld, as Cerberus was being dragged by Heracles from a cave, dazzled by the unaccustomed daylight, Cerberus spewed out a \"poison-foam\", which made the aconite plants growing there poisonous. Seneca\'s Cerberus too, like Ovid\'s, reacts violently to his first sight of daylight. Enraged, the previously submissive Cerberus struggles furiously, and Heracles and Theseus must together drag Cerberus into the light.
Pausanias reports that according to local legend Cerberus was brought up through a chasm in the earth dedicated to Clymenus (Hades) next to the sanctuary of Chthonia at Hermione, and in Euripides\' *Heracles*, though Euripides does not say that Cerberus was brought out there, he has Cerberus kept for a while in the \"grove of Chthonia\" at Hermione. Pausanias also mentions that at Mount Laphystion in Boeotia, that there was a statue of Heracles Charops (\"with bright eyes\"), where the Boeotians said Heracles brought up Cerberus. Other locations which perhaps were also associated with Cerberus being brought out of the underworld include, Hierapolis, Thesprotia, and Emeia near Mycenae.
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# Cerberus
## Twelfth Labour of Heracles {#twelfth_labour_of_heracles}
### Presented to Eurystheus, returned to Hades {#presented_to_eurystheus_returned_to_hades}
In some accounts, after bringing Cerberus up from the underworld, Heracles paraded the captured Cerberus through Greece. Euphorion has Heracles lead Cerberus through Midea in Argolis, as women and children watch in fear, and Diodorus Siculus says of Cerberus, that Heracles \"carried him away to the amazement of all and exhibited him to men.\" Seneca has Juno complain of Heracles \"highhandedly parading the black hound through Argive cities\" and Heracles greeted by laurel-wreathed crowds, \"singing\" his praises.
Then, according to Apollodorus, Heracles showed Cerberus to Eurystheus, as commanded, after which he returned Cerberus to the underworld. However, according to Hesychius of Alexandria, Cerberus escaped, presumably returning to the underworld on his own.
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# Cerberus
## Iconography
thumb\|upright=1.3\|One of the two earliest depictions of the capture of Cerberus (composed of the last five figures on the right) shows, from right to left: Cerberus, with a single dog head and snakes rising from his body, fleeing right, Hermes, with his characteristic hat (*petasos*) and caduceus, Heracles, with quiver on his back, stone in left hand, and bow in right, a goddess, standing in front of Hades\' throne, facing Heracles, and Hades, with scepter, fleeing left. Drawing of a lost Corinthian cup (c. 590--580 BC) from Argos.
The capture of Cerberus was a popular theme in ancient Greek and Roman art. The earliest depictions date from the beginning of the sixth century BC. One of the two earliest depictions, a Corinthian cup (c. 590--580 BC) from Argos (now lost), shows a naked Heracles, with quiver on his back and bow in his right hand, striding left, accompanied by Hermes. Heracles threatens Hades with a stone, who flees left, while a goddess, perhaps Persephone or possibly Athena, standing in front of Hades\' throne, prevents the attack. Cerberus, with a single canine head and snakes rising from his head and body, flees right. On the far right a column indicates the entrance to Hades\' palace. Many of the elements of this scene---Hermes, Athena, Hades, Persephone, and a column or portico---are common occurrences in later works. The other earliest depiction, a relief *pithos* fragment from Crete (c. 590--570 BC), is thought to show a single lion-headed Cerberus with a snake (open-mouthed) over his back being led to the right.
A mid-sixth-century BC Laconian cup by the Hunt Painter adds several new features to the scene which also become common in later works: three heads, a snake tail, Cerberus\' chain and Heracles\' club. Here Cerberus has three canine heads, is covered by a shaggy coat of snakes, and has a tail which ends in a snake head. He is being held on a chain leash by Heracles who holds his club raised over head.
In Greek art, the vast majority of depictions of Heracles and Cerberus occur on Attic vases. Although the lost Corinthian cup shows Cerberus with a single dog head, and the relief *pithos* fragment (c. 590--570 BC) apparently shows a single lion-headed Cerberus, in Attic vase painting Cerberus usually has two dog heads. In other art, as in the Laconian cup, Cerberus is usually three-headed. Occasionally in Roman art Cerberus is shown with a large central lion head and two smaller dog heads on either side.
As in the Corinthian and Laconian cups (and possibly the relief *pithos* fragment), Cerberus is often depicted as part snake. In Attic vase painting, Cerberus is usually shown with a snake for a tail or a tail which ends in the head of a snake. Snakes are also often shown rising from various parts of his body including snout, head, neck, back, ankles, and paws.
Two Attic amphoras from Vulci, one (c. 530--515 BC) by the Bucci Painter (Munich 1493), the other (c. 525--510 BC) by the Andokides painter (Louvre F204), in addition to the usual two heads and snake tail, show Cerberus with a mane down his necks and back, another typical Cerberian feature of Attic vase painting. Andokides\' amphora also has a small snake curling up from each of Cerberus\' two heads.
Besides this lion-like mane and the occasional lion-head mentioned above, Cerberus was sometimes shown with other leonine features. A pitcher (c. 530--500) shows Cerberus with mane and claws, while a first-century BC sardonyx cameo shows Cerberus with leonine body and paws. In addition, a limestone relief fragment from Taranto (c. 320--300 BC) shows Cerberus with three lion-like heads.
During the second quarter of the 5th century BC the capture of Cerberus disappears from Attic vase painting. After the early third century BC, the subject becomes rare everywhere until the Roman period. In Roman art the capture of Cerberus is usually shown together with other labors. Heracles and Cerberus are usually alone, with Heracles leading Cerberus.
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# Cerberus
## Cerberus rationalized {#cerberus_rationalized}
At least as early as the 6th century BC, some ancient writers attempted to explain away various fantastical features of Greek mythology; included in these are various rationalized accounts of the Cerberus story. The earliest such account (late 6th century BC) is that of Hecataeus of Miletus. In his account Cerberus was not a dog at all, but rather simply a large venomous snake, which lived on Tainaron. The serpent was called the \"hound of Hades\" only because anyone bitten by it died immediately, and it was this snake that Heracles brought to Eurystheus. The geographer Pausanias (who preserves for us Hecataeus\' version of the story) points out that, since Homer does not describe Cerberus, Hecataeus\' account does not necessarily conflict with Homer, since Homer\'s \"Hound of Hades\" may not in fact refer to an actual dog.
Other rationalized accounts make Cerberus out to be a normal dog. According to Palaephatus (4th century BC) Cerberus was one of the two dogs who guarded the cattle of Geryon, the other being Orthrus. Geryon lived in a city named Tricranium (in Greek *Tricarenia*, \"Three-Heads\"), from which name both Cerberus and Geryon came to be called \"three-headed\". Heracles killed Orthus, and drove away Geryon\'s cattle, with Cerberus following along behind. Molossus, a Mycenaen, offered to buy Cerberus from Eurystheus (presumably having received the dog, along with the cattle, from Heracles). But when Eurystheus refused, Molossus stole the dog and penned him up in a cave in Tainaron. Eurystheus commanded Heracles to find Cerberus and bring him back. After searching the entire Peloponnesus, Heracles found where it was said Cerberus was being held, went down into the cave, and brought up Cerberus, after which it was said: \"Heracles descended through the cave into Hades and brought up Cerberus.\"
In the rationalized account of Philochorus, in which Heracles rescues Theseus, Perithous is eaten by Cerberus. In this version of the story, Aidoneus (i.e., \"Hades\") is the mortal king of the Molossians, with a wife named Persephone, a daughter named Kore (another name for the goddess Persephone) and a large mortal dog named Cerberus, with whom all suitors of his daughter were required to fight. After having stolen Helen, to be Theseus\' wife, Theseus and Perithous, attempt to abduct Kore, for Perithous, but Aidoneus catches the two heroes, imprisons Theseus, and feeds Perithous to Cerberus. Later, while a guest of Aidoneus, Heracles asks Aidoneus to release Theseus, as a favor, which Aidoneus grants.
A 2nd-century AD Greek known as Heraclitus the paradoxographer (not to be confused with the 5th-century BC Greek philosopher Heraclitus)---claimed that Cerberus had two pups that were never away from their father, which made Cerberus appear to be three-headed.
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# Cerberus
## Cerberus allegorized {#cerberus_allegorized}
Servius, a medieval commentator on Virgil\'s *Aeneid*, derived Cerberus\' name from the Greek word *creoboros* meaning \"flesh-devouring\" (see above), and held that Cerberus symbolized the corpse-consuming earth, with Heracles\' triumph over Cerberus representing his victory over earthly desires. Later, the mythographer Fulgentius, allegorizes Cerberus\' three heads as representing the three origins of human strife: \"nature, cause, and accident\", and (drawing on the same flesh-devouring etymology as Servius) as symbolizing \"the three ages---infancy, youth, old age, at which death enters the world.\" The Byzantine historian and bishop Eusebius wrote that Cerberus was represented with three heads, because the positions of the sun above the earth are three---rising, midday, and setting.
The later Vatican Mythographers repeat and expand upon the traditions of Servius and Fulgentius. All three Vatican Mythographers repeat Servius\' derivation of Cerberus\' name from *creoboros*. The Second Vatican Mythographer repeats (nearly word for word) what Fulgentius had to say about Cerberus, while the Third Vatican Mythographer, in another very similar passage to Fugentius\', says (more specifically than Fugentius), that for \"the philosophers\" Cerberus represented hatred, his three heads symbolizing the three kinds of human hatred: natural, causal, and casual (i.e. accidental).
The Second and Third Vatican Mythographers, note that the three brothers Zeus, Poseidon and Hades each have tripartite insignia, associating Hades\' three-headed Cerberus, with Zeus\' three-forked thunderbolt, and Poseidon\'s three-pronged trident, while the Third Vatican Mythographer adds that \"some philosophers think of Cerberus as the tripartite earth: Asia, Africa, and Europe. This earth, swallowing up bodies, sends souls to Tartarus.\"
Virgil described Cerberus as \"ravenous\" (*fame rabida*), and a rapacious Cerberus became proverbial. Thus Cerberus came to symbolize avarice, and so, for example, in Dante\'s *Inferno,* Cerberus is placed in the Third Circle of Hell, guarding over the gluttons, where he \"rends the spirits, flays and quarters them,\" and Dante (perhaps echoing Servius\' association of Cerberus with earth) has his guide Virgil take up handfuls of earth and throw them into Cerberus\' \"rapacious gullets.\"
## Namesakes
In the constellation Cerberus introduced by Johannes Hevelius in 1687, Cerberus is drawn as a three-headed snake, held in Hercules\' hand (previously these stars had been depicted as a branch of the tree on which grew the Apples of the Hesperides).
In 1829, French naturalist Georges Cuvier gave the name *Cerberus* to a genus of Asian snakes, which are commonly called \"dog-faced water snakes\" in English.
In 1988 the Massachusetts Institute of Technology (MIT) developed Kerberos, a computer-network authentication protocol, named after Cerberus.
In 2023 European heatwaves, the most significant of which was named \"Cerberus Heatwave\", which brought the hottest temperatures ever recorded in Europe
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# Cardinal vowels
**Cardinal vowels** are a set of reference vowels used by phoneticians in describing the sounds of languages. They are classified depending on the position of the tongue relative to the roof of the mouth, how far forward or back is the highest point of the tongue, and the position of the lips (rounded or unrounded).
A cardinal vowel is a vowel sound produced when the tongue is in an extreme position, either front or back, high or low. The current system was systematised by Daniel Jones in the early 20th century, though the idea goes back to earlier phoneticians, notably Ellis and Bell.
## Table of cardinal vowels {#table_of_cardinal_vowels}
Three of the cardinal vowels---`{{IPA|[i]}}`{=mediawiki}, `{{IPA|[ɑ]}}`{=mediawiki} and `{{IPA|[u]}}`{=mediawiki}---have articulatory definitions. The vowel `{{IPA|[i]}}`{=mediawiki} is produced with the tongue as far forward and as high in the mouth as is possible (without producing friction), with spread lips. The vowel `{{IPA|[u]}}`{=mediawiki} is produced with the tongue as far back and as high in the mouth as is possible, with protruded lips. This sound can be approximated by adopting the posture to whistle a very low note, or to blow out a candle. And `{{IPA|[ɑ]}}`{=mediawiki} is produced with the tongue as low and as far back in the mouth as possible.
The other vowels are \'auditorily equidistant\' between these three \'corner vowels\', at four degrees of aperture or \'height\': close (high tongue position), close-mid, open-mid, and open (low tongue position).
These degrees of aperture plus the front-back distinction define eight reference points on a mixture of articulatory and auditory criteria. These eight vowels are known as the eight \'primary cardinal vowels\', and vowels like these are common in the world\'s languages.
The lip positions can be reversed with the lip position for the corresponding vowel on the opposite side of the front-back dimension, so that e.g. Cardinal 1 can be produced with rounding somewhat similar to that of Cardinal 8; these are known as \'secondary cardinal vowels\'. Sounds such as these are claimed to be less common in the world\'s languages. Other vowel sounds are also recognised on the vowel chart of the International Phonetic Alphabet.
Jones argued that to be able to use the cardinal vowel system effectively one must undergo training with an expert phonetician, working both on the recognition and the production of the vowels.
Cardinal vowels are not vowels of any particular language, but a measuring system. However, some languages contain vowel or vowels that are close to the cardinal vowel(s). An example of such language is Ngwe, which is spoken in Cameroon. It has been cited as a language with a vowel system that has eight vowels which are rather similar to the eight primary cardinal vowels (Ladefoged 1971:67).
Number IPA Description
-------- ----- -----------------------------------
1 Close front unrounded vowel
2 Close-mid front unrounded vowel
3 Open-mid front unrounded vowel
4 Open front unrounded vowel
5 Open back unrounded vowel
6 Open-mid back rounded vowel
7 Close-mid back rounded vowel
8 Close back rounded vowel
9 Close front rounded vowel
10 Close-mid front rounded vowel
11 Open-mid front rounded vowel
12 Open front rounded vowel
13 Open back rounded vowel
14 Open-mid back unrounded vowel
15 Close-mid back unrounded vowel
16 Close back unrounded vowel
17 Close central unrounded vowel
18 Close central rounded vowel
19 Close-mid central unrounded vowel
20 Close-mid central rounded vowel
21 Open-mid central unrounded vowel
22 Open-mid central rounded vowel
Cardinal vowels 19--22 were added by David Abercrombie. In IPA Numbers, cardinal vowels 1--18 have the same numbers but added to 300.
## Limits on the accuracy of the system {#limits_on_the_accuracy_of_the_system}
The usual explanation of the cardinal vowel system implies that the competent user can reliably distinguish between sixteen Primary and Secondary vowels plus a small number of central vowels. The provision of diacritics by the International Phonetic Association further implies that intermediate values may also be reliably recognized, so that a phonetician might be able to produce and recognize not only a close-mid front unrounded vowel `{{IPA|[e]}}`{=mediawiki} and an open-mid front unrounded vowel `{{IPA|[ɛ]}}`{=mediawiki} but also a mid front unrounded vowel `{{IPA|[e̞]}}`{=mediawiki}, a centralized mid front unrounded vowel `{{IPA|[ë]}}`{=mediawiki}, and so on. This suggests a range of vowels nearer to forty or fifty than to twenty in number. Empirical evidence for this ability in trained phoneticians is hard to come by.
Ladefoged, in a series of pioneering experiments published in the 1950s and 60s, studied how trained phoneticians coped with the vowels of a dialect of Scottish Gaelic. He asked eighteen phoneticians to listen to a recording of ten words spoken by a native speaker of Gaelic and to place the vowels on a cardinal vowel quadrilateral. He then studied the degree of agreement or disagreement among the phoneticians. Ladefoged himself drew attention to the fact that the phoneticians who were trained in the British tradition established by Daniel Jones were closer to each other in their judgments than those who had not had this training. However, the most striking result is the great divergence of judgments among *all* the listeners regarding vowels that were distant from Cardinal values
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# Cross-country skiing
**Cross-country skiing** is a form of skiing whereby skiers traverse snow-covered terrain without use of ski lifts or other assistance. Cross-country skiing is widely practiced as a sport and recreational activity; however, some still use it as a means of travel. Variants of cross-country skiing are adapted to a range of terrain which spans unimproved, sometimes mountainous terrain to groomed courses that are specifically designed for the sport.
Modern cross-country skiing is similar to the original form of skiing, from which all skiing disciplines evolved, including alpine skiing, ski jumping and Telemark skiing. Skiers propel themselves either by striding forward (classic style) or side-to-side in a skating motion (skate skiing), aided by arms pushing on ski poles against the snow. It is practised in regions with snow-covered landscapes, including Europe, Canada, Russia, the United States, Australia and New Zealand.
Competitive cross-country skiing is one of the Nordic skiing sports. Cross-country skiing and rifle marksmanship are the two components of biathlon. Ski orienteering is a form of cross-country skiing, which includes map navigation along snow trails and tracks.
## History
The word ski comes from the Old Norse word *skíð* which means stick of wood. Skiing started as a technique for traveling cross-country over snow on skis, starting almost five millennia ago with beginnings in Scandinavia. It may have been practised as early as 600 BCE in Daxing\'anling, in what is now China. Early historical evidence includes Procopius\'s (around CE 550) description of Sami people as *skrithiphinoi* translated as \"ski running samis\". Birkely argues that the Sami people have practiced skiing for more than 6000 years, evidenced by the very old Sami word *čuoigat* for skiing. Egil Skallagrimsson\'s 950 CE saga describes King Haakon the Good\'s practice of sending his tax collectors out on skis. The Gulating law (1274) stated that \"No moose shall be disturbed by skiers on private land.\" Cross-country skiing evolved from a utilitarian means of transportation to being a worldwide recreational activity and sport, which branched out into other forms of skiing starting in the mid-1800s.
Early skiers used one long pole or spear in addition to the skis. The first depiction of a skier with two ski poles dates to 1741. Traditional skis, used for snow travel in Norway and elsewhere into the 1800s, often comprised one short ski with a natural fur traction surface, the *andor*, and one long for gliding, the *langski*---one being up to 100 cm longer than the other---allowing skiers to propel themselves with a scooter motion. This combination has a long history among the Sami people. Skis up to 280 cm have been produced in Finland, and the longest recorded ski in Norway is 373 cm.
### Transportation
Ski warfare, the use of ski-equipped troops in war, is first recorded by the Danish historian Saxo Grammaticus in the 13th century. These troops were reportedly able to cover distances comparable to that of light cavalry. The garrison in Trondheim used skis at least from 1675, and the Danish-Norwegian army included specialized skiing battalions from 1747---details of military ski exercises from 1767 are on record. Skis were used in military exercises in 1747. In 1799 French traveller Jacques de la Tocnaye recorded his visit to Norway in his travel diary: Norwegian immigrants used skis (\"Norwegian snowshoes\") in the US midwest from around 1836. Norwegian immigrant \"Snowshoe Thompson\" transported mail by skiing across the Sierra Nevada between California and Nevada from 1856. In 1888 Norwegian explorer Fridtjof Nansen and his team crossed the Greenland icecap on skis. Norwegian workers on the Buenos Aires - Valparaiso railway line introduced skiing in South America around 1890. In 1910 Roald Amundsen used skis on his South Pole Expedition. In 1902 the Norwegian consul in Kobe imported ski equipment and introduced skiing to the Japanese, motivated by the death of Japanese soldiers during a snow storm. Starting in 1919, Vladimir Lenin helped popularize the activity in the Soviet Union.
### Sport
`{{main article|Cross-country skiing (sport)}}`{=mediawiki} Norwegian skiing regiments organized military skiing contests in the 18th century, divided in four classes: shooting at a target while skiing at \"top speed\", downhill racing among trees, downhill racing on large slopes without falling, and \"long racing\" on \"flat ground\". An early record of a public ski competition occurred in Tromsø, 1843. In Norwegian, *langrenn* refers to \"competitive skiing where the goal is to complete a specific distance in groomed tracks in the shortest possible time\". In Norway, *ski touring competitions* (*turrenn*) are long-distance cross-country competitions open to the public, competition is usually within age intervals.
A new technique, skate skiing, was experimented with early in the 20th Century, but was not widely adopted until the 1980s. Johan Grøttumsbråten used the skating technique at the 1931 World Championship in Oberhof, one of the earliest recorded use of skating in competitive cross-country skiing. This technique was later used in ski orienteering in the 1960s on roads and other firm surfaces. It became widespread during the 1980s after the success of Bill Koch (United States) in 1982 Cross-country Skiing Championships drew more attention to the skating style. Norwegian skier Ove Aunli started using the technique in 1984, when he found it to be much faster than classic style. Finnish skier, Pauli Siitonen, developed a one-sided variant of the style in the 1970s, leaving one ski in the track while skating to the side with the other one during endurance events; this became known as the \"marathon skate\".
### Terminology
The word *ski* comes from the Old Norse word *skíð* which means \"cleft wood\", \"stick of wood\" or \"ski\". Norwegian language does not use a verb-form equivalent in idiomatic speech, unlike English \"to ski\". In modern Norwegian, a variety of terms refer to cross-country skiing, including:
- (literally \"walk on skis\")---a general term for self-propelled skiing
- (literally \"hiking on skis\")---refers to ski touring as recreation
- (literally \"long race\")---refers to cross-country ski racing
In contrast, alpine skiing is referred to as *stå på ski* (literally \"stand on skis\").
Fridtjof Nansen, describes the crossing of Greenland as *På ski over Grønland*, literally \"On skis across Greenland\", while the English edition of the report was titled, *The first crossing of Greenland*. Nansen referred to the activity of traversing snow on skis as *skilöbning* (he used the term also in the English translation), which may be translated as *ski running*. Nansen used *skilöbning*, regarding all forms of skiing, but noted that ski jumping is purely a competitive sport and not for amateurs. He further noted that in some competitions the skier \"is also required to show his skill in turning his ski to one side or the other within given marks\" at full speed on a steep hill. Nansen regarded these forms (i.e., jumping and slalom) as \"special arts\", and believed that the most important branch of skiing was travel \"in an ordinary way across the country\". In Germany, Nansen\'s Greenland report was published as *Auf Schneeschuhen durch Grönland* (literally \"On snowshoes through Greenland\"). The German term, *Schneeschuh*, was supplanted by the borrowed Norwegian word, *Ski*, in the late 19th century. The Norwegian encyclopedia of sports also uses the term, *skiløping*, (literally \"ski running\") for all forms of skiing. Around 1900 the word *Skilaufen* was used in German in the same sense as *skiløping*.
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# Cross-country skiing
## Recreation
Recreational cross-country skiing includes ski touring and groomed-trail skiing, typically at resorts or in parklands. It is an accessible form of recreation for persons with vision and mobility impairments. A related form of recreation is dog skijoring---a winter sport where a cross-country skier is assisted by one or more dogs.
### Ski touring {#ski_touring}
Ski touring takes place off-piste and outside of ski resorts. Tours may extend over multiple days. Typically, skis, bindings, and boots allow for free movement of the heel to enable a walking pace, as with Nordic disciplines and unlike Alpine skiing. Ski touring\'s subgenre ski mountaineering involves independently navigating and route finding through potential avalanche terrain and often requires familiarity with meteorology along with skiing skills. Ski touring can be faster and easier than summer hiking in some terrain, allowing for traverses and ascents that would be harder in the summer. Skis can also be used to access backcountry alpine climbing routes when snow is off the technical route, but still covers the hiking trail. In some countries, organizations maintain a network of huts for use by cross-country skiers in wintertime. For example, the Norwegian Trekking Association maintains over 400 huts stretching across thousands of kilometres of trails which hikers can use in the summer and skiers in the winter.
### Groomed-trail skiing {#groomed_trail_skiing}
Groomed trail skiing occurs at facilities such as Nordmarka (Oslo), Royal Gorge Cross Country Ski Resort and Gatineau Park in Quebec, where trails are laid out and groomed for both classic and skate-skiing. Such grooming and track setting (for classic technique) requires specialized equipment and techniques that adapt to the condition of the snow. Trail preparation employs snow machines which tow snow-compaction, texturing and track-setting devices. Groomers must adapt such equipment to the condition of the snow---crystal structure, temperature, degree of compaction, moisture content, etc. Depending on the initial condition of the snow, grooming may achieve an increase in density for new-fallen snow or a decrease in density for icy or compacted snow. Cross-country ski facilities may incorporate a course design that meets homologation standards for such organizations as the International Olympic Committee, the International Ski Federation, or national standards. Standards address course distances, degree of difficulty with maximums in elevation difference and steepness---both up and downhill, plus other factors. Some facilities have night-time lighting on select trails---called *lysløype* (light trails) in Norwegian and *elljusspår* (electric-light trails) in Swedish. The first *lysløype* opened in 1946 in Nordmarka and at Byåsen (Trondheim).
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# Cross-country skiing
## Competition
Cross-country ski competition encompasses a variety of formats for races over courses of varying lengths according to rules sanctioned by the International Ski and Snowboard Federation (FIS) and by national organizations, such as the U.S. Ski and Snowboard Association and Cross Country Ski Canada. It also encompasses cross-country ski marathon events, sanctioned by the Worldloppet Ski Federation, cross-country ski orienteering events, sanctioned by the International Orienteering Federation, and Paralympic cross-country skiing, sanctioned by the International Paralympic Committee.
### FIS-sanctioned competition {#fis_sanctioned_competition}
The FIS Nordic World Ski Championships have been held in various numbers and types of events since 1925 for men and since 1954 for women. From 1924 to 1939, the World Championships were held every year, including the Winter Olympic Games. After World War II, the World Championships were held every four years from 1950 to 1982. Since 1985, the World Championships have been held in odd-numbered years. Notable cross-country ski competitions include the Winter Olympics, the FIS Nordic World Ski Championships, and the FIS World Cup events (including the Holmenkollen).
### Other sanctioned competition {#other_sanctioned_competition}
Cross-country ski marathons---races with distances greater than 40 kilometers---have two cup series, the Ski Classics, which started in 2011, and the Worldloppet. Skiers race in classic or free-style (skating) events, depending on the rules of the race. Notable ski marathons, include the *Vasaloppet* in Sweden, *Birkebeineren* in Norway, the Tartu Maraton in Estonia, the Engadin Skimarathon in Switzerland, the American Birkebeiner, the Tour of Anchorage in Anchorage, Alaska, and the Boreal Loppet, held in Forestville, Quebec, Canada.
Biathlon combines cross-country skiing and rifle shooting. Depending on the shooting performance, extra distance or time is added to the contestant\'s total running distance/time. For each shooting round, the biathlete must hit five targets; the skier receives a penalty for each missed target, which varies according to the competition rules.
Ski orienteering is a form of cross-country skiing competition that requires navigation in a landscape, making optimal route choices at racing speeds. Standard orienteering maps are used, but with special green overprinting of trails and tracks to indicate their navigability in snow; other symbols indicate whether any roads are snow-covered or clear. Standard skate-skiing equipment is used, along with a map holder attached to the chest. It is one of the four orienteering disciplines recognized by the International Orienteering Federation. Upper body strength is especially important because of frequent double poling along narrow snow trails.
Paralympic cross-country ski competition is an adaptation of cross-country skiing for athletes with disabilities. Paralympic cross-country skiing includes standing events, sitting events (for wheelchair users), and events for visually impaired athletes under the rules of the International Paralympic Committee. These are divided into several categories for people who are missing limbs, have amputations, are blind, or have any other physical disability, to continue their sport.
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# Cross-country skiing
## Techniques
thumb\|Video of skiers demonstrating a variety of techniques. Cross-country skiing has two basic propulsion techniques, which apply to different surfaces: classic (undisturbed snow and tracked snow) and skate skiing (firm, smooth snow surfaces). The classic technique relies on a wax or texture on the ski bottom under the foot for traction on the snow to allow the skier to slide the other ski forward in virgin or tracked snow. With the skate skiing technique a skier slides on alternating skis on a firm snow surface at an angle from each other in a manner similar to ice skating. Both techniques employ poles with baskets that allow the arms to participate in the propulsion. Specialized equipment is adapted to each technique and each type of terrain. A variety of turns are used, when descending.
Poles contribute to forward propulsion, either simultaneously (usual for the skate technique) or in alternating sequence (common for the classical technique as the \"diagonal stride\"). Double poling is also used with the classical technique when higher speed can be achieved on flats and slight downhills than is available in the diagonal stride, which is favored to achieve higher power going uphill.
### Classic
The classic style is often used on prepared trails (pistes) that have pairs of parallel grooves (tracks) cut into the snow. It is also the most usual technique where no tracks have been prepared. With this technique, each ski is pushed forward from the other stationary ski in a striding and gliding motion, alternating foot to foot. With the \"diagonal stride\" variant the poles are planted alternately on the opposite side of the forward-striding foot; with the \"kick-double-pole\" variant the poles are planted simultaneously with every other stride. At times, especially with gentle descents, double poling is the sole means of propulsion. On uphill terrain, techniques include the \"side step\" for steep slopes, moving the skis perpendicular to the fall line, the \"herringbone\" for moderate slopes, where the skier takes alternating steps with the skis splayed outwards, and, for gentle slopes, the skier uses the diagonal technique with shorter strides and greater arm force on the poles.
### Skate skiing {#skate_skiing}
With skate skiing, the skier provides propulsion on a smooth, firm snow surface by pushing alternating skis away from one another at an angle, in a manner similar to ice skating. Skate-skiing usually involves a coordinated use of poles and the upper body to add impetus. Three common techniques are \"V1\", \"V2\" and \"V2 alternate\". In \"V1\" the skier pushes with a double pole plant each time the ski is extended on a temporarily \"dominant\" side, this technique is optimal for climbing. In \"V2 alternate\" the skier performs the double pole plant before the \"dominant\" ski is extended, this technique allows for maintaining a higher speed and is often used on slightly downhill terrain. In \"V2\" the skier performs the double pole plant each time the ski is extended on either side, on flat ground and in slight inclines this technique is often the fastest and most efficient of the 3. Skiers climb hills with these techniques by widening the angle of the \"V\" and by making more frequent, shorter strides and more forceful use of poles. A variant of the technique is the \"marathon skate\" or \"Siitonen step\", where the skier leaves one ski in the track while skating outwards to the side with the other ski.
### Turns
Turns, used while descending or for braking, include the snowplough (or \"wedge turn\"), the stem christie (or \"wedge christie\"), parallel turn, and the Telemark turn. The step turn is used for maintaining speed during descents or out of track on flats.
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# Cross-country skiing
## Equipment
Equipment comprises skis, poles, boots and bindings; these vary according to:
- Technique, classic vs skate
- Terrain, which may vary from groomed trails to wilderness
- Performance level, from recreational use to competition at the elite level
### Skis
Skis used in cross-country are lighter and narrower than those used in alpine skiing. Ski bottoms are designed to provide a gliding surface and, for classic skis, a traction zone under foot. The base of the gliding surface is a plastic material that is designed both to minimize friction and, in many cases, to accept waxes. Glide wax may be used on the tails and tips of classic skis and across the length of skate skis.
#### Types
Each type of ski is sized and designed differently. Length affects maneuverability; camber affects pressure on the snow beneath the feet of the skier; side-cut affects the ease of turning; width affects forward friction; overall area on the snow affects bearing capacity; and tip geometry affects the ability to penetrate new snow or to stay in a track. Each of the following ski types has a different combination of these attributes:
- **Classic skis**: Designed for skiing in tracks. For adult skiers (between 155 cm/50 kg and 185 cm/75 kg), recommended lengths are between 180 and 210 centimetres (approximately 115% of the skier\'s height). Traction comes from a \"grip zone\" underfoot that when bearing the skier\'s weight engages either a textured gripping surface or a grip wax. Accordingly, these skis are classified as \"waxable\" or \"waxless\". Recreational waxless skis generally require little attention and are adapted for casual use. Waxable skis, if prepared correctly, provide better grip and glide.
: When the skier\'s weight is distributed on both skis, the ski\'s camber diminishes the pressure of the grip zone on the snow and promotes bearing on the remaining area of the ski---the \"glide zone\". A test for stiffness of camber is made with a piece of paper under the skier\'s foot, standing on skis on a flat, hard surface---the paper should be pinned throughout the grip zone of the ski on which all the skier\'s weight is placed, but slide freely when the skier\'s weight is bearing equally on both skis.
- **Skate skis**: Designed for skiing on groomed surfaces. The usual recommended length is skier length +5-15cm. The entire bottom of each skate ski is a glide zone---prepared for maximum glide. Traction comes from the skier pushing away from the edge of the previous ski onto the next ski.
- **Back country skis**: Designed for ski touring on natural snow conditions. Recommended lengths are between 150 and 195 centimeters for adult skiers, depending on height and weight of the user. Back country skis are typically heavier and wider than classic and skate skis; they often have metal edges for better grip on hard snow; and their greater sidecut helps to carve turns.
: The geometry of a back country ski depends on its purpose---skis suited for forested areas where loose powder can predominate may be shorter and wider than those selected for open, exposed areas where compacted snow may prevail. Sidecut on Telemark skis promotes turning in forest and rugged terrain. Width and short length aid turning in loose and deep snow. Longer, narrower and more rigid skis with sharp edges are suited for snow that has been compacted by wind or freeze-thaw. Touring ski design may represent a general-purpose compromise among these different ski conditions, plus being acceptable for use in groomed tracks. Traction may come from a textured or waxed grip zone, as with classic skis, or from ski skins, which are applied to the ski bottom for long, steep ascents and have hairs or mechanical texture that prevents sliding backwards.
#### Gliding surface {#gliding_surface}
Glide waxes enhance the speed of the gliding surface. The wax is either melted on the base using an iron or applied in a liquid form. The excess wax is first scraped off and then finished by brushing. Most glide waxes are based on paraffin that is combined with additive materials. The paraffin hardness and additives are varied based on snow type, humidity and temperature. Since the 2021-2022 race season, fluorinated products are banned in FIS sanctioned competitions. Before the ban, most race waxes combined fluorinated hydrocarbon waxes with fluorocarbon overlays. Fluorocarbons decrease surface tension and surface area of the water between the ski and the snow, increasing speed and glide of the ski under specific conditions. Either combined with the wax or applied after in a spray, powder, or block form, fluorocarbons significantly improve the glide of the ski.
#### Traction surface {#traction_surface}
Skis designed for classic technique, both in track and in virgin snow, rely on a traction zone, called the \"grip zone\" or \"kick zone\", underfoot. This comes either from a) *texture*, such as \"fish scales\" or mohair skins, designed to slide forward but not backwards, that is built into the grip zone of waxless skis, or from applied devices, e.g. climbing skins, or b) from *grip waxes*. Grip waxes are classified according to their hardness: harder waxes are for colder and newer snow. An incorrect choice of grip wax for the snow conditions encountered may cause ski slippage (wax too hard for the conditions) or snow sticking to the grip zone (wax too soft for the conditions). Grip waxes generate grip by interacting with snow crystals, which vary with temperature, age and compaction. Hard grip waxes do not work well for snow which has metamorphosed to having coarse grains, whether icy or wet. In these conditions, skiers opt for a stickier substance, called *klister*.
### Boots and bindings {#boots_and_bindings}
Ski boots are attached to the ski only at the toe, leaving the heel free. Depending on application, boots may be lightweight (performance skiing) or heavier and more supportive (back-country skiing).
Bindings connect the boot to the ski. There are three primary groups of binding systems used in cross-country skiing (in descending order of importance):
- **Standardized system**: Boots and bindings have an integrated connection, typically a bar across the front end of the sole of the boot, and platform on which the boot rests. Two families of standards prevail: NNN (New Nordic Norm) and SNS (Salomon Nordic System) Profil. Both systems have variants for skiing on groomed surfaces and in back country. These systems are the most common type of binding.
- **Three-pin**: The boot-gripping system comprises three pins that correspond to three holes in the sole of the boot\'s toe, used primarily for back-country skiing.
- **Cable**: A cable secures the free-moving heel and keeps the toe of the boot pushed into a boot-gripping section, used primarily for back-country and telemark skiing.
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# Cross-country skiing
## Equipment
### Poles
Ski poles are used for balance and propulsion. Modern cross-country ski poles are made from aluminium, fibreglass-reinforced plastic, or carbon fibre, depending on weight, cost and performance parameters. Formerly they were made of wood or bamboo. They feature a foot (called a basket) near the end of the shaft that provides a pushing platform, as it makes contact with the snow. Baskets vary in size, according to the expected softness/firmness of the snow. Racing poles feature smaller, lighter baskets than recreational poles. Poles designed for skating are longer than those designed for classic skiing. Traditional skiing in the 1800s used a single pole for both cross-country and downhill. The single pole was longer and stronger than the poles that are used in pairs. In competitive cross-country poles in pairs were introduced around 1900.
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# Cross-country skiing
## Gallery
Image:Skigudinne.jpg\|An early depiction of a skier---a Sami woman or goddess hunting on skis by Olaus Magnus (1553). <File:Birkebeinerne> ski01.jpg\|Loyal retainers transporting Prince Haakon IV of Norway to safety on skis during the winter of 1206---1869 depiction by Knud Bergslien. <File:138>. Kronprins Olav - no-nb digifoto 20150710 00006 bldsa pk kgl0061.jpg\|Olav V of Norway as crown-prince in 1939 Image:olympic skier in ice storm.jpg\|A skate-skier in Gatineau Park, Quebec, a North American groomed-trail ski venue. <File:AchenseeWinter01.JPG%7CA> recreational cross-country trail, groomed for classic skiing only, in Tyrol. <File:Blind> skier and guide.jpg\|A blind cross-country skier with guide at a regional Ski for Light event. <File:Skijor> worlds.jpg\|Dog skijoring---dogs provide added propulsion to the cross-country skier
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# Constantius II
Constantine II\|Julius Constantius\|Constantius III}} `{{Use dmy dates|date=September 2021}}`{=mediawiki}
**Constantius II** (*Flavius Julius Constantius*; *Kōnstántios*; 7 August 317 -- 3 November 361) was Roman emperor from 337 to 361. His reign saw constant warfare on the borders against the Sasanian Empire and Germanic peoples, while internally the Roman Empire went through repeated civil wars, court intrigues, and usurpations. His religious policies inflamed domestic conflicts that would continue after his death.
Constantius was a son of Constantine the Great, who elevated him to the imperial rank of *Caesar* on 8 November 324 and after whose death Constantius became *Augustus* together with his brothers, Constantine II and Constans on 9 September 337. He promptly oversaw the massacre of his father-in-law, an uncle, and several cousins, consolidating his hold on power. The brothers divided the empire among themselves, with Constantius receiving Greece, Thrace, the Asian provinces, and Egypt in the east. For the following decade a costly and inconclusive war against Persia took most of Constantius\'s time and attention. In the meantime, his brothers Constantine and Constans warred over the western provinces of the empire, leaving the former dead in 340 and the latter as sole ruler of the west. The two remaining brothers maintained an uneasy peace with each other until, in 350, Constans was overthrown and assassinated by the usurper Magnentius.
Unwilling to accept Magnentius as co-ruler, Constantius waged a civil war against the usurper, defeating him at the battles of Mursa Major in 351 and Mons Seleucus in 353. Magnentius died by suicide after the latter battle, leaving Constantius as sole ruler of the empire. In 351, Constantius elevated his cousin Constantius Gallus to the subordinate rank of *Caesar* to rule in the east, but had him executed three years later after receiving scathing reports of his violent and corrupt nature. Shortly thereafter, in 355, Constantius promoted his last surviving cousin, Gallus\'s younger half-brother Julian, to the rank of *Caesar*.
As emperor, Constantius promoted Arianism, banned pagan sacrifices, and issued laws against Jews. His military campaigns against Germanic tribes were successful: he defeated the Alamanni in 354 and campaigned across the Danube against the Quadi and Sarmatians in 357. The war against the Sasanians, which had been in a lull since 350, erupted with renewed intensity in 359 and Constantius travelled to the east in 360 to restore stability after the loss of several border fortresses. However, Julian claimed the rank of *Augustus* in 360, leading to war between the two after Constantius\'s attempts to persuade Julian to back down failed. No battle was fought, as Constantius became ill and died of fever on 3 November 361 in Mopsuestia, allegedly naming Julian as his rightful successor before his death.
## Early life {#early_life}
Flavius Julius Constantius was born in 317 at Sirmium, Pannonia, now Serbia. He was the third son of Constantine the Great, and second by his second wife Fausta, the daughter of Maximian. Constantius was made *caesar* by his father on 8 November 324. In 336, religious unrest in Armenia and tense relations between Constantine and king Shapur II caused war to break out between Rome and Sassanid Persia. Though he made initial preparations for the war, Constantine fell ill and sent Constantius east to take command of the eastern frontier. Before Constantius arrived, the Persian general Narses, who was possibly the king\'s brother, overran Mesopotamia and captured Amida. Constantius promptly attacked Narses, and after suffering minor setbacks defeated and killed Narses at the Battle of Narasara. Constantius captured Amida and initiated a major refortification of the city, enhancing the city\'s circuit walls and constructing large towers. He also built a new stronghold in the hinterland nearby, naming it *Antinopolis*.
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# Constantius II
## Augustus in the east {#augustus_in_the_east}
In early 337, Constantius hurried to Constantinople after receiving news that his father was near death. After Constantine died, Constantius buried him with lavish ceremony in the Church of the Holy Apostles. Soon after his father\'s death, the army massacred his relatives descended from the marriage of his paternal grandfather Constantius Chlorus to Flavia Maximiana Theodora, though the details are unclear. Two of Constantius\'s uncles (Julius Constantius and Flavius Dalmatius) and seven of his cousins were killed, including Hannibalianus and Dalmatius, rulers of Pontus and Moesia respectively, leaving Constantius, his two brothers Constantine II and Constans, and three cousins Gallus, Julian and Nepotianus as the only surviving male relatives of Constantine the Great. While the "official version" was that Constantius\'s relatives were merely the victims of a mutinous army, Ammianus Marcellinus, Zosimus, Libanius, Athanasius and Julian all blamed Constantius for the event. Burgess considered the latter version to be "consistent with all the evidence", pointing to multiple factors that he believed lined up with the massacre being a planned attack rather than a spontaneous mutiny - the lack of high-profile punishments as a response, the sparing of all women, the attempted damnatio memoriae on the deceased, and the exile of the survivors Gallus and Julian.
Soon after, Constantius met his brothers in Pannonia at Sirmium to formalize the partition of the empire. Constantius received the eastern provinces, including Constantinople, Thrace, Asia Minor, Syria, Egypt, and Cyrenaica; Constantine received Britannia, Gaul, Hispania, and Mauretania; and Constans, initially under the supervision of Constantine II, received Italy, Africa, Illyricum, Pannonia, Macedonia, and Achaea.
Constantius then hurried east to Antioch to resume the war with Persia. While Constantius was away from the eastern frontier in early 337, King Shapur II assembled a large army, which included war elephants, and launched an attack on Roman territory, laying waste to Mesopotamia and putting the city of Nisibis under siege. Despite initial success, Shapur lifted his siege after his army missed an opportunity to exploit a collapsed wall. When Constantius learned of Shapur\'s withdrawal from Roman territory, he prepared his army for a counter-attack.
Constantius repeatedly defended the eastern border against invasions by the Sassanid Empire under Shapur. These conflicts were mainly limited to Sassanid sieges of the major fortresses of Roman Mesopotamia, including Nisibis (Nusaybin), Singara, and Amida (Diyarbakir). Although Shapur seems to have been victorious in most of these confrontations, the Sassanids were able to achieve little. However, the Romans won a decisive victory at the Battle of Narasara, killing Shapur\'s brother, Narses. Ultimately, Constantius was able to push back the invasion, and Shapur failed to make any significant gains.
Meanwhile, Constantine II desired to retain control of Constans\'s realm, leading the brothers into open conflict. Constantine was killed in 340 near Aquileia during an ambush. As a result, Constans took control of his deceased brother\'s realms and became sole ruler of the Western two-thirds of the empire. This division lasted until January 350, when Constans was assassinated by forces loyal to the usurper Magnentius.
### War against Magnentius {#war_against_magnentius}
Constantius was determined to march west to fight the usurper. However, feeling that the east still required some sort of imperial presence, he elevated his cousin Constantius Gallus to *caesar* of the eastern provinces. As an extra measure to ensure the loyalty of his cousin, he married the elder of his two sisters, Constantina, to him.
Before facing Magnentius, Constantius first came to terms with Vetranio, a loyal general in Illyricum who had recently been acclaimed emperor by his soldiers. Vetranio immediately sent letters to Constantius pledging his loyalty, which Constantius may have accepted simply in order to stop Magnentius from gaining more support. These events may have been spurred by the action of Constantina, who had since traveled east to marry Gallus. Constantius subsequently sent Vetranio the imperial diadem and acknowledged the general\'s new position as *augustus*. However, when Constantius arrived, Vetranio willingly resigned his position and accepted Constantius\'s offer of a comfortable retirement in Bithynia.
In 351, Constantius clashed with Magnentius in Pannonia with a large army. The ensuing Battle of Mursa Major was one of the largest and bloodiest battles ever between two Roman armies. The result was a victory for Constantius, but a costly one. Magnentius survived the battle and, determined to fight on, withdrew into northern Italy. Rather than pursuing his opponent, however, Constantius turned his attention to securing the Danubian border, where he spent the early months of 352 campaigning against the Sarmatians along the middle Danube. After achieving his aims, Constantius advanced on Magnentius in Italy. This action led the cities of Italy to switch their allegiance to him and eject the usurper\'s garrisons. Again, Magnentius withdrew, this time to southern Gaul.
In 353, Constantius and Magnentius met for the final time at the Battle of Mons Seleucus in southern Gaul, and again Constantius emerged the victor. Magnentius, realizing the futility of continuing his position, committed suicide on 10 August 353.
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# Constantius II
## Solo reign {#solo_reign}
Constantius spent much of the rest of 353 and early 354 on campaign against the Alamanni on the Danube frontier. The campaign was successful and raiding by the Alamanni ceased temporarily. In the meantime, Constantius had been receiving disturbing reports regarding the actions of his cousin Gallus. Possibly as a result of these reports, Constantius concluded a peace with the Alamanni and traveled to Mediolanum (Milan).
In Mediolanum, Constantius first summoned Ursicinus, Gallus\'s *magister equitum*, for reasons that remain unclear. Constantius then summoned Gallus and Constantina. Although Gallus and Constantina complied with the order at first, when Constantina died in Bithynia, Gallus began to hesitate. However, after some convincing by one of Constantius\'s agents, Gallus continued his journey west, passing through Constantinople and Thrace to Poetovio (Ptuj) in Pannonia.
In Poetovio, Gallus was arrested by the soldiers of Constantius under the command of Barbatio. Gallus was then moved to Pola and interrogated. Gallus claimed that it was Constantina who was to blame for all the trouble while he was in charge of the eastern provinces. This angered Constantius so greatly that he immediately ordered Gallus\'s execution. He soon changed his mind, however, and recanted the order. Unfortunately for Gallus, this second order was delayed by Eusebius, one of Constantius\'s eunuchs, and Gallus was executed.
### Religious issues {#religious_issues}
*Main article: Religious policies of Constantius II*
#### Paganism
Laws dating from the 350s prescribed the death penalty for those who performed or attended pagan sacrifices, and for the worshipping of idols. Pagan temples were shut down, and the Altar of Victory was removed from the Senate meeting house. There were also frequent episodes of ordinary Christians destroying, pillaging and desecrating many ancient pagan temples, tombs and monuments. Paganism was still popular among the population at the time. The emperor\'s policies were passively resisted by many governors and magistrates.
In spite of this, Constantius never made any attempt to disband the various Roman priestly colleges or the Vestal Virgins. He never acted against the various pagan schools. At times, he actually made some effort to protect paganism. In fact, he even ordered the election of a priest for Africa. Also, he remained pontifex maximus and was deified by the Roman Senate after his death. His relative moderation toward paganism is reflected by the fact that it was over twenty years after his death, during the reign of Gratian, that any pagan senator protested his treatment of their religion.
#### Christianity
Although often considered an Arian, Constantius ultimately preferred a third, compromise version that lay somewhere in between Arianism and the Nicene Creed, retrospectively called Semi-Arianism. During his reign he attempted to mold the Christian church to follow this compromise position, convening several Christian councils. \"Unfortunately for his memory the theologians whose advice he took were ultimately discredited and the malcontents whom he pressed to conform emerged victorious,\" writes the historian A. H. M. Jones. \"The great councils of 359--60 are therefore not reckoned ecumenical in the tradition of the church, and Constantius II is not remembered as a restorer of unity, but as a heretic who arbitrarily imposed his will on the church.\"
According to the Greek historian Philostorgius (d. 439) in his *Ecclesiastical History*, Constantius sent an Arian bishop known as Theophilus the Indian (also known as \"Theophilus of Yemen\") to Tharan Yuhanim, then the king of the South Arabian Himyarite Kingdom to convert the people to Christianity. According to the report, Theophilus succeeded in establishing three churches, one of them in the capital Zafar.
#### Judaism
Judaism faced some severe restrictions under Constantius, who seems to have followed an anti-Jewish policy in line with that of his father. This included edicts to limit the ownership of slaves by Jewish people and banning marriages between Jews and Christian women. Later edicts sought to discourage conversions from Christianity to Judaism by confiscating the apostate\'s property. However, Constantius\'s actions in this regard may not have been so much to do with Jewish religion as with Jewish business---apparently, privately owned Jewish businesses were often in competition with state-owned businesses. As a result, Constantius may have sought to provide an advantage to state-owned businesses by limiting the skilled workers and slaves available to Jewish businesses.
### Further crises {#further_crises}
On 11 August 355, the *magister militum* Claudius Silvanus revolted in Gaul. Silvanus had surrendered to Constantius after the Battle of Mursa Major. Constantius had made him *magister militum* in 353 with the purpose of blocking the German threats, a feat that Silvanus achieved by bribing the German tribes with the money he had collected. A plot organized by members of Constantius\'s court led the emperor to recall Silvanus. After Silvanus revolted, he received a letter from Constantius recalling him to Milan, but which made no reference to the revolt. Ursicinus, who was meant to replace Silvanus, bribed some troops, and Silvanus was killed.
Constantius realised that too many threats still faced the Empire, however, and he could not possibly handle all of them by himself. So on 6 November 355, he elevated his last remaining male relative, Julian, to the rank of *caesar*. A few days later, Julian was married to Helena, the last surviving sister of Constantius. Constantius soon sent Julian off to Gaul. Constantius spent the next few years overseeing affairs in the western part of the empire primarily from his base at Mediolanum. In April--May 357 he visited Rome for the only time in his life. The same year, he forced Sarmatian and Quadi invaders out of Pannonia and Moesia Inferior, then led a successful counter-attack across the Danube.
In the winter of 357--58, Constantius received ambassadors from Shapur II who demanded that Rome restore the lands surrendered by Narseh. Despite rejecting these terms, Constantius tried to avert war with the Sassanid Empire by sending two embassies to Shapur II. Shapur II nevertheless launched another invasion of Roman Mesopotamia. In 360, when news reached Constantius that Shapur II had destroyed Singara (Sinjar), and taken Kiphas (Hasankeyf), Amida (Diyarbakır), and Ad Tigris (Cizre), he decided to travel east to face the re-emergent threat.
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# Constantius II
## Solo reign {#solo_reign}
### Usurpation of Julian and crises in the east {#usurpation_of_julian_and_crises_in_the_east}
In the meantime, Julian had won some victories against the Alamanni, who had once again invaded Roman Gaul. However, when Constantius requested reinforcements from Julian\'s army for the eastern campaign, the Gallic legions revolted and proclaimed Julian *augustus*.
On account of the immediate Sassanid threat, Constantius was unable to directly respond to his cousin\'s usurpation, other than by sending missives in which he tried to convince Julian to resign the title of *augustus* and be satisfied with that of *caesar*. By 361, Constantius saw no alternative but to face the usurper with force, and yet the threat of the Sassanids remained. Constantius had already spent part of early 361 unsuccessfully attempting to re-take the fortress of Ad Tigris. After a time he had withdrawn to Antioch to regroup and prepare for a confrontation with Shapur II. The campaigns of the previous year had inflicted heavy losses on the Sassanids, however, and they did not attempt another round of campaigns that year. This temporary respite in hostilities allowed Constantius to turn his full attention to facing Julian.
### Death
Constantius immediately gathered his forces and set off west. However, by the time he reached Mopsuestia in Cilicia, it was clear that he was fatally ill and would not survive to face Julian. The sources claim that realising his death was near, Constantius had himself baptised by Euzoius, the Semi-Arian bishop of Antioch, and then declared that Julian was his rightful successor. Constantius II died of fever on 3 November 361.
Like Constantine the Great, he was buried in the Church of the Holy Apostles, in a porphyry sarcophagus that was described in the 10th century by Constantine VII Porphyrogenitus in the *De Ceremoniis*.
## Marriages and children {#marriages_and_children}
Constantius II was married three times:
First to a daughter of his half-uncle Julius Constantius, whose name is unknown. She was a full-sister of Gallus and a half-sister of Julian. She died c. 352/3.
Second, to Eusebia, a woman of Macedonian origin, originally from the city of Thessalonica, whom Constantius married before his defeat of Magnentius in 353. She died before 361.
Third and lastly, in 361, to Faustina, who gave birth to Constantius\'s only child, a posthumous daughter named Constantia, who later married Emperor Gratian.
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# Constantius II
## Family tree {#family_tree}
Emperors are shown with a rounded-corner border with their dates as Augusti, names with a thicker border appear in both sections
**1: Constantine\'s parents and half-siblings** `{{Tree chart/start|align=center}}`{=mediawiki} `{{tree chart| | | | | | |CGOTH|CGOTH={{ubl|[[Claudius Gothicus]]|268–270|''fabricated ancestry''}}|boxstyle_CGOTH=border:2px solid; border-radius:1em}}`{=mediawiki} `{{tree chart| | | | | | | |Q|}}`{=mediawiki} `{{tree chart| | |HELEN|y|CCHLO|y|THEO1|HELEN=[[Helena, mother of Constantine I|Helena]]|boxstyle_HELEN=border:2px solid|CCHLO={{ubl|[[Constantius I]]|305–306}}|boxstyle_CCHLO=border:2px solid; border-radius:1em|THEO1=[[Flavia Maximiana Theodora]]}}`{=mediawiki} `{{tree chart| | | | | |!| | | |)|-|v|-|v|-|-|-|v|-|-|-|-|-|v|-|.| | | | | }}`{=mediawiki} `{{tree chart| | | | |CONST| |FLAVD|!|HANN1| |CONS2|y|LICI1|!|ANAST|~|BASSI|CONST={{ubl|'''Constantine I'''|306–337}}|boxstyle_CONST=border:3px solid; border-radius:1em|FLAVD=[[Flavius Dalmatius]]|HANN1=Hannibalianus|CONS2=[[Flavia Julia Constantia]]|LICI1={{ubl|[[Licinius]]|308–324}}|boxstyle_LICI1=border:2px solid; border-radius:1em|ANAST=Anastasia|BASSI=[[Bassianus (executed by Constantine)|Bassianus]]}}`{=mediawiki} `{{tree chart| |,|-|-|-|-|-|-|-|'| |!| | | | | | | |!| | | |!}}`{=mediawiki} `{{tree chart| |!| | | | |GALL1|y|JULIC|y|BASIL| |LICI2| |EUTR2|y|NEPO1|GALL1=[[Galla (wife of Julius Constantius)|Galla]]|JULIC=[[Julius Constantius]]|BASIL=[[Basilina]]|LICI2=[[Licinius II]]|EUTR2=[[Eutropia (sister of Constantine I)|Eutropia]]|NEPO1=Virius Nepotianus}}`{=mediawiki} `{{tree chart| |!| | | | | | | |!| | | |!| | | | | | | | | | | |!}}`{=mediawiki} `{{tree chart|HANN2|~|CONS6|~|GALLU| |JULIA|~|HELE2| | | | | |NEPO2|HANN2=[[Hannibalianus]]|boxstyle_HANN2=border:3px solid|CONS6=[[Constantina]]|boxstyle_CONS6=border:3px solid|GALLU=[[Constantius Gallus]]|boxstyle_GALLU=border:3px solid|JULIA={{ubl|[[Julian (emperor)|Julian]]|360–363}}|boxstyle_JULIA=border:3px solid; border-radius:1em|HELE2=[[Helena (wife of Julian)|Helena]]|boxstyle_HELE2=border:3px solid|NEPO2=[[Nepotianus]]}}`{=mediawiki} `{{tree chart/end}}`{=mediawiki} `{{break}}`{=mediawiki} **2: Constantine\'s children** `{{Tree chart/start|align=center}}`{=mediawiki} `{{tree chart|MINER|y|CONST|y|FAUS1|MINER=[[Minervina]]|CONST={{ubl|'''Constantine I'''|306–337}}|boxstyle_CONST=border:3px solid; border-radius:1em|FAUS1=[[Fausta]]}}`{=mediawiki} `{{tree chart| | | |!| | | |)|-|v|-|v|-|v|-|-|-|-|-|.|}}`{=mediawiki} `{{tree chart| | |CRISP| |CONS3|!|CONS5|!|HANN2|~|CONS6|~|GALLU|CRISP=[[Crispus]]|CONS3={{ubl|[[Constantine II (emperor)|Constantine II]]|337–340}}|boxstyle_CONS3=border:2px solid; border-radius:1em|CONS5={{ubl|[[Constans]]|337–350}}|boxstyle_CONS5=border:2px solid; border-radius:1em|HANN2=[[Hannibalianus]]|boxstyle_HANN2=border:3px solid|CONS6=[[Constantina]]|boxstyle_CONS6=border:3px solid|GALLU=[[Constantius Gallus]]|boxstyle_GALLU=border:3px solid}}`{=mediawiki} `{{tree chart| | | | | | | | | |!| | | |!}}`{=mediawiki} `{{tree chart| | | | |FAUS2|y|CONS4| |HELE2|~|JULIA|FAUS2=[[Faustina (wife of Constantius II)|Faustina]]|CONS4={{ubl|Constantius II|337–361}}|boxstyle_CONS4=border:2px solid; border-radius:1em|JULIA={{ubl|[[Julian (emperor)|Julian]]|360–363}}|boxstyle_JULIA=border:3px solid; border-radius:1em|HELE2=[[Helena (wife of Julian)|Helena]]|boxstyle_HELE2=border:3px solid}}`{=mediawiki} `{{tree chart| | | | | | | |!}}`{=mediawiki} `{{tree chart| | |GRATI|~|CONS7|GRATI={{ubl|[[Gratian]]|367–383}}|boxstyle_GRATI=border:2px solid; border-radius:1em|CONS7=[[Constantia (wife of Gratian)|Constantia]]}}`{=mediawiki} `{{Tree chart/end}}`{=mediawiki} `{{Chart bottom}}`{=mediawiki}
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# Constantius II
## Reputation
According to DiMaio and Frakes, "\...Constantius is hard for the modern historian to fully understand both due to his own actions and due to the interests of the authors of primary sources for his reign." A. H. M. Jones writes that he \"appears in the pages of Ammianus as a conscientious emperor but a vain and stupid man, an easy prey to flatterers. He was timid and suspicious, and interested persons could easily play on his fears for their own advantage.\" However, Kent and M. and A. Hirmer suggest that the emperor \"has suffered at the hands of unsympathetic authors, ecclesiastical and civil alike. To orthodox churchmen he was a bigoted supporter of the Arian heresy, to Julian the Apostate and the many who have subsequently taken his part he was a murderer, a tyrant and inept as a ruler\". They go on to add, \"Most contemporaries seem in fact to have held him in high esteem, and he certainly inspired loyalty in a way his brother could not\".
Eutropius wrote of him,
> He was a man of a remarkably tranquil disposition, good-natured, trusting too much to his friends and courtiers, and at last too much in the power of his wives. He conducted himself with great moderation in the commencement of his reign; he enriched his friends, and suffered none, whose active services he had experienced, to go unrewarded. He was however somewhat inclined to severity, whenever any suspicion of an attempt on the government was excited in him; otherwise he was gentle. His fortune is more to be praised in civil than in foreign wars
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# Cottingley Fairies
The **Cottingley Fairies** are the subject of a hoax which purports to provide evidence of the existence of fairies. They appear in a series of five photographs taken by Elsie Wright (1901--1988) and Frances Griffiths (1907--1986), two young cousins who lived in Cottingley, near Bradford in England. In 1917, when the first two photographs were taken, Elsie was 16 years old and Frances was 9. The pictures came to the attention of writer Sir Arthur Conan Doyle, who used them to illustrate an article on fairies he had been commissioned to write for the Christmas 1920 edition of *The Strand Magazine*. Doyle was enthusiastic about the photographs, and interpreted them as clear and visible evidence of supernatural phenomena. Public reaction was mixed; some accepted the images as genuine, others believed that they had been faked.
Interest in the Cottingley Fairies gradually declined after 1921. Both girls married and lived abroad for a time after they grew up, and yet the photographs continued to hold the public imagination. In 1966 a reporter from the *Daily Express* newspaper traced Elsie, who had by then returned to the United Kingdom. Elsie left open the possibility that she believed she had photographed her thoughts, and the media once again became interested in the story.
In the early 1980s Elsie and Frances admitted that the photographs were faked, using cardboard cutouts of fairies copied from a popular children\'s book of the time, but Frances maintained that the fifth and final photograph was genuine. As of 2019 the photographs and the cameras used are in the collections of the National Science and Media Museum in Bradford, England.
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