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# Homeopathy
## Ethics and safety {#ethics_and_safety}
The provision of homeopathic preparations has been described as unethical. Michael Baum, professor emeritus of surgery and visiting professor of medical humanities at University College London (UCL), has described homeopathy as a \"cruel deception\". Edzard Ernst, the first professor of complementary medicine in the United Kingdom and a former homeopathic practitioner, has expressed his concerns about pharmacists who violate their ethical code by failing to provide customers with \"necessary and relevant information\" about the true nature of the homeopathic products they advertise and sell. In 2013 the UK Advertising Standards Authority concluded that the Society of Homeopaths were targeting vulnerable ill people and discouraging the use of essential medical treatment while making misleading claims of efficacy for homeopathic products. In 2015 the Federal Court of Australia imposed penalties on a homeopathic company for making false or misleading statements about the efficacy of the whooping cough vaccine and recommending homeopathic remedies as an alternative.A 2000 review by homeopaths reported that homeopathic preparations are \"unlikely to provoke severe adverse reactions\". In 2012, a systematic review evaluating evidence of homeopathy\'s possible adverse effects concluded that \"homeopathy has the potential to harm patients and consumers in both direct and indirect ways\". A 2016 systematic review and meta-analysis found that, in homeopathic clinical trials, adverse effects were reported among the patients who received homeopathy about as often as they were reported among patients who received placebo or conventional medicine.
Some homeopathic preparations involve poisons such as Belladonna, arsenic, and poison ivy. In rare cases, the original ingredients are present at detectable levels. This may be due to improper preparation or intentional low dilution. Serious adverse effects such as seizures and death have been reported or associated with some homeopathic preparations. Instances of arsenic poisoning have occurred. In 2009, the FDA advised consumers to stop using three discontinued cold remedy Zicam products because it could cause permanent damage to users\' sense of smell.Sources:
-
- In 2016 the FDA issued a safety alert to consumers warning against the use of homeopathic teething gels and tablets following reports of adverse events after their use. A previous FDA investigation had found that these products were improperly diluted and contained \"unsafe levels of belladonna\" and that the reports of serious adverse events in children using this product were \"consistent with belladonna toxicity\".
Patients who choose to use homeopathy rather than evidence-based medicine risk missing timely diagnosis and effective treatment, thereby worsening the outcomes of serious conditions such as cancer. The Russian Commission on Pseudoscience has said homeopathy is not safe because \"patients spend significant amounts of money, buying medicines that do not work and disregard already known effective treatment.\" Critics have cited cases of patients failing to receive proper treatment for diseases that could have been easily managed with conventional medicine and who have died as a result. In 1978, Anthony Campbell, a consultant physician at the Royal London Homeopathic Hospital, criticized statements by George Vithoulkas claiming that syphilis, when treated with antibiotics, would develop into secondary and tertiary syphilis with involvement of the central nervous system. Vithoulkas\' claims echo the idea that treating a disease with external medication used to treat the symptoms would only drive it deeper into the body and conflict with scientific studies, which indicate that penicillin treatment produces a complete cure of syphilis in more than 90% of cases.
The use of homeopathy as a preventive for serious infectious diseases, called homeoprophylaxis, is especially controversial. Some homeopaths (particularly those who are non-physicians) advise their patients against immunization. Others have suggested that vaccines be replaced with homeopathic \"nosodes\". While Hahnemann was opposed to such preparations, modern homeopaths often use them although there is no evidence to indicate they have any beneficial effects. Promotion of homeopathic alternatives to vaccines has been characterized as dangerous, inappropriate and irresponsible. In December 2014, the Australian homeopathy supplier Homeopathy Plus! was found to have acted deceptively in promoting homeopathic alternatives to vaccines. In 2019, an investigative journalism piece by the *Telegraph* revealed that homeopathy practitioners were actively discouraging patients from vaccinating their children. Cases of homeopaths advising against the use of anti-malarial drugs have also been identified, putting visitors to the tropics in severe danger.
A 2006 review recommends that pharmacy colleges include a required course where ethical dilemmas inherent in recommending products lacking proven safety and efficacy data be discussed and that students should be taught where unproven systems such as homeopathy depart from evidence-based medicine.
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# Homeopathy
## Regulation and prevalence {#regulation_and_prevalence}
Homeopathy is fairly common in some countries while being uncommon in others; is highly regulated in some countries and mostly unregulated in others. It is practiced worldwide and professional qualifications and licences are needed in most countries. A 2019 WHO report found that 100 out of 133 Member States surveyed in 2012 acknowledged that their population used homeopathy, with 22 saying the practice was regulated and 13 providing health insurance coverage. In some countries, there are no specific legal regulations concerning the use of homeopathy, while in others, licences or degrees in conventional medicine from accredited universities are required. In 2001 homeopathy had been integrated into the national health care systems of many countries, including India, Mexico, Pakistan, Sri Lanka, and the United Kingdom.
### Regulation
Some homeopathic treatment is covered by the public health service of several European countries, including Scotland, and Luxembourg. It used to be covered in France until 2021. In other countries, such as Belgium, homeopathy is not covered. In Austria, the public health service requires scientific proof of effectiveness in order to reimburse medical treatments and homeopathy is listed as not reimbursable, but exceptions can be made; private health insurance policies sometimes include homeopathic treatments. In 2018, Austria\'s Medical University of Vienna stopped teaching homeopathy. The Swiss government withdrew coverage of homeopathy and four other complementary treatments in 2005, stating that they did not meet efficacy and cost-effectiveness criteria, but following a referendum in 2009 the five therapies were reinstated for a further 6-year trial period. In Germany, homeopathic treatments are covered by 70 percent of government medical plans, and available in almost every pharmacy. In January 2024, German health minister Karl Lauterbach announced plans to withdraw all statutory health insurance coverage for homeopathic and anthroposophic treatments, citing a lack of scientific evidence for their efficacy.
The English NHS recommended against prescribing homeopathic preparations in 2017. In 2018, prescriptions worth £55,000 were written in defiance of the guidelines, representing less than 0.001% of the total NHS prescribing budget. In 2016 the UK\'s Committee of Advertising Practice compliance team wrote to homeopaths in the UK to \"remind them of the rules that govern what they can and can\'t say in their marketing materials\". The letter told homeopaths to \"ensure that they do not make any direct or implied claims that homeopathy can treat medical conditions\" and asks them to review their marketing communications \"including websites and social media pages\" to ensure compliance. Homeopathic services offered at Bristol Homeopathic Hospital in the UK ceased in October 2015.
Member states of the European Union are required to ensure that homeopathic products are registered, although this process does not require any proof of efficacy. In Spain, the Association for the protection of patients from pseudo-scientific therapies is lobbying to get rid of the easy registration procedure for homeopathic remedies. In Bulgaria, Hungary, Latvia, Romania and Slovenia homeopathy, by law, can only be practiced by medical practitioners. However, in Slovenia if doctors practice homeopathy their medical license will be revoked. In Germany, to become a homeopathic physician, one must attend a three-year training program, while France, Austria and Denmark mandate licences to diagnose any illness or dispense of any product whose purpose is to treat any illness. Homeopaths in the UK are under no legal regulations, meaning anyone can call themselves homeopaths and administer homeopathic remedies. The Indian government recognizes homeopathy as one of its national systems of medicine and they are sold with medical claims. It has established the Department of Ayurveda, Yoga and Naturopathy, Unani, Siddha and Homoeopathy (AYUSH) under the Ministry of Health & Family Welfare. The south Indian state of Kerala also has a cabinet-level AYUSH department. The Central Council of Homoeopathy was established in 1973 to monitor higher education in homeopathy, and the National Institute of Homoeopathy in 1975. Principals and standards for homeopathic products are covered by the *Homoeopathic pharmacopoeia of India*. A minimum of a recognized diploma in homeopathy and registration on a state register or the Central Register of Homoeopathy is required to practice homeopathy in India.
In the United States each state is responsible for the laws and licensing requirements for homeopathy. In 2015, the FDA held a hearing on homeopathic product regulation. At the hearing, representatives from the Center for Inquiry and the Committee for Skeptical Inquiry summarized the harm that is done to the general public from homeopathics and proposed regulatory actions: In 2016 the United States Federal Trade Commission (FTC) issued an \"Enforcement Policy Statement Regarding Marketing Claims for Over-the-Counter Homeopathic Drugs\" which specified that the FTC will apply the same standard to homeopathic drugs that it applies to other products claiming similar benefits. A related report concluded that claims of homeopathy effectiveness \"are not accepted by most modern medical experts and do not constitute competent and reliable scientific evidence that these products have the claimed treatment effects.\" In 2019, the FDA removed an enforcement policy that permitted unapproved homeopathics to be sold. Currently no homeopathic products are approved by the FDA.
Homeopathic remedies are regulated as natural health products in Canada. Ontario became the first province in the country to regulate the practice of homeopathy, a move that was widely criticized by scientists and doctors. Health Canada requires all products to have a licence before being sold and applicants have to submit evidence on \"the safety, efficacy and quality of a homeopathic medicine\". In 2015 the Canadian Broadcasting Corporation tested the system by applying for and then receiving a government approved licence for a made-up drug aimed at kids.
In Australia, the sale of homeopathic products is regulated by the Therapeutic Goods Administration. In 2015, the National Health and Medical Research Council of Australia concluded that there is \"no reliable evidence that homeopathy is effective and should not be used to treat health conditions that are chronic, serious, or could become serious\". They recommended anyone considering using homeopathy should first get advice from a registered health practitioner. A 2017 review into Pharmacy Remuneration and Regulation recommended that products be banned from pharmacies; while noting the concerns the government did not adopt the recommendation. In New Zealand there are no regulations specific to homeopathy and the New Zealand Medical Association does not oppose the use of homeopathy, a stance that has been called unethical by some doctors.
### Prevalence
Homeopathy is one of the most commonly used forms of alternative medicines and it has a large worldwide market. The exact size is uncertain, but information available on homeopathic sales suggests it forms a large share of the medical market.
In 1999, about 1000 UK doctors practiced homeopathy, most being general practitioners who prescribe a limited number of remedies. A further 1500 homeopaths with no medical training are also thought to practice. Over ten thousand German and French doctors use homeopathy. In the United States a National Health Interview Survey estimated 5 million adults and 1 million children used homeopathy in 2011. An analysis of this survey concluded that most cases were self-prescribed for colds and musculoskeletal pain. Major retailers like Walmart, CVS, and Walgreens sell homeopathic products that are packaged to resemble conventional medicines.
The homeopathic drug market in Germany is worth about 650 million euro with a 2014 survey finding that 60 percent of Germans reported trying homeopathy. A 2009 survey found that only 17 percent of respondents knew how homeopathic medicine was made. France spent more than US\$408 million on homeopathic products in 2008. In the United States the homeopathic market is worth about \$3 billion-a-year; with 2.9 billion spent in 2007. Australia spent US\$7.3 million on homeopathic medicines in 2008.
In India, a 2014 national health survey found that homeopathy was used by about 3% of the population. Homeopathy is used in China, although it arrived a lot later than in many other countries, partly due to the restriction on foreigners that persisted until late in the nineteenth century. Throughout Africa there is a high reliance on traditional medicines, which can be attributed to the cost of modern medicines and the relative prevalence of practitioners. Many African countries do not have any official training facilities.
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# Homeopathy
## Veterinary use {#veterinary_use}
Using homeopathy as a treatment for animals is termed \"veterinary homeopathy\" and dates back to the inception of homeopathy; Hahnemann himself wrote and spoke of the use of homeopathy in animals other than humans. The use of homeopathy in the organic farming industry is heavily promoted. Given that homeopathy\'s effects in humans are due to the placebo effect and the counseling aspects of the consultation, such treatments are even less effective in animals. Studies have also found that giving animals placebos can play active roles in influencing pet owners to believe in the effectiveness of the treatment when none exists. This means that animals given homeopathic remedies will continue to suffer, resulting in animal welfare concerns.
Little existing research on the subject is of a high enough scientific standard to provide reliable data on efficacy. A 2016 review of peer-reviewed articles from 1981 to 2014 by scientists from the University of Kassel, Germany, concluded that there is not enough evidence to support homeopathy as an effective treatment of infectious diseases in livestock. The UK\'s Department for Environment, Food and Rural Affairs (Defra) has adopted a robust position against use of \"alternative\" pet preparations including homeopathy. The British Veterinary Association\'s position statement on alternative medicines says that it \"cannot endorse\" homeopathy, and the Australian Veterinary Association includes it on its list of \"ineffective therapies\"
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# Hairpin
A **hairpin** or **hair pin** is a long device used to hold a person\'s hair in place. It may be used simply to secure long hair out of the way for convenience or as part of an elaborate hairstyle or coiffure. The earliest evidence for dressing the hair may be seen in carved \"Venus figurines\" such as the Venus of Brassempouy and the Venus of Willendorf. The creation of different hairstyles, especially among women, seems to be common to all cultures and all periods and many past, and current, societies use hairpins.
Hairpins made of metal, ivory, bronze, carved wood, etc. were used in ancient Egypt. for securing decorated hairstyles. Such hairpins suggest, as graves show, that many were luxury objects among the Egyptians and later the Greeks, Etruscans, and Romans. Major success came in 1901 with the invention of the spiral hairpin by New Zealand inventor Ernest Godward. This was a predecessor of the hair clip.
The hairpin may be decorative and encrusted with jewels and ornaments, or it may be utilitarian, and designed to be almost invisible while holding a hairstyle in place. Some hairpins are a single straight pin, but modern versions are more likely to be constructed from different lengths of wire that are bent in half with a u-shaped end and a few kinks along the two opposite portions. The finished pin may vary from two to six inches in last length. The length of the wires enables placement in several designs of hairstyles to hold the nature in place. The kinks enable retaining the pin during normal movements.
A hairpin patent was issued to Kelly Chamandy in 1925.
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# Hairpin
## Hairpins in Chinese culture {#hairpins_in_chinese_culture}
Hairpins (generally known as `{{Transliteration|zh|fa-zan}}`{=mediawiki}; `{{lang-zh|髮簪}}`{=mediawiki}) are an important symbol in Chinese culture. In ancient China, hairpins were worn by men as well as women, and they were essential items for everyday hairstyling, mainly for securing and decorating a hair bun. Furthermore, hairpins worn by women could also represent their social status.
In Han Chinese culture, when young girls reached the age of fifteen, they were allowed to take part in a rite of passage known as `{{Transliteration|zh|[[ji Li (ceremony)|ji li]]}}`{=mediawiki} (`{{lang-zh|筓禮}}`{=mediawiki}), or \"hairpin initiation\". This ceremony marked the coming of age of young women. Particularly, before the age of fifteen, girls did not use hairpins as they wore their hair in braids, and they were considered as children. When they turned fifteen, they could be considered as young women after the ceremony, and they started to style their hair as buns secured and embellished by hairpins. This practice indicated that these young women could now enter into marriage. However, if a young woman had not been consented to marriage before age twenty, or she had not yet participated in a coming of age ceremony, she would attend a ceremony when she turned twenty.
In comparison with `{{Transliteration|zh|ji li}}`{=mediawiki}, the male equivalent known as `{{Transliteration|zh|[[Guan Li|guan li]]}}`{=mediawiki} (`{{lang-zh|冠禮}}`{=mediawiki}) or \"hat initiation\", usually took place five years later, at the age of twenty. In the 21st century hanfu movement, an attempt to revive the traditional Han Chinese coming-of-age ceremonies has been made, and the ideal age to attend the ceremony is twenty years old for all genders.
While hairpins can symbolize the transition from childhood to adulthood, they were closely connected to the concept of marriage as well. At the time of an engagement, the fiancée may take a hairpin from her hair and give it to her fiancé as a pledge: this can be seen as a reversal of the Western tradition, in which the future groom presents an engagement ring to his betrothed. After the wedding ceremony, the husband should put the hairpin back into his spouse\'s hair.
Hair has always carried many psychological, philosophical, romantic, and cultural meanings in Chinese culture. In Han culture, people call the union between two people `{{Transliteration|zh|jie-fa}}`{=mediawiki} (`{{lang-zh|結髮}}`{=mediawiki}), literally \"tying hair\". During the wedding ceremony, some Chinese couples exchange a lock of hair as a pledge, while others break a hairpin into two parts, and then, each of the betrothed take one part with them for keeping. If this couple were ever to get separated in the future, when they reunite, they can piece the two halves together, and the completed hairpin would serve as a proof of their identities as well as a symbol of their reunion. In addition, a married couple is sometimes referred to as `{{Transliteration|zh|jie-fa fu-qi}}`{=mediawiki} (`{{lang-zh|結髮夫妻}}`{=mediawiki}), an idiom which implies the relationship between the pair is very intimate and happy, just like how their hair has been tied together.
## Gallery
<File:Hairpin>, China, Tang dynasty, 618-907, silver, gilt - Royal Ontario Museum - DSC04137.JPG\|Chinese Tang dynasty (618--907) hairpin <File:Ming> Dynasty Silver-gilt Hairpin 6.jpg\|Chinese Ming dynasty (1368--1644) hairpin <File:Ming> Dynasty Silver-gilt Hairpin 7.jpg\|Chinese Ming dynasty (1368--1644) hairpin <File:Tomb> of Prince Chuang of Liang (梁莊王) - Hairpins 1.jpg\|Chinese Ming dynasty hairpins, 15th century <File:Tomb> of Prince Chuang of Liang (梁莊王) - Hairpins 2.jpg\|Chinese Ming dynasty hairpins, 15th century <File:Kanzashi1.jpg%7CJapanese> `{{Transliteration|ja|hirauchi [[kanzashi]]}}`{=mediawiki}, period unknown <File:Hairpins> moscow.jpg\|Russian hairpins from Moscow, probably 18th or 19th century <File:Modern> U-shaped hairpin
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# HMS Resolution
Several ships of the Royal Navy have borne the name **HMS *Resolution***:
- a first rate launched as *Prince Royal* in 1610 was renamed *Resolution* in 1650 following the inauguration of the Commonwealth, and continued to bear that name until 1660, when the name *Prince Royal* was restored
- , a 50-gun third-rate frigate launched 1654 as *Tredagh*; renamed *Resolution* 1660; destroyed after grounding by a Dutch fireship in the St James\'s Day Battle 4 August 1666.
- , a 70-gun third-rate ship of the line launched 1667; rebuilt 1698; foundered in 1703.
- , a 70-gun third rate launched 1705; run ashore to avoid capture 1707.
- , a 70-gun third rate launched 1708; wrecked 1711.
- , a 74-gun third rate launched 1758; run aground and lost 1759 at the Battle of Quiberon Bay.
- , a 74-gun third rate launched 1770; broken up 1813.
- , the vessel of Captain James Cook in his explorations.
- , a cutter purchased 1779; went missing in the North Sea June 1797, presumed to have foundered.
- , a `{{sclass|Royal Sovereign|battleship}}`{=mediawiki} in service from 1893 to 1914.
- , a `{{sclass|Revenge|battleship|2}}`{=mediawiki} in service from 1915 to 1944.
- , lead ship of the `{{sclass|Resolution|submarine|0}}`{=mediawiki} ballistic missile submarines in service from 1966 to 1994.
## Battle honours {#battle_honours}
Ships named *Resolution* of the Royal Navy have earned the following battle honours: `{{div col|colwidth=20em}}`{=mediawiki}
- Kentish Knock, 1652
- Gabbard, 1653
- Scheveningen, 1653
- Lowestoft, 1665
- Four Days\' Battle, 1666
- Orfordness, 1666
- Sole Bay, 1672
- Schooneveld, 1673
- Texel, 1673
- Barfleur, 1692
- Quiberon Bay, 1759
- St Vincent, 1780
- St Kitts, 1782
- The Saints, 1782
- Basque Roads, 1809
- Atlantic, 1939−40
- Norway, 1940
## Other British warships named *Resolution* {#other_british_warships_named_resolution}
- *Resolution* was a gunboat that the garrison at Gibraltar launched in June 1782 during the Great Siege of Gibraltar. She was one of 12. Each was armed with an 18-pounder gun, and received a crew of 21 men drawn from Royal Navy vessels stationed at Gibraltar. `{{HMS|Brilliant|1779|2}}`{=mediawiki} provided *Resolution*{{\'}}s crew.
- HMS *Resolution*, a cutter in the West Indies, date of acquisition unknown and date of loss unknown. On 10 November 1800 Captain Peter Halkett of `{{HMS|Apollo|1799|6}}`{=mediawiki} captured the Spanish sloop of war *Resolution* in the West Indies. She was armed with 18 guns and had a crew of 149 men, under the command of Don Francisco Darrichena. Halkett reported that she was the former British navy cutter *Resolution*. *Resolution* was in such an irreparable state that after a few days Halkett destroyed her.
- *Resolution*, a victualing hoy, of 75 tons, offered for sale on 22 September 1828, lying at Deptford
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# Haddocks' Eyes
\"**Haddocks\' Eyes**\" is the nickname of the name of a song sung by The White Knight from Lewis Carroll\'s 1871 novel *Through the Looking-Glass*, chapter VIII.
\"Haddocks\' Eyes\" is an example used to elaborate on the symbolic status of the concept of \"name\": a name as identification marker may be assigned to anything, including another name, thus introducing different levels of symbolization. It has been discussed in several works on logic and philosophy.
## Haddock\'s Eyes {#haddocks_eyes}
The White Knight explains to Alice a confusing nomenclature for the song.
*Haddocks\' Eyes*{{\'}}.\" \"Oh, that\'s the name of the song, is it?\" Alice said, trying to feel interested. \"No, you don\'t understand,\" the Knight said, looking a little vexed. \"That\'s what the name is `{{em|called}}`{=mediawiki}. The name really `{{em|is}}`{=mediawiki} {{\'}}*The Aged Aged Man*{{\'}}.\" \"Then I ought to have said \'That\'s what the `{{em|song}}`{=mediawiki} is called\'?\" Alice corrected herself. \"No, you oughtn\'t: that\'s quite another thing! The `{{em|song}}`{=mediawiki} is called {{\'}}*Ways And Means*{{\'}}: but that\'s only what it\'s `{{em|called}}`{=mediawiki}, you know!\" \"Well, what `{{em|is}}`{=mediawiki} the song, then?\" said Alice, who was by this time completely bewildered. \"I was coming to that,\" the Knight said. \"The song really `{{em|is}}`{=mediawiki} {{\'}}*A-sitting On A Gate*{{\'}}: and the tune\'s my own invention.\" }}
To summarize:
- The song\'s **name** is **called** *Haddocks\' Eyes*
- The song\'s **name** is *The Aged Aged Man*
- The song is **called** *Ways and Means*
- The song **is** *A-sitting on a Gate*
The complicated terminology distinguishing between \'the song, what the song is called, the name of the song, and what the name of the song is called\' both uses and mentions the use--mention distinction.
## The song {#the_song}
The White Knight sings the song to a tune he claims as his own invention, but which Alice recognises as \"I give thee all, I can no more\". By the time Alice heard it, she was already tired of poetry.
The song parodies the plot, but not the style or metre, of \"Resolution and Independence\" by William Wordsworth.
## Upon the Lonely Moor {#upon_the_lonely_moor}
Like \"Jabberwocky\", another poem published in *Through the Looking Glass*, \"Haddocks\' Eyes\" appears to have been revised over the course of many years. In 1856, Carroll published the following poem anonymously under the name *Upon the Lonely Moor*. It bears an obvious resemblance to \"Haddocks\' Eyes\"
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# Horner's method
In mathematics and computer science, **Horner\'s method** (or **Horner\'s scheme**) is an algorithm for polynomial evaluation. Although named after William George Horner, this method is much older, as it has been attributed to Joseph-Louis Lagrange by Horner himself, and can be traced back many hundreds of years to Chinese and Persian mathematicians. After the introduction of computers, this algorithm became fundamental for computing efficiently with polynomials.
The algorithm is based on **Horner\'s rule**, in which a polynomial is written in *nested form*: $\begin{align}
&a_0 + a_1x + a_2x^2 + a_3x^3 + \cdots + a_nx^n \\
={} &a_0 + x \bigg(a_1 + x \Big(a_2 + x \big(a_3 + \cdots + x(a_{n-1} + x \, a_n) \cdots \big) \Big) \bigg).
\end{align}$
This allows the evaluation of a polynomial of degree `{{mvar|n}}`{=mediawiki} with only $n$ multiplications and $n$ additions. This is optimal, since there are polynomials of degree `{{mvar|n}}`{=mediawiki} that cannot be evaluated with fewer arithmetic operations.
Alternatively, **Horner\'s method** and **`{{vanchor|Horner–Ruffini method}}`{=mediawiki}** also refers to a method for approximating the roots of polynomials, described by Horner in 1819. It is a variant of the Newton--Raphson method made more efficient for hand calculation by application of Horner\'s rule. It was widely used until computers came into general use around 1970.
## Polynomial evaluation and long division {#polynomial_evaluation_and_long_division}
Given the polynomial $p(x) = \sum_{i=0}^n a_i x^i = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + \cdots + a_n x^n,$ where $a_0, \ldots, a_n$ are constant coefficients, the problem is to evaluate the polynomial at a specific value $x_0$ of $x.$
For this, a new sequence of constants is defined recursively as follows: `{{NumBlk||<math display="block">\begin{align}
b_n & := a_n \\
b_{n-1} & := a_{n-1} + b_n x_0 \\
& ~~~ \vdots \\
b_1 & := a_1 + b_2 x_0 \\
b_0 & := a_0 + b_1 x_0.
\end{align}</math>|{{EquationRef|1}}}}`{=mediawiki} Then $b_0$ is the value of $p(x_0)$.
To see why this works, the polynomial can be written in the form $p(x) = a_0 + x \bigg(a_1 + x \Big(a_2 + x \big(a_3 + \cdots + x(a_{n-1} + x \, a_n) \cdots \big) \Big) \bigg) \ .$
Thus, by iteratively substituting the $b_i$ into the expression, $\begin{align}
p(x_0) & = a_0 + x_0\Big(a_1 + x_0\big(a_2 + \cdots + x_0(a_{n-1} + b_n x_0) \cdots \big)\Big) \\
& = a_0 + x_0\Big(a_1 + x_0\big(a_2 + \cdots + x_0 b_{n-1}\big)\Big) \\
& ~~ \vdots \\
& = a_0 + x_0 b_1 \\
& = b_0.
\end{align}$
Now, it can be proven that; `{{NumBlk||<math display="block">
p(x) = \left(b_1 + b_2 x + b_3 x^2 + b_4x^3 + \cdots + b_{n-1} x^{n-2} +b_nx^{n-1}\right) \left(x - x_0\right) + b_0
</math>|{{EquationRef|2}}}}`{=mediawiki} This expression constitutes Horner\'s practical application, as it offers a very quick way of determining the outcome of; $p(x) / (x-x_0)$ with $b_0$ (which is equal to $p(x_0)$) being the division\'s remainder, as is demonstrated by the examples below. If $x_0$ is a root of $p(x)$, then $b_0 = 0$ (meaning the remainder is $0$), which means you can factor $p(x)$ as $x-x_0$.
To finding the consecutive $b$-values, you start with determining $b_n$, which is simply equal to $a_n$. Then you then work recursively using the formula: $b_{n-1} = a_{n-1} + b_{n}x_0$ till you arrive at $b_0$.
### Examples
Evaluate $f(x)=2x^3-6x^2+2x-1$ for $x=3$.
We use synthetic division as follows:
` `*`x`*`{{sub|0}}`{=mediawiki}`│ `*`x`*`{{sup|3}}`{=mediawiki}` `*`x`*`{{sup|2}}`{=mediawiki}` `*`x`*`{{sup|1}}`{=mediawiki}` `*`x`*`{{sup|0}}`{=mediawiki}\
` 3 │ 2 −6 2 −1`\
` │ 6 0 6`\
` └────────────────────────`\
` 2 0 2 5`
The entries in the third row are the sum of those in the first two. Each entry in the second row is the product of the `{{mvar|x}}`{=mediawiki}-value (`{{val|3}}`{=mediawiki} in this example) with the third-row entry immediately to the left. The entries in the first row are the coefficients of the polynomial to be evaluated. Then the remainder of $f(x)$ on division by $x-3$ is `{{val|5}}`{=mediawiki}.
But by the polynomial remainder theorem, we know that the remainder is $f(3)$. Thus, $f(3) = 5$.
In this example, if $a_3 = 2, a_2 = -6, a_1 = 2, a_0 = -1$ we can see that $b_3 = 2, b_2 = 0, b_1 = 2, b_0 = 5$, the entries in the third row. So, synthetic division (which was actually invented and published by Ruffini 10 years before Horner\'s publication) is easier to use; it can be shown to be equivalent to Horner\'s method.
As a consequence of the polynomial remainder theorem, the entries in the third row are the coefficients of the second-degree polynomial, the quotient of $f(x)$ on division by $x-3$. The remainder is `{{val|5}}`{=mediawiki}. This makes Horner\'s method useful for polynomial long division.
Divide $x^3-6x^2+11x-6$ by $x-2$:
` 2 │ 1 −6 11 −6`\
` │ 2 −8 6`\
` └────────────────────────`\
` 1 −4 3 0`
The quotient is $x^2-4x+3$.
Let $f_1(x)=4x^4-6x^3+3x-5$ and $f_2(x)=2x-1$. Divide $f_1(x)$ by $f_2\,(x)$ using Horner\'s method.
` 0.5 │ 4 −6 0 3 −5`\
` │ 2 −2 −1 1`\
` └───────────────────────`\
` 2 −2 −1 1 −4`
The third row is the sum of the first two rows, divided by `{{val|2}}`{=mediawiki}. Each entry in the second row is the product of `{{val|1}}`{=mediawiki} with the third-row entry to the left. The answer is $\frac{f_1(x)}{f_2(x)}=2x^3-2x^2-x+1-\frac{4}{2x-1}.$
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# Horner's method
## Polynomial evaluation and long division {#polynomial_evaluation_and_long_division}
### Efficiency
Evaluation using the monomial form of a degree $n$ polynomial requires at most $n$ additions and $(n^2+n)/2$ multiplications, if powers are calculated by repeated multiplication and each monomial is evaluated individually. The cost can be reduced to $n$ additions and $2n-1$ multiplications by evaluating the powers of $x$ by iteration.
If numerical data are represented in terms of digits (or bits), then the naive algorithm also entails storing approximately $2n$ times the number of bits of $x$: the evaluated polynomial has approximate magnitude $x^n$, and one must also store $x^n$ itself. By contrast, Horner\'s method requires only $n$ additions and $n$ multiplications, and its storage requirements are only $n$ times the number of bits of $x$. Alternatively, Horner\'s method can be computed with $n$ fused multiply--adds. Horner\'s method can also be extended to evaluate the first $k$ derivatives of the polynomial with $kn$ additions and multiplications.
Horner\'s method is optimal, in the sense that any algorithm to evaluate an arbitrary polynomial must use at least as many operations. Alexander Ostrowski proved in 1954 that the number of additions required is minimal. Victor Pan proved in 1966 that the number of multiplications is minimal. However, when $x$ is a matrix, Horner\'s method is not optimal.
This assumes that the polynomial is evaluated in monomial form and no preconditioning of the representation is allowed, which makes sense if the polynomial is evaluated only once. However, if preconditioning is allowed and the polynomial is to be evaluated many times, then faster algorithms are possible. They involve a transformation of the representation of the polynomial. In general, a degree-$n$ polynomial can be evaluated using only `{{floor|''n''/2}}`{=mediawiki}+2 multiplications and $n$ additions.
#### Parallel evaluation {#parallel_evaluation}
A disadvantage of Horner\'s rule is that all of the operations are sequentially dependent, so it is not possible to take advantage of instruction level parallelism on modern computers. In most applications where the efficiency of polynomial evaluation matters, many low-order polynomials are evaluated simultaneously (for each pixel or polygon in computer graphics, or for each grid square in a numerical simulation), so it is not necessary to find parallelism within a single polynomial evaluation.
If, however, one is evaluating a single polynomial of very high order, it may be useful to break it up as follows: $\begin{align}
p(x)
& = \sum_{i=0}^n a_i x^i \\[1ex]
& = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + \cdots + a_n x^n \\[1ex]
& = \left( a_0 + a_2 x^2 + a_4 x^4 + \cdots\right) + \left(a_1 x + a_3 x^3 + a_5 x^5 + \cdots \right) \\[1ex]
& = \left( a_0 + a_2 x^2 + a_4 x^4 + \cdots\right) + x \left(a_1 + a_3 x^2 + a_5 x^4 + \cdots \right) \\[1ex]
& = \sum_{i=0}^{\lfloor n/2 \rfloor} a_{2i} x^{2i} + x \sum_{i=0}^{\lfloor n/2 \rfloor} a_{2i+1} x^{2i} \\[1ex]
& = p_0(x^2) + x p_1(x^2).
\end{align}$
More generally, the summation can be broken into *k* parts: $p(x)
= \sum_{i=0}^n a_i x^i
= \sum_{j=0}^{k-1} x^j \sum_{i=0}^{\lfloor n/k \rfloor} a_{ki+j} x^{ki}
= \sum_{j=0}^{k-1} x^j p_j(x^k)$ where the inner summations may be evaluated using separate parallel instances of Horner\'s method. This requires slightly more operations than the basic Horner\'s method, but allows *k*-way SIMD execution of most of them. Modern compilers generally evaluate polynomials this way when advantageous, although for floating-point calculations this requires enabling (unsafe) reassociative math. Another use of breaking a polynomial down this way is to calculate steps of the inner summations in an alternating fashion to take advantage of instruction-level parallelism.
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# Horner's method
## Polynomial evaluation and long division {#polynomial_evaluation_and_long_division}
### Application to floating-point multiplication and division {#application_to_floating_point_multiplication_and_division}
Horner\'s method is a fast, code-efficient method for multiplication and division of binary numbers on a microcontroller with no hardware multiplier. One of the binary numbers to be multiplied is represented as a trivial polynomial, where (using the above notation) $a_i = 1$, and $x = 2$. Then, *x* (or *x* to some power) is repeatedly factored out. In this binary numeral system (base 2), $x = 2$, so powers of 2 are repeatedly factored out.
#### Example
For example, to find the product of two numbers (0.15625) and *m*: $\begin{align}
(0.15625) m & = (0.00101_b) m = \left( 2^{-3} + 2^{-5} \right) m = \left( 2^{-3})m + (2^{-5} \right)m \\
& = 2^{-3} \left(m + \left(2^{-2}\right)m\right) = 2^{-3} \left(m + 2^{-2} (m)\right).
\end{align}$
#### Method
To find the product of two binary numbers *d* and *m*:
1. A register holding the intermediate result is initialized to *d*.
2. Begin with the least significant (rightmost) non-zero bit in *m*. `{{ordered list | list-style-type = lower-alpha | start = 2
| Count (to the left) the number of bit positions to the next most significant non-zero bit. If there are no more-significant bits, then take the value of the current bit position.
| Using that value, perform a left-shift operation by that number of bits on the register holding the intermediate result}}`{=mediawiki}
3. If all the non-zero bits were counted, then the intermediate result register now holds the final result. Otherwise, add d to the intermediate result, and continue in step 2 with the next most significant bit in *m*.
#### Derivation
In general, for a binary number with bit values ($d_3 d_2 d_1 d_0$) the product is $(d_3 2^3 + d_2 2^2 + d_1 2^1 + d_0 2^0)m = d_3 2^3 m + d_2 2^2 m + d_1 2^1 m + d_0 2^0 m.$ At this stage in the algorithm, it is required that terms with zero-valued coefficients are dropped, so that only binary coefficients equal to one are counted, thus the problem of multiplication or division by zero is not an issue, despite this implication in the factored equation: $= d_0\left(m + 2 \frac{d_1}{d_0} \left(m + 2 \frac{d_2}{d_1} \left(m + 2 \frac{d_3}{d_2} (m)\right)\right)\right).$
The denominators all equal one (or the term is absent), so this reduces to $= d_0(m + 2 {d_1} (m + 2 {d_2} (m + 2 {d_3} (m)))),$ or equivalently (as consistent with the \"method\" described above) $= d_3(m + 2^{-1} {d_2} (m + 2^{-1}{d_1} (m + {d_0} (m)))).$
In binary (base-2) math, multiplication by a power of 2 is merely a register shift operation. Thus, multiplying by 2 is calculated in base-2 by an arithmetic shift. The factor (2^−1^) is a right arithmetic shift, a (0) results in no operation (since 2^0^ = 1 is the multiplicative identity element), and a (2^1^) results in a left arithmetic shift. The multiplication product can now be quickly calculated using only arithmetic shift operations, addition and subtraction.
The method is particularly fast on processors supporting a single-instruction shift-and-addition-accumulate. Compared to a C floating-point library, Horner\'s method sacrifices some accuracy, however it is nominally 13 times faster (16 times faster when the \"canonical signed digit\" (CSD) form is used) and uses only 20% of the code space.
### Other applications {#other_applications}
Horner\'s method can be used to convert between different positional numeral systems -- in which case *x* is the base of the number system, and the *a*~*i*~ coefficients are the digits of the base-*x* representation of a given number -- and can also be used if *x* is a matrix, in which case the gain in computational efficiency is even greater. However, for such cases faster methods are known.
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# Horner's method
## Polynomial root finding {#polynomial_root_finding}
Using the long division algorithm in combination with Newton\'s method, it is possible to approximate the real roots of a polynomial. The algorithm works as follows. Given a polynomial $p_n(x)$ of degree $n$ with zeros $z_n < z_{n-1} < \cdots < z_1,$ make some initial guess $x_0$ such that $z_1 < x_0$. Now iterate the following two steps:
1. Using Newton\'s method, find the largest zero $z_1$ of $p_n(x)$ using the guess $x_0$.
2. Using Horner\'s method, divide out $(x-z_1)$ to obtain $p_{n-1}$. Return to step 1 but use the polynomial $p_{n-1}$ and the initial guess $z_1$.
These two steps are repeated until all real zeros are found for the polynomial. If the approximated zeros are not precise enough, the obtained values can be used as initial guesses for Newton\'s method but using the full polynomial rather than the reduced polynomials.
### Example {#example_1}
Consider the polynomial $p_6(x) = (x+8)(x+5)(x+3)(x-2)(x-3)(x-7)$ which can be expanded to $p_6(x) = x^6 + 4x^5 - 72x^4 -214x^3 + 1127x^2 + 1602x -5040.$
From the above we know that the largest root of this polynomial is 7 so we are able to make an initial guess of 8. Using Newton\'s method the first zero of 7 is found as shown in black in the figure to the right. Next $p(x)$ is divided by $(x-7)$ to obtain $p_5(x) = x^5 + 11x^4 + 5x^3 - 179x^2 - 126x + 720$ which is drawn in red in the figure to the right. Newton\'s method is used to find the largest zero of this polynomial with an initial guess of 7. The largest zero of this polynomial which corresponds to the second largest zero of the original polynomial is found at 3 and is circled in red. The degree 5 polynomial is now divided by $(x-3)$ to obtain $p_4(x) = x^4 + 14x^3 + 47x^2 - 38x - 240$ which is shown in yellow. The zero for this polynomial is found at 2 again using Newton\'s method and is circled in yellow. Horner\'s method is now used to obtain $p_3(x) = x^3 + 16x^2 + 79x + 120$ which is shown in green and found to have a zero at −3. This polynomial is further reduced to $p_2(x) = x^2 + 13x + 40$ which is shown in blue and yields a zero of −5. The final root of the original polynomial may be found by either using the final zero as an initial guess for Newton\'s method, or by reducing $p_2(x)$ and solving the linear equation. As can be seen, the expected roots of −8, −5, −3, 2, 3, and 7 were found.
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# Horner's method
## Divided difference of a polynomial {#divided_difference_of_a_polynomial}
Horner\'s method can be modified to compute the divided difference $(p(y) - p(x))/(y - x).$ Given the polynomial (as before) $p(x) = \sum_{i=0}^n a_i x^i = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + \cdots + a_n x^n,$ proceed as follows $\begin{align}
b_n & = a_n, &\quad d_n &= b_n, \\
b_{n-1} & = a_{n-1} + b_n x, &\quad d_{n-1} &= b_{n-1} + d_n y, \\
& {}\ \ \vdots &\quad & {}\ \ \vdots\\
b_1 & = a_1 + b_2 x, &\quad d_1 &= b_1 + d_2 y,\\
b_0 & = a_0 + b_1 x.
\end{align}$
At completion, we have $\begin{align}
p(x) &= b_0, \\
\frac{p(y) - p(x)}{y - x} &= d_1, \\
p(y) &= b_0 + (y - x) d_1.
\end{align}$ This computation of the divided difference is subject to less round-off error than evaluating $p(x)$ and $p(y)$ separately, particularly when $x \approx y$. Substituting $y = x$ in this method gives $d_1 = p'(x)$, the derivative of $p(x)$.
## History
Horner\'s paper, titled \"A new method of solving numerical equations of all orders, by continuous approximation\", was [read](http://hdl.handle.net/2027/mdp.39015014105277?urlappend=%3Bseq=158) before the Royal Society of London, at its meeting on July 1, 1819, with a sequel in 1823. Horner\'s paper in Part II of *Philosophical Transactions of the Royal Society of London* for 1819 was warmly and expansively welcomed by a [reviewer](http://turing.une.edu.au/~ernie/Horner/Horner1820MonthlyRev91-4.pdf)`{{Dead link|date=January 2020|bot=InternetArchiveBot|fix-attempted=yes}}`{=mediawiki} in the issue of *The Monthly Review: or, Literary Journal* for April, 1820; in comparison, a technical paper by Charles Babbage is dismissed curtly in this review. The sequence of reviews in *The Monthly Review* for September, 1821, concludes that Holdred was the first person to discover a direct and general practical solution of numerical equations. Fuller showed that the method in Horner\'s 1819 paper differs from what afterwards became known as \"Horner\'s method\" and that in consequence the priority for this method should go to Holdred (1820).
Unlike his English contemporaries, Horner drew on the Continental literature, notably the work of Arbogast. Horner is also known to have made a close reading of John Bonneycastle\'s book on algebra, though he neglected the work of Paolo Ruffini.
Although Horner is credited with making the method accessible and practical, it was known long before Horner. In reverse chronological order, Horner\'s method was already known to:
- Paolo Ruffini in 1809 (see Ruffini\'s rule)
- Isaac Newton in 1669
- the Chinese mathematician Zhu Shijie in the 14th century
- the Chinese mathematician Qin Jiushao in his *Mathematical Treatise in Nine Sections* in the 13th century
- the Persian mathematician Sharaf al-Dīn al-Ṭūsī in the 12th century (the first to use that method in a general case of cubic equation)
- the Chinese mathematician Jia Xian in the 11th century (Song dynasty)
- *The Nine Chapters on the Mathematical Art*, a Chinese work of the Han dynasty (202 BC -- 220 AD) edited by Liu Hui (fl. 3rd century).
Qin Jiushao, in his *Shu Shu Jiu Zhang* (*Mathematical Treatise in Nine Sections*; 1247), presents a portfolio of methods of Horner-type for solving polynomial equations, which was based on earlier works of the 11th century Song dynasty mathematician Jia Xian; for example, one method is specifically suited to bi-quintics, of which Qin gives an instance, in keeping with the then Chinese custom of case studies. Yoshio Mikami in *Development of Mathematics in China and Japan* (Leipzig 1913) wrote:`{{Blockquote | style=font-size:100% | text="... who can deny the fact of Horner's illustrious process being used in China at least nearly six long centuries earlier than in Europe ... We of course don't intend in any way to ascribe Horner's invention to a Chinese origin, but the lapse of time sufficiently makes it not altogether impossible that the Europeans could have known of the Chinese method in a direct or indirect way."<ref>{{harvnb|Mikami|1913|p=77}}</ref>}}`{=mediawiki} Ulrich Libbrecht concluded: *It is obvious that this procedure is a Chinese invention \... the method was not known in India*. He said, Fibonacci probably learned of it from Arabs, who perhaps borrowed from the Chinese. The extraction of square and cube roots along similar lines is already discussed by Liu Hui in connection with Problems IV.16 and 22 in *Jiu Zhang Suan Shu*, while Wang Xiaotong in the 7th century supposes his readers can solve cubics by an approximation method described in his book Jigu Suanjing
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# Hapworth 16, 1924
\"**Hapworth 16, 1924**\" is an uncollected work of short fiction by J. D. Salinger that appeared in the June 19, 1965, issue of *The New Yorker*.
The story is the last original work Salinger published during his lifetime, and filled almost the entire magazine. It is the \"youngest\" of his Glass family stories, in the sense that the narrated events happen chronologically before those in the rest of the series.
## Plot
46-year-old Buddy Glass reproduces the contents of a letter written by his older brother Seymour, who died by suicide 17 years earlier in 1948. Seymour wrote the letter to their parents while he and Buddy (two years his junior) were attending Camp Simon Hapworth, Maine, in 1924. The literary voice conveyed in the letter is that of a highly articulate and strikingly precocious boy of seven. The letter, written from the camp infirmary (Seymour has injured his leg) is a wide-ranging commentary on the camp personnel, the camp attendees, and his relationships with his family, humanity and God. Seymour and Buddy largely prefer to occupy themselves writing poems and short stories rather than participate in group activities. They therefore meet with some hostility.
Seymour devotes a large part of the letter to enumerating his reading list and requests for further reading material from his parents. He offers critical appraisals of a number of major literary figures. The letter closes with a lengthy discourse on the significance of God.
## Publishing history {#publishing_history}
The circumstances and considerations that led chief fiction editor William Shawn at *The New Yorker* to devote virtually the entire June 19, 1965, edition to \"Hapworth 16, 1924\" are obscure. Biographer Kenneth Slawenki writes, \"the files of *The New Yorker* are unusually silent on the details of the novella\'s reception by the editorial staff and its eventual reception by William Shawn.\" The correspondence between Salinger and Shawn chronicling the decision may have been deliberately suppressed. Slawenski speculates that the appearance of Salinger\'s piece in the journal was \"a *fait accompli* rather than a topic of debate\".
After the story\'s appearance in *The New Yorker*, Salinger---who had already withdrawn to his New Hampshire home---stopped publishing altogether. Since the story never appeared in book form, readers had to seek out that issue or find it on microfilm. Finally, with the release of *The Complete New Yorker* on DVD in 2005, the story was once again widely available.
In 1996, Orchises Press, a small Virginia publishing house, started a process of publishing \"Hapworth\" in book form. Orchises Press owner Roger Lathbury has described the effort in *The Washington Post* and, three months after Salinger\'s death, in *New York* magazine*.* According to Lathbury, Salinger was deeply concerned with the proposed book\'s appearance, even visiting Washington to examine the cloth for the binding. Salinger also sent Lathbury numerous \"infectious and delightful and loving\" letters.
Following publishing norms, Lathbury applied for Library of Congress Cataloging in Publication data, unaware of how publicly available the information would be. A writer in Seattle, researching an article on Jeff Bezos, came across the \"Hapworth\" publication date, and told his sister, a journalist for the *Washington Business Journal*, who wrote an article about the upcoming book. This led to substantial coverage in the press. Shortly before the books were to be shipped, Salinger changed his mind, and Orchises withdrew the book. New publication dates were repeatedly announced, but it never appeared. Lathbury said, \"I never reached back out. I thought about writing some letters, but it wouldn\'t have done any good.\"
## Reception and assessment {#reception_and_assessment}
Both contemporary and later literary critics harshly panned \"Hapworth 16, 1924\"; writing in *The New York Times*, Michiko Kakutani called it \"a sour, implausible and, sad to say, completely charmless story \.... filled with digressions, narcissistic asides and ridiculous shaggy-dog circumlocutions.\"
Calling it \"virtually unreadable\" and \"an enigma\", critic John Wenke compares \"Hapworth\" to viewing a neighbor\'s unedited family home movies. He writes:
Wenke adds that the story is a striking departure from the \"urbane, pithy and wry\" short fiction *The New Yorker*\'s editors and readership favored.
Biographer Kenneth Slawenski considers the piece \"professionally, a disaster\" and ponders what may have motivated Salinger to submit the work for publication:
Biographer Ian Hamilton concurs that Salinger appears to abandon his loyal readership and retreat into the exclusive realm of his characters. He writes, \"The Glass family has, in this last story, become Salinger\'s subject and his readership, his creatures and his companions. His life is finally made one with art.\"
Salinger is said to have considered the story a \"high point of his writing\" and made tentative steps to have it reprinted, though those came to nothing
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# Hubris
**Hubris** (`{{IPAc-en|ˈ|h|juː|b|r|ɪ|s}}`{=mediawiki}; `{{etymology|grc|''{{wikt-lang|grc|ὕβρις}}'' ({{grc-transl|ὕβρις}})|pride, insolence, outrage}}`{=mediawiki}), or less frequently **hybris** (`{{IPAc-en|ˈ|h|aɪ|b|r|ɪ|s}}`{=mediawiki}), is extreme or excessive pride or dangerous overconfidence and complacency, often in combination with (or synonymous with) **arrogance**.
Hubris, arrogance, and pretension are related to the need for victory (even if it does not always mean winning) instead of reconciliation, which \"friendly\" groups might promote. Hubris is usually perceived as a characteristic of an individual rather than a group, although the group the offender belongs to may suffer collateral consequences from wrongful acts. Hubris often indicates a loss of contact with reality and an overestimation of one\'s own competence, accomplishments, or capabilities.
The term *hubris* originated in Ancient Greek, where it had several different meanings depending on the context. In legal usage, it meant assault or sexual crimes and theft of public property, and in religious usage it meant emulation of divinity or transgression against a god.
## Ancient Greek origin {#ancient_greek_origin}
In ancient Greek, *hubris* referred to \"outrage\": actions that violated natural order, or which shamed and humiliated the victim, sometimes for the pleasure or gratification of the abuser.
### Mythological usage {#mythological_usage}
Hesiod and Aeschylus used the word \"hubris\" to describe transgressions against the gods. A common way that hubris was committed was when a mortal claimed to be better than a god in a particular skill or attribute. Claims like these were rarely left unpunished, and so Arachne, a talented young weaver, was transformed into a spider when she said that her skills exceeded those of the goddess Athena. Additional examples include Icarus, Phaethon, Salmoneus, Niobe, Cassiopeia, Tantalus, and Tereus.
The goddess Hybris is described in the Encyclopædia Britannica Eleventh Edition as having \"insolent encroachment upon the rights of others\".
These events were not limited to myth, and certain figures in history were considered to have been punished for committing hubris through their arrogance. One such person was the king Xerxes I as portrayed in Aeschylus\'s play *The Persians*, and who allegedly threw chains to bind the Hellespont sea as punishment for daring to destroy his fleet.
What is common in all of these examples is the breaching of limits, as the Greeks believed that the Fates (Μοῖραι) had assigned each being with a particular area of freedom, an area that even the gods could not breach.
### Legal usage {#legal_usage}
In ancient Athens, hubris was defined as the use of violence to shame the victim (this sense of hubris could also characterize rape). In legal terms, hubristic violations of the law included what might today be termed assault-and-battery, sexual crimes, or the theft of public or sacred property. In some contexts, the term had a sexual connotation. Shame was frequently reflected upon the perpetrator, as well.
Crucial to this definition are the ancient Greek concepts of honour (τιμή, *timē*) and shame (αἰδώς, *aidōs*). The concept of honour included not only the exaltation of the one receiving honour, but also the shaming of the one overcome by the act of hubris. This concept of honour is akin to a zero-sum game. Rush Rehm simplifies this definition of hubris to the contemporary concept of \"insolence, contempt, and excessive violence\".
Two well-known cases are found in the speeches of Demosthenes, a prominent statesman and orator in ancient Greece. These two examples occurred when first Midias punched Demosthenes in the face in the theatre (*Against Midias*), and second when (in *Against Conon*) a defendant allegedly assaulted a man and crowed over the victim. Yet another example of hubris appears in Aeschines\' *Against Timarchus*, where the defendant, Timarchus, is accused of breaking the law of hubris by submitting himself to prostitution and anal intercourse. Aeschines brought this suit against Timarchus to bar him from the rights of political office and his case succeeded. Aristotle defined hubris as shaming the victim, not because of anything that happened to the committer or might happen to the committer, but merely for that committer\'s own gratification:
> to cause shame to the victim, not in order that anything may happen to you, nor because anything has happened to you, but merely for your own gratification. Hubris is not the requital of past injuries; this is revenge. As for the pleasure in hubris, its cause is this: naive men think that by ill-treating others they make their own superiority the greater.
### Early Christianity {#early_christianity}
In the Septuagint, the \"hubris is overweening pride, superciliousness or arrogance, often resulting in fatal retribution or nemesis\". The word *hubris* as used in the New Testament parallels the Hebrew word *pesha*, meaning \"transgression\". It represents a pride that \"makes a man defy God\", sometimes to the degree that he considers himself an equal.
## Modern usage {#modern_usage}
In its modern usage, hubris denotes overconfident pride combined with arrogance. Hubris is also referred to as \"pride that blinds\" because it often causes a committer of hubris to act in foolish ways that belie common sense.
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# Hubris
## Modern usage {#modern_usage}
### Arrogance
The Oxford English Dictionary defines \"arrogance\" in terms of \"high or inflated opinion of one\'s own abilities, importance, etc., that gives rise to presumption or excessive self-confidence, or to a feeling or attitude of being superior to others \[\...\].\" Adrian Davies sees arrogance as more generic and less severe than hubris
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# Hussites
thumb\|upright=1.2\|Battle between Hussites (left) and Catholic crusaders in the 15th century thumb\|upright=1.2\|The Lands of the Bohemian Crown during the Hussite Wars. The movement began during the Renaissance in Prague and quickly spread south and then through the rest of the Kingdom of Bohemia. Eventually, it expanded into the remaining domains of the Bohemian Crown as well. The **Hussites** (Czech: *Husité* or *Kališníci*, \"Chalice People\"; Latin: *Hussitae*) were a Czech proto-Protestant Christian movement influenced by both the Byzantine Rite and John Wycliffe that followed the teachings of reformer Jan Hus (fl. 1401--1415), a part of the Bohemian Reformation.
The Czech lands had originally been Christianized by Byzantine Greek missionaries Saints Cyril and Methodius, who introduced the Byzantine Rite in the Old Church Slavonic liturgical language and the Byzantine tradition of Communion in both kinds administered by the holy spoon. Over the centuries that followed, however, the Roman Rite in Ecclesiastical Latin, which is less easily understood than Slavonic by native speakers of Old Czech, was imposed upon the Czech people despite considerable public resistance, by German-speaking bishops, beginning with Wiching, from the Holy Roman Empire. (See also Sázava Monastery). As a cultural memory of both communion in both kinds and the Divine Liturgy in a language closer to the vernacular is believed to have survived well into the Renaissance, the ideas of Jan Hus and others like him swiftly gained a wide public following. After the trial and execution of Hus at the Council of Constance, a series of crusades, civil wars, victories and compromises between various factions with different theological agendas broke out. At the end of the Hussite Wars (1420--1434), the now Catholic-supported Utraquist side came out victorious from protracted conflict against Jan Žižka and the Taborites, who embraced the more radical theological teachings of John Wycliffe and the Lollards, and became the dominant Hussite group in Bohemia.
Catholics and Utraquists were given legal equality in Bohemia after the religious peace of Kutná Hora in 1485. Bohemia and Moravia, or what is now the territory of the Czech Republic, remained majority Hussite for two centuries. Roman Catholicism was only reimposed by the Holy Roman Emperor Ferdinand II following the 1620 Battle of White Mountain and during the Thirty Years\' War.
The Hussite tradition continues in the Moravian Church, Unity of the Brethren and, since the dissolution of Austria-Hungary, by the re-founded Czechoslovak Hussite Church. The revived legacy of Saints Cyril and Methodius also continues in both the Orthodox Church in the Czech Lands and the Apostolic Exarchate of the Greek Catholic Church in the Czech Republic.
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# Hussites
## History
The Hussite movement began in the Kingdom of Bohemia and quickly spread throughout the remaining Lands of the Bohemian Crown, including Moravia and Silesia. It also made inroads into the northern parts of the Kingdom of Hungary (now Slovakia), but was rejected and gained infamy for the plundering behaviour of the Hussite soldiers. There were also very small temporary communities in Poland-Lithuania and Transylvania which moved to Bohemia after being confronted with religious intolerance. It was a regional movement that failed to expand farther. Hussites emerged as a majority Utraquist movement with a significant Taborite faction, and smaller regional ones that included Adamites, Orebites and Orphans.
Major Hussite theologians included Petr Chelčický and Jerome of Prague. A number of Czech national heroes were Hussite, including Jan Žižka, who led a fierce resistance to five consecutive crusades proclaimed on Hussite Bohemia by the Papacy. Hussites were one of the most important forerunners of the Protestant Reformation. This predominantly religious movement was propelled by social issues and strengthened Czech national awareness.
### Hus\'s death {#huss_death}
thumb\|left\|upright=0.9\|Execution of Jan Hus (1415) that sparked outrage in the Kingdom of Bohemia
The Council of Constance lured Jan Hus in with a letter of indemnity, then tried him for heresy and put him to death at the stake on 6 July 1415.
The arrest of Hus in 1414 caused considerable resentment in Czech lands. The authorities of both countries appealed urgently and repeatedly to King Sigismund to release Jan Hus.
When news of his death at the Council of Constance arrived, disturbances broke out, directed primarily against the clergy and especially against the monks. Even the Archbishop narrowly escaped from the effects of this popular anger. The treatment of Hus was felt to be a disgrace inflicted upon the whole country and his death was seen as a criminal act. King Wenceslaus IV., prompted by his grudge against Sigismund, at first gave free vent to his indignation at the course of events in Constance. His wife openly favoured the friends of Hus. Avowed Hussites stood at the head of the government.
A league was formed by certain lords,`{{Who|date=April 2011}}`{=mediawiki} who pledged themselves to protect the free preaching of the Gospel upon all their possessions and estates and to obey the power of the Bishops only where their orders accorded with the injunctions of the Bible. The university would arbitrate any disputed points. The entire Hussite nobility joined the league. Other than verbal protest of the council\'s treatment of Hus, there was little evidence of any actions taken by the nobility until 1417. At that point several of the lesser nobility and some barons, signatories of the 1415 protest letter, removed Catholic priests from their parishes, replacing them with priests willing to give communion in both wine and bread. The chalice of wine became the central identifying symbol of the Hussite movement. If the king had joined, its resolutions would have received the sanction of the law; but he refused, and approached the newly formed Roman Catholic League of lords, whose members pledged themselves to support the king, the Catholic Church, and the council. The prospect of a civil war began to emerge.
Prior to becoming pope, Martin V, then known as Cardinal Otto of Colonna had attacked Hus with relentless severity. He energetically resumed the battle against Hus\'s teaching after the enactments of the Council of Constance. He wished to eradicate completely the doctrine of Hus, for which purpose the co-operation of King Wenceslaus had to be obtained. In 1418, Sigismund succeeded in winning his brother over to the standpoint of the council by pointing out the inevitability of a religious war if the heretics in Bohemia found further protection. Hussite statesmen and army leaders had to leave the country and Roman Catholic priests were reinstated. These measures caused a general commotion which hastened the death of King Wenceslaus by a paralytic stroke in 1419. His heir was Sigismund.
### Hussite Wars (1419--1434) {#hussite_wars_14191434}
thumb\|left\|upright=0.9\|alt=Painting of battle between mounted knights\|The Battle of Kratzau between Hussites and Catholic forces led by Hans von Polenz thumb\|upright=1.0\|right\|The Hussite Wagenburg right\|thumb\|upright=0.7\|Recreation of Hussite pavise from an original in the Museum of Prague
The news of the death of King Wenceslaus in 1419 produced a great commotion among the people of Prague. A revolution swept over the country: churches and monasteries were destroyed, and church property was seized by the Hussite nobility. It was then, and remained till much later, in question whether Bohemia was a hereditary or an elective monarchy, especially as the line through which Sigismund claimed the throne had accepted that the Kingdom of Bohemia was an elective monarchy elected by the nobles, and thus the regent of the kingdom (Čeněk of Wartenberg) also explicitly stated that Sigismund had not been elected as reason for Sigismund\'s claim to not be accepted. Sigismund could get possession of \"his\" kingdom only by force of arms. Pope Martin V called upon Catholics of the West to take up arms against the Hussites, declaring a crusade, and twelve years of warfare followed.
The Hussites initially campaigned defensively, but after 1427 they assumed the offensive. Apart from their religious aims, they fought for the national interests of the Czechs. The moderate and radical parties were united, and they not only repelled the attacks of the army of crusaders but crossed the borders into neighboring countries. On March 23, 1430, Joan of Arc dictated a letter that threatened to lead a crusading army against the Hussites unless they returned to the Catholic faith, but her capture by English and Burgundian troops two months later would keep her from carrying out this threat.
### Council of Basel and Compacta of Prague {#council_of_basel_and_compacta_of_prague}
Eventually, the opponents of the Hussites found themselves forced to consider an amicable settlement. The Hussites were sent an invitation to attend the ecumenical Council of Basel on October 15, 1431. The discussions began on 10 January 1432, focusing chiefly on the four articles of Prague. No agreement emerged. After repeated negotiations between the Basel Council and Bohemia, a Bohemian--Moravian state assembly in Prague accepted the *\"Compactata\"* of Prague on 30 November 1433. The agreement granted communion in both kinds to all who desired it, but with the understanding that Christ was entirely present in each kind, though on the condition that the rest of the Hussite reforms would no longer be emphasised. Free preaching was granted conditionally: the Church hierarchy had to approve and place priests, and the power of the bishop must be considered. The article which prohibited the secular power of the clergy was almost reversed.
The Taborites refused to conform. The Calixtines united with the Roman Catholics and destroyed the Taborites at the Battle of Lipany on 30 May 1434. From that time, the Taborites lost their importance, though the Hussite movement would continue in Poland for another five years, until the Royalist forces of Poland defeated the Polish Hussites at the Battle of Grotniki. The state assembly of Jihlava in 1436 confirmed the *\"Compactata\"* and gave them the sanction of law. This accomplished the reconciliation of Bohemia with Rome and the Western Church, and at last Sigismund obtained possession of the Bohemian crown. His reactionary measures caused a ferment in the whole country, but he died in 1437. The state assembly in Prague rejected Wyclif\'s doctrine of the Lord\'s Supper, which was obnoxious to the Utraquists, as heresy in 1444. Most of the Taborites now went over to the party of the Utraquists; the rest joined the \"Brothers of the Law of Christ\" (*\"Unitas Fratrum\"*) (see history of the Moravian Church).
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# Hussites
## History
### Hussite Bohemia, Luther and the Reformation (1434--1618) {#hussite_bohemia_luther_and_the_reformation_14341618}
thumb\|upright=0.9\|Painting celebrating the Catholic victory at the Battle of White Mountain (1620). In the coming years, Bohemia and Moravia were converted from Hussitism to Roman Catholicism by the Habsburgs.
In 1462, Pope Pius II declared the *\"Compacta\"* null and void, prohibited communion in both kinds, and acknowledged King George of Podebrady as king on condition that he would promise an unconditional harmony with the Roman Church. This he refused, leading to the Bohemian--Hungarian War (1468--1478). His successor, King Vladislaus II, favored the Roman Catholics and proceeded against some zealous clergymen of the Calixtines. The troubles of the Utraquists increased from year to year. In 1485, at the Diet of Kutná Hora, an agreement was made between the Roman Catholics and Utraquists that lasted for thirty-one years. It was only later, at the Diet of 1512, that the equal rights of both religions were permanently established. The appearance of Martin Luther was hailed by the Utraquist clergy, and Luther himself was astonished to find so many points of agreement between the doctrines of Hus and his own. But not all Utraquists approved of the German Reformation; a schism arose among them, and many returned to the Roman doctrine, while other elements had organised the *\"Unitas Fratrum\"* already in 1457.
### Bohemian Revolt and harsh persecution under the Habsburgs (1618--1918) {#bohemian_revolt_and_harsh_persecution_under_the_habsburgs_16181918}
Under Emperor Maximilian II, the Bohemian state assembly established the Confessio Bohemica, upon which Lutherans, Reformed, and Bohemian Brethren agreed. From that time forward Hussitism began to die out. After the Battle of White Mountain on 8 November 1620 the Roman Catholic Faith was re-established with vigour, which fundamentally changed the religious conditions of the Czech lands.
Leaders and members of Unitas Fratrum were forced to choose to either leave the many and varied southeastern principalities of what was the Holy Roman Empire (mainly Austria, Hungary, Bohemia, Moravia and parts of Germany and its many states), or to practice their beliefs secretly. As a result, members were forced underground and dispersed across northwestern Europe. The largest remaining communities of the Brethren were located in Lissa (Leszno) in Poland, which had historically strong ties with the Czechs, and in small, isolated groups in Moravia. Some, among them Jan Amos Comenius, fled to western Europe, mainly the Low Countries. A settlement of Hussites in Herrnhut, Saxony, now Germany, in 1722 caused the emergence of the Moravian Church.
### Post-Habsburg era and modern times (1918--present) {#post_habsburg_era_and_modern_times_1918present}
thumb\|upright=0.7\|left\|The modern Hussite flag *Main article: Moravian Church, Czechoslovak Hussite Church, Unity of the Brethren (Texas)*
In 1918, as a result of World War I, the Czech lands regained independence from Austria-Hungary controlled by the Habsburg monarchy as Czechoslovakia (due to Masaryk and Czechoslovak legions with Hussite tradition, in the name of the troops).
Today, the Hussite tradition is represented in the Moravian Church, Unity of the Brethren, and Czechoslovak Hussite Church.
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# Hussites
## Factions
{{ multiple image\|total_width=600 \| image1 = Luther und Hus-Abendmahl.jpg \| caption1 = *Luther and Hus serving communion under both kinds together*, an imaginary woodcut from 16th century Saxony demonstrating the affinity of Lutherans and Moderate Hussites \| image2 = Jensky kodex Zizka.jpg \| caption2 = Jan Žižka leading troops of Radical Hussites \| image3 = Jagiełło dispute.JPG \| caption3 = Hussite theologians dispute in the presence of King Władysław II Jagiełło of Poland }}
Hussitism organised itself during the years 1415--1419. Hussites were not a unitary movement, but a diverse one with multiple factions that held different views and opposed each other in the Hussite Wars. From the beginning, there formed two parties, with a smaller number of people withdrawing from both parties around the pacifist Petr Chelčický, whose teachings would form the foundation of the Unitas Fratrum. Hussites can be divided into:
- Moderate Hussites
- Prague Hussites
- Bohemian Hussite nobility
- Hussites of Žatec and Louny
- Other Utraquists/Calixtines
- Radical Hussites
- Taborites
- Orebites
- Adamites
- Orphans
- Other Radical Hussites
### Moderates `{{Anchor|Four Articles of Prague}}`{=mediawiki}
The more conservative Hussites (the moderate party, or Utraquists), who followed Hus more closely, sought to conduct reform while leaving the whole hierarchical and liturgical order of the Church untouched.
Their programme is contained in the Four Articles of Prague, which were written by Jacob of Mies and agreed upon in July 1420, promulgated in the Latin, Czech, and German languages. They can be summarised as follows:
- Free preaching of the Word of God throughout the Kingdom of Bohemia and the Margravate of Moravia.
- Celebration of the communion under both kinds (bread and wine to priests and laity alike)
- The removal of secular power from the clergy.
- Secular punishment for mortal sins among clergy and laity alike.
The views of the moderate Hussites were widely represented at the university and among the citizens of Prague; they were therefore called the Prague Party, but also Calixtines (Latin *calix* chalice) or Utraquists (Latin *utraque* both), because they emphasized the second article of Prague, and the chalice became their emblem.
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# Hussites
## Factions
### Radicals
The more radical parties, the Taborites, Orebites and Orphans, identified itself more boldly with the doctrines of John Wycliffe, sharing his passionate hatred of the monastic clergy, and his desire to return the Church to its supposed condition during the time of the apostles. This required the removal of the existing hierarchy and the secularisation of ecclesiastical possessions. Above all they clung to Wycliffe\'s doctrine of the Lord\'s Supper, denying transubstantiation, and this is the principal point by which they are distinguished from the moderate party, the Utraquists.
The radicals preached the *\"sufficientia legis Christi\"*---the divine law (i.e. the Bible) is the sole rule and canon for human society, not only in the church, but also in political and civil matters. They rejected therefore, as early as 1416, everything that they believed had no basis in the Bible, such as the veneration of saints and images, fasts, superfluous holidays, the oath, intercession for the dead, auricular Confession, indulgences, the sacraments of Confirmation and the Anointing of the Sick, and chose their own priests.
The radicals had their gathering-places all around the country. Their first armed assault fell on the small town of Ústí, on the river Lužnice, south of Prague (today\'s Sezimovo Ústí). However, as the place did not prove to be defensible, they settled in the remains of an older town upon a hill not far away and founded a new town, which they named Tábor (a play on words, as \"Tábor\" not only meant \"camp\" or \"encampment\" in Czech, but is also the traditional name of the mountain on which Jesus was expected to return; see Mark 13); hence they were called Táborité (Taborites). They comprised the essential force of the radical Hussites.
Their aim was to destroy the enemies of the law of God, and to defend his kingdom (which had been expected to come in a short time) by the sword. Their end-of-world visions did not come true. In order to preserve their settlement and spread their ideology, they waged bloody wars; in the beginning they observed a strict regime, inflicting the severest punishment equally for murder, as for less severe faults as adultery, perjury, and usury, and also tried to apply rigid Biblical standards to the social order of the time. The Taborites usually had the support of the Orebites (later called Orphans), an eastern Bohemian sect of Hussitism based in Hradec Králové
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# HMS Ark Royal
Five ships of the Royal Navy have borne the name **HMS *Ark Royal***:
- , the flagship of the English fleet during the Spanish Armada campaign of 1588
- , planned as freighter, built as seaplane carrier during the First World War, renamed *Pegasus* in 1934
- , British aircraft carrier launched in 1937 which participated in the Second World War and was sunk by a U-boat in 1941
- , an `{{sclass|Audacious|aircraft carrier|2}}`{=mediawiki} launched in 1950, decommissioned in 1979
- , an `{{sclass|Invincible|aircraft carrier|2}}`{=mediawiki}, launched in 1981, decommissioned in 2011
## Battle honours {#battle_honours}
- Armada 1588
- Cádiz 1596
- Dardanelles 1915
- Norway 1940
- Spartivento 1940
- Mediterranean 1940--1941
- *Bismarck* 1941
- Malta Convoys 1941
- Al Faw 2003
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# Hausdorff dimension
thumb\|upright=1.25\|Example of non-integer dimensions. The first four iterations of the Koch curve, where after each iteration, all original line segments are replaced with four, each a self-similar copy that is 1/3 the length of the original. One formalism of the Hausdorff dimension uses the scale factor (S = 3) and the number of self-similar objects (N = 4) to calculate the dimension, D, after the first iteration to be D = (log N)/(log S) = (log 4)/(log 3) ≈ 1.26.
In mathematics, **Hausdorff dimension** is a measure of *roughness*, or more specifically, fractal dimension, that was introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners---the shapes of traditional geometry and science---the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects---including fractals---have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or \"rough\" sets, this dimension is also commonly referred to as the *Hausdorff--Besicovitch dimension.*
More specifically, the Hausdorff dimension is a dimensional number associated with a metric space, i.e. a set where the distances between all members are defined. The dimension is drawn from the extended real numbers, $\overline{\mathbb{R}}$, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.
In mathematical terms, the Hausdorff dimension generalizes the notion of the dimension of a real vector space. That is, the Hausdorff dimension of an *n*-dimensional inner product space equals *n*. This underlies the earlier statement that the Hausdorff dimension of a point is zero, of a line is one, etc., and that irregular sets can have noninteger Hausdorff dimensions. For instance, the Koch snowflake shown at right is constructed from an equilateral triangle; in each iteration, its component line segments are divided into 3 segments of unit length, the newly created middle segment is used as the base of a new equilateral triangle that points outward, and this base segment is then deleted to leave a final object from the iteration of unit length of 4. That is, after the first iteration, each original line segment has been replaced with N=4, where each self-similar copy is 1/S = 1/3 as long as the original. Stated another way, we have taken an object with Euclidean dimension, D, and reduced its linear scale by 1/3 in each direction, so that its length increases to N=S^D^. This equation is easily solved for D, yielding the ratio of logarithms (or natural logarithms) appearing in the figures, and giving---in the Koch and other fractal cases---non-integer dimensions for these objects.
The Hausdorff dimension is a successor to the simpler, but usually equivalent, box-counting or Minkowski--Bouligand dimension.
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# Hausdorff dimension
## Intuition
The intuitive concept of dimension of a geometric object *X* is the number of independent parameters one needs to pick out a unique point inside. However, any point specified by two parameters can be instead specified by one, because the cardinality of the real plane is equal to the cardinality of the real line (this can be seen by an argument involving interweaving the digits of two numbers to yield a single number encoding the same information). The example of a space-filling curve shows that one can even map the real line to the real plane surjectively (taking one real number into a pair of real numbers in a way so that all pairs of numbers are covered) and *continuously*, so that a one-dimensional object completely fills up a higher-dimensional object.
Every space-filling curve hits some points multiple times and does not have a continuous inverse. It is impossible to map two dimensions onto one in a way that is continuous and continuously invertible. The topological dimension, also called Lebesgue covering dimension, explains why. This dimension is the greatest integer *n* such that in every covering of *X* by small open balls there is at least one point where *n* + 1 balls overlap. For example, when one covers a line with short open intervals, some points must be covered twice, giving dimension *n* = 1.
But topological dimension is a very crude measure of the local size of a space (size near a point). A curve that is almost space-filling can still have topological dimension one, even if it fills up most of the area of a region. A fractal has an integer topological dimension, but in terms of the amount of space it takes up, it behaves like a higher-dimensional space.
The Hausdorff dimension measures the local size of a space taking into account the distance between points, the metric. Consider the number *N*(*r*) of balls of radius at most *r* required to cover *X* completely. When *r* is very small, *N*(*r*) grows polynomially with 1/*r*. For a sufficiently well-behaved *X*, the Hausdorff dimension is the unique number *d* such that N(*r*) grows as 1/*r^d^* as *r* approaches zero. More precisely, this defines the box-counting dimension, which equals the Hausdorff dimension when the value *d* is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.
For shapes that are smooth, or shapes with a small number of corners, the shapes of traditional geometry and science, the Hausdorff dimension is an integer agreeing with the topological dimension. But Benoit Mandelbrot observed that fractals, sets with noninteger Hausdorff dimensions, are found everywhere in nature. He observed that the proper idealization of most rough shapes one sees is not in terms of smooth idealized shapes, but in terms of fractal idealized shapes:
> Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
For fractals that occur in nature, the Hausdorff and box-counting dimension coincide. The packing dimension is yet another similar notion which gives the same value for many shapes, but there are well-documented exceptions where all these dimensions differ.`{{Example needed|s|date=January 2022}}`{=mediawiki}
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# Hausdorff dimension
## Formal definition {#formal_definition}
The formal definition of the Hausdorff dimension is arrived at by defining first the d-dimensional Hausdorff measure, a fractional-dimension analogue of the Lebesgue measure. First, an outer measure is constructed: Let $X$ be a metric space. If $S\subset X$ and $d\in [0,\infty)$,
$$H^d_\delta(S)=\inf\left \{\sum_{i=1}^\infty (\operatorname{diam} U_i)^d: \bigcup_{i=1}^\infty U_i\supseteq S, \operatorname{diam} U_i<\delta\right \},$$
where the infimum is taken over all countable covers $U$ of $S$. The Hausdorff d-dimensional outer measure is then defined as $\mathcal{H}^d(S)=\lim_{\delta\to 0}H^d_\delta(S)$, and the restriction of the mapping to measurable sets justifies it as a measure, called the $d$-dimensional Hausdorff Measure.
### Hausdorff dimension {#hausdorff_dimension}
The **Hausdorff dimension** $\dim_{\operatorname{H}}{(X)}$ of $X$ is defined by
$$\dim_{\operatorname{H}}{(X)}:=\inf\{d\ge 0: \mathcal{H}^d(X)=0\}.$$
This is the same as the supremum of the set of $d\in [0,\infty)$ such that the $d$-dimensional Hausdorff measure of $X$ is infinite (except that when this latter set of numbers $d$ is empty the Hausdorff dimension is zero).
### Hausdorff content {#hausdorff_content}
The $d$-dimensional **unlimited Hausdorff content** of $S$ is defined by
$$C_H^d(S):= H_\infty^d(S) = \inf\left \{ \sum_{k=1}^\infty (\operatorname{diam} U_k)^d: \bigcup_{k=1}^\infty U_k\supseteq S \right \}$$
In other words, $C_H^d(S)$ has the construction of the Hausdorff measure where the covering sets are allowed to have arbitrarily large sizes. (Here we use the standard convention that $\inf\varnothing=\infty$.) The Hausdorff measure and the Hausdorff content can both be used to determine the dimension of a set, but if the measure of the set is non-zero, their actual values may disagree.
## Examples
thumb\|upright=1.2\|Dimension of a further fractal example. The Sierpinski triangle, an object with Hausdorff dimension of log(3)/log(2)≈1.58.
- Countable sets have Hausdorff dimension 0.
- The Euclidean space $\R^n$ has Hausdorff dimension $n$, and the circle $S^1$ has Hausdorff dimension 1.
- Fractals often are spaces whose Hausdorff dimension strictly exceeds the topological dimension. For example, the Cantor set, a zero-dimensional topological space, is a union of two copies of itself, each copy shrunk by a factor 1/3; hence, it can be shown that its Hausdorff dimension is ln(2)/ln(3) ≈ 0.63. The Sierpinski triangle is a union of three copies of itself, each copy shrunk by a factor of 1/2; this yields a Hausdorff dimension of ln(3)/ln(2) ≈ 1.58. These Hausdorff dimensions are related to the \"critical exponent\" of the Master theorem for solving recurrence relations in the analysis of algorithms.
- Space-filling curves like the Peano curve have the same Hausdorff dimension as the space they fill.
- The trajectory of Brownian motion in dimension 2 and above is conjectured to be Hausdorff dimension 2.
thumb\|upright=1.2\|Estimating the Hausdorff dimension of the coast of Great Britain
- Lewis Fry Richardson performed detailed experiments to measure the approximate Hausdorff dimension for various coastlines. His results have varied from 1.02 for the coastline of South Africa to 1.25 for the west coast of Great Britain.
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# Hausdorff dimension
## Properties of Hausdorff dimension {#properties_of_hausdorff_dimension}
### Hausdorff dimension and inductive dimension {#hausdorff_dimension_and_inductive_dimension}
Let *X* be an arbitrary separable metric space. There is a topological notion of inductive dimension for *X* which is defined recursively. It is always an integer (or +∞) and is denoted dim~ind~(*X*).
**Theorem**. Suppose *X* is non-empty. Then
$$\dim_{\mathrm{Haus}}(X) \geq \dim_{\operatorname{ind}}(X).$$ Moreover,
$$\inf_Y \dim_{\operatorname{Haus}}(Y) =\dim_{\operatorname{ind}}(X),$$ where *Y* ranges over metric spaces homeomorphic to *X*. In other words, *X* and *Y* have the same underlying set of points and the metric *d*~*Y*~ of *Y* is topologically equivalent to *d*~*X*~.
These results were originally established by Edward Szpilrajn (1907--1976), e.g., see Hurewicz and Wallman, Chapter VII.`{{full citation needed|date=March 2015}}`{=mediawiki}
### Hausdorff dimension and Minkowski dimension {#hausdorff_dimension_and_minkowski_dimension}
The Minkowski dimension is similar to, and at least as large as, the Hausdorff dimension, and they are equal in many situations. However, the set of rational points in \[0, 1\] has Hausdorff dimension zero and Minkowski dimension one. There are also compact sets for which the Minkowski dimension is strictly larger than the Hausdorff dimension.
### Hausdorff dimensions and Frostman measures {#hausdorff_dimensions_and_frostman_measures}
If there is a measure μ defined on Borel subsets of a metric space *X* such that *μ*(*X*) \> 0 and *μ*(*B*(*x*, *r*)) ≤ *r^s^* holds for some constant *s* \> 0 and for every ball *B*(*x*, *r*) in *X*, then dim~Haus~(*X*) ≥ *s*. A partial converse is provided by Frostman\'s lemma.
### Behaviour under unions and products {#behaviour_under_unions_and_products}
If $X=\bigcup_{i\in I}X_i$ is a finite or countable union, then
$$\dim_{\operatorname{Haus}}(X) =\sup_{i\in I} \dim_{\operatorname{Haus}}(X_i).$$
This can be verified directly from the definition.
If *X* and *Y* are non-empty metric spaces, then the Hausdorff dimension of their product satisfies
$$\dim_{\operatorname{Haus}}(X\times Y)\ge \dim_{\operatorname{Haus}}(X)+ \dim_{\operatorname{Haus}}(Y).$$
This inequality can be strict. It is possible to find two sets of dimension 0 whose product has dimension 1. In the opposite direction, it is known that when *X* and *Y* are Borel subsets of **R**^*n*^, the Hausdorff dimension of *X* × *Y* is bounded from above by the Hausdorff dimension of *X* plus the upper packing dimension of *Y*. These facts are discussed in Mattila (1995).
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# Hausdorff dimension
## Self-similar sets {#self_similar_sets}
Many sets defined by a self-similarity condition have dimensions which can be determined explicitly. Roughly, a set *E* is self-similar if it is the fixed point of a set-valued transformation ψ, that is ψ(*E*) = *E*, although the exact definition is given below.
> **Theorem**. Suppose
>
> $$\psi_i: \mathbf{R}^n \rightarrow \mathbf{R}^n, \quad i=1, \ldots , m$$
>
> are each a contraction mapping on **R**^*n*^ with contraction constant *r~i~* \< 1. Then there is a unique *non-empty* compact set *A* such that
>
> $$A = \bigcup_{i=1}^m \psi_i (A).$$
The theorem follows from Stefan Banach\'s contractive mapping fixed point theorem applied to the complete metric space of non-empty compact subsets of **R**^*n*^ with the Hausdorff distance.
### The open set condition {#the_open_set_condition}
To determine the dimension of the self-similar set *A* (in certain cases), we need a technical condition called the *open set condition* (OSC) on the sequence of contractions ψ~*i*~.
There is an open set *V* with compact closure, such that
$$\bigcup_{i=1}^m\psi_i (V) \subseteq V,$$
where the sets in union on the left are pairwise disjoint.
The open set condition is a separation condition that ensures the images ψ~*i*~(*V*) do not overlap \"too much\".
**Theorem**. Suppose the open set condition holds and each ψ~*i*~ is a similitude, that is a composition of an isometry and a dilation around some point. Then the unique fixed point of ψ is a set whose Hausdorff dimension is *s* where *s* is the unique solution of
$$\sum_{i=1}^m r_i^s = 1.$$
The contraction coefficient of a similitude is the magnitude of the dilation.
In general, a set *E* which is carried onto itself by a mapping
: $A \mapsto \psi(A) = \bigcup_{i=1}^m \psi_i(A)$
is self-similar if and only if the intersections satisfy the following condition:
$$H^s\left(\psi_i(E)\cap \psi_j(E)\right) =0,$$
where *s* is the Hausdorff dimension of *E* and *H^s^* denotes s-dimensional Hausdorff measure. This is clear in the case of the Sierpinski gasket (the intersections are just points), but is also true more generally:
**Theorem**. Under the same conditions as the previous theorem, the unique fixed point of ψ is self-similar
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# Heckler & Koch
\(2022\) \| operating_income = `{{increase}}`{=mediawiki} €46.23 million (2022) \| net_income = `{{increase}}`{=mediawiki} €50.639 million (2022) \| assets = `{{nowrap|{{increase}} €328.194 million (2022)<ref name=IR/>}}`{=mediawiki} \| equity = `{{Decrease}}`{=mediawiki} €70.313 million (2022) }}
**Heckler & Koch GmbH** (**HK** or **H&K**; `{{IPA|de|ˌhɛklɐ ʔʊnt ˈkɔx}}`{=mediawiki}) is a German firearms manufacturer that produces handguns, rifles, submachine guns, and grenade launchers. The company is located in Oberndorf am Neckar, Baden-Württemberg and also has subsidiaries in the United Kingdom, France, and the United States.
Heckler & Koch was founded in 1949 by former Mauser engineers Edmund Heckler, Theodor Koch, and Alex Seidel, who founded the company out of the shuttered Mauser factory in Oberndorf. The company initially produced machine tool and metal parts until 1956 when, in response to a *\[\[Bundeswehr\]\]* contract for a new service rifle, HK developed the Heckler & Koch G3. The success of the G3 rifle prompted HK to transition to the defense industry. HK was owned by Royal Ordnance from 1991 to 2002, and is currently part of the Heckler & Koch Group, comprising Heckler & Koch GmbH, Heckler & Koch Defense, NSAF Ltd., and Heckler & Koch France SAS. The company\'s motto is \"*Keine Kompromisse!*\" (No Compromises!).
Nicolas Walewski\'s financial holding company CDE has held a majority stake in Heckler & Koch since July 2020.
## History
With the fall of Nazi Germany and the following Allied occupation of Germany, Oberndorf came under French control, and the entire Waffenfabrik Mauser AG factory was dismantled by French occupying forces. All factory records were destroyed on orders of the local French Army commander. In 1948, three former Mauser engineers, Edmund Heckler, Theodor Koch, and Alex Seidel, saved what they could from the factory and used what they had salvaged to start a machine tool plant in the vacant factory that became known as the Engineering Office Heckler & Co.
On 28 December 1949, the Engineering Office Heckler & Co. changed its name and was registered officially as Heckler & Koch GmbH. Initially the new company manufactured machine tools, bicycle and sewing machine parts, gauges, and other precision parts. In 1956, Heckler & Koch responded to the West German government\'s tender for a new infantry rifle for the *Bundeswehr* with the proposal of the G3 battle rifle, based on the Spanish CETME Model 58 rifle and developed in cooperation with CETME. The German government awarded Heckler & Koch the tender and in 1959 declared the G3 the standard rifle of the *Bundeswehr*. Later in 1961, Heckler & Koch developed the 7.62×51mm HK21 general-purpose machine gun, based on the G3.
In 1966, Heckler & Koch introduced the HK54 machine pistol, which eventually launched in 1969 as the MP5 submachine gun. Two years later, the company introduced the HK33 assault rifle, a smaller version of the G3 chambered in 5.56×45mm NATO.
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# Heckler & Koch
## History
### Diversification
In 1974, Heckler & Koch diversified into two more areas, HK Defense and Law Enforcement Technology and HK Hunting and Sports Firearms. Since then, HK has designed and manufactured more than 100 different types of firearms and devices for the world\'s military and law enforcement organizations as well as sports shooters and hunters. In 1990, Heckler & Koch completed two decades of development of their caseless weapon system and produced prototypes of the G11 rifle. The company also produced prototypes of the G41 assault rifle intended for the *Bundeswehr*. Due to the international political climate at the time (East and West Germany uniting and defense budget cuts) the company was unable to secure funded contracts from the German government to support production of either weapon system and became financially vulnerable. The following year, Heckler & Koch was sold to British Aerospace\'s Royal Ordnance division.
During 1994 and 1995, the German government awarded Heckler & Koch contracts for producing an updated standard assault rifle and updated standard sidearm for the *Bundeswehr*. Heckler & Koch developed and produced the Project HK50, a lightweight carbon fiber assault rifle, which became the G36 assault rifle. In addition, Heckler & Koch produced the P8 pistol, derived from its USP handguns produced since 1989. The USP was adopted as the standard sidearm of the *Bundeswehr* in 1994, and the G36 was adopted as their standard-issue rifle in 1995.
As the result of a 1999 merger between British Aerospace and Marconi Electronic Systems, Heckler & Koch was owned by the resulting BAE Systems; it was contracted to refurbish the British Army\'s SA80 rifles (which had been manufactured by Royal Ordnance) This contract entailed a modification program to the SA80 series of rifles to address a number of reliability issues with the design. In 2002, BAE Systems restructured and sold Heckler & Koch to a group of private investors, who created the German group holding company HK Beteiligungs GmbH.
In 2003, HK Beteiligungs GmbH\'s business organization restructured as Heckler & Koch Jagd und Sportwaffen GmbH (HKJS), and its business was separated into the two business areas similar to the 1974 business mission areas: Defense, and Law Enforcement and Sporting Firearms. In 2004, Heckler & Koch was awarded a major handgun contract for the United States Department of Homeland Security, worth a potential \$26.2 million for up to 65,000 handguns. This contract ranks as the single largest handgun procurement contract in U.S. law enforcement history.
HK was contracted by the United States Army to produce the kinetic energy subsystem (see: kinetic projectiles or kinetic energy penetrator) of the Objective Individual Combat Weapon, a planned replacement for the M16 rifle/M203 grenade launcher combination. The OICW was designed to fire 5.56 mm rounds and 25 mm grenades. The kinetic energy component was also developed separately as the XM8, though both the OICW and XM8 are now indefinitely suspended.
Heckler & Koch developed an AR-15/M4 carbine variant, marketed as the HK416. HK replaced the direct impingement system used by the Stoner design on the original M16 with a short-stroke piston operating system. The civilian models are named the MR223 and, in the U.S., the MR556A1.
In 2007, United States Secretary of the Army Pete Geren agreed to hold a \"dust chamber\" test pitting the M4 against the Heckler & Koch HK416 and XM8, as well as the rival FN SCAR design. The Heckler & Koch XM8 and FN SCAR had the fewest failures in the test, closely followed by the HK416, while the M4 had by far the most. In 2007, the Norwegian Army became the first to field the HK416 as a standard-issue rifle.
HK sells its pistols in the United States to both law enforcement and civilian markets, through its HK USA subsidiary. The company has locations in Virginia, New Hampshire, and Georgia.
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# Heckler & Koch
## Products
Heckler & Koch has produced a variety of firearms including the G3, HK21, MP5, HK4, HK33, HK69, VP70, PSG1, USP, G36, MG4, UMP, MP7, and HK416 which have become some of the most iconic and widely adopted firearms in the world, used by dozens of militaries, police forces, and paramilitaries worldwide. Many of its prototype weapons including the G11, HK CAWS, XM29 OICW, and XM8, have also become recognizable. HK firearms use blowback operation, short-recoil, roller-delayed blowback, gas-delayed blowback, and short-stroke piston gas operation. HK is responsible for several innovations in firearms, such as the use of polymers in weapon designs, modern polygonal rifling, the feasibility of high-velocity caseless ammunition in prototype service rifles, and integral rails for handgun attachments.
### HK naming system {#hk_naming_system}
Heckler & Koch products use an internal naming system, consisting of an abbreviation and a two- or three-digit *Werknummern* designation popularly referred to as the \"HK 3-digit system\". Each letter and digit is assigned a specific meaning outlined in the convention to make them easier to identify and differentiate by name.
The HK naming convention is not a fixed convention, but rather a guideline, and not all HK products follow it; this is typically done for marketing purposes or quirks in the weapon\'s development or intended role. For instance, the HK416 does not use a proper abbreviation (\"HK\" does not mean anything specific), nor does it use proper digits (the HK416 was originally two models, the \"HK M4\" and \"HK M16\", that were later amalgamated into the HK416); using the 3-digit system, the standard HK416 would likely be referred to as the G333. Such products tend to have proper internal designations anyway; the HK416 is internally referred to as the HK333.
#### Abbreviations
Most HK products have a prefix of between one and three letters, corresponding to a word or term in German (though some refer to English terms instead, with no German equivalent). Several were only used for a single model, such as the \"Universal\" weapons (UMP, UCP, USC, and USP). Some abbreviations are used as a suffix to designate specific variants.
Letter German meaning English equivalent Placement Designation Example
--------- -------------------------------------- -------------------------------- ----------- ------------------------------------------------------------------------------------------------------------- -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
**HK** N/A Heckler & Koch Prefix Basic prefix for HK products with no specific meaning HK417, HK45
**A** *Ausführung* Model Variant Version Suffix Variants of existing designs \"G3\" refers to the original G3 rifle with a wooden handguard and fixed stock; \"G3A1\" refers to the G3 variant with a wooden handguard and a retractable stock; \"G3A2\" refers to the G3 variant with a plastic handguard and fixed stock; etc.
**G** *Gewehr* Rifle Prefix Rifles, primarily those intended to be issued as service rifles G41
**K** *Kurz* Short Suffix Compact, shortened variants of handguns and submachine guns MP5K
*Karabiner* Carbine Carbine variants of rifles G36K
**C** N/A Compact Suffix Compact, shortened variants of rifles G36C
**AG** *Anbau-Gerät* Attached Device Prefix Weapon attachments, primarily underbarrel grenade launchers AG-C/EGLM
*Anbaugranatwerfer* Attached Grenade Launcher
**GMG** N/A Grenade Machine Gun Full name Automatic grenade launchers GMG/GMW
**GMW** *Granatmaschinenwaffe* Automatic Grenade Launcher
**MG** *Maschinengewehr* Machine Gun Prefix Machine guns and squad automatic weapons MG4
**MP** *Maschinenpistole* Machine Pistol Submachine Gun Prefix Submachine guns, machine pistols, and personal defense weapons MP5
**MSG** *Militärisches Scharfschützengewehr* Military Sharpshooting Rifle Prefix Sharpshooting rifles designed specifically for military use MSG90
**PSG** *Präzisionsschützengewehr* Precision Sharpshooter Rifle Prefix Sharpshooting rifles in general PSG1
**PSP** *Polizei-Selbstlade-Pistole* Police Self-Loading Pistol Full name Self-loading handguns designed specifically for law enforcement use PSP
**SD** *Schalldämpfer* Sound Dampener Suppressor Suffix Weapon variants which are integrally-suppressed or designed to be used with a suppressor MP5SD (for integrally-suppressed weapons) USP9 SD (for weapons with an extended threaded barrel intended for suppressors)
**SG** *Scharfschützengewehr* Sharpshooters Rifle Suffix Weapon variants designed for sharpshooting G3SG/1
**SK** *Subkompakt* Subcompact Suffix Extra-compact variants of handguns, usually for concealed carry P2000 SK
**SL** *Selbstlader* Autoloader Prefix Self-loading semi-automatic firearms, usually rifles, intended for hunting and the civilian market SL8
**UMP** N/A Universal Machine Pistol Prefix A specific submachine gun intended to replace the MP5 as a universal-role submachine gun UMP
**UCP** N/A Universal Combat Pistol Prefix A specific handgun intended to be the companion sidearm to the MP7 UCP
**USC** N/A Universal Self-Loading Carbine Prefix The semi-automatic civilian market variant of the UMP submachine gun USC
**USP** *Universale Selbstladepistole* Universal Self-Loading Pistol Prefix A specific handgun designed for the American civilian market USP
**VP** *Volkspistole* People\'s Pistol Prefix Handguns, usually polymer-framed, intended for the civilian market VP70, VP9, VP40
**ZF** *Zielfernrohr* Telescopic Sight Postfix Weapon variants not necessarily intended for sharpshooting that come with a telescopic sight and claw mount G3A3ZF
Prefix Telescopic sight models, typically those produced in cooperation with Hensoldt ZF 6x42 PSG1
#### *Werknummern* designations {#werknummern_designations}
The *Werknummern* designation system assigns two or three digits which correspond to the product\'s technical specifics. They are placed after (or if a suffix, before) the abbreviation and denote the generation, form factor, and caliber or munition of the weapon.
First Second
------- ---------------- --- ---------------------------------------------- ---
None 1st Generation 1 Magazine-fed machine gun 1
1 2nd Generation 2 Belt-fed machine gun 2
2 3rd Generation 3 Full-size rifle 3
3 4th Generation 4 Semi-automatic military carbine 4
4 5th Generation 5 Selective fire carbine 5
5 6th Generation 6 Shoulder-fired standalone grenade launcher 6
6 7th Generation 7 Underbarrel firearm-mounted grenade launcher 7
7 8th Generation 8 Hunting rifles and repeaters 8
8 9th Generation 9 N/A 9
#### Date code {#date_code}
The date code is a two-letter combination used to specify the year a weapon was manufactured in. These are not part of the product\'s name, but are printed for identification directly on the weapon itself. They are only used on handguns.
Letter Number Examples
---------------------------------------------- -------- ------------------------
**A** 0 **AF** -- *05* -- 2005
**B** 1
**C** 2
**D** 3 **BG** -- *16* -- 2016
**E** 4
**F** 5
**G** 6
**H** 7 **CE** -- *24* -- 2024
**I** 8
**K** 9
The letter **J** is not used as a date code.
Heckler & Koch handguns produced at HK\'s German facilities are marked with \"DE\", Germany\'s ISO 3166-1 code. Handguns manufactured in HK facilities outside Germany, or those produced in Germany before 2008, do not have the DE marking.
### Trigger group {#trigger_group}
Heckler & Koch long arms mostly follow a set of shared trigger group standards for selective fire and safety, with corresponding markings and pictograms.
Type Positions Settings Location
-------------------- ------------ ------------------------------------------------------------------------------- --------------
SEF 3-position Safe (*Sicher*), semi-automatic (*Einzelfeuer*), full automatic (*Feuerstoß*) Left-side
0-1-20 3-position Safe, semi-automatic, full automatic Left-side
SE / 0-1 2-position Safe, semi-automatic Ambidextrous
Navy 3-position Safe, semi-automatic, full automatic Ambidextrous
Navy 3-Round Burst 4-position Safe, semi-automatic, 3-round burst, full automatic Ambidextrous
Navy 2-Round Burst 4-position Safe, semi-automatic, 2-round burst, full automatic Ambidextrous
Setting Marking system
---------------- --------------------
Number Letter
Safe White \"0\"
Semi-automatic Red \"1\"
Burst fire Red \"2\" or \"3\"
Full automatic Red \"30\"
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# Heckler & Koch
## Trafficking
H&K has been accused of shipping small arms to conflict regions such as Bosnia and Nepal, and has licensed its weapons for production by governments with poor human rights records such as Sudan, Thailand and Myanmar. It has been argued that the company effectively evaded EU export restrictions when these licensees sold HK weapons to conflict zones including Indonesia, Sri Lanka and Sierra Leone.
According to the newspaper *Stuttgarter Nachrichten* (31 August 2011), as well as the state broadcaster ARD, a large stockpile of G36 assault rifles fell into rebel hands during the August 2011 attack on Muammar Gaddafi\'s compound in Tripoli. It is unclear how many were exported to Libya and by whom.
### Illegal arms sales to Mexico {#illegal_arms_sales_to_mexico}
On 11 December 2011, federal, state and local Mexican police officers used battle rifles to fire on Ayotzinapa Rural Teachers\' College students and peasant organizations to disperse a blockade on Mexican Federal Highway 95D, resulting in the deaths of students Jorge Alexis Herrera and Gabriel Echeverría de Jesús. According to media reports, 7.62×51mm NATO round casings were found at the scene, matching those used by H&K G3 rifles. In Iguala and Cocula, corrupt police officers and cartelmen are known to have used H&K G36 rifles during the 2014 Iguala mass kidnapping on 26--27 September 2013. At least six teaching students were murdered by cartelmen and corrupt local police, and 43 others are missing and presumed dead. Other than the six identified persons, no other bodies have been found, and they are believed to have been incinerated.
As a result of efforts by civil society and human rights organizations in Mexico and Germany, H&K and two of its former employees were brought before the Provincial Court of Stuttgart. After ten months of trial, on 21 February 2019, the court convicted them of illegally selling arms to Mexican governmental institutions which failed to acknowledge their due observance of human rights. The two former employees (sales manager Sahlmann and administrative employee Beuter) had been found to have used fraudulent permits in the sale of 4,700 rifles and large quantities of ammunition. H&K was issued a fine of 3.7 million euros, and the two men received suspended sentences of 17 and 22 months. The spokesman of the Presidency of the Republic of Mexico, Jesús Ramírez Cuevas, said that the amount of the fine should go to the victims and their families.
On 30 March 2021, Germany\'s Federal Court of Justice (BGH) upheld the lower court\'s decision, finding that H&K employees knowingly falsified information on the nature and destination of arms sold by the company in order to attain federal export licenses
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# British Aerospace HOTOL
**HOTOL**, for **Horizontal Take-Off and Landing**, was a 1980s British design for a single-stage-to-orbit (SSTO) spaceplane that was to be powered by an airbreathing jet engine. Development was being conducted by a consortium led by Rolls-Royce and British Aerospace (BAe).
Designed as a single-stage-to-orbit (SSTO) reusable winged launch vehicle, HOTOL was to be fitted with a unique air-breathing engine, the RB545 or Swallow, that was under development by British engine manufacturer Rolls-Royce. The propellant for the engine technically consisted of a combination of liquid hydrogen/liquid oxygen; however, it was to employ a new means of dramatically reducing the amount of oxidizer needed to be carried on board by utilising atmospheric oxygen as the spacecraft climbed through the lower atmosphere. Since the oxidizer typically represents the majority of the takeoff weight of a rocket, HOTOL was to be considerably smaller than normal pure-rocket designs, roughly the size of a medium-haul airliner such as the McDonnell Douglas DC-9/MD-80.
While HOTOL\'s proof-of-concept design study was being carried out, attempts were made by both industry and the British government to establish international cooperation to develop, produce, and deploy the spacecraft. In spite of American interest in the programme, there was little appetite amongst the members of the European Space Agency (ESA), and the British government was not prepared to depart from ESA cooperation. Additionally, technical issues were encountered, and there were allegations that comparisons with alternative launch systems such as conventional rocket vehicle using similar construction techniques failed to show much advantage to HOTOL. In 1989, funding for the project ended. The termination of development work on HOTOL led to the formation of Reaction Engines Limited (REL) to develop and produce Skylon, a proposed spacecraft based on HOTOL technologies, including its air-breathing engine.
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# British Aerospace HOTOL
## Development
### Origins
The ideas behind HOTOL originated from work done by British engineer Alan Bond in the field of pre-cooled jet engines. Bond had specifically performed this research with the intention of producing a viable engine for powering a space launch system. In 1982, British Aerospace (BAe), which was Europe\'s principal satellite-builder, began studying a prospective new launch system with the aim of providing launch costs that were 20 per cent of the American Space Shuttle operated by NASA. BAe became aware of work by British engine manufacturer Rolls-Royce on a suitable engine, and soon conceived of an uncrewed, fully reusable single-stage-to-orbit (SSTO) winged spaceplane as a launch vehicle.
Thus, the project had soon become a joint venture between BAe and Rolls-Royce, led by John Scott-Scott and Bob Parkinson. Early on, there was an ambition to \'Europeanise\' the project and to involve other nations in its development and manufacture as it was recognised that an estimated £4 billion would be needed to fund full-scale development. In August 1984, BAe unveiled a public display of the HOTOL satellite launcher project and released details on its proposed operations.
In December 1984, a Department of Trade and Industry (DTI) memorandum noted that West Germany was interested in the programme, while France had adopted a critical attitude towards HOTOL, which the ministry viewed as potentially due to it being seen as a competitor to French-led projects. According to Minister of Trade and Industry Geoffrey Pattie, French diplomatic pressure to gather support for its own proposed Hermes space vehicle had inadvertently generated support and interest amongst European Space Agency (ESA) members in the HOTOL project. Despite this climate of tentative interest and possible European support, there was a general attitude of reluctance within the British government to take the lead on a new space launcher.
### American interest and design study {#american_interest_and_design_study}
In March 1985, there were claims that Rolls-Royce was in the process of conducting licensing talks for HOTOL engine technology with American propulsion company Rocketdyne. In April 1985, Pattie wrote to Secretary of State for Defence Michael Heseltine to propose a two-year £3 million proof of concept study be performed under a public-private partnership arrangement, consisting of £1 million provided by the UK government and the remainder being financed by Rolls-Royce and BAe themselves. Pattie reasoned that the project would serve Britain\'s \"strategic capability\", and that tests of key technologies could foster international collaboration. According to aerospace publication *Flight International*, the support of the Ministry of Defense (MoD) was critical as the design of HOTOL\'s engine had been classified.
In July 1985, Rolls-Royce\'s technical director Gordon Lewis stated that the firm sought the involvement of the Royal Aircraft Establishment\'s (RAE) propulsion group, and that Rolls-Royce was not prepared to invest its own funds into engine development for HOTOL. By the second half of 1985, work had commenced on the two-year concept-of-proof study. Early on, there was considerable pressure to demonstrate the project\'s feasibility and credibility in advance of final decisions being taken by ESA on the Hermes and what would become the Ariane 5 launch system, thus the work concentrated on the validation of critical technologies involved.
By November 1985, DTI and RAE discussions noted that Rolls-Royce were seeking American data on ramjet technology to support their work on the engine, which it referred to by the name *Swallow*. Reportedly, the United States Air Force were interested in the technology used in the Swallow engine for its own purposes. In November 1985, discussions between Prime Minister Margaret Thatcher, Minister without portfolio David Young and US President Ronald Reagan\'s scientific adviser George Keyworth noted American interest in collaboration on developing hypersonic vehicles such as HOTOL, and that a prototype could be flying as early as 1990.
According to British government files, neither BAe nor the MoD were enthusiastic for the prospects of American involvement in the programme, expressing reluctance out of a belief that the outcome of such a move could result in the UK becoming a junior member in a project that it once led. There was also a belief that if Britain chose to pair up with the United States, it would find itself frozen out of work on future European launchers. However, Rolls-Royce viewed transatlantic cooperation as necessary. BAe\'s head of future business, Peter Conchie, stated that, if possible, HOTOL should become a part of the European space framework. In early 1986, the British government formally approved the two-year study.
### Problems and criticism {#problems_and_criticism}
In December 1984, project management consultant David Andrews issued an eight-page critique of the programme, noting that the design was optimised for the ascent while exposing itself to extended thermal loads during descent due to a low level of drag. He also claimed that the vehicle offered no capability that was not already available; BAe responded that the criticisms made had been answered. In April 1985, the Ministry of Defence\'s research and development department deputy controller James Barnes claimed that HOTOL lacked a justification, and that there was no defence requirement for such vehicles. He also noted that the \"engineering problems are considerable\" and that it was unlikely to enter service until the 2020s; Barnes also observed the HOTOL engine to be \"ingenious\".
In November 1985, the RAE issued an assessment of HOTOL\'s study proposal; the organisation believed that HOTOL would take up to 20 years to develop, rather than the 12-year timetable that had been envisioned by industry. The RAE also projected that the project would have an estimated total cost of £5 billion (as of its value in 1985), £750 million of which would be required in a six-year definition phase and an estimated £25 million in a pre-definition feasibility study.
During development, it was found that the comparatively heavy rear-mounted engine moved the centre of mass of the vehicle rearwards. This meant that the vehicle had to be designed to push the centre of drag as far rearward as possible to ensure stability during the entire flight regime. Redesign of the vehicle to do this required a large mass of hydraulic systems, which cost a significant proportion of the payload, and made the economics unclear. In particular, some of the analysis seemed to indicate that similar technology applied to a pure rocket approach would give approximately the same performance at less cost.
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# British Aerospace HOTOL
## Development
### Shutdown
By 1989, the outlook for HOTOL had become bleak. From the onset of the project, support between the British government and industrial partners had been uneven, while the United States had emerged as the only foreign nation that showed willingness to contribute to the programme, in part because of the secrecy surrounding it. There was little prospect for European involvement, ESA having elected to pursue development of what would become the Ariane 5, a conventional space launch system. Rolls-Royce withdrew from the project, judging the eventual market for the engine was unlikely to be large enough to repay the development costs. The British government declined to offer further funding for HOTOL. The project was almost at the end of its concept-design phase while much of the plans remained in a speculative state; the craft was reportedly still dogged with aerodynamic problems and operational disadvantages at this point.
### Successors
A cheaper redesign, **Interim HOTOL** or **HOTOL 2**, which was to be launched from the back of a modified Antonov An-225 transport aircraft, specifically was promoted by BAe in 1991; however, this proposal was rejected as well. The design for Interim HOTOL was to have dispensed with an air-breathing engine cycle and was designed to use a more conventional mix of LOX and liquid hydrogen as fuel instead.
In 1989, HOTOL co-creator Alan Bond and engineers John Scott-Scott and Richard Varvill formed Reaction Engines Limited (REL) which worked on a new air-breathing engine, SABRE, which used alternative designs to work around (and improve upon) the Rolls-Royce patents, and the Skylon vehicle intended to solve the problems of HOTOL. They first published these engine and spacecraft concepts in 1993, and continued developing the core technologies, particularly the engine and its frost-controlled pre-cooler; initially supported by private funding, but latterly with support from the European Space Agency, the British National Space Centre, the United Kingdom Space Agency, BAe, and the Air Force Research Laboratory. `{{As of|2017}}`{=mediawiki} REL planned to demonstrate a flight-ready pre-cooler operating under simulated flight conditions in 2018, and statically test a demonstration engine core in 2020. REL fell into administration in 2024, ceasing all operations. Neither SABRE (a full-scale working engine; partial prototypes and components for testing not counted) nor Skylon were ever built.
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# British Aerospace HOTOL
## Design
### Overview
HOTOL was envisioned as an uncrewed, fully reusable single-stage-to-orbit (SSTO) winged spaceplane. The uncrewed craft was intended to put a payload of around 7 to 8 tonnes in orbit, at 300 km altitude. It was intended to take off from a runway, mounted on the back of a large rocket-boosted trolley that would help get the craft up to \"working speed\". The engine was intended to switch from jet propulsion to pure rocket propulsion at 26--32 km high, by which time the craft would be travelling at Mach 5 to 7. After reaching low Earth orbit (LEO), HOTOL was intended to re-enter the atmosphere and glide down to land on a conventional runway (approx 1,500 metres minimum). Only a single payload would have been carried at a time as BAe had judged this to be more economic as it removed any need for satellite interfacing and allowed for missions to be tailored to individual requirements.
During its high-altitude phase, its flight control system would have been linked to ground stations and to space-based global navigation system navigation, while radar would have been used during the take-off and landing phases. In addition to the placing of satellites into geosynchronous orbit or LEO, HOTOL was also projected as being able to also perform the retrieval of satellites and hardware from LEO. BAe promotional material depicts HOTOL docking with the International Space Station (ISS), a feat that the company claimed would have required crewed operation as automated systems were not capable of performing such docking manoeuvres at that time. HOTOL was designed to conduct fully automated uncrewed flights; however, it had been intended at a later stage to potentially re-introduce a pilot. Crewed operations would have required the installation of a dedicated pressurised module within the payload bay.
As designed, HOTOL would have been 62 metres long, 12.8 metres high, a fuselage diameter of 5.7 metres and a wingspan of 19.7 metres.
The final vehicle design (HOTOL-K) had a take-off mass of 275 tonnes. Approximately 82% of that mass was propellant with the vehicle structure being a further 16%. This left just 2% (approximately 5 tonnes) for the payload, leaving little margin for design changes to the basic vehicle structure.
It featured a wing design that had been derived from that of Concorde; its large area resulted in relatively low wing loading, which would have resulted in lower reentry temperatures (never rising above 1,400 °C). Built out of carbon composite materials, there would have been no need for the use of insulating tiles akin to those that comprised the Space Shuttle thermal protection system. The internally stowed landing gear would have been too small to carry the weight of the fully fuelled rocket, so emergency landings would have required the fuel to be dumped.
Almost the entire forward fuselage, ahead of the payload bay, comprised a single hydrogen tank.
HOTOL was designed to have a vertical fin, just aft of the nose, for lateral stability. However, later discussions with NPO Molniya about Interim Hotol made it clear that the fin would have been subject to excessive heating on re-entry (due to interactions between two shock-waves). Consequently, Interim Hotol switched back to a more conventional (but larger) tail-fin.
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# British Aerospace HOTOL
## Design
### Engine
The **RB545**, which was given the name \"**Swallow**\" by its manufacturer, British engine maker Rolls-Royce, was an air-breathing rocket engine. It would have functioned as an integrated dual-role powerplant, having been capable of air-breathing while operating within the atmosphere and operating in a similar manner to that of a rocket when having attained close to and within LEO. This engine would have also been capable of powering the spacecraft to hypersonic speeds. It was a crucial element of the programme, having been publicly attributed as \"the heart of Hotol\'s very low launch costs\".
The exact details of this engine were covered by the Official Secrets Act of the United Kingdom; consequently, there is relatively little public information about its development and on its operation. However, material was later declassified when government policy changed to prevent the keeping of secret patents without an attributed justification.
Within the atmosphere, air would be taken in through two vertically mounted intake ramps, then the flow would be split, passing the correct amount to the pre-coolers, and the excess to spill ducts. Hydrogen from the fuel tanks would be passed through two heat exchangers to pre-cool the air prior to entering a high overall pressure-ratio turbojet-like engine cycle --- the heated hydrogen driving a compressor to compress and feed the cooled air into the rocket engine, where it was combusted with some of the hydrogen used to cool the air. The majority of the remaining hot hydrogen was released from the back of the engine, with a small amount drawn off to reheat the air in the spill ducts in a ramjet arrangement to produce \"negative intake momentum drag\".
To prevent the pre-coolers from icing up, the first pre-cooler cooled the air to around 10 degrees above freezing point, to liquefy the water vapour in the air. Then liquid oxygen (LOX) would have been injected into the airflow to drop the temperature to -50 C flash freezing the water into microscopic ice crystals, sufficiently cold that they wouldn\'t melt due to kinetic heating if they struck the second pre-cooler elements. A water trap could have been added after the first pre-cooler if operating conditions resulted in an excess of moisture.
When it was no longer possible to use the atmosphere for combustion, the RB545 would switch to using on-board LOX to burn with the hydrogen as a high-efficiency hydrogen/oxygen rocket
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# Hawker Harrier
The **Hawker Harrier** was a British experimental biplane torpedo bomber aircraft built by Hawker Aircraft to a specification issued in the 1920s for the Royal Air Force.
## Development
In 1925, the British Air Ministry laid down specifications for a high altitude bomber to replace the Hawker Horsley and for a coastal torpedo bomber (Specifications 23/25 and 24/25). As these specifications were similar, the Air Ministry announced that a single competition would be held to study aircraft submitted for both specifications.
Sydney Camm of Hawker Aircraft designed the Harrier to meet the requirements of Specification 23/25, with the prototype (*J8325*) first flying in February 1927, the first of the competitors for the two specifications to fly. The Harrier was a two-seat biplane with single-bay wings powered by a geared Bristol Jupiter VIII radial engine. It was armed with one .303 in (7.7 mm) Vickers machine gun and one .303 in (7.7 mm) Lewis gun carrying a maximum of 1000 lb of bombs.
The prototype Harrier was tested at the Aeroplane and Armament Experimental Establishment (A & AEE) at Martlesham Heath in November 1927, where, while it met the requirements of Specification 23/25 and had satisfactory handling, the geared engine meant that it was underpowered, and it had an inferior bombload to the Hawker Horsley, the aircraft it was meant to replace. It was therefore modified to carry a torpedo. On testing the modified aircraft, however, it was found to still be underpowered, being incapable of taking off with a torpedo, gunner and full fuel load. It was therefore not considered further, the competition ultimately being won by the Vickers Vildebeest.
The prototype was used by Bristol as an engine testbed, flying with the 870 hp Bristol Hydra and the 495 hp Bristol Orion engines
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# Haggis
**Haggis** (*taigeis* `{{IPA|gd|ˈtʰakʲɪʃ|}}`{=mediawiki}) is a savoury pudding containing sheep\'s pluck (heart, liver, and lungs), minced with chopped onion, oatmeal, suet, spices, and salt, mixed with stock, and cooked while traditionally encased in the animal\'s stomach though now an artificial casing is often used instead. According to the 2001 English edition of the *Larousse Gastronomique*: \"Although its description is not immediately appealing, haggis has an excellent nutty texture and delicious savoury flavour\".
It is believed that food similar to haggis --- perishable offal quickly cooked inside an animal\'s stomach, all conveniently available after a hunt --- was eaten from ancient times.
Although the name \"hagws\" or \"hagese\" was first recorded in England c. 1430, the dish is considered traditionally of Scottish origin. It is even the national dish as a result of Scots poet Robert Burns\' poem \"Address to a Haggis\" of 1786. Haggis is traditionally served with \"neeps and tatties\", boiled and mashed separately, and a dram (a glass of Scotch whisky), especially as the main course of a Burns supper.
## History and etymology {#history_and_etymology}
### Scottish theory {#scottish_theory}
Haggis is popularly assumed to be of Scottish origin, but many countries have produced similar dishes with different names. However, the recipes as known and standardised now are distinctly Scottish. The first known written recipes for a dish of the name, made with offal and herbs, are as \"hagese\", in the verse cookbook *Liber Cure Cocorum* dating from around 1430 in Lancashire, north west England, and, as \"hagws of a schepe\" from an English cookbook also of c. 1430.
The earlier (1390) book *The Forme of Cury* by Richard II\'s master cooks includes a dish of grated meat in a pig\'s caul, without using such a name.
The Scottish poem \"Flyting of Dunbar and Kennedy\", which is dated before 1520 (the generally accepted date prior to the death of William Dunbar, one of the composers), refers to \"haggeis\".
An early printed recipe for haggis appears in 1615 in *The English Huswife* by Gervase Markham. It contains a section entitled \"Skill in Oate meale\": \"The use and vertues of these two severall kinds of Oate-meales in maintaining the Family, they are so many (according to the many customes of many Nations) that it is almost impossible to recken all\"; and then proceeds to give a description of \"oat-meale mixed with blood, and the Liver of either Sheepe, Calfe or Swine, maketh that pudding which is called the Haggas or Haggus, of whose goodnesse it is in vaine to boast, because there is hardly to be found a man that doth not affect them.\" (Gervase Markham, *The English Huswife*)
In her book *The Haggis: A Little History*, Dickson Wright suggests that haggis was invented as a way of cooking quick-spoiling offal near the site of a hunt, without the need to carry along an additional cooking vessel. The liver and kidneys could be grilled directly over a fire, but this treatment was unsuitable for the stomach, intestines, or lungs. Chopping up the lungs and stuffing the stomach with them and whatever fillers might have been on hand, then boiling the assembly -- probably in a vessel made from the animal\'s hide -- was one way to make sure these parts were not wasted.
### Roman theory {#roman_theory}
Food writer Alan Davidson suggests that the ancient Romans were the first known to have made products of the haggis type. Haggis was \"born of necessity, as a way to utilize the least expensive cuts of meat and the innards as well\".
### Norse theory {#norse_theory}
Clarissa Dickson Wright says that it \"came to Scotland in a longship \[i.e., from Scandinavia\] even before Scotland was a single nation\". She cites etymologist Walter William Skeat as further suggestion of possible Scandinavian origins: Skeat claimed that the *hag--* element of the word is derived from *haggw* or the Old Icelandic *hoggva*, meaning \'to hew → chop → hack\', same as in Modern Scots: *hag*, \'to hew\' or strike with a sharp weapon, relating to the chopped-up contents of the dish.
The related Nordic variations of the root dish are traditionally called "hew/chop-food": *hakkemad*, *hakkemat\]\]*, *hackmat*, in modern Swedish renamed to *pölsa*.
## Folklore
In the absence of hard facts as to haggis\' origins, popular folklore has provided some notions. One is that the dish originates from the days of the old Scottish cattle drovers. When the men left the Highlands to drive their cattle to market in Edinburgh, the women would prepare rations for them to eat during the long journey down through the glens. They used the ingredients that were most readily available in their homes and conveniently packaged them in a sheep\'s stomach allowing for easy transport during the journey. Other speculations have been based on Scottish slaughtering practices. When a chieftain or laird required an animal to be slaughtered for meat (whether sheep or cattle) the workmen were allowed to keep the offal as their share.
A joke sometimes maintained is that a haggis is a small Scottish animal with longer legs on one side, so that it can run around the steep hills of the Scottish highlands without falling over. According to one poll, 33 percent of American visitors to Scotland believed haggis to be an animal.
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# Haggis
## Modern use {#modern_use}
Haggis is traditionally served as part of the Burns supper on or near January 25, the birthday of Scotland\'s national poet Robert Burns. Burns wrote the poem \"Address to a Haggis\", which starts \"Fair fa\' your honest, sonsie face, Great chieftain o\' the puddin-race!\" In Burns\'s lifetime haggis was a common dish of the poor as it was nourishing yet very cheap, being made from leftover parts of sheep otherwise discarded.
Haggis is widely available in supermarkets in Scotland all year, with cheaper brands normally packed in artificial casings, rather than stomachs. Sometimes haggis is sold in tins or a container which can be cooked in a microwave or conventional oven. Some commercial haggis is largely made from pig, rather than sheep, offal. Kosher haggis, not only pork-free but fully conformant to Jewish dietary laws, is produced.
Haggis is often served in Scottish fast-food establishments, in the shape of a large sausage and deep fried in batter. Together with chips, this comprises a \"haggis supper\". A \"haggis burger\" is a patty of fried haggis served on a bun. A \"haggis pakora\" is another deep fried variant, available in some Indian restaurants in Scotland. Haggis can be used as an ingredient in other dishes, even pizza, rather than the main part of a dish.
A traditional haggis recipe describes haggis as \"sheep\'s \'pluck\' (heart, liver, and lungs), minced with onion, oatmeal, suet, spices, and salt, mixed with stock, and traditionally encased in the animal\'s stomach and boiled\". Ingredients are sheep stomach, heart and lungs of one lamb, onions, oatmeal, salt, pepper, stock, and water, with optional ingredients dried coriander, cinnamon, and nutmeg. It can be boiled, baked, or deep fried.
In the north-east of Scotland, from Aberdeen northwards, in addition to the customary neeps and tatties, haggis is commonly served with mince.
### Vegetarian
Vegetarian haggis was first available commercially in 1984, and now can account for between 25% and 40% of haggis sales. It substitutes various pulses, nuts and vegetables for the meat. Oats and barley may be included as may different types of lentils, split peas, adzuki beans, kidney beans, borlotti beans, peanuts, other nuts and mushrooms, onions, and carrots.
## Outside Scotland {#outside_scotland}
Haggis remains popular with Scottish immigrants in the United States, Canada, Australia, and New Zealand, owing to the strong influence of Scottish culture, especially for Burns Suppers. It can be made in any country, but is sometimes imported from Scotland.
### Legality
In 1971, it became illegal to import haggis into the US from the UK due to a ban on food containing sheep lung, which constitutes 10--15% of the traditional recipe. The ban encompasses all lungs, as fluids such as stomach acid and phlegm may enter the lung during slaughter. The situation was further complicated in 1989 when all UK beef and lamb was banned from importation to the US due to a BSE crisis. The ban on importing British lamb to the US was lifted in 2022 but the ban on food containing sheep lung remained in force.
As haggis cannot be exported to the United States, it is instead made there, sometimes by Scottish companies. In one such use, which is stated to be otherwise the same 150-year-old recipe having the same ingredients as in Scotland, sheep lung is not used and the casing is artificial rather than stomach
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# Holy Grail
The **Holy Grail** (*Saint Graal*, *Graal Santel*, *Greal Sanctaidd*, *Gral*) is a treasure that serves as an important motif in Arthurian literature. Various traditions describe the Holy Grail as a cup, dish, or stone with miraculous healing powers, sometimes providing eternal youth or sustenance in infinite abundance, often guarded in the custody of the Fisher King and located in the hidden Grail castle. By analogy, any elusive object or goal of great significance may be perceived as a \"holy grail\" by those seeking such.
A mysterious \"grail\" (Old French: *graal* or *greal*), wondrous but not unequivocally holy, first appears in *Perceval, the Story of the Grail*, an unfinished chivalric romance written by Chrétien de Troyes around 1190. Chrétien\'s story inspired many continuations, translators and interpreters in the later-12th and early-13th centuries, including Wolfram von Eschenbach, who portrayed the Grail as a stone in *Parzival*. The Christian, Celtic or possibly other origins of the Arthurian grail trope are uncertain and have been debated among literary scholars and historians.
Writing soon after Chrétien, Robert de Boron in *Joseph d\'Arimathie (poem)* portrayed the Grail as Jesus\'s vessel from the Last Supper, which Joseph of Arimathea used to catch Christ\'s blood at the crucifixion. Thereafter, the Holy Grail became interwoven with the legend of the Holy Chalice, the Last Supper cup, an idea continued in works such as the *Lancelot-Grail* cycle, and subsequently the 15th-century *Le Morte d\'Arthur*. In this form, it is now a popular theme in modern culture, and has become the subject of folklore studies, pseudohistorical writings, works of fiction, and conspiracy theories.
## Etymology
The word *graal*, as it is spelled in its earliest appearances, comes from Old French common noun *graal* or *greal*, cognate with Old Occitan *grazal* and Old Catalan *gresal*, meaning \"a cup or bowl of earth, wood, or metal\" (or other various types of vessels in different Occitan dialects). Its origin is uncertain. One unlikely is the Old Welsh word *griol*. The most commonly accepted etymology derives it from Latin *gradalis* or *gradale* via an earlier form, *cratalis*, a derivative of *crater* or *cratus*, which was, in turn, borrowed from Ancient Greek *\[\[krater\]\]* (`{{wikt-lang|grc|κρᾱτήρ}}`{=mediawiki}, a large wine-mixing vessel). Alternative suggestions include a derivative of *cratis*, a name for a type of woven basket that came to refer to a dish, or a derivative of Latin *gradus* meaning {{\"\'}}by degree\', \'by stages\', applied to a dish brought to the table in different stages or services during a meal\".
In the 15th century, English writer John Hardyng invented a fanciful new etymology for Old French *san-graal* (or *san-gréal*), meaning \"Holy Grail\", by parsing it as *sang réal*, meaning \"royal blood\". This etymology was used by some later medieval British writers such as Thomas Malory, and became prominent in the conspiracy theory developed in the book *The Holy Blood and the Holy Grail*, in which *sang real* refers to the Jesus bloodline.
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# Holy Grail
## Medieval literature {#medieval_literature}
### Overview
The literature surrounding the Grail can be divided into two branches. The first concerns King Arthur\'s knights visiting the Grail castle or questing after the object:
- *Perceval, the Story of the Grail*, a chivalric romance poem by Chrétien de Troyes where a girl mysteriously carries it in a procession. When first described by Chrétien, the marvelous nature of \"a grail\" is mysteriously unexplained. There, it is a salver, a tray used to serve at a feast.
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- The four continuations of Chrétien\'s unfinished poem, by authors of differing vision, designed to bring the story to a close.
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- The Didot Perceval, purportedly a prosification of Robert de Boron\'s lost sequel to his romance poems *Joseph d\'Arimathie (poem)* and *Merlin*.
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- *Parzival* by Wolfram von Eschenbach, where it is a gemstone linked to the fall of the angels.
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- Welsh romance *Peredur son of Efrawg*, a loose translation of Chrétien\'s poem and the Continuations, with some influence from native Welsh literature. It had no Grail as such, presenting the hero instead with a platter containing his kinsman\'s bloody, severed head.
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- *Perlesvaus*, an alternative work inspired by *Perceval*.
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- German poem *Diu Crône* (*The Crown*), in which Gawain, rather than Perceval, achieves the Grail.
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- The Prose *Lancelot* section of the vast Lancelot-Grail (Vulgate) cycle introduced the new Grail hero, Galahad. The Vulgate *Queste del Saint Graal*, a follow-up part of the cycle, ends with the eventual achievement of the Grail by Galahad. The story was rewritten in the Post-Vulgate Cycle and other derivative works.
The other branch tells the Grail\'s earlier history since the time of Joseph of Arimathea:
- Robert de Boron\'s *Joseph d\'Arimathie* and *Merlin* (the Little Grail Cycle), establishing the Grail as the vessel of the Last Supper.
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- The Vulgate *Estoire del Saint Graal* and the Vulgate *Merlin*, parts of the Lancelot-Grail cycle (but written after *Lancelot* and the *Queste*) based on Robert\'s telling but expanding it greatly with many new details. It, too, was then rewritten in the Post-Vulgate.
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# Holy Grail
## Medieval literature {#medieval_literature}
### Chrétien de Troyes {#chrétien_de_troyes}
The subject is first featured in *Perceval, le Conte du Graal* (*The Story of the Grail*) by Chrétien de Troyes, who claims he was working from a source book given to him by his patron, Count Philip of Flanders. In this incomplete poem, dated sometime between 1180 and 1191, the object has not yet acquired the implications it would have in later works.
While dining in the magical castle of the Fisher King, Perceval witnesses a wondrous procession in which youths carry magnificent objects from one chamber to another, passing before him at each course of the meal. First comes a young man carrying a bleeding lance, then two boys carrying candelabras. Finally, a beautiful young girl emerges bearing an elaborately decorated *graal*, or \"grail\". Perceval, who had been warned against talking too much, remains silent through all of this and wakes up the next morning alone. Later, a hermit informs Perceval that the latter is a \"very holy thing\" in which a host is served that miraculously keeps the crippled Fisher King alive. If Perceval had asked the appropriate questions about the meaning of the lance and the grail, he would have healed his maimed host.
Chrétien refers to this object not as \"the Grail\" but as \"a grail\" (*un graal*), showing the word was used, in its earliest literary context, as a common noun. For Chrétien, a grail was a wide, somewhat deep, dish or bowl, interesting because it contained not a pike, salmon, or lamprey, as the audience may have expected for such a container, but a single Communion wafer. The story of the Wounded King\'s mystical fasting is not unique; several saints were said to have lived without food besides communion, for instance Saint Catherine of Genoa. This may imply that Chrétien intended the Communion wafer to be the significant part of the ritual, and the Grail to be a mere prop. Hélinand of Froidmont\'s *Chronicon* described it as a \"wide and deep saucer\" (*scutella lata et aliquantulum profunda*). It is also mentioned by others such as Rigaut de Barbezieux.
Chrétien\'s Perceval does not achieve the quest, but four different authors attempted to completed his unfinished story in their own poems known as *Perceval Continuations* that include two successive follow up tales and then two alternative endings. In these works, the mysteries left unsolved by Chrétien (the bleeding lance, the broken sword, the wounded king) develop an explicitly Christian character, transforming a chivalric adventure into a mystical religious quest, undertaken by not only Perceval but also Gawain.
The *First Continuation* (*Gawain Continuation*) seemingly features two grails: a floating dish and a carved head of Jesus. The *Third Continuation* has it again as carried by a girl. Here, the Fisher King dies and is replaced by Perceval, after whose death the Grail is taken to the Heaven.
### Wolfram von Eschenbach {#wolfram_von_eschenbach}
In *Parzival*, the author Wolfram von Eschenbach, citing the authority of a certain (probably fictional) Kyot the Provençal, claimed the Grail was a gemstone, the sanctuary of the neutral angels who took neither side during Lucifer\'s rebellion. It is called *lapis exillis* (other forms *lapsis*, *lapsit*, *exilis*), which in alchemy is the name of the philosopher\'s stone.
In Wolfram\'s telling, the Grail was kept safe at the castle of Munsalvaesche (*mons salvationis*), entrusted to Titurel, the first Grail King. The stone grants eternal life to its guardian. In the end, Parzival replaces the maimed and long suffering Anfortas as the new Grail King, having finally released him by correctly answering his question.
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# Holy Grail
## Medieval literature {#medieval_literature}
### Robert de Boron {#robert_de_boron}
Though Chrétien\'s account is the earliest and most influential of all Grail texts, it was in the work of Robert de Boron that the Grail truly became the \"Holy Grail\" and assumed the form most familiar to modern readers in its Christian context. In his *Joseph d\'Arimathie*, composed between 1191 and 1202, Robert tells the story of Joseph of Arimathea acquiring the chalice of the Last Supper to collect Christ\'s blood upon his removal from the cross. Joseph is thrown in prison, where Christ visits him and explains the mysteries of the blessed cup. Upon his release, Joseph gathers his in-laws and other followers and travels west to Britain, where he founds a dynasty of Grail keepers that eventually includes Perceval.
Robert returned to the subject of the Grail as a major theme in *Merlin* where he linked it to the figure of Merlin, turned by him into a Grail prophet who orders the construction of the Round Table as a successor item to the previous Grail tables of Jesus and Joseph. Perceval himself is the subject of the *Prose Perceval* (*Perceval en prose*), a rare work sometimes attributed to Robert that presents a revised and completed version of Chrétien\'s story while simultaneously also serving as a continuation to *Joseph* and *Merlin*.
In the anonymous prose *Perlesvaus*, another but markedly different continuation of Chrétien\'s *Perceval*, the Grail is a holy blood relic creating mystical visions and appearing in the form of a hovering chalice, apparently as inspired by the works of de Boron. It a religious militant work where its hero Perlesvaus (i.e. Perceval) punishes infidels and conquers the Grail castle in an allegory for establishing the Kingdom of Jerusalem.
The vast prose *Vulgate Cycle* (*Lancelot-Grail*) finished the story set up by Robert de Boron in *Joseph* and *Merlin*, the works themselves incorporated into the cycle in an expanded form as the Vulgate *Estoire dou Graal* (*History of the Grail*) and the Vulgate *Merlin*, in the continuation known as the Vulgate *Queste del Saint Graal* (*Quest for the Holy Grail*). Here, the main Grail hero is Galahad, son of the world\'s hitherto greatest knight, Lancelot, and the Fisher King\'s daughter and the Grail Bearer at the castle of Corbenic, Elaine. Both of his parents come from Biblical lineages and he is destined to achieve the Grail, a symbol of divine grace, as the virgin Galahad\'s spiritual purity makes him superior to even his illustrious father.
In the *Estoire*, the definition and characterization of the Grail change over the course of the story. It is initially only mentioned as the holy \"bowl\", then is referred to as a \"vase\", before definitively becoming a cup and the \"grail\". It is also kept in a marvelous ark and forbidden to ordinary mortals, reminiscent of the Ark of the Covenant. The Grail again appears in the Vulgate *Lancelot*, featured in a story loosely based on Chrétien (the procession here is witnessed by Lancelot and later by Bors), as well as in a new original episode of Elaine using it to cure Lancelot\'s madness (having also physically healed Hector and Bors in previous chapter). In the *Queste*, the corruption of the inhabitants of Britain resulted in the loss of the Grail and its return to the Middle Eastern city of Sarras.
The *Queste* tells of the adventures of various Knights of the Round Table in their eponymous great quest in search of the Grail, who embark on it against the worried Arthur\'s reservations and wander throughout Britain and the broader world alone or in small groups. Perceval and Bors the Younger eventually join Galahad, who had been earlier proved uniquely worthy and predestined for it by surviving the Siege Perilous. They are present as his companions at the successful end of the Grail Quest, when they witness his ascension to Heaven. The mystery of the Grail is finally unveiled as containing an incarnation of Christ. Perceval himself dies on their voyage back. A total of 72 knights perish and the Round Table never fully recovers, setting the stage for the collapse of the Arthurian world in the cycle\'s final part, the *Mort Artu*.
Alternative versions of the Grail Quest based on that from the *Vulgate Cycle* are featured in the *Prose Tristan* (long version) and the *Post-Vulgate Cycle*. The Galahad-centered tradition was later picked by Thomas Malory for his *Le Morte d\'Arthur* and remains popular today. Based on the Vulgate *Queste* in an abridged form, Malory\'s telling accordingly elevates Galahad above Perceval (Percivale), the latter reduced to a secondary role in the Quest. Uniquely, Malory described the Grail as invisible, apparently confused by his French source text\'s mention of an invisible Grail bearer.
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# Holy Grail
## Later traditions {#later_traditions}
### Relics
In the wake of the Arthurian romances, several artifacts came to be identified as the Holy Grail in medieval relic veneration. These artifacts are said to have been the vessel used at the Last Supper, but other details vary. Despite the prominence of the Grail literature, traditions about a Last Supper relic remained rare in contrast to other items associated with Jesus\' last days, such as the True Cross and Holy Lance.
One tradition predates the Grail romances: in the 7th century, the pilgrim Arculf reported that the Last Supper chalice was displayed near Jerusalem. In the wake of Robert de Boron\'s Grail works, several other items came to be claimed as the true Last Supper vessel. In the late 12th century, one was said to be in Byzantium; Albrecht von Scharfenberg\'s Grail romance *Der Jüngere Titurel* associated it explicitly with the Arthurian Grail, but claimed it was only a copy. This item was said to have been looted in the Fourth Crusade and brought to Troyes in France, but it was lost during the French Revolution.
Two relics associated with the Grail survive today. The *Sacro Catino* (Sacred Basin, also known as the Genoa Chalice) is a green glass dish held at the Genoa Cathedral said to have been used at the Last Supper. Its provenance is unknown, and there are two divergent accounts of how it was brought to Genoa by Crusaders in the 12th century. It was not associated with the Last Supper until later, in the wake of the Grail romances; the first known association is in Jacobus de Voragine\'s chronicle of Genoa in the late 13th century, which draws on the Grail literary tradition. The Catino was moved and broken during Napoleon\'s conquest in the early 19th century, revealing that it is glass rather than emerald.
The Holy Chalice of Valencia is an agate dish with a mounting for use as a chalice. The bowl may date to Greco-Roman times, but its dating is unclear, and its provenance is unknown before 1399, when it was gifted to Martin I of Aragon. By the 14th century, an elaborate tradition had developed that this object was the Last Supper chalice. This tradition mirrors aspects of the Grail material, with several major differences, suggesting a separate tradition entirely. It is not associated with Joseph of Arimathea or Jesus\' blood; it is said to have been taken to Rome by Saint Peter and later entrusted to Saint Lawrence. Early references do not call the object the \"Grail\". The first evidence connecting it to the Grail tradition is from the 15th century, when the monarchy sold the cup to Valencia Cathedral. It remains a significant local icon.
Several objects were identified with the Holy Grail in the 17th century. In the 20th century, a series of new items became associated with it. These include the Nanteos Cup, a medieval wooden bowl found near Rhydyfelin, Wales; a glass dish found near Glastonbury, England; the Antioch chalice, a 6th-century silver-gilt object that became attached to the Grail legend in the 1930s; and the Chalice of Doña Urraca, a cup made between 200 BC and 100 AD, kept in León's Basilica of Saint Isidore.
### Locations associated with the Holy Grail {#locations_associated_with_the_holy_grail}
In the modern era, a number of places have become associated with the Holy Grail. One of the most prominent is Glastonbury in Somerset, England. Glastonbury was associated with King Arthur and his resting place of Avalon by the 12th century. In the 13th century, a legend arose that Joseph of Arimathea was the founder of Glastonbury Abbey. Early accounts of Joseph at Glastonbury focus on his role as the evangelist of Britain rather than as the custodian of the Holy Grail, but from the 15th century, the Grail became a more prominent part of the legends surrounding Glastonbury. Interest in Glastonbury resurged in the late 19th century, inspired by renewed interest in the Arthurian legend and contemporary spiritual movements centered on ancient sacred sites. In the late 19th century, John Goodchild hid a glass bowl near Glastonbury; a group of his friends, including Wellesley Tudor Pole, retrieved the cup in 1906 and promoted it as the original Holy Grail. Glastonbury and its Holy Grail legend have since become a point of focus for various New Age and Neopagan groups.
Some, not least the Benedictine monks, have identified the castle from *Parzival* with their real sanctuary of Montserrat in Catalonia. In the early 20th century, esoteric writers identified Montségur, a stronghold of the heretical Cathar sect in the 13th century, as the Grail castle. Similarly, the 14th-century Rosslyn Chapel in Midlothian, Scotland, became attached to the Grail legend in the mid-20th century when a succession of conspiracy books identified it as a secret hiding place of the Grail.
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# Holy Grail
## Modern interpretations {#modern_interpretations}
### Scholarly hypotheses {#scholarly_hypotheses}
Scholars have long speculated on the origins of the Holy Grail before Chrétien, suggesting that it may contain elements of the trope of magical cauldrons from Celtic mythology and later Welsh mythology, combined with Christian legend surrounding the Eucharist, the latter found in Eastern Christian sources, conceivably in that of the Byzantine Mass, or even Persian sources. The view that the \"origin\" of the Grail legend should be seen as deriving from Celtic mythology was championed by Roger Sherman Loomis (*The Grail: From Celtic Myth to Christian Symbol*), Alfred Nutt (*Studies on the Legend of the Holy Grail*, available at Wikisource), and Jessie Weston (*From Ritual to Romance* and *The Quest of the Holy Grail*). Loomis traced a number of parallels between medieval Welsh literature and Irish material, and the Grail romances, including similarities between the *Mabinogion*{{\'}}s Bran the Blessed and the Arthurian Fisher King, and between Bran\'s life-restoring cauldron and the Grail.
The opposing view dismissed the \"Celtic\" connections as spurious, and interpreted the legend as essentially Christian in origin. Joseph Goering identified sources for Grail imagery in 12th-century wall paintings from churches in the Catalan Pyrenees (now mostly moved to the Museu Nacional d\'Art de Catalunya), which present unique iconic images of the Virgin Mary holding a bowl that radiates tongues of fire, images that predate the first literary account by Chrétien de Troyes. Goering argues that they were the original inspiration for the Grail legend.
Psychologists Emma Jung and Marie-Louise von Franz used analytical psychology to interpret the Grail as a series of symbols in their book *The Grail Legend*. They directly expanded on interpretations by Carl Jung, which were later invoked by Joseph Campbell. Philosopher Henry Corbin, a member of the Eranos circle founded by Jung, also commented on the esoteric significance of the grail, relating it to the Iranian Islamic symbols that he studied.
Daniel Scavone (1999, 2003) argued that the \"Grail\" originally referred to the Image of Edessa. According to Richard Barber (2004), the Grail legend is connected to the introduction of \"more ceremony and mysticism\" surrounding the sacrament of the Eucharist in the high medieval period, proposing that the first Grail stories may have been connected to the \"renewal in this traditional sacrament\". Goulven Peron (2016) suggested that the Holy Grail may reflect the horn of the river-god Achelous, as described by Ovid in the *Metamorphoses*.
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# Holy Grail
## Modern interpretations {#modern_interpretations}
### Pseudohistory and conspiracy theories {#pseudohistory_and_conspiracy_theories}
Since the 19th century, the Holy Grail has been linked to various conspiracy theories. In 1818, Austrian pseudohistorical writer Joseph von Hammer-Purgstall connected the Grail to contemporary myths surrounding the Knights Templar that cast the order as a secret society dedicated to mystical knowledge and relics. In Hammer-Purgstall\'s work, the Grail is not a physical relic, but a symbol of the secret knowledge that the Templars sought. There is no historical evidence linking the Templars to a search for the Grail, but subsequent writers have elaborated on the Templar theories.
Starting in the early 20th century, writers, particularly in France, further connected the Templars and Grail to the Cathars. In 1906, French esoteric writer Joséphin Péladan identified the Cathar castle of Montségur with Munsalväsche or Montsalvat, the Grail castle in Wolfram\'s *Parzival*. This identification has inspired a wider legend asserting that the Cathars possessed the Holy Grail. According to these stories, the Cathars guarded the Grail at Montségur, and smuggled it out when the castle fell in 1244.
Beginning in 1933, German writer Otto Rahn published a series of books tying the Grail, Templars, and Cathars to modern German nationalist mythology. According to Rahn, the Grail was a symbol of a pure Germanic religion repressed by Christianity. Rahn\'s books inspired interest in the Grail within Nazi occultist circles, and led to the SS chief Heinrich Himmler\'s abortive sponsorship of Rahn\'s search for the Grail, as well as many subsequent conspiracy theories and fictional works about the Nazis searching for the Grail.
In the late 20th century, writers Michael Baigent, Richard Leigh, and Henry Lincoln created one of the most widely known conspiracy theories about the Holy Grail. The theory first appeared on the BBC documentary series *Chronicle* in the 1970s, and was elaborated upon in the bestselling 1982 book *Holy Blood, Holy Grail*. The theory combines myths about the Templars and Cathars with various other legends, and a prominent hoax about a secret order called the Priory of Sion. According to this theory, the Holy Grail is not a physical object, but a symbol of the bloodline of Jesus. The blood connection is based on the etymological reading of *san greal* (holy grail) as *sang real* (royal blood), which dates to the 15th century. The narrative developed is that Jesus was not divine, and had children with Mary Magdalene, who took the family to France where their descendants became the Merovingian dynasty. Supposedly, while the Catholic Church worked to destroy the dynasty, they were protected by the Priory of Sion and their associates, including the Templars, Cathars, and other secret societies. The book, its arguments, and its evidence have been widely dismissed by scholars as pseudohistorical, but it has had a vast influence on conspiracy and alternate history books. It has also inspired fiction, most notably Dan Brown\'s 2003 novel *The Da Vinci Code* and its 2006 film adaptation.
### Music and painting {#music_and_painting}
The combination of hushed reverence, chromatic harmonies and sexualized imagery in Richard Wagner\'s final music drama *Parsifal*, premiered in 1882, developed this theme, associating the Grail -- now periodically producing blood -- directly with female fertility. The high seriousness of the subject was also epitomized in Dante Gabriel Rossetti\'s painting in which a woman modeled by Alexa Wilding holds the Grail with one hand, while adopting a gesture of blessing with the other.
A major mural series depicting the Quest for the Holy Grail was done by the artist Edwin Austin Abbey during the first decade of the 20th century for the Boston Public Library. Other artists, including George Frederic Watts and William Dyce, also portrayed grail subjects.
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# Holy Grail
## Modern interpretations {#modern_interpretations}
### Literature
The story of the Grail and of the quest to find it became increasingly popular in the 19th century, referred to in literature such as Alfred, Lord Tennyson\'s Arthurian cycle *Idylls of the King*. A sexualised interpretation of the grail, now identified with female genitalia, appeared in 1870 in Hargrave Jennings\' book *The Rosicrucians, Their Rites and Mysteries*.
- T. S. Eliot\'s poem *The Waste Land* (1922) loosely follows the legend of the Holy Grail and the Fisher King combined with vignettes of contemporary British society. In his first note to the poem, Eliot attributes the title to Jessie Weston\'s book on the Grail legend, *From Ritual to Romance*. The allusion is to the wounding of the Fisher King and the subsequent sterility of his lands. A poem of the same title, though otherwise dissimilar, written by Madison Cawein, was published in 1913 in *Poetry*.
- In John Cowper Powys\'s *A Glastonbury Romance* (1932), the \"heroine is the Grail,\" and its central concerns are with the various myths and legends, along with the history associated with Glastonbury. It is also possible to see most of the main characters as undertaking a Grail quest.
- The Grail is central in Charles Williams\' novel *War in Heaven* (1930) and his two collections of poems about Taliessin, *Taliessin Through Logres* and *Region of the Summer Stars* (1938).
- *The Silver Chalice* (1952) is a non-Arthurian historical Grail novel by Thomas B. Costain.
- A quest for the Grail appears in Nelson DeMille\'s adventure novel *The Quest* (1975), set during the 1970s.
- Marion Zimmer Bradley\'s Arthurian revisionist fantasy novel *The Mists of Avalon* (1983) presented the Grail as a symbol of water, part of a set of objects representing the four classical elements.
- The main theme of Rosalind Miles\' *Child of the Holy Grail* (2000) in her *Guenevere* series is the story of the Grail quest by the 14-year-old Galahad.
- The Grail motif features heavily in Umberto Eco\'s 2000 novel *Baudolino*, set in the 12th century.
- It is the subject of Bernard Cornwell\'s historical fiction series of books *The Grail Quest* (2000--2012), set during the Hundred Years War. In his earlier series *The Warlord Chronicles*, an adaptation of the Arthurian legend, Cornwell also reimagines the Grail quest as a quest for a cauldron that is one of the Thirteen Treasures of Britain from Celtic mythology.
- Influenced by the 1982 publication of the ostensibly non-fiction *The Holy Blood and the Holy Grail*, Dan Brown\'s *The Da Vinci Code* (2003) has the \"grail\" taken to refer to Mary Magdalene as the \"receptacle\" of Jesus\' bloodline (playing on the *sang real* etymology). In Brown\'s novel, it is hinted that this Grail was long buried beneath Rosslyn Chapel in Scotland, but that in recent decades, its guardians had it moved to a secret chamber embedded in the floor beneath the Inverted Pyramid in the entrance of the Louvre museum.
- Michael Moorcock\'s fantasy novel *The War Hound and the World\'s Pain* (1981) depicts a supernatural Grail quest set in the era of the Thirty Years\' War.
- German history and fantasy novel author Rainer M. Schröder wrote the trilogy *Die Bruderschaft vom Heiligen Gral* (*The Brotherhood of the Holy Grail*) about a group of four Knights Templar who save the Grail from the Fall of Acre in 1291 and go through an odyssey to bring it to the Temple in Paris in the first two books, *Der Fall von Akkon* (2006) and *Das Amulett der Wüstenkrieger* (2006), while defending the holy relic from the attempts of a Satanic sect called Iscarians to steal it. In the third book, *Das Labyrinth der schwarzen Abtei* (2007), the four heroes must reunite to smuggle the Holy Grail out of the Temple in Paris after the trials of the Knights Templar in 1307, again pursued by the Iscarians. Schröder indirectly addresses the Cathar theory by letting the four heroes encounter Cathars -- among them old friends from their flight from Acre -- on their way to Portugal to seek refuge with the King of Portugal and travel further west.
- The 15th novel in *The Dresden Files* series by Jim Butcher, *Skin Game* (2014), features Harry Dresden being recruited by Denarian and longtime enemy Nicodemus into a heist team seeking to retrieve the Holy Grail from the vault of Hades, the lord of the Underworld. The properties of the item are not explicit, but the relic itself makes an appearance and is in the hands of Nicodemus by the end of the novel\'s events.
- The Holy Grail features prominently in Jack Vance\'s *Lyonesse Trilogy*, where it is the subject of an earlier quest, several generations before the birth of King Arthur. However, in contrast to the Arthurian canon, Vance\'s Grail is a common object lacking any magical or spiritual qualities, and the characters finding it derive little benefit.
- *Grails: Quests of the Dawn* (1994), edited by Richard Gilliam, Martin H. Greenberg, and Edward E. Kramer is a collection of 25 short stories about the grail by various science fiction and fantasy writers.
- In Robert Bruton\'s *Empire in Apocalypse* (2023), the Holy Grail appears as General Belisarius\'s Vandal chalice, recovered with other treasures the Vandals had stolen during the sacking of Rome.
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# Holy Grail
## Modern interpretations {#modern_interpretations}
### Film and other media {#film_and_other_media}
In the cinema, the Holy Grail debuted in the 1904 silent film *Parsifal*, an adaptation of Wagner\'s opera by Edwin S. Porter. More recent cinematic adaptations include Costain\'s *The Silver Chalice* made into a 1954 film by Victor Saville and Brown\'s *The Da Vinci Code* turned into a 2006 film by Ron Howard.
- The silent drama film *The Light in the Dark* (1922) involves discovery of the Grail in modern times.
- Robert Bresson\'s fantasy film *Lancelot du Lac* (1974) includes a more realistic version of the Grail quest from Arthurian romances.
- *Monty Python and the Holy Grail* (1975) is a comedic take on the Arthurian Grail quest, adapted in 2004 as the stage production *Spamalot*.
- John Boorman, in his fantasy film *Excalibur* (1981), attempted to restore a more traditional heroic representation of an Arthurian tale, in which the Grail is revealed as a mystical means to revitalise Arthur and the barren land to which his depressive sickness is connected.
- Steven Spielberg\'s adventure film *Indiana Jones and the Last Crusade* (1989) features Indiana Jones and his father in a race for the Grail against the Nazis.
- In a pair of fifth-season episodes (September 1989), entitled \"Legend of the Holy Rose,\" MacGyver undertakes a quest for the Grail.
- Terry Gilliam\'s comedy-drama film *The Fisher King* (1991) features the Grail quest in the modern New York City.
- In the season one episode \"Grail\" (1994) of the television series *Babylon 5*, a man named Aldous Gajic visits Babylon 5 in his continuing quest to find the Holy Grail. His quest is primarily a plot device, as the episode\'s action revolves not around the quest but rather around his presence and impact on the life of a station resident.
- The video game *Gabriel Knight 3: Blood of the Sacred, Blood of the Damned* (1999) features an alternate version of the Grail, interwoven with the mythology of the Knights Templar. The Holy Grail is revealed in the story to be the blood of Jesus Christ that contains his power, only accessible to those descended from him, with the vessel of the Grail being defined as his body itself which the Templars uncovered in the Holy Lands.
- In *Pretty Guardian Sailor Moon,* the Holy Grail (Sehai in the anime, or Rainbow Moon Chalice) is the magical object with which Sailor Moon transforms in her Super form.
- A science fiction version of the Grail Quest is central theme in the *Stargate SG-1* season 10 episode \"The Quest\" (2006).
- The song \"Holy Grail\" by Australian band Hunters & Collectors was released in 1993.
- The song \"Holy Grail\" by Jay-Z featuring Justin Timberlake was released in 2013.
- In the video game *Persona 5* (2016), the Holy Grail is the Treasure of the game\'s final Palace, representing the combined desires of all of humanity for a higher power to take control of their lives and make a world that has no sense of individuality.
- In the television series *Knightfall* (2017), the search for the Holy Grail by the Knights Templar is a major theme of the series\' first season. The Grail, which appears as a simple earthenware cup, is coveted by various factions including the Pope, who thinks that possession of it will enable him to ignite another Crusade.
- In the *Fate* franchise, the Holy Grail serves as the prize of the Holy Grail War, granting a single wish to the victor of the battle royale. However, it is hinted at throughout the series that this Grail is not the real chalice of Christ, but is actually an item of uncertain nature created by mages some generations ago.
- In the *Assassin\'s Creed* video game franchise the Holy Grail is mentioned. In the original game, one Templar refers to the main relic of the game as the Holy Grail, although it was later discovered to be one of many Apples of Eden. The Holy Grail was mentioned again in Templar Legends, ending up in either Scotland or Spain by different accounts. The Holy Grail appears again in *Assassin\'s Creed: Altaïr\'s Chronicles*, by the name of the Chalice, however this time not as an object but as a woman named Adha, similar to the sang rael, or royal blood, interpretation.
- In the fourth series of *The Grand Tour*, the trio goes to Nosy Boraha where they accidentally find the Holy Grail while searching for La Buse\'s buried treasure.\"A massive Hunt\", The Grand Tour:
- Hammond: \"There\'s something there!\"
- Clarkson: \"What\'s that?\"
- May: \"What is it?\"
- Hammond: \"I think it\'s the Holy Grail.\"
- May: \"Oh cock.\"
- Clarkson: \"And on that terrible disappointment, it\'s time to end.\"
- In the 17th episode of *Little Witch Academia*, \"Amanda O\'Neill and the Holy Grail\", the Holy Grail is used as a plot device in which witches Amanda O\'Neill and Akko Kagari set out to find the item itself at Appleton School.
- In the 12th episode of season 9 of the American show *The Office*, Jim Halpert sends Dwight Schrute on a wild goose chase to find the Holy Grail. After Dwight completing all the clues to find it, but coming up empty handed, the camera cuts to Glenn drinking out of it in his office.
- In the 2022 Christmas special episode of the British TV series *Detectorists*, \"Special\", Lance finds a crockery cup, eyes only, in a field that turns out to be where a historic battle took place and a reliquary containing the Holy Grail was lost. A montage shows how the same crockery cup went from the hands of Jesus at the Last Supper (implied) to being lost in the field.
- The 2023 limited television series *Mrs. Davis* revolves around Sister Simone\'s quest to find and destroy the Holy Grail, both as the central plot device and also as metacommentary on quests for the Holy Grail, which one character observes might be the \"most overused MacGuffin ever\"
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# Hunt the Wumpus
***Hunt the Wumpus*** is a text-based adventure game developed by Gregory Yob in 1973. In the game, the player moves through a series of connected caves, arranged as the vertices of a dodecahedron, as they hunt a monster named the Wumpus. The turn-based game has the player trying to avoid fatal bottomless pits and \"super bats\" that will move them around the cave system; the goal is to fire one of their \"crooked arrows\" through the caves to kill the Wumpus. Yob created the game in early 1973 due to his annoyance at the multiple hide-and-seek games set in caves in a grid pattern, and multiple variations of the game were sold via mail order by Yob and the People\'s Computer Company. The source code to the game was published in *Creative Computing* in 1975 and republished in *The Best of Creative Computing* the following year.
The game sparked multiple variations and expanded versions and was ported to several systems, including the TI-99/4A home computer. It has been cited as an early example of the survival horror genre, and was listed in 2012 on *Time*{{\'}}s All-Time 100 greatest video games list. The Wumpus monster has appeared in several forms in media since 1973, including other video games, a novella, and *Magic: The Gathering* cards.
## Gameplay
*Hunt the Wumpus* is a text-based adventure game set in a series of caves connected by tunnels. In one of the twenty caves is a \"Wumpus\", which the player is attempting to kill. Additionally, two of the caves contain bottomless pits, while two others contain \"super bats\" which will pick up the player and move them to a random cave. The game is turn-based; each cave is given a number by the game, and each turn begins with the player being told which cave they are in and which caves are connected to it by tunnels. The player then elects to either move to one of those connected caves or shoot one of their five \"crooked arrows\", named for their ability to change direction while in flight. Each cave is connected to three others, and the system as a whole is equivalent to a dodecahedron.
The caves are in complete darkness, so the player cannot see into adjacent caves; instead, upon moving to a new empty cave, the game describes if they can smell a Wumpus, hear a bat, or feel a draft from a pit in one of the connected caves. Entering a cave with a pit ends the game due to the player falling in, while entering the cave with the Wumpus startles it; the Wumpus will either move to another cave or remain and kill the player. If the player chooses to fire an arrow, they first select how many caves, up to five, that the arrow will travel through, and then enters each cave that the arrow moves through. If the player enters a cave number that is not connected to where the arrow is, the game picks a valid option at random. If the arrow hits the player while it is travelling, the player loses; if it hits the Wumpus, they win. If the arrow does not hit anything, then the Wumpus is startled and may move to a new cave; unlike the player, the Wumpus is not affected by super bats or pits. If the Wumpus moves to the player\'s location, they lose.
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# Hunt the Wumpus
## Development
In early 1973, Gregory Yob was looking through some of the games published by the People\'s Computer Company (PCC), and grew annoyed that there were multiple games, including *Hurkle* and *Mugwump*, that had the player \"hide and seek\" in a 10 by 10 grid. Yob was inspired to make a game that used a non-grid pattern, where the player would move through points connected through some other type of topology. Yob came up with the name \"Hunt the Wumpus\" that afternoon, and decided from there that the player would traverse through rooms arranged in a non-grid pattern, with a monster called a Wumpus somewhere in them. `{{multiple image
| align = right
| total_width = 320
| image1 = Hunt_the_Wumpus_map_3d.svg
| image2 = Hunt_the_Wumpus_map.svg
| footer =Yob designed the original ''Hunt the Wumpus'' map with the caves arranged as the vertices of a [[dodecahedron]] (left). They can also be mapped in two dimensions (right).
}}`{=mediawiki} Yob chose a dodecahedron because it was his favorite platonic solid, and because he had once made a kite shaped like one. From there, Yob added the arrows to shoot between rooms, terming it the \"crooked arrow\" as it would need to change directions to go through multiple caves, and decided that the player could only sense nearby caves by smell, as a light would wake the Wumpus up. He then added the bottomless pits, and a couple days later the super bats. Finally, feeling that players would want to create a map, he made the cave map fixed and gave each cave a number. Yob later claimed that, to his knowledge, most players did not create maps of the cave system, nor follow his expected strategy of carefully moving around the system to determine exactly where the Wumpus was before firing an arrow. While playtesting the game, Yob found it unexciting that the Wumpus always stayed in one place, and so changed it to be able to move. He then delivered a copy of the game, written in BASIC, to the PCC.
In May 1973, one month after he had finished coding the game, Yob went to a conference at Stanford University and discovered that in the section of the conference where the PCC had set up computer terminals, multiple players were engrossed in playing *Wumpus*, making it, in his opinion, a hit game. The PCC first mentioned the game in its newsletter in September as a \"cave game\" that would be available to order through them soon, and gave it a full two-page description in its next issue in November of the same year. Tapes containing *Wumpus* were sold via mail order by both the PCC and Yob himself. The PCC description was republished along with source code in its book *What to Do After You Hit Return* in 1977, while a description of the game and its source code was published in *Creative Computing* in its October 1975 issue, and republished in *The Best of Creative Computing* the following year. It also appeared in other books of BASIC games, such as *Computer Programs in BASIC* in 1981.
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# Hunt the Wumpus
## Legacy
Multiple versions of *Hunt the Wumpus* were created and distributed after the game\'s release. Yob made *Wumpus 2* and *Wumpus 3*, beginning immediately after finishing the original game, with *Wumpus 2* adding different cave arrangements and *Wumpus 3* adding more hazards. The source code for *Wumpus 2* was published in *Creative Computing* and republished in *The Best of Creative Computing 2* (1977), along with a description of *Wumpus 3*. The PCC announced in the same November 1973 newsletter issue as it discussed the original game that a version from them titled *Super Wumpus* would be available soon, and listed it in its order catalog in its January 1974 issue under both that name and *Wumpus 3*. In 1978, a book titled *Superwumpus*, by Jack Emmerichs, was published containing source code for both BASIC and assembly language versions of his unrelated version of *Hunt the Wumpus*.
In addition to the original BASIC games, versions of *Hunt the Wumpus* have been created for numerous other systems. Yob had seen or heard of versions in several languages, such as IBM RPG and Fortran, by 1975. A version in C, written in November 1973 by Ken Thompson, creator of the Unix operating system, was released in 1974; a later C version can still be found in the bsdgames package on modern BSD and Linux operating systems. In 1978, Danny Hillis, working as a summer intern on the TMS9918 graphics chip, wrote a graphical version of the game as a demonstration with the pattern of caves displayed as a torus instead of a dodecahedron, which was later published as a commercial game for the TI-99/4A. In 1981, a version was released for the HP-41C calculator.
*Hunt the Wumpus* has been cited as an early example of a survival horror game; the book *Vampires and Zombies* claims that it was an early example of the genre, while the paper \"Restless dreams in Silent Hill\" states that \"from a historical perspective the genre\'s roots lie in *Hunt the Wumpus*\". Other sources, however, such as the book *The World of Scary Video Games*, claim that the game lacks elements needed for a \"horror\" game, as the player hunts rather than is hunted by the Wumpus, and nothing in the game is explicitly intended to frighten the player, making it more of an early adventure or puzzle game. Kevin Cogger of 1Up.com claimed that *Wumpus*, whether or not it is an adventure game, \"introduced a number of concepts that would come to define the adventure genre\", such as presenting the game from the perspective of the player-character, and non-grid-based map design. In 2012, *Hunt the Wumpus* was listed on *Time*{{\'}}s All-Time 100 greatest video games list.
The Wumpus monster has appeared in several different forms of media, such as several \"Wumpus\" creature cards in *Magic: The Gathering* including a \"Hunted Wumpus\", video games such as *M.U.L.E.* (1983), and Cory Doctorow\'s 2011 novella *The Great Big Beautiful Tomorrow*. The textbook *Artificial Intelligence: A Modern Approach*, with editions published since 1995, uses a version of this game as one of the examples. An interactive audio-only version of the game was displayed by Jared Bendis as *Treasure of the Wumpus in the Azimuth Cave* at festivals in Ohio from 2011 to 2018, and an interactive touch screen version of the game, *Return to Wumpus Cave*, was presented in 2022
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# HMS Hercules
Five ships of the Royal Navy have borne the name **HMS *Hercules**\'\', or**HMS*Hercule**\'\', after the Greek and Roman hero Hercules. Another was launched, but never served in the Navy:
- was a 74-gun third rate launched in 1759 and sold in 1784.
- HMS *Hercule* was a 74-gun third rate captured by `{{HMS|Mars|1794|6}}`{=mediawiki} in 1798 and broken up in 1810.
- was a 74-gun third rate launched in 1815. She was used for harbour service from 1853 and was sold in 1865.
- was an ironclad battleship launched in 1868. She was used for harbour service from 1881, as a barracks from 1905, was renamed HMS *Calcutta* in 1909, HMS *Fisgard II* in 1915, and was sold in 1932.
- was a `{{sclass|Colossus|battleship (1910)|0}}`{=mediawiki} battleship launched in 1910 and sold for breaking up in 1921.
- was a `{{sclass|Majestic|aircraft carrier|0}}`{=mediawiki} light fleet aircraft carrier launched in 1945, but not completed until purchased by India in 1957. Commissioned in 1961 as `{{INS|Vikrant|1961|6}}`{=mediawiki}, she was paid off in 1997 and was a museum ship between 2001 and 2012. She was scrapped in 2014
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# Historicism
**Historicism** is an approach to explaining the existence of phenomena, especially social and cultural practices (including ideas and beliefs), by studying the process or history by which they came about. The term is widely used in philosophy, anthropology, and sociology.
This historical approach to explanation differs from and complements the approach known as functionalism, which seeks to explain a phenomenon, such as for example a social form, by providing reasoned arguments about how that social form fulfills some function in the structure of a society. In contrast, rather than taking the phenomenon as a given and then seeking to provide a justification for it from reasoned principles, the historical approach asks \"Where did this come from?\" and \"What factors led up to its creation?\"; that is, historical explanations often place a greater emphasis on the role of process and contingency.
Historicism is often used to help contextualize theories and narratives, and may be a useful tool to help understand how social and cultural phenomena came to be.
The historicist approach differs from individualist theories of knowledge such as strict empiricism and rationalism, which does not take into account traditions. Historicism can be reductionist, often tends to be, and is usually contrasted with theories that posit that historical changes occur entirely at random.
David Summers, building on the work of E. H. Gombrich, defines historicism negatively, writing that it posits \"that laws of history are formulatable and that in general the outcome of history is predictable,\" adding \"the idea that history is a universal matrix prior to events, which are simply placed in order within that matrix by the historian.\" This approach, he writes, \"seems to make the ends of history visible, thus to justify the liquidation of groups seen not to have a place in the scheme of history\" and that it has led to the \"fabrication of some of the most murderous myths of modern times.\"
## History of the term {#history_of_the_term}
The term *historicism* (*Historismus*) was coined by German philosopher Karl Wilhelm Friedrich Schlegel. Over time, what historicism is and how it is practiced have developed different and divergent meanings. Elements of historicism appear in the writings of French essayist Michel de Montaigne (1533--1592) and Italian philosopher G. B. Vico (1668--1744), and became more fully developed with the dialectic of Georg Wilhelm Friedrich Hegel (1770--1831), influential in 19th-century Europe. The writings of Karl Marx, influenced by Hegel, also occasionally include historicism. The term is also associated with the empirical social sciences and with the work of Franz Boas. Historicism tends to be hermeneutic because it values cautious, rigorous, and contextualized interpretation of information; or relativist, because it rejects notions of universal, fundamental and immutable interpretations.
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# Historicism
## Variants
### Hegelian
Hegel viewed the realization of human freedom as the ultimate purpose of history, which could be achieved only through the creation of the perfect state. Historical progress toward this state would occur through a dialectical process: the tension between the purpose of humankind (freedom) and humankind\'s current condition would produce the attempt by humankind to change its condition to one more in accord with its nature. However, because humans are often not aware of the goal of humanity and history, the process of achieving freedom is necessarily one of self-discovery.
Hegel saw progress toward freedom as conducted by the \"spirit\" (Geist), a seemingly supernatural force that directs all human actions and interactions. Yet Hegel makes clear that the spirit is a mere abstraction that comes into existence \"through the activity of finite agents\". Thus, Hegel\'s determining forces of history may not have a metaphysical nature, though many of his opponents and interpreters have understood him as holding metaphysical and determinist views.
Hegel\'s historicism also suggests that any human society and all human activities such as science, art, or philosophy, are defined by their history. Consequently, their essence can be sought only by understanding said history. The history of any such human endeavor, moreover, not only continues but also reacts against what has gone before; this is the source of Hegel\'s famous dialectic teaching usually summarized by the slogan \"thesis, antithesis, and synthesis\". (Hegel did not use these terms, although Johann Fichte did.) Hegel\'s famous aphorism, \"Philosophy is the history of philosophy\", describes it bluntly.
Hegel\'s position is perhaps best illuminated when contrasted against the atomistic and reductionist opinion of human societies and social activities self-defining on an *ad hoc* basis through the sum of dozens of interactions. Yet another contrasting model is the persistent metaphor of a social contract. Hegel considers the relationship between individuals and societies as organic, not atomic: even their social discourse is mediated by language, and language is based on etymology and unique character. It thus preserves the culture of the past in thousands of half-forgotten metaphors. To understand why a person is the way he is, you must examine that person in his society: and to understand that society, you must understand its history, and the forces that influenced it. The *Zeitgeist*, the \"Spirit of the Age\", is the concrete embodiment of the most important factors that are acting in human history at any given time. This contrasts with teleological theories of activity, which suppose that the end is the determining factor of activity, as well as those who believe in a tabula rasa, or blank slate, opinion, such that individuals are defined by their interactions.
These ideas can be interpreted variously. The Right Hegelians, working from Hegel\'s opinions about the organicism and historically determined nature of human societies, interpreted Hegel\'s historicism as a justification of the unique destiny of national groups and the importance of stability and institutions. Hegel\'s conception of human societies as entities greater than the individuals who constitute them influenced nineteenth-century romantic nationalism and its twentieth-century excesses. The Young Hegelians, by contrast, interpreted Hegel\'s thoughts on societies influenced by social conflict for a doctrine of social progress, and attempted to manipulate these forces to cause various results. Karl Marx\'s doctrine of \"historical inevitabilities\" and historical materialism is one of the more influential reactions to this part of Hegel\'s thought. Significantly, Karl Marx\'s theory of alienation argues that capitalism disrupts traditional relationships between workers and their work.
Hegelian historicism is related to his ideas on the means by which human societies progress, specifically the dialectic and his conception of logic as representing the inner essential nature of reality. Hegel attributes the change to the \"modern\" need to interact with the world, whereas ancient philosophers were self-contained, and medieval philosophers were monks. In his History of Philosophy Hegel writes:
> In modern times things are very different; now we no longer see philosophic individuals who constitute a class by themselves. With the present day all difference has disappeared; philosophers are not monks, for we find them generally in connection with the world, participating with others in some common work or calling. They live, not independently, but in the relation of citizens, or they occupy public offices and take part in the life of the state. Certainly they may be private persons, but if so, their position as such does not in any way isolate them from their other relationship. They are involved in present conditions, in the world and its work and progress. Thus their philosophy is only by the way, a sort of luxury and superfluity. This difference is really to be found in the manner in which outward conditions have taken shape after the building up of the inward world of religion. In modern times, namely, on account of the reconciliation of the worldly principle with itself, the external world is at rest, is brought into order --- worldly relationships, conditions, modes of life, have become constituted and organized in a manner which is conformable to nature and rational. We see a universal, comprehensible connection, and with that individuality likewise attains another character and nature, for it is no longer the plastic individuality of the ancients. This connection is of such power that every individuality is under its dominion, and yet at the same time can construct for itself an inward world.
This opinion that entanglement in society creates an indissoluble bond with expression, would become an influential question in philosophy, namely, the requirements for individuality. It would be considered by Nietzsche, John Dewey and Michel Foucault directly, as well as in the work of numerous artists and authors. There have been various responses to Hegel\'s challenge. The Romantic period emphasized the ability of individual genius to transcend time and place, and use the materials from their heritage to fashion works which were beyond determination. The modern would advance versions of John Locke\'s infinite malleability of the human animal. Post-structuralism would argue that since history is not present, but only the image of history, that while an individual era or power structure might emphasize a particular history, that the contradictions within the story would hinder the very purposes that the history was constructed to advance.
### Anthropological
In the context of anthropology and other sciences which study the past, historicism has a different meaning. Historical Particularism is associated with the work of Franz Boas. His theory used the diffusionist concept that there were a few \"cradles of civilization\" which grew outwards, and merged it with the idea that societies would adapt to their circumstances. The school of historicism grew in response to unilinear theories that social development represented adaptive fitness, and therefore existed on a continuum. While these theories were espoused by Charles Darwin and many of his students, their application as applied in social Darwinism and general evolution characterized in the theories of Herbert Spencer and Leslie White, historicism was neither anti-selection, nor anti-evolution, as Darwin never attempted nor offered an explanation for cultural evolution. However, it attacked the notion that there was one normative spectrum of development, instead emphasizing how local conditions would create adaptations to the local environment. Julian Steward refuted the viability of globally and universally applicable adaptive standards proposing that culture was honed adaptively in response to the idiosyncrasies of the local environment, the cultural ecology, by specific evolution. What was adaptive for one region might not be so for another. This conclusion has likewise been adopted by modern forms of biological evolutionary theory.
The primary method of historicism was empirical, namely that there were so many requisite inputs into a society or event, that only by emphasizing the data available could a theory of the source be determined. In this opinion, grand theories are unprovable, and instead intensive field work would determine the most likely explanation and history of a culture, and hence it is named \"historicism\".
This opinion would produce a wide range of definition of what, exactly, constituted culture and history, but in each case the only means of explaining it was in terms of the historical particulars of the culture itself.
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# Historicism
## Variants
### New Historicism {#new_historicism}
Since the 1950s, when Jacques Lacan and Michel Foucault argued that each epoch has its own knowledge system, within which individuals are inexorably entangled, many post-structuralists have used *historicism* to describe the opinion that all questions must be settled within the cultural and social context in which they are raised. Answers cannot be found by appeal to an external truth, but only within the confines of the norms and forms that phrase the question. This version of historicism holds that there are only the raw texts, markings and artifacts that exist in the present, and the conventions used to decode them. This school of thought is sometimes given the name of *New Historicism*. The same term, *new historicism* is also used for a school of literary scholarship which interprets a poem, drama, etc. as an expression of or reaction to the power-structures of its society. Stephen Greenblatt is an example of this school.
### Modern Historicism {#modern_historicism}
Within the context of 20th-century philosophy, debates continue as to whether ahistorical and immanent methods were sufficient to understand the meaning (that is to say, \"what you see is what you get\" positivism) or whether context, background and culture are important beyond the mere need to decode words, phrases and references. While post-structural historicism is relativist in its orientation---that is, it sees each culture as its own frame of reference---a large number of thinkers have embraced the need for historical context, not because culture is self-referential, but because there is no more compressed means of conveying all of the relevant information except through history. This opinion is often seen as deriving from the work of Benedetto Croce. Recent historians using this tradition include Thomas Kuhn.
Talcott Parsons criticized historicism as a case of idealistic fallacy in *The Structure of Social Action* (1937). Post-structuralism uses the term *new historicism*, which has some associations with both anthropology and Hegelianism.
### Christian Historicism {#christian_historicism}
#### Eschatological
In Christianity, the term *historicism* refers to the confessional Protestant form of prophetical interpretation which holds that the fulfillment of biblical prophecy has occurred throughout history and continues to occur; as opposed to other methods which limit the time-frame of prophecy-fulfillment to the past or to the future.
#### Dogmatic and ecclesiastic {#dogmatic_and_ecclesiastic}
There is also a particular opinion in ecclesiastical history and in the history of dogmas which has been described as historicist by Pope Pius XII in the encyclical *Humani generis*. \"They add that the history of dogmas consists in the reporting of the various forms in which revealed truth has been clothed, forms that have succeeded one another in accordance with the different teachings and opinions that have arisen over the course of the centuries.\" \"There is also a certain historicism, which attributing value only to the events of man\'s life, overthrows the foundation of all truth and absolute law, both on the level of philosophical speculations and especially to Christian dogmas.\"
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# Historicism
## Critics
### Marxism
Western Marxists such as Karl Korsch, Antonio Gramsci and the early Georg Lukacs emphasise the roots of Marx\'s thought in Hegel. They interpret Marxism as a historically relativist philosophy, which views ideas (including Marxist theory) as products of the historical epochs that create them. In this view, Marxism is not an objective social science, but rather a theoretical expression of the class consciousness of the working class within a historical process. This understanding of Marxism is strongly criticised by the structural Marxist Louis Althusser, who affirms that Marxism is an objective science, autonomous from interests of society and class. Marxism is, therefore, often associated with deterministic claims of future historical development, but these are not structural parts of Marxism as a style of critique which requires distinction between various critical registers, which at once develops an understanding of broad historical-geographical tensions without prophesying a specific outcome.
### Karl Popper {#karl_popper}
Karl Popper used the term *historicism* in his influential books *The Poverty of Historicism* and *The Open Society and Its Enemies*, to mean: \"an approach to the social sciences which assumes that *historical prediction* is their primary aim, and which assumes that this aim is attainable by discovering the \'rhythms\' or the \'patterns\', the \'laws\' or the \'trends\' that underlie the evolution of history\". Popper condemned historicism along with the determinism and holism which he argued formed its basis, claiming that historicism had the potential to inform dogmatic, ideological beliefs not predicated upon facts that were falsifiable. In *The Poverty of Historicism*, he identified historicism with the opinion that there are \"inexorable laws of historical destiny\", an opinion he warned against. If this seems to contrast with what proponents of historicism argue for, in terms of contextually relative interpretation, this happens, according to Popper, only because such proponents are unaware of the type of causality they ascribe to history. Popper wrote with reference to Hegel\'s theory of history, which he criticized extensively.
In *The Open Society and Its Enemies*, Popper attacks \"historicism\" and its proponents, among whom he identifies and singles out Hegel, Plato and Marx---calling them all \"enemies of the open society\". The objection he makes is that historicist positions, by claiming that there is an inevitable and deterministic pattern to history, evade the responsibility of the individual to make free contributions to the evolution of society, hence leading to totalitarianism. Throughout this work, he defines his conception of historicism as: \"The central historicist doctrine---the doctrine that history is controlled by specific historical or evolutionary laws whose discovery would enable us to prophesy the destiny of man.\" As mentioned above, such characterizations of Marx in particular are not entirely accurate to Marx in his own right, and have drawn criticism from philosophers such as Lakatos for mischaracterizing the defense of induction in historical materialism. Other philosophers such as Walter Kaufmann have also been critical of Popper, calling his reading of Hegel a "myth," "known largely through secondary sources..."
Another of his targets is what he terms \"moral historicism\", the attempt to infer moral values from the course of history; in Hegel\'s words, that \"history is the world\'s court of justice\". Popper says that he does not believe \"that success proves anything or that history is our judge\". Futurism must be distinguished from prophecies that the right will prevail: these attempt to infer history from ethics, rather than ethics from history, and are therefore historicism in the normal sense rather than moral historicism.
He also attacks what he calls \"Historism\", which he regards as distinct from historicism. By historism, he means the tendency to regard every argument or idea as completely accounted for by its historical context, as opposed to assessing it by its merits.
### Leo Strauss {#leo_strauss}
Leo Strauss used the term *historicism* and reportedly termed it the single greatest threat to intellectual freedom insofar as it denies any attempt to address injustice-pure-and-simple (such is the significance of historicism\'s rejection of \"natural right\" or \"right by nature\"). Strauss argued that historicism \"rejects political philosophy\" (insofar as this stands or falls by questions of permanent, trans-historical significance) and is based on the belief that \"all human thought, including scientific thought, rests on premises which cannot be validated by human reason and which came from historical epoch to historical epoch.\" Strauss further identified R. G. Collingwood as the most coherent advocate of historicism in the English language. Countering Collingwood\'s arguments, Strauss warned against historicist social scientists\' failure to address real-life problems---most notably that of tyranny---to the extent that they relativize (or \"subjectivize\") all ethical problems by placing their significance strictly in function of particular or ever-changing socio-material conditions devoid of inherent or \"objective\" \"value\". Similarly, Strauss criticized Eric Voegelin\'s abandonment of ancient political thought as guide or vehicle in interpreting modern political problems.
In his books, *Natural Right and History* and *On Tyranny*, Strauss offers a complete critique of historicism as it emerges in the works of Hegel, Marx, and Heidegger. Many believe that Strauss also found historicism in Edmund Burke, Tocqueville, Augustine, and John Stuart Mill. Although it is largely disputed whether Strauss himself was a historicist, he often indicated that historicism grew out of and against Christianity and was a threat to civic participation, belief in human agency, religious pluralism, and, most controversially, an accurate understanding of the classical philosophers and religious prophets themselves. Throughout his work, he warns that historicism, and the understanding of progress that results from it, expose us to tyranny, totalitarianism, and democratic extremism. In a collection of his works by Kenneth Hart entitled *Jewish Philosophy and the Crisis of Modernity*, he argues that Islam, traditional Judaism, and ancient Greece, share a concern for sacred law that makes them especially susceptible to historicism, and therefore to tyranny
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# Human sexual activity
`{{Close relationships}}`{=mediawiki} **Human sexual activity**, **human sexual practice** or **human sexual behaviour** is the manner in which humans experience and express their sexuality. People engage in a variety of sexual acts, ranging from activities done alone (e.g., masturbation) to acts with another person (e.g., sexual intercourse, non-penetrative sex, oral sex, etc.) or persons (e.g., orgy) in varying patterns of frequency, for a wide variety of reasons. Sexual activity usually results in sexual arousal and physiological changes in the aroused person, some of which are pronounced while others are more subtle. Sexual activity may also include conduct and activities which are intended to arouse the sexual interest of another or enhance the sex life of another, such as strategies to find or attract partners (courtship and display behaviour), or personal interactions between individuals (for instance, foreplay or BDSM). Sexual activity may follow sexual arousal.
Human sexual activity has sociological, cognitive, emotional, behavioural and biological aspects. It involves personal bonding, sharing emotions, the physiology of the reproductive system, sex drive, sexual intercourse, and sexual behaviour in all its forms.
In some cultures, sexual activity is considered acceptable only within marriage, while premarital and extramarital sex are taboo. Some sexual activities are illegal either universally or in some countries or subnational jurisdictions, while some are considered contrary to the norms of certain societies or cultures. Two examples that are criminal offences in most jurisdictions are sexual assault and sexual activity with a person below the local age of consent.
## Types
Sexual activity can be classified in a number of ways. The practices may be preceded by or consist solely of foreplay. Acts involving one person (autoeroticism) may include sexual fantasy or masturbation. If two people are involved, they may engage in vaginal sex, anal sex, oral sex or manual sex. Penetrative sex between two people may be described as sexual intercourse, but definitions vary. If there are more than two participants in a sex act, it may be referred to as group sex. Autoerotic sexual activity can involve use of dildos, vibrators, butt plugs, and other sex toys, though these devices can also be used with a partner.
Sexual activity can be classified into the gender and sexual orientation of the participants, as well as by the relationship of the participants. The relationships can be ones of marriage, intimate partners, casual sex partners or anonymous. Sexual activity can be regarded as conventional or as alternative, involving, for example, fetishism or BDSM activities.
Fetishism can take many forms, including the desire for certain body parts (partialism) such as breasts, navels, or feet. The object of desire can be shoes, boots, lingerie, clothing, leather or rubber items. Some non-conventional autoerotic practices can be dangerous. These include autoerotic asphyxiation and self-bondage. The potential for injury or even death that exists while engaging in the partnered versions of these fetishes (choking and bondage, respectively) becomes drastically increased in the autoerotic case due to the isolation and lack of assistance in the event of a problem.
Sexual activity that is consensual is sexual activity in which both or all participants agree to take part and are of the age that they can consent. If sexual activity takes place under force or duress, it is considered rape or another form of sexual assault. In different cultures and countries, various sexual activities may be lawful or illegal in regards to the age, gender, marital status or other factors of the participants, or otherwise contrary to social norms or generally accepted sexual morals.
## Mating strategies {#mating_strategies}
In evolutionary psychology and behavioral ecology, human mating strategies are a set of behaviors used by individuals to attract, select, and retain mates. Mating strategies overlap with reproductive strategies, which encompass a broader set of behaviors involving the timing of reproduction and the trade-off between quantity and quality of offspring (see life history theory).
Relative to other animals, human mating strategies are unique in their relationship with cultural variables such as the institution of marriage. Humans may seek out individuals with the intention of forming a long-term intimate relationship, marriage, casual relationship, or friendship. The human desire for companionship is one of the strongest human drives. It is an innate feature of human nature, and may be related to the sex drive. The human mating process encompasses the social and cultural processes whereby one person may meet another to assess suitability, the courtship process and the process of forming an interpersonal relationship. Commonalities, however, can be found between humans and nonhuman animals in mating behavior.
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# Human sexual activity
## Stages of physiological arousal during sexual stimulation {#stages_of_physiological_arousal_during_sexual_stimulation}
The physiological responses during sexual stimulation are fairly similar for both men and women and there are four phases.
- During the excitement phase, muscle tension and blood flow increase in and around the sexual organs, heart and respiration increase and blood pressure rises. Men and women experience a \"sex flush\" on the skin of the upper body and face. For women, the vagina becomes lubricated and the clitoris engorges. For men, the penis becomes erect.
- During the plateau phase, heart rate and muscle tension increase further. A man\'s urinary bladder closes to prevent urine from mixing with semen. A woman\'s clitoris may withdraw slightly and there is more lubrication, outer swelling and muscles tighten and reduction of diameter.
- During the orgasm phase, breathing becomes extremely rapid and the pelvic muscles begin a series of rhythmic contractions. Both men and women experience quick cycles of muscle contraction of lower pelvic muscles and women often experience uterine and vaginal contractions; this experience can be described as intensely pleasurable, but roughly 15% of women never experience orgasm, and half report having faked it. A large genetic component is associated with how often women experience orgasm.
- During the resolution phase, muscles relax, blood pressure drops, and the body returns to its resting state. Though generally reported that women do not experience a refractory period and thus can experience an additional orgasm, or multiple orgasms soon after the first, some sources state that both men and women experience a refractory period because women may also experience a period after orgasm in which further sexual stimulation does not produce excitement. This period may last from minutes to days and is typically longer for men than women.
Sexual dysfunction is the inability to react emotionally or physically to sexual stimulation in a way projected of the average healthy person; it can affect different stages in the sexual response cycles, which are desire, excitement and orgasm. In the media, sexual dysfunction is often associated with men, but in actuality, it is more commonly observed in females (43 percent) than males (31 percent).
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# Human sexual activity
## Psychological aspects {#psychological_aspects}
Sexual activity can lower blood pressure and overall stress levels. It serves to release tension, elevate mood, and possibly create a profound sense of relaxation, especially in the postcoital period. From a biochemical perspective, sex causes the release of oxytocin and endorphins and boosts the immune system.
### Motivations
People engage in sexual activity for any of a multitude of possible reasons. Although the primary evolutionary purpose of sexual activity is reproduction, research on college students suggested that people have sex for four general reasons: *physical attraction*, as a *means to an end*, to increase *emotional connection*, and to *alleviate insecurity*.
Most people engage in sexual activity because of pleasure they derive from the arousal of their sexuality, especially if they can achieve orgasm. Sexual arousal can also be experienced from foreplay and flirting, and from fetish or BDSM activities, or other erotic activities. Most commonly, people engage in sexual activity because of the sexual desire generated by a person to whom they feel sexual attraction; but they may engage in sexual activity for the physical satisfaction they achieve in the absence of attraction for another, as in the case of casual or social sex. At times, a person may engage in a sexual activity solely for the sexual pleasure of their partner, such as because of an obligation they may have to the partner or because of love, sympathy or pity they may feel for the partner.
A person may engage in sexual activity for purely monetary considerations, or to obtain some advantage from either the partner or the activity. A man and woman may engage in sexual intercourse with the objective of conception. Some people engage in hate sex which occurs between two people who strongly dislike or annoy each other. It is related to the idea that opposition between two people can heighten sexual tension, attraction and interest.
#### Self-determination theory {#self_determination_theory}
Research has found that people also engage in sexual activity for reasons associated with self-determination theory. The self-determination theory can be applied to a sexual relationship when the participants have positive feelings associated with the relationship, not from the social pressures of their partner, but *intrinsically motivated* to engage in intercourse on their own accord. These participants do not feel guilty or coerced into the partnership. Researchers have proposed the model of self-determined sexual motivation. The purpose of this model is to connect self-determination and sexual motivation. This model has helped to explain how people are sexually motivated when involved in self-determined dating relationships. This model also links the positive outcomes, (satisfying the need for autonomy, competence, and relatedness) gained from sexual motivations.
According to the completed research associated with this model, it was found that people of both sexes who engaged in sexual activity for self-determined motivation had more positive psychological well-being. While engaging in sexual activity for self-determined reasons, the participants also had a higher need for fulfillment. When this need was satisfied, they felt better about themselves. This was correlated with greater closeness to their partner and higher overall satisfaction in their relationship. Though both sexes engaged in sexual activity for self-determined reasons, there were some differences found between males and females. It was concluded that females had more motivation than males to engage in sexual activity for self-determined reasons. Females also had higher satisfaction and relationship quality than males did from the sexual activity. Overall, research concluded that psychological well-being, sexual motivation, and sexual satisfaction were all positively correlated when dating couples partook in sexual activity for self-determined reasons.
#### Human connection {#human_connection}
According to Havelock Ellis, a fulfilling marriage is one that possesses both the \"art of love\" and \"science of procreation\". `{{Blockquote|text=Without the factor of mutual love the proper conditions for procreation cannot exist; without the factor of procreation the sexual union, however beautiful and sacred a relationship it may in itself be, remains, in essence, a private relationship, incomplete as a marriage and without public significance.|author=Havelock Ellis (1921)|title=Studies in the Psychology of Sex, Volume VI, Sex in Relation to Society, p. 508}}`{=mediawiki} Ellis states that a genuine and mutual connection to the other is needed for proper sexual intercourse. However, if the marriage lacks procreation, the relationship may lack understanding between partners and become superficial. Love is believed to have a nurturing aspect and is not wholly determined by instinct. \"They believe, no art of love to be either learnt or taught; it comes by nature. Nothing could be further from the truth, most of all as regards civilized man.\" The role of love has a direct impact on proper sexual intercourse, which shares many similarities to the principles of marriage and thus a fulfilling happiness beyond the act of procreation. `{{Blockquote|text=The art of love certainly includes such primary facts of sexual hygiene, but it involves also the whole erotic discipline of marriage, and that is why its significance is so great, for the welfare and happiness of the individual, for the stability of sexual unions, and indirectly for the race, since the art of love is ultimately the art of attaining the right conditions for procreation.|author=Havelock Ellis (1921)|title=Studies in the Psychology of Sex, Volume VI, Sex in Relation to Society, p. 511}}`{=mediawiki}
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# Human sexual activity
## Frequency
The frequency of sexual activity might range from zero to 15 or 20 times a week. Frequency of intercourse tends to decline with age. Some post-menopausal women experience decline in frequency of sexual intercourse, while others do not. According to the Kinsey Institute, the average frequency of sexual intercourse in the US for individuals with partners is 112 times per year (age 18--29), 86 times per year (age 30--39), and 69 times per year (age 40--49). The rate of sexual activity has been declining in the 21st century, a phenomenon that has been described as a sex recession.
### Adolescents
The age at which adolescents become sexually active varies considerably between different cultures and times. (See Prevalence of virginity.) The first sexual act of a child or adolescent is sometimes referred to as the sexualization of the child, and may be considered a milestone or a change of status, as the loss of virginity or innocence. Youth are legally free to have intercourse after they reach the age of consent.
A 1999 survey of students indicated that approximately 40% of ninth graders across the United States report having had sexual intercourse. This figure rises with each grade. Males are more sexually active than females at each of the grade levels surveyed. Sexual activity of young adolescents differs in ethnicity as well. A higher percentage of African American and Hispanic adolescents are more sexually active than white adolescents.
Research on sexual frequency has also been conducted solely on female adolescents who engage in sexual activity. Female adolescents tended to engage in more sexual activity due to positive mood. In female teenagers, engaging in sexual activity was directly positively correlated with being older, greater sexual activity in the previous week or prior day, and more positive mood the previous day or the same day as the sexual activity occurred. Decreased sexual activity was associated with prior or same-day negative mood or menstruation.
Although opinions differ, researchers suggest that sexual activity is an essential part of humans, and that teenagers need to experience sex. According to a study, sexual experiences help teenagers understand pleasure and satisfaction. In relation to hedonic and eudaimonic well-being, it stated that teenagers can positively benefit from sexual activity. The cross-sectional study was conducted in 2008 and 2009 at a rural upstate New York community. Teenagers who had their first sexual experience at age 16 revealed a higher well-being than those who were sexually inexperienced or who became sexually active at age 17. Furthermore, teenagers who had their first sexual experience at age 15 or younger, or who had many sexual partners were not negatively affected and did not have associated lower well-being.
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# Human sexual activity
## Health and safety {#health_and_safety}
Sexual activity is an innately physiological function, but like other physical activity, it comes with risks. There are four main types of risks that may arise from sexual activity: unwanted pregnancy, contracting a sexually transmitted infection (STI), physical injury, and psychological injury.
### Unwanted pregnancy {#unwanted_pregnancy}
Any sexual activity that involves the introduction of semen into a woman\'s vagina, such as during sexual intercourse, or contact of semen with her vulva, may result in a pregnancy. To reduce the risk of unintended pregnancies, some people who engage in penile--vaginal sex may use contraception, such as birth control pills, a condom, diaphragms, spermicides, hormonal contraception or sterilization. The effectiveness of the various contraceptive methods in avoiding pregnancy varies considerably, and depends on the method rather than the user.
### Sexually transmitted infections {#sexually_transmitted_infections}
Sexual activity that involves skin-to-skin contact, exposure to an infected person\'s bodily fluids or mucous membranes carries the risk of contracting a sexually transmitted infection. People may not be able to detect that their sexual partner has one or more STIs, for example if they are asymptomatic (show no symptoms). The risk of STIs can be reduced by safe sex practices, such as using condoms. Both partners may opt to be tested for STIs before engaging in sex. The exchange of body fluids is not necessary to contract an infestation of crab lice. Crab lice typically are found attached to hair in the pubic area but sometimes are found on coarse hair elsewhere on the body (for example, eyebrows, eyelashes, beard, mustache, chest, armpits, etc.). Pubic lice infestations (pthiriasis) are spread through direct contact with someone who is infested with the louse.
Some STIs like HIV/AIDS can also be contracted by using IV drug needles after their use by an infected person, as well as through childbirth or breastfeeding.
### Aging
Factors such as biological and psychological factors, diseases, mental conditions, boredom with the relationship, and widowhood have been found to contribute to a decrease in sexual interest and activity in old age, but older age does not eliminate the ability to enjoy sexual activity.
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# Human sexual activity
## Orientations and society {#orientations_and_society}
### Heterosexuality
Heterosexuality is the romantic or sexual attraction to the opposite sex. Heterosexual practices are institutionally privileged in most countries. In some countries, mostly those where religion has a strong influence on social policy, marriage laws serve the purpose of encouraging people to have sex only within marriage. Sodomy laws have been used to discourage same-sex sexual practices, but they may also affect opposite-sex sexual practices. Laws also ban adults from committing sexual abuse, committing sexual acts with anyone under an age of consent, performing sexual activities in public, and engaging in sexual activities for money (prostitution). Though these laws cover both same-sex and opposite-sex sexual activities, they may differ in regard to punishment, and may be more frequently (or exclusively) enforced on those who engage in same-sex sexual activities.
Different-sex sexual practices may be monogamous, serially monogamous, or polyamorous, and, depending on the definition of sexual practice, abstinent or autoerotic (including masturbation). Additionally, different religious and political movements have tried to influence or control changes in sexual practices including courting and marriage, though in most countries changes occur at a slow rate.
### Homosexuality
Homosexuality is the romantic or sexual attraction to the same sex. People with a homosexual orientation can express their sexuality in a variety of ways, and may or may not express it in their behaviors. Research indicates that many gay men and lesbians want, and succeed in having, committed and durable relationships. For example, survey data indicate that between 40% and 60% of gay men and between 45% and 80% of lesbians are currently involved in a romantic relationship.
It is possible for a person whose sexual identity is mainly heterosexual to engage in sexual acts with people of the same sex. Gay and lesbian people who pretend to be heterosexual are often referred to as being closeted (hiding their sexuality in \"the closet\"). \"Closet case\" is a derogatory term used to refer to people who hide their sexuality. Making that orientation public can be called \"coming out of the closet\" in the case of voluntary disclosure or \"outing\" in the case of disclosure by others against the subject\'s wishes (or without their knowledge). Among some communities (called \"men on the DL\" or \"down-low\"), same-sex sexual behavior is sometimes viewed as solely for physical pleasure. Men who have sex with men, as well as women who have sex with women, or men on the \"down-low\" may engage in sex acts with members of the same sex while continuing sexual and romantic relationships with the opposite sex.
People who engage exclusively in same-sex sexual practices may not identify themselves as gay or lesbian. In sex-segregated environments, individuals may seek relationships with others of their own gender (known as situational homosexuality). In other cases, some people may experiment or explore their sexuality with same (or different) sex sexual activity before defining their sexual identity. Despite stereotypes and common misconceptions, there are no forms of sexual acts exclusive to same-sex sexual behavior that cannot also be found in opposite-sex sexual behavior, except those involving the meeting of the genitalia between same-sex partners -- tribadism (generally vulva-to-vulva rubbing) and frot (generally penis-to-penis rubbing).
### Bisexuality and pansexuality {#bisexuality_and_pansexuality}
People who have a romantic or sexual attraction to both sexes are referred to as bisexual. People who have a distinct but not exclusive preference for one sex/gender over the other may also identify themselves as bisexual. Like gay and lesbian individuals, bisexual people who pretend to be heterosexual are often referred to as being closeted.
Pansexuality (also referred to as omnisexuality) may or may not be subsumed under bisexuality, with some sources stating that bisexuality encompasses sexual or romantic attraction to all gender identities. Pansexuality is characterized by the potential for aesthetic attraction, romantic love, or sexual desire towards people without regard for their gender identity or biological sex. Some pansexuals suggest that they are gender-blind; that gender and sex are insignificant or irrelevant in determining whether they will be sexually attracted to others. As defined in the *Oxford English Dictionary,* pansexuality \"encompasses all kinds of sexuality; not limited or inhibited in sexual choice with regards to gender or practice\".
### Avoidance of inbreeding {#avoidance_of_inbreeding}
Although the main adaptive function of human sexual activity is reproduction, human sexual activity also includes the adaptive constraint of avoiding close inbreeding, since inbreeding can have deleterious effects on progeny. Charles Darwin, who was married to his first cousin Emma Wedgwood, considered that the ill health that plagued his family was a consequence of inbreeding. In general, inbreeding between individuals who are closely genetically related leads to the expression of deleterious recessive mutations. The avoidance of inbreeding as a constraint on human sexual activity is apparent in the near universal cultural inhibitions in human societies of sexual activity between closely related individuals. Human outcrossing sexual activity provides the adaptive benefit of the masking of expression of deleterious recessive mutations.
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# Human sexual activity
## Other social aspects {#other_social_aspects}
### General attitudes {#general_attitudes}
Alex Comfort and others propose three potential social aspects of sexual intercourse in humans, which are not mutually exclusive: reproductive, relational, and recreational. The development of the contraceptive pill and other highly effective forms of contraception in the mid- and late 20th century has increased people\'s ability to segregate these three functions, which still overlap a great deal and in complex patterns. For example: A fertile couple may have intercourse while using contraception to experience sexual pleasure (recreational) and also as a means of emotional intimacy (relational), thus deepening their bonding, making their relationship more stable and more capable of sustaining children in the future (deferred reproductive). This same couple may emphasize different aspects of intercourse on different occasions, being playful during one episode of intercourse (recreational), experiencing deep emotional connection on another occasion (relational), and later, after discontinuing contraception, seeking to achieve pregnancy (reproductive, or more likely reproductive and relational).
### Religious and ethical {#religious_and_ethical}
Human sexual activity is generally influenced by social rules that are culturally specific and vary widely.
Sexual ethics, morals, and norms relate to issues including deception/honesty, legality, fidelity and consent. Some activities, known as sex crimes in some locations, are illegal in some jurisdictions, including those conducted between (or among) consenting and competent adults (examples include sodomy law and adult--adult incest).
Some people who are in a relationship but want to hide polygamous activity (possibly of opposite sexual orientation) from their partner, may solicit consensual sexual activity with others through personal contacts, online chat rooms, or, advertising in select media.
Swinging involves singles or partners in a committed relationship engaging in sexual activities with others as a recreational or social activity. The increasing popularity of swinging is regarded by some as arising from the upsurge in sexual activity during the sexual revolution of the 1960s.
Some people engage in various sexual activities as a business transaction. When this involves having sex with, or performing certain actual sexual acts for another person in exchange for money or something of value, it is called prostitution. Other aspects of the adult industry include phone sex operators, strip clubs, and pornography.
### Gender roles and the expression of sexuality {#gender_roles_and_the_expression_of_sexuality}
Social gender roles can influence sexual behavior as well as the reaction of individuals and communities to certain incidents; the World Health Organization states that, \"Sexual violence is also more likely to occur where beliefs in male sexual entitlement are strong, where gender roles are more rigid, and in countries experiencing high rates of other types of violence.\" Some societies, such as those where the concepts of family honor and female chastity are very strong, may practice violent control of female sexuality, through practices such as honor killings and female genital mutilation.
The relation between gender equality and sexual expression is recognized, and promotion of equity between men and women is crucial for attaining sexual and reproductive health, as stated by the UN International Conference on Population and Development Program of Action:
: \"Human sexuality and gender relations are closely interrelated and together affect the ability of men and women to achieve and maintain sexual health and manage their reproductive lives. Equal relationships between men and women in matters of sexual relations and reproduction, including full respect for the physical integrity of the human body, require mutual respect and willingness to accept responsibility for the consequences of sexual behaviour. Responsible sexual behaviour, sensitivity and equity in gender relations, particularly when instilled during the formative years, enhance and promote respectful and harmonious partnerships between men and women.\"
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# Human sexual activity
## BDSM
BDSM is a variety of erotic practices or roleplaying involving bondage, dominance and submission, sadomasochism, and other interpersonal dynamics. Given the wide range of practices, some of which may be engaged in by people who do not consider themselves as practicing BDSM, inclusion in the BDSM community or subculture usually being dependent on self-identification and shared experience. BDSM communities generally welcome anyone with a non-normative streak who identifies with the community; this may include cross-dressers, extreme body modification enthusiasts, animal players, latex or rubber aficionados, and others.
B/D (bondage and discipline) is a part of BDSM. Bondage includes the restraint of the body or mind. D/s means \"Dominant and submissive\". A Dominant is one who takes control of a person who wishes to surrender control and a submissive is one who surrenders control to a person who wishes to take control. S/M (sadism and masochism) is the other part of BDSM. A sadist is an individual who takes pleasure in the pain or humiliation of others and a masochist is an individual who takes pleasure from their own pain or humiliation.
Unlike the usual \"power neutral\" relationships and play styles commonly followed by couples, activities and relationships within a BDSM context are often characterized by the participants\' taking on complementary, but unequal roles; thus, the idea of informed consent of both the partners becomes essential. Participants who exert dominance (sexual or otherwise) over their partners are known as Dominants or Tops, while participants who take the passive, receiving, or obedient role are known as submissives or bottoms.
These terms are sometimes shortened so that a dominant person may be referred to as a \"Dom\" (a woman may choose to use the feminine \"Domme\") and a submissive may be referred to as a \"sub\". Individuals who can change between Top/Dominant and bottom/submissive roles -- whether from relationship to relationship or within a given relationship -- are known as *switches*. The precise definition of roles and self-identification is a common subject of debate within the community. In a 2013 study, researchers stated that BDSM is a sexual act where participants play role games, use restraint, use power exchange, use suppression and pain is sometimes involved depending on individual(s). The study serves to challenge the widespread notion that BDSM could be in some way linked to psychopathology. According to the findings, one who participates in BDSM may have greater strength socially and mentally as well as greater independence than those who do not practice BDSM. It suggests that people who participate in BDSM play have higher subjective well-being, and that this might be because BDSM play requires extensive communication. Before any act occurs, the partners must discuss their agreement of their relationship. They discuss how long the play will last, the intensity, their actions, what each participant needs or desires, and what, if any, sexual activities may be included. All acts must be consensual and pleasurable to both parties.
In a 2015 study, interviewed BDSM participants have mentioned that the activities have helped to create higher levels of connection, intimacy, trust and communication between partners. The study suggests that Dominants and submissives exchange control for each other\'s pleasure and to satisfy a need. The participants have remarked that they enjoy pleasing their partner in any way they can and many surveyed have felt that this is one of the best things about BDSM. It gives a submissive pleasure to do things in general for their Dominant while a Dominant enjoys making their encounters all about their submissive and enjoy doing things that makes their submissive happy. The findings indicate that the surveyed submissives and Dominants found BDSM makes play more pleasurable and fun. The participants have also mentioned improvements in their personal growth, romantic relationships, sense of community and self, the dominant\'s confidence, and their coping with everyday things by giving them a psychological release.
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# Human sexual activity
## Legal issues {#legal_issues}
There are many laws and social customs which prohibit, or in some way affect sexual activities. These laws and customs vary from country to country, and have varied over time. They cover, for example, a prohibition to non-consensual sex, to sex outside marriage, to sexual activity in public, besides many others. Many of these restrictions are non-controversial, but some have been the subject of public debate.
Most societies consider it a serious crime to force someone to engage in sexual acts or to engage in sexual activity with someone who does not consent. This is called sexual assault, and if sexual penetration occurs it is called rape, the most serious kind of sexual assault. The details of this distinction may vary among different legal jurisdictions. Also, what constitutes effective consent in sexual matters varies from culture to culture and is frequently debated. Laws regulating the minimum age at which a person can consent to have sex (age of consent) are frequently the subject of debate, as is adolescent sexual behavior in general. Some societies have forced marriage, where consent may not be required.
### Same-sex laws {#same_sex_laws}
Many locales have laws that limit or prohibit same-sex sexual activity.
### Sex outside marriage {#sex_outside_marriage}
In the West, sex before marriage is not illegal. There are social taboos and many religions condemn pre-marital sex. In many Muslim countries, such as Saudi Arabia, Pakistan, Afghanistan, Iran, Kuwait, Maldives, Morocco, Oman, Mauritania, United Arab Emirates, Sudan, and Yemen, any form of sexual activity outside marriage is illegal. Those found guilty, especially women, may be forced to wed the sexual partner, may be publicly beaten, or may be stoned to death. In many African and native tribes, sexual activity is not viewed as a privilege or right of a married couple, but rather as the unification of bodies and is thus not frowned upon.
Other studies have analyzed the changing attitudes about sex that American adolescents have outside marriage. Adolescents were asked how they felt about oral and vaginal sex in relation to their health, social, and emotional well-being. Overall, teenagers felt that oral sex was viewed as more socially positive amongst their demographic. Results stated that teenagers believed that oral sex for dating and non-dating adolescents was less threatening to their overall values and beliefs than vaginal sex was. When asked, teenagers who participated in the research viewed oral sex as more acceptable to their peers, and their personal values than vaginal sex.
### Minimum age of sexual activity (age of consent) {#minimum_age_of_sexual_activity_age_of_consent}
The laws of each jurisdiction set the minimum age at which a young person is allowed to engage in sexual activity. This age of consent is typically between 14 and 18 years, but laws vary. In many jurisdictions, age of consent is a person\'s mental or functional age. As a result, those above the set age of consent may still be considered unable to legally consent due to mental immaturity. Many jurisdictions regard any sexual activity by an adult involving a child as child sexual abuse.
Age of consent may vary by the type of sexual act, the sex of the actors, or other restrictions such as abuse of a position of trust. Some jurisdictions also make allowances for young people engaged in sexual acts with each other.
### Incestuous relationships {#incestuous_relationships}
Most jurisdictions prohibit sexual activity between certain close relatives. These laws vary to some extent; such acts are called incestuous.
Incest laws may involve restrictions on marriage rights, which also vary between jurisdictions. When incest involves an adult and a child, it is considered to be a form of child sexual abuse.
### Sexual abuse {#sexual_abuse}
Non-consensual sexual activity or subjecting an unwilling person to witnessing a sexual activity are forms of sexual abuse, as well as (in many countries) certain non-consensual paraphilias such as frotteurism, telephone scatophilia (indecent phonecalls), and non-consensual exhibitionism and voyeurism (known as \"indecent exposure\" and \"peeping tom\" respectively).
### Prostitution and survival sex {#prostitution_and_survival_sex}
People sometimes exchange sex for money or access to other resources. Work takes place under many varied circumstances. The person who receives payment for sexual services is known as a prostitute and the person who receives such services is referred to by a multitude of terms, such as being a client. Prostitution is one of the branches of the sex industry. The legal status of prostitution varies from country to country, from being a punishable crime to a regulated profession. Estimates place the annual revenue generated from the global prostitution industry to be over \$100 billion. Prostitution is sometimes referred to as \"the world\'s oldest profession\". Prostitution may be a voluntary individual activity or facilitated or forced by pimps.
Survival sex is a form of prostitution engaged in by people in need, usually when homeless or otherwise disadvantaged people trade sex for food, a place to sleep, or other basic needs, or for drugs. The term is used by sex trade and poverty researchers and aid workers
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# Hydraulic ram
A **hydraulic ram pump**, **ram pump**, or **hydram** is a cyclic water pump powered by hydropower. It takes in water at one \"hydraulic head\" (pressure) and flow rate, and outputs water at a higher hydraulic head and lower flow rate. The device uses the water hammer effect to develop pressure that allows a portion of the input water that powers the pump to be lifted to a point higher than where the water originally started. The hydraulic ram is sometimes used in remote areas, where there is both a source of low-head hydropower and a need for pumping water to a destination higher in elevation than the source. In this situation, the ram is often useful, since it requires no outside source of power other than the kinetic energy of flowing water.
## History
In 1772, John Whitehurst of Cheshire, England, invented a manually controlled precursor of the hydraulic ram called the \"pulsation engine\" and installed the first one at Oulton, Cheshire to raise water to a height of 4.9 m. In 1783, he installed another in Ireland. He did not patent it, and details are obscure, but it is known to have had an air vessel.
The first self-acting ram pump was invented by the Frenchman Joseph Michel Montgolfier (best known as a co-inventor of the hot air balloon) in 1796 for raising water in his paper mill at Voiron. His friend Matthew Boulton took out a British patent on his behalf in 1797. The sons of Montgolfier obtained a British patent for an improved version in 1816, and this was acquired, together with Whitehurst\'s design, in 1820 by Josiah Easton, a Somerset-born engineer who had just moved to London.
Easton\'s firm, inherited by his son James (1796--1871), grew during the nineteenth century to become one of the more important engineering manufacturers in England, with a large works at Erith, Kent. They specialised in water supply and sewerage systems worldwide, as well as land drainage projects. Eastons had a good business supplying rams for water supply purposes to large country houses, farms, and village communities. Some of their installations still survived as of 2004, one such example being at the hamlet of Toller Whelme, in Dorset. Until about 1958 when the mains water arrived, the hamlet of East Dundry just south of Bristol had three working rams -- their noisy \"thump\" every minute or so resonated through the valley night and day: these rams served farms that needed much water for their dairy herds.
The firm closed in 1909, but the ram business was continued by James R. Easton. In 1929, it was acquired by Green & Carter of Winchester, Hampshire, who were engaged in the manufacturing and installation of Vulcan and Vacher Rams.
The first US patent was issued to Joseph Cerneau (or Curneau) and Stephen (Étienne) S. Hallet (1755-1825) in 1809.See:
- *Executive Documents of the House of Representatives at the Second Session of the Twenty-first Congress*, vol. 2 (Washington, D.C.: Duff Green, 1831), [pages 328 and 332](https://books.google.com/books?id=YYlHAQAAIAAJ&pg=RA4-PA1828).
- Letter from Stephen S. Hallet to U.S. President James Madison, September 9, 1808. Available on-line at: [U.S. National Archives](https://founders.archives.gov/documents/Madison/03-01-02-0404).
US interest in hydraulic rams picked up around 1840, as further patents were issued and domestic companies started offering rams for sale. Toward the end of the 19th century, interest waned as electricity and electric pumps became widely available.
Priestly\'s Hydraulic Ram, built in 1890 in Idaho, was a \"marvelous\" invention, apparently independent, which lifted water 110 ft to provide irrigation. The ram survives and is listed on the U.S. National Register of Historic Places.
By the end of the twentieth century, interest in hydraulic rams has revived, due to the needs of sustainable technology in developing countries, and energy conservation in developed ones. An example is Aid Foundation International in the Philippines, who won an Ashden Award for their work developing ram pumps that could be easily maintained for use in remote villages. The hydraulic ram principle has been used in some proposals for exploiting wave power, one of which was discussed as long ago as 1931 by Hanns Günther in his book *In hundert Jahren*.
Some later ram designs in the UK called **compound rams** were designed to pump treated water using an untreated drive water source, which overcomes some of the problems of having drinking water sourced from an open stream.
In 1996 English engineer Frederick Philip Selwyn patented a more compact hydraulic ram pump where the waste valve used the venturi effect and was arranged concentrically around the input pipe. Initially patented as a fluid pressure amplifier due to its different design, it is currently sold as the \"Papa Pump\". Additionally to this a large scale version named the \"Venturo Pump\" is also being manufactured.
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# Hydraulic ram
## Construction and principle of operation {#construction_and_principle_of_operation}
A traditional hydraulic ram has only two moving parts, a spring or weight loaded \"waste\" valve sometimes known as the \"clack\" valve and a \"delivery\" check valve, making it cheap to build, easy to maintain, and very reliable.
Priestly\'s Hydraulic Ram, described in detail in the 1947 Encyclopedia Britannica, has no moving parts.
### Sequence of operation {#sequence_of_operation}
A simplified hydraulic ram is shown in Figure 2. Initially, the waste valve \[4\] is open (i.e. lowered) because of its own weight, and the delivery valve \[5\] is closed under the pressure caused by the water column from the outlet \[3\]. The water in the inlet pipe \[1\] starts to flow under the force of gravity and picks up speed and kinetic energy until the increasing drag force lifts the waste valve\'s weight and closes it. The momentum of the water flow in the inlet pipe against the now closed waste valve causes a water hammer that raises the pressure in the pump beyond the pressure caused by the water column pressing down from the outlet. This pressure differential now opens the delivery valve \[5\], and forces some water to flow into the delivery pipe \[3\]. Because this water is being forced uphill through the delivery pipe farther than it is falling downhill from the source, the flow slows; when the flow reverses, the delivery check valve \[5\] closes. Meanwhile, the water hammer from the closing of the waste valve also produces a pressure pulse which propagates back up the inlet pipe to the source where it converts to a suction pulse that propagates back down the inlet pipe. This suction pulse, with the weight or spring on the valve, pulls the waste valve back open and allows the process to begin again.
A pressure vessel \[6\] containing air cushions the hydraulic pressure shock when the waste valve closes, and it also improves the pumping efficiency by allowing a more constant flow through the delivery pipe. Although the pump could in theory work without it, the efficiency would drop drastically and the pump would be subject to extraordinary stresses that could shorten its life considerably. One problem is that the pressurized air will gradually dissolve into the water until none remains. One solution to this problem is to have the air separated from the water by an elastic diaphragm (similar to an expansion tank); however, this solution can be problematic in developing countries where replacements are difficult to procure. Another solution is a snifting valve installed close to the drive side of the delivery valve. This automatically inhales a small amount of air each time the delivery valve shuts and the partial vacuum develops. Another solution is to insert an inner tube of a car or bicycle tire into the pressure vessel with some air in it and the valve closed. This tube is in effect the same as the diaphragm, but it is implemented with more widely available materials. The air in the tube cushions the shock of the water the same as the air in other configurations does.
### Efficiency
A typical energy efficiency is 60%, but up to 80% is possible. This should not be confused with the volumetric efficiency, which relates the volume of water delivered to total water taken from the source. The portion of water available at the delivery pipe will be reduced by the ratio of the delivery head to the supply head. Thus if the source is 2 m above the ram and the water is lifted to 10 m above the ram, only 20% of the supplied water can be available, the other 80% being spilled via the waste valve. These ratios assume 100% energy efficiency. Actual water delivered will be further reduced by the energy efficiency factor. In the above example, if the energy efficiency is 70%, the water delivered will be 70% of 20%, i.e. 14%. Assuming a 2-to-1 supply-head-to-delivery-head ratio and 70% efficiency, the delivered water would be 70% of 50%, i.e. 35%. Very high ratios of delivery to supply head usually result in lowered energy efficiency. Suppliers of rams often provide tables giving expected volume ratios based on actual tests.
### Drive and delivery pipe design {#drive_and_delivery_pipe_design}
Since both efficiency and reliable cycling depend on water hammer effects, the drive pipe design is important. It should be between 3 and 7 times longer than the vertical distance between the source and the ram. Commercial rams may have an input fitting designed to accommodate this optimum slope. The diameter of the supply pipe would normally match the diameter of the input fitting on the ram, which in turn is based on its pumping capacity. The drive pipe should be of constant diameter and material, and should be as straight as possible. Where bends are necessary, they should be smooth, large diameter curves. Even a large spiral is allowed, but elbows are to be avoided. PVC will work in some installations, but steel pipe is preferred, although much more expensive. If valves are used they should be a free flow type such as a ball valve or gate valve.
The delivery pipe is much less critical since the pressure vessel prevents water hammer effects from traveling up it. Its overall design would be determined by the allowable pressure drop based on the expected flow. Typically the pipe size will be about half that of the supply pipe, but for very long runs a larger size may be indicated. PVC pipe and any necessary valves are not a problem.
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# Hydraulic ram
## Construction and principle of operation {#construction_and_principle_of_operation}
### Starting operation {#starting_operation}
A ram newly placed into operation or which has stopped cycling should start automatically if the waste valve weight or spring pressure is adjusted correctly, but it can be restarted as follows: If the waste valve is in the raised (closed) position, it must be pushed down manually into the open position and released. If the flow is sufficient, it will then cycle at least once. If it does not continue to cycle, it must be pushed down repeatedly until it cycles continuously on its own, usually after three or four manual cycles. If the ram stops with the waste valve in the down (open) position it must be lifted manually and kept up for as long as necessary for the supply pipe to fill with water and for any air bubbles to travel up the pipe to the source. This may take some time, depending on supply pipe length and diameter. Then it can be started manually by pushing it down a few times as described above. Having a valve on the delivery pipe at the ram makes starting easier. Closing the valve until the ram starts cycling, then gradually opening it to fill the delivery pipe. If opened too quickly it will stop the cycle. Once the delivery pipe is full the valve can be left open.
### Common operational problems {#common_operational_problems}
Failure to deliver sufficient water may be due to improper adjustment of the waste valve, having too little air in the pressure vessel, or simply attempting to raise the water higher than the level of which the ram is capable.
The ram may be damaged by freezing in winter, or loss of air in the pressure vessel leading to excess stress on the ram parts. These failures will require welding or other repair methods and perhaps parts replacement.
It is not uncommon for an operating ram to require occasional restarts. The cycling may stop due to poor adjustment of the waste valve, or insufficient water flow at the source. Air can enter if the supply water level is not at least a few inches above the input end of the supply pipe. Other problems are blockage of the valves with debris, or improper installation, such as using a supply pipe of non-uniform diameter or material, having sharp bends or a rough interior, or one that is too long or short for the drop, or is made of an insufficiently rigid material. A PVC supply pipe will work in some installations but a steel pipe is better
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# Huygens–Fresnel principle
The **Huygens--Fresnel principle** (named after Dutch physicist Christiaan Huygens and French physicist Augustin-Jean Fresnel) states that every point on a wavefront is itself the source of spherical wavelets, and the secondary wavelets emanating from different points mutually interfere. The sum of these spherical wavelets forms a new wavefront. As such, the Huygens-Fresnel principle is a method of analysis applied to problems of luminous wave propagation both in the far-field limit and in near-field diffraction as well as reflection.
## History
In 1678, Huygens proposed that every point reached by a luminous disturbance becomes a source of a spherical wave. The sum of these secondary waves determines the form of the wave at any subsequent time; the overall procedure is referred to as **Huygens\' construction**. He assumed that the secondary waves travelled only in the \"forward\" direction, and it is not explained in the theory why this is the case. He was able to provide a qualitative explanation of linear and spherical wave propagation, and to derive the laws of reflection and refraction using this principle, but could not explain the deviations from rectilinear propagation that occur when light encounters edges, apertures and screens, commonly known as diffraction effects.
In 1818, Fresnel showed that Huygens\'s principle, together with his own principle of interference, could explain both the rectilinear propagation of light and also diffraction effects. To obtain agreement with experimental results, he had to include additional arbitrary assumptions about the phase and amplitude of the secondary waves, and also an obliquity factor. These assumptions have no obvious physical foundation, but led to predictions that agreed with many experimental observations, including the Poisson spot.
Poisson was a member of the French Academy, which reviewed Fresnel\'s work. He used Fresnel\'s theory to predict that a bright spot ought to appear in the center of the shadow of a small disc, and deduced from this that the theory was incorrect. However, Fran%C3%A7ois Arago, another member of the committee, performed the experiment and showed that the prediction was correct. This success was important evidence in favor of the wave theory of light over then predominant corpuscular theory.
In 1882, Gustav Kirchhoff analyzed Fresnel\'s theory in a rigorous mathematical formulation, as an approximate form of an integral theorem. Very few rigorous solutions to diffraction problems are known however, and most problems in optics are adequately treated using the Huygens-Fresnel principle.
In 1939 Edward Copson, extended the Huygens\' original principle to consider the polarization of light, which requires a vector potential, in contrast to the scalar potential of a simple ocean wave or sound wave.
In antenna theory and engineering, the reformulation of the Huygens--Fresnel principle for radiating current sources is known as surface equivalence principle.
Issues in Huygens-Fresnel theory continue to be of interest. In 1991, David A. B. Miller suggested that treating the source as a dipole (not the monopole assumed by Huygens) will cancel waves propagating in the reverse direction, making Huygens\' construction quantitatively correct. In 2021, Forrest L. Anderson showed that treating the wavelets as Dirac delta functions, summing and differentiating the summation is sufficient to cancel reverse propagating waves.
## Examples
### Refraction
The apparent change in direction of a light ray as it enters a sheet of glass at angle can be understood by the Huygens construction. Each point on the surface of the glass gives a secondary wavelet. These wavelets propagate at a slower velocity in the glass, making less forward progress than their counterparts in air. When the wavelets are summed, the resulting wavefront propagates at an angle to the direction of the wavefront in air.
In an inhomogeneous medium with a variable index of refraction, different parts of the wavefront propagate at different speeds. Consequently the wavefront bends around in the direction of higher index.
### Diffraction
## Huygens\' principle as a microscopic model {#huygens_principle_as_a_microscopic_model}
The Huygens--Fresnel principle provides a reasonable basis for understanding and predicting the classical wave propagation of light. However, there are limitations to the principle, namely the same approximations done for deriving the Kirchhoff\'s diffraction formula and the approximations of near field due to Fresnel. These can be summarized in the fact that the wavelength of light is much smaller than the dimensions of any optical components encountered.
Kirchhoff\'s diffraction formula provides a rigorous mathematical foundation for diffraction, based on the wave equation. The arbitrary assumptions made by Fresnel to arrive at the Huygens--Fresnel equation emerge automatically from the mathematics in this derivation.
A simple example of the operation of the principle can be seen when an open doorway connects two rooms and a sound is produced in a remote corner of one of them. A person in the other room will hear the sound as if it originated at the doorway. As far as the second room is concerned, the vibrating air in the doorway is the source of the sound.
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# Huygens–Fresnel principle
## Mathematical expression of the principle {#mathematical_expression_of_the_principle}
Consider the case of a point source located at a point **P**~0~, vibrating at a frequency *f*. The disturbance may be described by a complex variable *U*~0~ known as the complex amplitude. It produces a spherical wave with wavelength λ, wavenumber `{{math|''k'' {{=}}`{=mediawiki} 2*π*/*λ*}}. Within a constant of proportionality, the complex amplitude of the primary wave at the point **Q** located at a distance *r*~0~ from **P**~0~ is:
$$U(r_0) \propto \frac {U_0 e^{ikr_0}}{r_0}.$$
Note that magnitude decreases in inverse proportion to the distance traveled, and the phase changes as *k* times the distance traveled.
Using Huygens\'s theory and the principle of superposition of waves, the complex amplitude at a further point **P** is found by summing the contribution from each point on the sphere of radius *r*~0~. In order to get an agreement with experimental results, Fresnel found that the individual contributions from the secondary waves on the sphere had to be multiplied by a constant, −*i*/λ, and by an additional inclination factor, *K*(χ). The first assumption means that the secondary waves oscillate at a quarter of a cycle out of phase with respect to the primary wave and that the magnitude of the secondary waves are in a ratio of 1:λ to the primary wave. He also assumed that *K*(χ) had a maximum value when χ = 0, and was equal to zero when χ = π/2, where χ is the angle between the normal of the primary wavefront and the normal of the secondary wavefront. The complex amplitude at **P**, due to the contribution of secondary waves, is then given by:
$$U(P) = -\frac{i}{\lambda} U(r_0) \int_{S} \frac {e^{iks}}{s} K(\chi)\,dS$$
where *S* describes the surface of the sphere, and *s* is the distance between **Q** and **P**.
Fresnel used a zone construction method to find approximate values of *K* for the different zones, which enabled him to make predictions that were in agreement with experimental results. The integral theorem of Kirchhoff includes the basic idea of Huygens--Fresnel principle. Kirchhoff showed that in many cases, the theorem can be approximated to a simpler form that is equivalent to the formation of Fresnel\'s formulation.
For an aperture illumination consisting of a single expanding spherical wave, if the radius of the curvature of the wave is sufficiently large, Kirchhoff gave the following expression for *K*(χ):
$$~K(\chi )= \frac{1}{2}(1+\cos \chi)$$
*K* has a maximum value at χ = 0 as in the Huygens--Fresnel principle; however, *K* is not equal to zero at χ = π/2, but at χ = π.
Above derivation of *K*(χ) assumed that the diffracting aperture is illuminated by a single spherical wave with a sufficiently large radius of curvature. However, the principle holds for more general illuminations. An arbitrary illumination can be decomposed into a collection of point sources, and the linearity of the wave equation can be invoked to apply the principle to each point source individually. *K*(χ) can be generally expressed as:
$$~K(\chi )= \cos \chi$$
In this case, *K* satisfies the conditions stated above (maximum value at χ = 0 and zero at χ = π/2).
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# Huygens–Fresnel principle
## Generalized Huygens\' principle {#generalized_huygens_principle}
Many books and references -- e.g. (Greiner, 2002) and (Enders, 2009) - refer to the Generalized Huygens\' Principle using the definition in (Feynman, 1948).
Feynman defines the generalized principle in the following way: `{{bquote| "Actually Huygens’ principle is not correct in optics. It is replaced by Kirchoff’s [sic] modification which requires that both the amplitude and its derivative must be known on the adjacent surface. This is a consequence of the fact that the wave equation in optics is second order in the time. The wave equation of quantum mechanics is first order in the time; therefore, Huygens’ principle is correct for matter waves, action replacing time."}}`{=mediawiki}
This clarifies the fact that in this context the generalized principle reflects the linearity of quantum mechanics and the fact that the quantum mechanics equations are first order in time. Finally only in this case the superposition principle fully apply, i.e. the wave function in a point P can be expanded as a superposition of waves on a border surface enclosing P. Wave functions can be interpreted in the usual quantum mechanical sense as probability densities where the formalism of Green\'s functions and propagators apply. What is note-worthy is that this generalized principle is applicable for \"matter waves\" and not for light waves any more. The phase factor is now clarified as given by the action and there is no more confusion why the phases of the wavelets are different from those of the original wave and modified by the additional Fresnel parameters.
As per Greiner the generalized principle can be expressed for $t'>t$ in the form:
$$\psi'(\mathbf{x}',t') = i \int d^3x \, G(\mathbf{x}',t';\mathbf{x},t)\psi(\mathbf{x},t)$$ where *G* is the usual Green function that propagates in time the wave function $\psi$. This description resembles and generalize the initial Fresnel\'s formula of the classical model.
## Feynman\'s path integral and the modern photon wave function {#feynmans_path_integral_and_the_modern_photon_wave_function}
Huygens\' theory served as a fundamental explanation of the wave nature of light interference and was further developed by Fresnel and Young but did not fully resolve all observations such as the low-intensity double-slit experiment first performed by G. I. Taylor in 1909. It was not until the early and mid-1900s that quantum theory discussions, particularly the early discussions at the 1927 Brussels Solvay Conference, where Louis de Broglie proposed his de Broglie hypothesis that the photon is guided by a wave function.
The wave function presents a much different explanation of the observed light and dark bands in a double slit experiment. In this conception, the photon follows a path which is a probabilistic choice of one of many possible paths in the electromagnetic field. These probable paths form the pattern: in dark areas, no photons are landing, and in bright areas, many photons are landing. The set of possible photon paths is consistent with Richard Feynman\'s path integral theory, the paths determined by the surroundings: the photon\'s originating point (atom), the slit, and the screen and by tracking and summing phases. The wave function is a solution to this geometry. The wave function approach was further supported by additional double-slit experiments in Italy and Japan in the 1970s and 1980s with electrons.
## Quantum field theory {#quantum_field_theory}
Huygens\' principle can be seen as a consequence of the homogeneity of space---space is uniform in all locations. Any disturbance created in a sufficiently small region of homogeneous space (or in a homogeneous medium) propagates from that region in all geodesic directions. The waves produced by this disturbance, in turn, create disturbances in other regions, and so on. The superposition of all the waves results in the observed pattern of wave propagation.
Homogeneity of space is fundamental to quantum field theory (QFT) where the wave function of any object propagates along all available unobstructed paths. When integrated along all possible paths, with a phase factor proportional to the action, the interference of the wave-functions correctly predicts observable phenomena. Every point on the wavefront acts as the source of secondary wavelets that spread out in the light cone with the same speed as the wave. The new wavefront is found by constructing the surface tangent to the secondary wavelets.
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# Huygens–Fresnel principle
## In other spatial dimensions {#in_other_spatial_dimensions}
In 1900, Jacques Hadamard observed that Huygens\' principle was broken when the number of spatial dimensions is even. From this, he developed a set of conjectures that remain an active topic of research. In particular, it has been discovered that Huygens\' principle holds on a large class of homogeneous spaces derived from the Coxeter group (so, for example, the Weyl groups of simple Lie algebras).
The traditional statement of Huygens\' principle for the D\'Alembertian gives rise to the KdV hierarchy; analogously, the Dirac operator gives rise to the AKNS hierarchy
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# Hero System
The ***Hero System*** is a generic role-playing game system that was developed from the superhero RPG *Champions*. After *Champions* fourth edition was released in 1989, a stripped-down version of its ruleset with no superhero or other genre elements was released as The *Hero System Rulesbook* in 1990. As a spinoff of *Champions*, the *Hero System* is considered to have started with 4th edition (as it is mechanically identical to *Champions* 4th edition), rather than on its own with a 1st edition. However, the first three editions of the game are typically referred to as *Champions*, rather than the Hero System, as the game for its first three editions was not sold as a universal toolkit, instead largely focusing on superheroes.
The *Hero System* is used as the underlying mechanics of other Hero Games role-playing games such as *Fantasy Hero*, *Star Hero*, and *Pulp Hero*. It is characterized by point-based character creation and the rigor with which it measures character abilities. It uses only six-sided dice.
## System features {#system_features}
The *Hero System* uses *Champions*\' key system features. Tasks are resolved using three six-sided dice and power effects (especially damage) are resolved by rolling a number of dice based on the power\'s strength.
Like *Champions*, it uses a tool-kit approach to creating effects. While the system does have more typical features of many RPGs, such as a skill system, most abilities in the *Hero System* rules are listed as generic \"powers\". Most powers are meant to be able to model a vast number of potential effects. When creating a character, a player decides on what effect they wish to create, then constructs this effect by consulting the powers in the rulebook. Most powers have a set of modifiers that alter their base performance to more finely-tune their representation of the effect desired. Each such modifier makes the power more or less capable, and correspondingly more or less expensive to purchase with character points (the \"currency\" used to buy powers; see the section following). The result is that many effects are possible from exactly the same base power. For example, while systems such as Dungeons & Dragons would list a wide variety of separate ranged attack powers that deal damage (such as a fireball, a lightning bolt, an acid spray, a magic missile, and dozens more), the vast majority of such effects in the *Hero System* would be constructed out of the same base two powers, \"Blast\" or \"Killing Attack\".
The *Hero System* rules only define an ability\'s very basic mechanical effects---the player is the one who defines what the ability looks like when used. For example, if a player wishes to model the ability to project a jet of fire, they could choose the \"Blast\" power. However, the power\'s text has no mention of what it looks like or how it operates beyond some very base notes concerning damage and range. To make it a jet of fire, the player simply states that this Blast is a jet of fire. To some degree this is simply cosmetic. However, in the game, that power now is treated as a fire attack, with all that implies as decided by the gamemaster in each situation: it has the possibility of starting secondary fires; it looks, smells and sounds like a jet of fire; will not work in water; will terrify people with a phobia of fire; etc. The system does have mechanical effect alterations as well: a Blast could be altered by any number of power modifiers such as \"Explosion\", \"Area of Effect\", \"Megascale\", etc.: both advantages and disadvantages are available. As players are typically attempting to model something with at least a partial real-life analogue, limitations on a power are as much about making it more accurate a representation as they are making it less expensive to purchase (for example, to model a firearm, the limitation that it requires ammunition is expected, regardless of the fact that this happens to make a firearm cost fewer character points). The system also allows players to construct very exacting modifiers not specifically detailed in the base rules. For example, a player could define one or more powers as not working when the moon is full, or when it is Tuesday, or any other limitation that the player can imagine and the gamemaster feels is applicable.
Also like *Champions*, the *Hero System* uses a point-based system for character creation. Instead of templates which define what a character is, how it performs mechanically, and the new abilities gained after a certain amount of play, a player is given a fixed number of points and allowed to create what they want. As this is a much more freeform process than in most games, the system encourages close involvement between players and gamemasters to ensure that all participants have the same understanding regarding the type of effects permitted, relative power levels, and the like.
### Character creation {#character_creation}
Each player creates their character starting with a pool of points to buy abilities (such as \"Energy Blast\" and \"Armor\"), increase characteristics (such as \"Strength\" and \"Intelligence\") and buy skills (such as \"Computer Programming\" and \"Combat Driving\"). This pool can be increased by taking disadvantages for your character (such as being hunted by an enemy, a dependency of some sort or having people who depend on your character in some way). The initial pool, as well as the final pool size, is determined by the Game Master (GM), as well as the point limits on each individual ability.
Unlike the d20 System and many other game systems, experience awards are in the form of character points, which have the same value as those used in character creation and can be applied directly to the character\'s abilities upon receipt.
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# Hero System
## System features {#system_features}
### Powers
The powers system are the variables players can manipulate in the characters of Hero System. The powers in the Hero System are categorized roughly as follows:
:\***Adjustment Powers** --- Modify the Characteristics of self or another.
:\***Attack Powers** --- Inflict physical damage or some other negative effect on an opponent.
:\***Body-Affecting Powers** --- Change shape, size, density, etc.
:\***Defense Powers** --- Protect against an attack or mishap.
:\***Mental Powers** --- Detect and/or affect the mind of another.
:\***Movement Powers** --- Employ various forms of movement.
:\***Sense-Affecting Powers** --- Alter or hinder a character\'s senses.
:\***Sensory Powers** --- Improve or expand upon the sensory abilities.
:\***Size Powers** --- Growth and Shrinking.
:\***Special Powers** --- Powers with some unusual quality, including ones that do not fall into the other categories.
:\***Standard Powers** --- A \"catch-all\" for Powers that are not Adjustment, Mental, Movement, Size, or Special Powers.
Within each of these categories are multiple Powers that have more specialized effects. Thus for the movement category there are powers that can be used for Running, Swimming, Climbing, Leaping, Gliding, Flying, Tunneling through solid surfaces, and even Teleportation. For certain game genres there are even powers for traveling to other dimensions or moving faster than light.
Also, many Powers appear in at least two categories. For example, most Attack Powers are also Standard Powers, and Size Powers are basically just a subcategory of Body-Affecting Powers. Darkness is in three categories --- Standard, Attack, and Sense-Affecting.
#### Point Cost {#point_cost}
Each power has a base point cost for a given effect. This could be, for example, a certain number of points per six-sided-die (or \"d6\") of damage inflicted upon a foe.
Powers can have both advantages and limitations. Both are modifiers applied at different stages in calculating cost. These modifiers are typically changes of ±`{{frac|1|4}}`{=mediawiki}, but can range up to ±2 or even higher.
After the base cost is calculated, advantages are applied. These, which can make a power more useful, typically expand its effectiveness or make it more powerful, and thus make it more expensive. Once advantages are applied, the base cost becomes the Active Cost.
The Active Cost is calculated as an intermediate step as it is required to calculate certain figures, such as range, END usage, difficulty of activation rolls, and other things.
The formula for calculating the Active Cost is:
: **Active Cost** = **Base Cost** × (1 + *Advantages*)
Once Active Cost is calculated, limitations are applied. These represent shortcomings in the power, lessened reliability or situations in which the power can not be used. Limitations are added separately as positive numbers, even though they are listed as negative.
The Real Cost of the power is then determined by:
: **Real Cost** = **Active Cost** / (1 + *Limitations*)
The Real Cost is the amount the character must actually pay for the Power.
#### Power Frameworks {#power_frameworks}
The rules also include schemes for providing a larger number of powers to a character for a given cost. These power frameworks reduce the cost either by requiring the group of powers to have a common theme as in an Elemental Control Framework, or by limiting the number of powers that can be active at one time with a Multipower Framework. Powers within a framework can share common limitations, further reducing the cost. A third type of power framework, the Variable Power Pool (VPP), trades thrift for flexibility. With it, powers can be arbitrarily chosen on the fly, granting enhanced in-game flexibility. The price is a premium on points, called the Control Cost. Additionally, it is marked as potentially unbalancing, so not all GMs will permit VPP\'s.
Elemental Controls were eliminated in the Sixth Edition.
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# Hero System
## Publishing history {#publishing_history}
Although several games based on what would become known as the *Hero System* were published in the 1980s, including *Champions*, *Danger International*, *Justice, Inc.*, *Robot Warriors* and the original versions of *Fantasy Hero* and *Star Hero*, each of the RPGs was self-contained, much as Chaosium\'s Basic Role-Playing games are. The *Hero System* itself was not released as an independent entity until 1990, as Steve Jackson Games\' *GURPS* (*Generic Universal Roleplaying System*) became more popular. As a joint venture between Hero Games and Iron Crown Enterprises, a stand-alone *Hero System Rulebook* was published alongside the fourth edition of Champions. The content was identical to the opening sections of the Champions rules, but all genre-related material was removed. Afterward, genre books such as *Ninja Hero* (written by Aaron Allston) and *Fantasy Hero* were published as sourcebooks for the *Hero System Rulebook* as opposed to being independent games.
With the collapse of the Hero-ICE alliance, the *Hero System* went into limbo for several years. The *Champions* franchise released a new version under the Fuzion system, which had been a joint development with R. Talsorian Games, called *Champions: the New Millennium*. Although two editions were published, it was very poorly received by *Champions* fans. In 2001, a reconstituted Hero Games was formed under the leadership of Steven S. Long, who had written several books for the earlier version of the system. It regained the rights to the *Hero System* and to the *Champions* trademark.
In 2001, the Fifth Edition of the *Hero System Rulebook* was released, incorporating heavy revisions by Long. A large black hardcover, it was critically well received and attained a degree of commercial success. (Following problems with fragile bindings on Fourth Edition rulebooks, the planned binding for the larger Fifth Edition was tested using a clothes dryer.) The Fifth Edition is often referred to as \"FREd\", which is a backronym for \"Fifth Rules Edition\". The name actually comes from Steve S. Long\'s reply when asked what the standard abbreviation for the Fifth Edition would be: \"I don\'t care if you call it \'Fred\', as long as you buy it.\" This was made the unofficial nickname by several replies on the same board affirming it after a reply from Willpower, who coined the backronym by saying, \"OK. FREd it is, \"Fifth Rules Edition\"!\"
A revised version (`{{ISBN|1-58366-043-7}}`{=mediawiki}) was issued in 2004, along with *Hero System Sidekick*, a condensed version of the rulebook with a cover price of under \$10. Fans often call the revised Fifth Edition \"Fiver,\" ReFREd,\" or \"5ER\" (from \"Fifth Edition revised\"; \"Fiver\" also alludes to *Watership Down*). This rulebook is so big (592 pages) that some fans speculated that it might be bulletproof, and it did indeed stop some bullets when tested by Hero Games staffers.
On February 28, 2008, Cryptic Studios purchased the *Champions* intellectual property, and sold the rights back to Hero Games to publish the 6th edition books. One of the new features will be to allow players to adapt their *Champions Online* characters to the pen-and-paper game.
In late 2009, Hero Games released the 6th Edition of the Hero System. The game has so far had a mostly positive reception, with little in the way of \'Edition Wars\'.`{{fact|date=November 2022}}`{=mediawiki} The largest rules change was the removal of Figured Characteristics (meaning that character stats that were previously linked intrinsically---such as Speed automatically increasing when sufficient amounts of Dexterity were purchased---were no longer connected, and instead bought entirely separately). Other, more minor rules changes include folding Armor and Force field into Resistant Defense and reestablishing Regeneration as a separate power. The rules were released in two volumes, with the first covering character creation in depth and the second describing campaigns and the running of games. The new genre book for Champions came out shortly thereafter, and a new *Fantasy Hero* was released in the summer of 2010. A new version of Sidekick was released in late 2009 under the title *The Hero System Basic Rulebook*, while an *Advanced Player Guide* was published that had additional options for character creation. Other recent releases included a large book of pre-constructed Powers, a set of pre-generated Martial Arts styles, abilities and skills, a large bestiary, a new grimoire for Fantasy Hero and a three-volume set of villains for *Champions*. A new edition of *Star Hero* was released in 2011, along with a second *Advanced Player Guide*.
On 28 November 2011, Hero Games announced a restructuring, with Darren Watts and long-time developer Steven S. Long relinquishing their full-time statuses to work freelance. In late 2012 *Champions Complete* was released, which contained all of the core 6th edition rules as well as enough information to play a superhero campaign in a single 240-page book. This compact presentation reflected criticism that the 6th edition rules had become too unwieldy.
Hero Games now maintains an irregular release schedule, with a minimal staff, and has successfully used Kickstarter to raise funds for new projects. One of these new products, *Fantasy Hero Complete*, was released in early 2015.
### Computer Release {#computer_release}
*Heromaker*, an MS-DOS program, was distributed with some versions of *Champions*. Today, *Hero Designer* for the Fifth and Sixth Editions is available on several platforms, and is supported by numerous character packs and other extensions linked to Hero Games book releases. In late 2008, Hero released a licensed RPG for Aaron Williams\'s popular comic PS238 using a simplified version of the Fifth Edition rules
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# History of Finland
`{{Scandinavia|History}}`{=mediawiki}
The **history of Finland** began around 9000 BC during the end of the last glacial period. Stone Age cultures were Kunda, Comb Ceramic, Corded Ware, Kiukainen, and Pöljä culture. The Finnish Bronze Age started in approximately 1500 BC and the Iron Age started in 500 BC and lasted until 1300 AD. Finnish Iron Age cultures can be separated into Finnish proper, Tavastian and Karelian cultures. The earliest written sources mentioning Finland start to appear from the 12th century onwards when the Catholic Church started to gain a foothold in Southwest Finland.
Due to the Northern Crusades and Swedish colonisation of some Finnish coastal areas, most of the region became a part of the Kingdom of Sweden and the realm of the Catholic Church from the 13th century onwards. After the Finnish War in 1809, Finland was ceded to the Russian Empire, making this area the autonomous Grand Duchy of Finland. The Lutheran religion dominated. Finnish nationalism emerged in the 19th century. It focused on Finnish cultural traditions, folklore, and mythology, including music and---especially---the highly distinctive language and lyrics associated with it. One product of this era was the *Kalevala*, one of the most significant works of Finnish literature. The catastrophic Finnish famine of 1866--1868 was followed by eased economic regulations and extensive emigration.
In 1917, Finland declared independence. A civil war between the Finnish Red Guards and the White Guard ensued a few months later, with the Whites gaining the upper hand during the springtime of 1918. After the internal affairs stabilized, the still mainly agrarian economy grew relatively quickly. Relations with the West, especially Sweden and Britain, were strong but tensions remained with the Soviet Union. During World War II, Finland fought twice against the Soviet Union, first defending its independence in the Winter War and then invading the Soviet Union in the Continuation War. In the peace settlement Finland ended up ceding a large part of Karelia and some other areas to the Soviet Union. However, Finland remained an independent democracy in Northern Europe.
In the latter half of its independent history, Finland has maintained a mixed economy. Since its post--World War II economic boom in the 1970s, Finland\'s GDP per capita has been among the world\'s highest. The expanded welfare state of Finland from 1970 and 1990 increased the public sector employees and spending and the tax burden imposed on the citizens. In 1992, Finland simultaneously faced economic overheating and depressed Western, Russian, and local markets. Finland joined the European Union in 1995, and replaced the Finnish markka with the euro in 2002. Following the Russian invasion of Ukraine in 2022, public opinion shifted in favour of joining NATO, and Finland eventually joined the alliance on 4 April 2023.
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# History of Finland
## Stone Age {#stone_age}
### Paleolithic
The Susiluola Cave near Kristinestad in Ostrobothnia has been suggested as a possible Neanderthal settlement, potentially dating back 120,000 years to the Last Interglacial. If confirmed, it would represent the earliest known human settlement in Fennoscandia. However, the interpretation of the findings is disputed, and the claim remains controversial within the scientific community.
### Mesolithic
The last ice age in the area of the modern-day Finland ended c. 9000 BC. Starting about that time, people migrated to the area of Finland from the south and southeast. Their culture represented a mixture of Kunda, Butovo, and Veretje culture. At the same time, northern Finland was inhabited via the coast of Norway. The oldest confirmed evidence of post-glacial human settlements in Finland is from the area of Ristola in Lahti and from Orimattila, from c. 8900 BC. Finland has been continuously inhabited at least since the end of the last ice age up to the present. The earliest post-glacial inhabitants of the present-day area of Finland were probably mainly seasonal hunter-gatherers. Among finds is the net of Antrea, the oldest fishing net known ever to have been excavated (calibrated carbon dating: ca. 8300 BC).
### Neolithic
By 5300 BC, pottery was present in Finland. The earliest samples belong to the Comb Ceramic cultures, known for their distinctive decorating patterns. This marks the beginning of the Neolithic period for Finland, although subsistence was still based on hunting and fishing. Extensive networks of exchange existed across Finland and northeastern Europe during the 5th millennium BC. For example, flint from Scandinavia and the Valdai Hills, amber from Scandinavia and the Baltic region, and slate from Scandinavia and Lake Onega found their way into Finnish archaeological sites, while asbestos and soap stone from Finland (e.g. the area of Saimaa) were found in other regions. Rock paintings---apparently related to shamanistic and totemistic belief systems---have been found, especially in Eastern Finland, e.g. Astuvansalmi.
Between 3500 and 2000 BC, monumental stone enclosures, colloquially known as Giant\'s Churches (*Jätinkirkko*), were constructed in the Ostrobothnia region. The purpose of the enclosures is unknown.
In recent years, a dig at the Kierikki site north of Oulu on the River Ii has changed the image of Finnish neolithic Stone Age culture. The site had been inhabited year-round and its inhabitants traded extensively. Kierikki culture is also seen as a subtype of Comb Ceramic culture. More of the site is excavated annually.
From 3200 BC onwards, either immigrants or a strong cultural influence from south of the Gulf of Finland settled in southwestern Finland. This culture was a part of the European Battle Axe cultures, which have often been associated with the movement of the Indo-European speakers. The Battle Axe, or Cord Ceramic, culture seems to have practiced agriculture and animal husbandry outside of Finland, but the earliest confirmed traces of agriculture in Finland date later, approximately to the 2nd millennium BC. Further inland, societies retained their hunting-gathering lifestyles for the time being.
The Battle Axe and Comb Ceramic cultures eventually merged, giving rise to the Kiukainen culture that existed between 2300 BC and 1500 BC, and was fundamentally a comb ceramic tradition with cord ceramic characteristics.
## Bronze Age {#bronze_age}
The Bronze Age began some time after 1500 BC. The coastal regions of Finland were a part of the Nordic Bronze Culture, whereas in the inland regions the influences came from the bronze-using cultures of northern and eastern Russia.
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# History of Finland
## Iron Age {#iron_age}
The Iron Age in Finland is considered to have lasted from c. 500 BC until c. 1300 AD. Written records of Finland become more common due to the Northern Crusades led by the Catholic Church in the 12th and 13th centuries. As the Finnish Iron Age lasted almost two millennia, it is further divided into six sub-periods:
- Pre-Roman period: 500 BC -- 1 BC
- Roman period: 1 AD -- 400 AD
- Migration period: 400 AD -- 575 AD
- Merovingian period: 575 AD -- 800 AD
- Viking age period: 800 AD -- 1025 AD
- Crusade period: 1033 AD -- 1300 AD
Very few written records of Finland or its people remain in any language of the era. Written sources are of foreign origin and include Tacitus\'s description of *Fenni* in his work *Germania*, runestones, the sagas written down by Snorri Sturluson, as well as the 12th- and 13th-century ecclesiastical letters by the Pope. Numerous other sources from the Roman period onwards contain brief mentions of ancient Finnish kings and place names, as such defining Finland as a kingdom and noting the culture of its people.
The oldest surviving mention of the word *Suomi* (Finland in Finnish) is in the annals of the Frankish Empire written between 741 and 829. At 811, annals mention a person named Suomi in connection with a peace agreement. The name Suomi as the name of Finland is nowadays used in Finnic languages, Sámi, Latvian, Lithuanian and Scottish Gaelic.
Currently the oldest known Scandinavian documents mentioning Finland are two runestones: Söderby, Sweden, with the inscription *finlont* (U 582), and Gotland with the inscription *finlandi* (G 319) dating from the 11th century. However, as the long continuum of the Finnish Iron Age into the historical Medieval period of Europe suggests, the primary source of information of the era in Finland is based on archaeological findings and modern applications of natural scientific methods like those of DNA analysis or computer linguistics.
Production of iron during the Finnish Iron Age was adopted from the neighboring cultures in the east, west and south about the same time as the first imported iron artifacts appear. This happened almost simultaneously in various parts of the country.
### Pre-Roman period: 500 BC -- 1 BC {#pre_roman_period_500_bc_1_bc}
The Pre-Roman period of the Finnish Iron Age is scarcest in findings, but the known ones suggest that cultural connections to other Baltic cultures were already established. The archeological findings of Pernå and Savukoski provides proof of this argument. Many of the era\'s dwelling sites are the same as those of the Neolithic. Most of the iron of the era was produced on site.
### Roman period: 1 AD -- 400 AD {#roman_period_1_ad_400_ad}
The Roman period brought along an influx of imported iron (and other) artifacts like Roman wine glasses and dippers as well as various coins of the Empire. During this period the (proto) Finnish culture stabilized on the coastal regions and larger graveyards become commonplace. The prosperity of the Finns rose to the level that the vast majority of gold treasures found within Finland date back to this period.
### Migration period: 400 AD -- 575 AD {#migration_period_400_ad_575_ad}
The Migration period saw the expansion of land cultivation inland, especially in Southern Bothnia, and the growing influence of Germanic cultures, both in artifacts like swords and other weapons and in burial customs. However most iron as well as its forging was of domestic origin, probably from bog iron.
### Merovingian period: 575 AD -- 800 AD {#merovingian_period_575_ad_800_ad}
The Merovingian period in Finland gave rise to a distinctive fine crafts culture of its own, visible in the original decorations of domestically produced weapons and jewelry. The finest luxury weapons, however, were imported from Western Europe. The very first Christian burials are from the latter part of this era as well. In the Leväluhta burial findings, the average height of a man was originally thought to be just 158 cm and that of a woman 147 cm, but recent research has corrected these numbers upwards and has confirmed that the people buried in Leväluhta were of average height for that era in Europe.
Recent findings suggest that Finnish trade connections became more active during the 8th century, bringing an influx of silver onto Finnish markets. The opening of the eastern route to Constantinople via Finland\'s southern coastline archipelago brought Arabic and Byzantine artifacts into the excavation findings of the era.
The earliest findings of imported iron blades and local iron working appear in 500 BC. From about 50 AD, there are indications of a more intense long-distance exchange of goods in coastal Finland. Inhabitants exchanged their products, presumably mostly furs, for weapons and ornaments with the Balts and the Scandinavians, as well as with the peoples along the traditional eastern trade routes. The existence of richly furnished burials, usually with weapons, suggests that there was a chiefly elite in the southern and western parts of the country. Hillforts spread over most of southern Finland at the end of the Iron and early Medieval Ages. There is no commonly accepted evidence of early state formations in Finland, and the presumably Iron Age origins of urbanization are contested.
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# History of Finland
## Iron Age {#iron_age}
### Chronology of languages in Finland {#chronology_of_languages_in_finland}
The question of the timelines for the evolution and the spreading of the current Finnic languages is controversial, and new theories challenging older ones have been introduced continuously.
It was for a long time widely`{{dubious|date=October 2021}}`{=mediawiki} believed that Finno-Ugric (the western branch of the Uralic) languages were first spoken in Finland and the adjacent areas during the Comb Ceramic period, around 4000 BC at the latest. During the 2nd millennium BC these evolved---possibly under an Indo-European (most likely Baltic) influence---into proto-Sami (inland) and Proto-Finnic (coastland). In contrast, A. Aikio and J. Häkkinen propose that the Finno-Ugric languages arrived in the Gulf of Finland area during the Late Bronze Age. Valter Lang has proposed that the Finnic and Saami languages arrived there in the early Bronze Age, possibly connected to the Seima-Turbino phenomenon. This would also imply that Finno-Ugric languages in Finland were preceded by a Northwestern Indo-European language, at least to the extent the latter can be associated with the Cord Ceramic culture, as well as by hitherto unknown Paleo-European languages. The center of expansion for the Proto-Finnic language is posited to have been located on the southern coast of the Gulf of Finland. The Finnish language is thought to have started to differentiate during the Iron Age starting from the earliest centuries of the Common Era.
Cultural influences from a variety of places are visible in the Finnish archaeological finds from the very first settlements onwards. For example, archaeological finds from Finnish Lapland suggest the presence of the Komsa culture from Norway. The Sujala finds, which are equal in age with the earliest Komsa artifacts, may also suggest a connection to the Swiderian culture. Southwestern Finland belonged to the Nordic Bronze Age, which may be associated with Indo-European languages, and according to Finnish Germanist Jorma Koivulehto speakers of Proto-Germanic language in particular. Artifacts found in Kalanti and the province of Satakunta, which have long been monolingually Finnish, and their place names have made several scholars argue for an existence of a proto-Germanic speaking population component a little later, during the Early and Middle Iron Age.
The Swedish colonisation of the Åland Islands, Turku archipelago and Uusimaa could possibly have started in the 12th century but reached its height in the 13th and 14th centuries, when it also affected the Eastern Uusimaa and Ostrobothnia. The oldest Swedish place names in Finland are from this period as well as the Swedish-speaking population of Finland.
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# History of Finland
## Finland under Swedish rule {#finland_under_swedish_rule}
### Middle Ages {#middle_ages}
Contact between Sweden and what is now Finland was considerable even during pre-Christian times; the Vikings were known to the Finns due to their participation in both commerce and plundering. There is possible evidence of Viking settlement in the Finnish mainland. The Åland Islands probably had Swedish settlement during the Viking Period. However, some scholars claim that the archipelago was deserted during the 11th century.
According to the archaeological finds, Christianity gained a foothold in Finland during the 11th century. According to the very few written documents that have survived, the church in Finland was still in its early development in the 12th century. Later medieval legends from late 13th century describe Swedish attempts to conquer and Christianize Finland sometime in the mid-1150s. Danish troops raided the Finnish coastline several times between 1191 and 1202. The Finnish tribes were able to wage war and engage in trade, but over time, were increasingly drawn into Latin Christendom.
In the early 13th century, Bishop Thomas became the first known bishop of Finland. There were several secular powers who aimed to bring the Finnish tribes under their rule. These were Sweden, Denmark, the Republic of Novgorod in northwestern Russia, and probably the German crusading orders as well. Finns had their own chiefs, but most probably no central authority. At the time there can be seen three cultural areas or tribes in Finland: Finns, Tavastians and Karelians. Russian chronicles indicate there were several conflicts between Novgorod and the Finnic tribes from the 11th or 12th century to the early 13th century. The influence of Russian Orthodoxy was extended to the area around Lake Onega and Lake Ladoga and the *Häme* (Tavastians) there were converted.
It was the Swedish regent, Birger Jarl, who allegedly established Swedish rule in Finland through the Second Swedish Crusade, most often dated to 1249. *Erik\'s Chronicle*, the only source narrating the crusade, describes that it was aimed at Tavastians. A papal letter from 1237 states that the Tavastians had reverted from Christianity to their old ethnic faith. Historians have raised doubts that the Second Swedish Crusade took place in 1249 due to Sweden and Norway being locked in conflict at the time, and some have suggested that it instead took place before Swedish forces were supposedly defeated by Alexander Nevsky in the 1240 Battle of the Neva.
Novgorod gained control in Karelia in 1278, the region inhabited by speakers of Eastern Finnish dialects. Sweden however gained the control of Western Karelia with the Third Swedish Crusade in 1293. Western Karelians were from then on viewed as part of the western cultural sphere, while eastern Karelians turned culturally to Russia and Orthodoxy. While eastern Karelians remain linguistically and ethnically closely related to the Finns, they are generally considered a separate people. Thus, the northern part of the border between Catholic and Orthodox Christendom came to lie at the eastern border of what would become Finland with the Treaty of Nöteborg with Novgorod in 1323.
During the 13th century, Finland was integrated into medieval European civilization. The Dominican order arrived in Finland around 1249 and came to exercise great influence there. In the early 14th century, the first records of Finnish students at the Sorbonne appear. In the southwestern part of the country, an urban settlement evolved in Turku. Turku was one of the biggest towns in the Kingdom of Sweden, and its population included German merchants and craftsmen. Otherwise the degree of urbanization was very low in medieval Finland. Southern Finland and the long coastal zone of the Gulf of Bothnia had sparse farming settlements, organized as parishes and castellanies. In the other parts of the country a small population of Sami hunters, fishermen, and small-scale farmers lived. These were exploited by the Finnish and Karelian tax collectors. During the 12th and 13th centuries, great numbers of Swedish settlers moved to the southern and northwestern coasts of Finland, to the Åland Islands, and to the archipelago between Turku and the Åland Islands. In these regions, the Swedish language is widely spoken even today. Swedish came to be the language of the upper class in many other parts of Finland as well.
The first known mention of Finland is in runestone Gs 13 from the 11th century. Pope Gregory IX declared that *Finlandia* was passed under his protection in 1229. The area called by the name of Finland remained vague and was used to indicate the consolidation of a central authority. Sources from before the consolidation of Swedish authority more often referred to particular tribes. After the consolidation of the kingdom of the Svea and the Göta, it expanded to include Norrland, Dalarna and what came to be known as Finland Proper, what is now a southwestern province of Finland. The original Swedish term for the realm\'s eastern part was *Österlands* (\'Eastern Lands\'), a plural, meaning the area of Finland Proper, Tavastia, and Karelia. This was later replaced by the singular form *Österland*, which was in use between 1350 and 1470. In the 15th century, *Finland* began to be used synonymously with *Österland*. The concept of a Finnish country in the modern sense developed slowly from the 15th to 18th centuries.
During the 13th century, the bishopric of Turku was established. Turku Cathedral was the center of the cult of Saint Henry of Uppsala, and naturally the cultural center of the bishopric. The bishop had ecclesiastical authority over much of today\'s Finland, and was usually the most powerful man there. Bishops were often Finns, whereas the commanders of castles were more often Scandinavian or German noblemen. In 1362, representatives from Finland were called to participate in the elections for the king of Sweden. As such, that year is often considered when Finland was incorporated into the Kingdom of Sweden. As in the Scandinavian part of the kingdom, the gentry or (lower) nobility consisted of magnates and yeomen who could afford armament for a man and a horse; these were concentrated in the southern part of Finland.
The strong fortress of Viborg (Finnish: *Viipuri*, Russian: *Vyborg*) guarded the eastern border of Finland. Sweden and Novgorod signed the Treaty of Nöteborg (*Pähkinäsaari* in Finnish) in 1323, but that did not last long. In 1348 the Swedish king Magnus Eriksson staged a failed crusade against Orthodox \"heretics\", managing only to alienate his supporters and ultimately lose his crown. The bones of contention between Sweden and Novgorod were the northern coastline of the Gulf of Bothnia and the wilderness regions of Savo in Eastern Finland. Novgorod considered these as hunting and fishing grounds of its Karelian subjects, and protested against the slow infiltration of Catholic settlers from the West. Occasional raids and clashes between Swedes and Novgorodians occurred during the late 14th and 15th centuries, but for most of the time an uneasy peace prevailed.
During the 1380s, a civil war in the Scandinavian part of Sweden brought unrest to Finland as well. The victor of this struggle was Queen Margaret I of Denmark, who brought the three Scandinavian kingdoms of Sweden, Denmark and, Norway under her rule (the Kalmar Union) in 1389. One of the phenomena that appeared in those days with the unrest, was the notorious pirates, known as the Victual Brothers, who operated in the Baltic Sea in the Middle Ages to terrorize the coastal areas of Finland, and among other things, Korsholm Castle in Ostrobothnia, Turku Castle in the Finland Proper and also the Turku\'s Archipelago Sea were the most significant domains for the pirates. The next 130 years or so were characterized by attempts of different Swedish factions to break out of the Union. Finland was sometimes involved in these struggles, but in general the 15th century seems to have been a relatively prosperous time, characterized by population growth and economic development. However, towards the end of the 15th century, the situation on the eastern border became more tense. The Grand Principality of Moscow conquered Novgorod, preparing the way for a unified Russia, and from 1495 to 1497 a war was fought between Sweden and Russia. The fortress-town of Viborg withstood a Russian siege; according to a contemporary legend, it was saved by a miracle.
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# History of Finland
## Finland under Swedish rule {#finland_under_swedish_rule}
### Middle Ages {#middle_ages}
### 16th century {#th_century}
In 1521, the Kalmar Union collapsed and Gustav Vasa became the King of Sweden. During his rule, the Swedish church was reformed. The state administration underwent extensive reforms and development too, giving it a much stronger grip on the life of local communities---and ability to collect higher taxes. Following the policies of the Reformation, in 1551 Mikael Agricola, bishop of Turku, published his translation of the New Testament into the Finnish language. In 1550, Helsinki was founded by Gustav Vasa under the name *Helsingfors*, but remained little more than a fishing village for more than two centuries. His second second son Johan became the duke of Finland in the early 1560s.
King Gustav Vasa died in 1560 and his crown was passed to his three sons in separate turns. King Erik XIV started an era of expansion when the Swedish crown took the city of Tallinn in Estonia under its protection in 1561. This action contributed to the early stages of the Livonian War which was a warlike era which lasted for 160 years. In the first phase, Sweden fought for the lordship of Estonia and Latvia against Denmark, Poland and Russia. The common people of Finland suffered because of drafts, high taxes, and abuse by military personnel. This resulted in the Cudgel War of 1596--1597, a desperate peasant rebellion, which was suppressed brutally and bloodily. A peace treaty (the Treaty of Teusina) with Russia in 1595 moved the border of Finland further to the east and north, very roughly where the modern border lies.
An important part of the 16th-century history of Finland was growth of the area settled by the farming population. The crown encouraged farmers from the province of Savonia to settle the vast wilderness regions in Middle Finland. This often forced the original Sami population to leave. Some of the wilderness settled was traditional hunting and fishing territory of Karelian hunters. During the 1580s, this resulted in a bloody guerrilla warfare between the Finnish settlers and Karelians in some regions, especially in Ostrobothnia.
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# History of Finland
## Finland under Swedish rule {#finland_under_swedish_rule}
### 17th century {#th_century_1}
From 1611 to 1632, Sweden was ruled by King Gustavus Adolphus, whose military reforms transformed the Swedish army from a peasant militia into an efficient fighting machine, possibly the best in Europe. The conquest of Livonia was now completed, and some territories were taken from internally divided Russia in the Treaty of Stolbovo. In 1630, the Swedish (and Finnish) armies marched into Central Europe, as Sweden had decided to take part in the great struggle between Protestant and Catholic forces in Germany, known as the Thirty Years\' War. The Finnish light cavalry was known as the Hakkapeliitat. Gustavus Adolphus also created the office of governor-general for Finland as part of his restructuring of the administration of the Swedish realm.
After the Peace of Westphalia in 1648, the Swedish Empire was one of the most powerful countries in Europe. During the war, several important reforms had been made in Finland:
- 1637--1640 and 1648--1654: Count Per Brahe functioned as general governor of Finland. Many important reforms were made and many towns were founded. His period of administration is generally considered very beneficial to the development of Finland.
- 1640: Finland\'s first university, the Academy of Åbo, was founded in Turku at the proposal of Count Per Brahe by Queen Christina of Sweden.
- 1642: the whole Bible was published in Finnish.
However, the high taxation, continuing wars and the cold climate (the Little Ice Age) made the Imperial era of Sweden rather gloomy times for Finnish peasants. In 1655--1660, the Northern Wars were fought, taking Finnish soldiers to the battle-fields of Livonia, Poland and Denmark. In 1676, the political system of Sweden was transformed into an absolute monarchy.
In Middle and Eastern Finland, great amounts of tar were produced for export. European nations needed this material for the maintenance of their fleets. According to some theories, the spirit of early capitalism in the tar-producing province of Ostrobothnia may have been the reason for the witch-hunt wave that happened in this region during the late 17th century. The people were developing more expectations and plans for the future, and when these were not realized, they were quick to blame witches---according to a belief system the Lutheran church had imported from Germany.
The Empire had a colony in the New World in the modern-day Delaware-Pennsylvania area between 1638 and 1655. At least half of the immigrants were of Finnish origin.
The 17th century was an era of very strict Lutheran orthodoxy. In 1608, the law of Moses was declared the law of the land, in addition to secular legislation. Every subject of the realm was required to confess the Lutheran faith and church attendance was mandatory. Ecclesiastical penalties were widely used. The rigorous requirements of orthodoxy were revealed in the dismissal of the Bishop of Turku, Johan Terserus, who wrote a catechism which was decreed heretical in 1664 by the theologians of the academy of Åbo. On the other hand, the Lutheran requirement of the individual study of Bible prompted the first attempts at wide-scale education. The church required from each person a degree of literacy sufficient to read the basic texts of the Lutheran faith. Although the requirements could be fulfilled by learning the texts by heart, also the skill of reading became known among the population.
From 1696 to 1699, a famine caused by climate decimated Finland. A combination of an early frost, the freezing temperatures preventing grain from reaching Finnish ports, and a lackluster response from the Swedish government saw about one-third of the population die. Soon afterwards, another war determining Finland\'s fate began (the Great Northern War of 1700--21).
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# History of Finland
## Finland under Swedish rule {#finland_under_swedish_rule}
### 18th century {#th_century_2}
The Great Northern War (1700--1721) was devastating, as Sweden and Russia fought for control of the Baltic. Harsh conditions---worsening poverty and repeated crop failures---among peasants undermined support for the war, leading to Sweden\'s defeat. Finland was a battleground as both armies ravaged the countryside, leading to famine, epidemics, social disruption and the loss of nearly half the population. By 1721 only 250,000 remained. Landowners had to pay higher wages to keep their peasants. Russia was the winner, annexing the south-eastern part, including the town of Viborg, after the Treaty of Nystad. The border with Russia came to lie roughly where it returned to after World War II. Sweden\'s status as a European great power was forfeited, and Russia was now the leading power in the North. The absolute monarchy ended in Sweden. During this Age of Liberty, the Parliament ruled the country, and the two parties of the Hats and Caps struggled for control leaving the lesser Court party, i.e. parliamentarians with close connections to the royal court, with little to no influence. The Caps wanted to have a peaceful relationship with Russia and were supported by many Finns, while other Finns longed for revenge and supported the Hats.
Finland by this time was depopulated, with a population in 1749 of 427,000. However, with peace the population grew rapidly, and doubled before 1800. 90% of the population were typically classified as peasants, most being free taxed yeomen. Society was divided into four Estates: peasants (free taxed yeomen), the clergy, nobility and burghers. A minority, mostly cottagers, were estateless, and had no political representation. Forty-five percent of the male population were enfranchised with full political representation in the legislature---although clerics, nobles and townsfolk had their own chambers in the parliament, boosting their political influence and excluding the peasantry on matters of foreign policy.
The mid-18th century was a relatively good time, partly because life was now more peaceful. However, during the Lesser Wrath (1741--1742), Finland was again occupied by the Russians after the government, during a period of Hat party dominance, had made a botched attempt to reconquer the lost provinces. Instead the result of the Treaty of Åbo was that the Russian border was moved further to the west. During this time, Russian propaganda hinted at the possibility of creating a separate Finnish kingdom.
Both the ascending Russian Empire and pre-revolutionary France aspired to have Sweden as a client state. Parliamentarians and others with influence were susceptible to taking bribes which they did their best to increase. The integrity and the credibility of the political system waned, and in 1771 the young and charismatic king Gustav III staged a coup d\'état, abolished parliamentarism and reinstated royal power in Sweden---more or less with the support of the parliament. In 1788, he started a new war against Russia. Despite a couple of victorious battles, the war was fruitless, managing only to bring disturbance to the economic life of Finland. The popularity of King Gustav III waned considerably. During the war, a group of officers made the famous Anjala declaration demanding peace negotiations and calling of the *Riksdag* (Parliament). An interesting sideline to this process was the conspiracy of some Finnish officers, who attempted to create an independent Finnish state with Russian support. After an initial shock, Gustav III crushed this opposition. In 1789, the new constitution of Sweden strengthened the royal power further, as well as improving the status of the peasantry. However, the continuing war had to be finished without conquests---and many Swedes now considered the king as a tyrant.
With the interruption of the Gustav III\'s war (1788--1790), the last decades of the 18th century had been an era of development in Finland. New things were changing even everyday life, such as starting of potato farming after the 1750s. New scientific and technical inventions were seen. The first hot air balloon in Finland (and in the whole Swedish kingdom) was made in Oulu (Uleåborg) in 1784, only a year after it was invented in France. Trade increased and the peasantry was growing more affluent and self-conscious. The Age of Enlightenment\'s climate of broadened debate in the society on issues of politics, religion and morals would in due time highlight the problem that the overwhelming majority of Finns spoke only Finnish, but the cascade of newspapers, belles-lettres and political leaflets was almost exclusively in Swedish---when not in French.
The two Russian occupations had been harsh and were not easily forgotten. These occupations were a seed of a feeling of separateness and otherness, that in a narrow circle of scholars and intellectuals at the university in Turku was forming a sense of a separate Finnish identity representing the eastern part of the realm. The shining influence of the Russian imperial capital Saint Petersburg was also much stronger in southern Finland than in other parts of Sweden, and contacts across the new border dispersed the worst fears for the fate of the educated and trading classes under a Russian régime. At the turn of the 19th century, the Swedish-speaking educated classes of officers, clerics and civil servants were mentally well prepared for a shift of allegiance to the strong Russian Empire.
King Gustav III was assassinated in 1792, and his son Gustav IV Adolf assumed the crown after a period of regency. The new king was not a particularly talented ruler; at least not talented enough to steer his kingdom through the dangerous era of the French Revolution and Napoleonic wars.
Meanwhile, the Finnish areas belonging to Russia after the peace treaties in 1721 and 1743 (not including Ingria), called \"Old Finland\", were initially governed with the old Swedish laws (a not uncommon practice in the expanding Russian Empire in the 18th century). However, gradually the rulers of Russia granted large estates of land to their non-Finnish favorites, ignoring the traditional landownership and peasant freedom laws of Old Finland. There were even cases where the noblemen punished peasants corporally, for example by flogging. The overall situation caused decline in the economy and morale in Old Finland, worsened since 1797 when the area was forced to send men to the Imperial Army. The construction of military installations in the area brought thousands of non-Finnish people to the region. In 1812, after the Russian conquest of Finland, \"Old Finland\" was attached to the rest of the country, though the landownership question remained a serious problem until the 1870s.
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# History of Finland
## Finland under Swedish rule {#finland_under_swedish_rule}
### Peasants
While the king of Sweden sent in his governor to rule Finland, in day to day reality the villagers ran their own affairs using traditional local assemblies (called the ting) which selected a local *lagman*, or lawman, to enforce the norms. The Swedes used the parish system to collect taxes. The *socken* (local parish) was at once a community religious organization and a judicial district that administered the king\'s law. The ting participated in the taxation process; taxes were collected by the bailiff, a royal appointee.
In contrast to serfdom in Germany and Russia, the Finnish peasant was typically a freeholder who owned and controlled his small plot of land. There was no serfdom in which peasants were permanently attached to specific lands, and were ruled by the owners of that land. In Finland (and Sweden) the peasants formed one of the four estates and were represented in the parliament. Outside the political sphere, however, the peasants were considered at the bottom of the social order---just above vagabonds. The upper classes looked down on them as excessively prone to drunkenness and laziness, as clannish and untrustworthy, and especially as lacking honor and a sense of national spirit. This disdain dramatically changed in the 19th century when everyone idealised the peasant as the true carrier of Finnishness and the national ethos, as opposed to the Swedish-speaking elites.
The peasants were not passive; they were proud of their traditions and would band together and fight to uphold their traditional rights in the face of burdensome taxes from the king or new demands by the landowning nobility. The great Cudgel War in the south in 1596--1597 attacked the nobles and their new system of state feudalism; this bloody revolt was similar to other contemporary peasant wars in Europe. In the north, there was less tension between nobles and peasants and more equality among peasants, due to the practice of subdividing farms among heirs, to non farm economic activities, and to the small numbers of nobility and gentry. Often the nobles and landowners were paternalistic and helpful. The Crown usually sided with the nobles, but after the \"restitution\" of the 1680s it ended the practice of the nobility extracting labor from the peasants and instead began a new tax system whereby royal bureaucrats collected taxes directly from the peasants, who disliked the efficient new system. After 1800 growing population pressure resulted in larger numbers of poor crofters and landless laborers and the impoverishment of small farmers.
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# History of Finland
## Historical population of Finland {#historical_population_of_finland}
: 1150: 20,000--40,000
: 1550: 300,000
: 1750: 428,000
: 1770: 561,000
: 1790: 706,000
: 1810: 863,000
: 1830: 1,372,000
: 1850: 1,637,000
: 1870: 1,769,000
: 1890: 2,380,000
: 1910: 2,943,000
: 1930: 3,463,000
: 1950: 4,030,000
: 1970: 4,598,000
: 1990: 4,977,000
: 2010: 5,375,000
: 2015: 5,500,000
: 2020: 5,531,000
## Grand Duchy of Finland {#grand_duchy_of_finland}
During the Finnish War between Sweden and Russia, Finland was again conquered by the armies of Tsar Alexander I. The four Estates of occupied Finland were assembled at the Diet of Porvoo on 29 March 1809, to pledge allegiance to Alexander I of Russia. Following the Swedish defeat in the war and the signing of the Treaty of Fredrikshamn on 17 September 1809, Finland remained a grand duchy under the Russian Empire until the end of 1917, with the title of grand duke of Finland being transferred to the Russian emperor. Russia assigned Karelia (\"Old Finland\") to the grand duchy in 1812. During the years of Russian rule the degree of autonomy varied. Periods of censorship and political prosecution occurred, particularly in the two last decades of Russian control, but the Finnish peasantry remained free (unlike the Russian serfs) as the old Swedish law remained effective (including the relevant parts from Gustav III\'s Constitution of 1772). The old four-chamber Diet was re-activated in the 1860s agreeing to supplementary new legislation concerning internal affairs. In addition, Finns remained free of obligations connected to the empire, such as the duty to serve in tsarist armies, and they enjoyed certain rights that citizens from other parts of the empire did not have.
### Economy
Before 1860 overseas merchant firms and the owners of landed estates had accumulated wealth that became available for industrial investments. After 1860 the government liberalized economic laws and began to build a suitable physical infrastructure of ports, railroads and telegraph lines. The domestic market was small but rapid growth took place after 1860 in export industries drawing on forest resources and mobile rural laborers. Industrialization began during the mid-19th century from forestry to industry, mining and machinery and laid the foundation of Finland\'s current day prosperity, even though agriculture employed a relatively large part of the population until the post--World War II era.
The beginnings of industrialism took place in Helsinki. Alfred Kihlman (1825--1904) began as a Lutheran priest and director of the elite Helsingfors boys\' school, the Swedish Normal Lyceum. He became a financier and member of the diet. There was little precedent in Finland in the 1850s for raising venture capital. Kihlman was well connected and enlisted businessmen and capitalists to invest in new enterprises. In 1869, he organized a limited partnership that supported two years of developmental activities that led to the founding of the Nokia company in 1871.
After 1890 industrial productivity stagnated because entrepreneurs were unable to keep up with technological innovations made by competitors in Germany, Britain and the United States. However, Russification opened up a large Russian market especially for machinery.
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# History of Finland
## Grand Duchy of Finland {#grand_duchy_of_finland}
### Nationalism
The Finnish national awakening in the mid-19th century was the result of members of the Swedish-speaking upper classes deliberately choosing to promote Finnish culture and language as a means of nation building, i.e. to establish a feeling of unity among all people in Finland including (and not of least importance) between the ruling elite and the ruled peasantry. The publication in 1835 of the Finnish national epic, the *Kalevala*, a collection of traditional myths and legends which is the folklore of the Karelian people (the Finnic Eastern Orthodox people who inhabit the Lake Ladoga-region of eastern Finland and present-day NW Russia), stirred the nationalism that later led to Finland\'s independence from Russia.
Particularly following Finland\'s incorporation into the Swedish central administration during the 16th and 17th centuries, Swedish was spoken by about 15% of the population, especially the upper and middle classes. Swedish was the language of administration, public institutions, education and cultural life. Only the peasants spoke Finnish. The emergence of Finnish to predominance resulted from a 19th-century surge of Finnish nationalism, aided by Russian bureaucrats attempting to separate Finns from Sweden and to ensure the Finns\' loyalty.
In 1863, the Finnish language gained an official position in administration. In 1892 Finnish became an equal official language and gained a status comparable to that of Swedish. Nevertheless, the Swedish language continued to be the language of culture, arts and business all the way to the 1920s.
Movements toward Finnish national pride, as well as liberalism in politics and economics involved ethnic and class dimensions. The nationalist movement against Russia began with the Fennoman movement led by Hegelian philosopher Johan Vilhelm Snellman in the 1830s. Snellman sought to apply philosophy to social action and moved the basis of Finnish nationalism to establishment of the language in the schools, while remaining loyal to the czar. Fennomania became the Finnish Party in the 1860s.
Liberalism was the central issue of the 1860s to 1880s. The language issue overlapped both liberalism and nationalism, and showed some a class conflict as well, with the peasants pitted against the conservative Swedish-speaking landowners and nobles. Finnish activists divided themselves into \"old\" (no compromise on the language question and conservative nationalism) and \"young\" (liberation from Russia) Finns. The leading liberals were Swedish-speaking intellectuals who called for more democracy; they became the radical leaders after 1880. The liberals organized for social democracy, labor unions, farmer cooperatives, and women\'s rights.
Nationalism was contested by the pro-Russian element and by the internationalism of the labor movement. The result was a tendency to class conflict over nationalism, but the early 1900s the working classes split into the Valpas (class struggle emphasis) and Mäkelin (nationalist emphasis).
### Religion
During that period Lutheranism and Eastern Orthodoxy were official religions of the Finnish Grand Duchy. The Evangelical Lutheran Church of Finland was separated from Church of Sweden in the early 19th century. Immediately after the Finnish War, Finnish Lutheran clergy feared state-led proselytism to Orthodoxy. The majority of Finns were Lutheran Christians, but an ancient prominent Orthodox minority lived in Karelian Isthmus and Ladoga Karelia. The monasteries of Valaam and Konevets were important religious centres and pilgrimage sites of Orthodox faithful. There were also Orthodox churches built in Finnish cities and towns, where there were Russian garrisons. During this period, Roman Catholism, Judaism and Islam came to Finland with Russian soldiers and merchants.
While the vast majority of Finns were Lutheran, there were two strains to Lutheranism that eventually merged to form the modern Finnish church. On the one hand was the high-church emphasis on ritual, with its roots in traditional peasant collective society. Paavo Ruotsalainen (1777--1852) on the other hand was a leader of the new pietism, with its subjectivity, revivalism, emphasis on personal morality, lay participation, and the social gospel. The pietism appealed to the emerging middle class. The Ecclesiastical Law of 1869 combined the two strains. Finland\'s political and Lutheran leaders considered both Eastern Orthodoxy and Roman Catholicism to be threats to the emerging nation. Eastern Orthodoxy was rejected as a weapon of Russification, while anti-Catholicism was long-standing. Anti-Semitism was also a factor, so the Dissenter Law of 1889 upgraded the status only of the minor Protestant sects. Founding monasteries was forbidden.
### Music
Before 1790 music was found in Lutheran churches and in folk traditions. In 1790 music lovers founded the Åbo Musical Society; it gave the first major stimulus to serious music by Finnish composers. In the 1880s, new institutions, especially the Helsinki Music Institute (since 1939 called the Sibelius Academy), the Institute of Music of Helsinki University and the Helsinki Philharmonic Orchestra, integrated Finland into the mainstream of European music. By far the most influential composer was Jean Sibelius (1865--1957); he composed nearly all his music before 1930. In April 1892 Sibelius presented his new symphony *Kullervo* in Helsinki. It featured poetry from the *Kalevala,* and was celebrated by critics as truly Finnish music.
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# History of Finland
## Grand Duchy of Finland {#grand_duchy_of_finland}
### Politics
Despite certain freedoms granted to Finland, the Grand Duchy was not a democratic state. The tsar retained supreme power and ruled through the highest official in the land, the governor general, almost always a Russian officer. Alexander dissolved the Diet of the Four Estates shortly after convening it in 1809, and it did not meet again for half a century. The tsar\'s actions were in accordance with the royalist constitution Finland had inherited from Sweden. The Finns had no guarantees of liberty, but depended on the tsar\'s goodwill for any freedoms they enjoyed. When Alexander II convened the Diet again in 1863, he did so not to fulfill any obligation but to meet growing pressures for reform within the empire as a whole. In the remaining decades of the century, the Diet enacted numerous legislative measures that modernized Finland\'s system of law, made its public administration more efficient, removed obstacles to commerce, and prepared the ground for the country\'s independence in the next century.
#### Russification
The policy of Russification of Finland (1899--1905 and 1908--1917, called *sortokaudet**/**sortovuodet* (\'times/years of oppression\') in Finnish) was the policy of the Russian czars designed to limit the special status of the Grand Duchy of Finland and fully integrate it politically, militarily, and culturally into the empire. Finns were strongly opposed and fought back by passive resistance and a strengthening of Finnish cultural identity. Key provisions were, first, the February Manifesto of 1899 which asserted the imperial government\'s right to rule Finland without the consent of local legislative bodies; second, the Language Manifesto of 1900 which made Russian the language of administration of Finland; and third, the conscription law of 1901 which incorporated the Finnish army into the imperial army and sent conscripts away to Russian training camps.
#### Democratic change {#democratic_change}
In 1906, as a result of the Russian Revolution of 1905 and the associated Finnish general strike of 1905, the old four-chamber Diet was replaced by a unicameral Parliament of Finland (the **Eduskunta**)*.* For the first time in Europe, universal suffrage (right to vote) and eligibility was implemented to include women: Finnish women were the first in Europe to gain full eligibility to vote; and have membership in an estate; land ownership or inherited titles were no longer required. However, on the local level things were different, as in the municipal elections the number of votes was tied to amount of tax paid. Thus, rich people could cast a number of votes, while the poor perhaps none at all. The municipal voting system was changed to universal suffrage in 1917 when a left-wing majority was elected to Parliament.
### Emigration trends {#emigration_trends}
*Main article: Finnish Americans, Canadians of Finnish ancestry* Emigration was especially important 1890--1914, with many young men and some families headed to Finnish settlements in the United States, and also to Canada. They typically worked in lumber and mining, and many were active in Marxist causes on the one hand, or the Finnish Evangelical Lutheran Church of America on the other. In the 21st century about 700,000 Americans and 140,000 Canadians claim Finnish ancestry.
: 1880s: 26,000
: 1890s: 59,000
: 20th century: 159,000
: 1910s: 67,000
: 1920s: 73,000
: 1930s: 3,000
: 1940s: 7,000
: 1950s: 32,000
By 2000 about 6% of the population spoke Swedish as their first language, or 300,000 people. However, since the late 20th century there has been a steady migration of older, better educated Swedish speakers to Sweden.
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# History of Finland
## Independence and Civil War {#independence_and_civil_war}
*Main article: Finnish Declaration of Independence, Timeline of Independence of Finland (1917--1920), Finnish Civil War* `{{See also|History of Finland (1917–present)}}`{=mediawiki} In the aftermath of the February Revolution in Russia, Finland received a new Senate, and a coalition Cabinet with the same power distribution as the Finnish Parliament. Based on the general election in 1916, the Social Democrats had a small majority, and the Social Democrat Oskari Tokoi became prime minister. The new Senate was willing to cooperate with the Provisional government of Russia, but no agreement was reached. Finland considered the personal union with Russia to be over after the dethroning of the Tsar---although the Finns had *de facto* recognized the Provisional government as the Tsar\'s successor by accepting its authority to appoint a new Governor General and Senate. They expected the Tsar\'s authority to be transferred to Finland\'s Parliament, which the Provisional government refused, suggesting instead that the question should be settled by the Russian Constituent Assembly.
For the Finnish Social Democrats it seemed as though the bourgeoisie was an obstacle on Finland\'s road to independence as well as on the proletariat\'s road to power. The non-Socialists in Tokoi\'s Senate were, however, more confident. They, and most of the non-Socialists in the Parliament, rejected the Social Democrats\' proposal on parliamentarism (the so-called \"Power Act\") as being too far-reaching and provocative. The act restricted Russia\'s influence on domestic Finnish matters, but did not touch the Russian government\'s power on matters of defence and foreign affairs. For the Russian Provisional government this was, however, far too radical, exceeding the Parliament\'s authority, and so the Provisional government dissolved the Parliament.
The minority of the Parliament, and of the Senate, were content. New elections promised a chance for them to gain a majority, which they were convinced would improve the chances to reach an understanding with Russia. The non-Socialists were also inclined to cooperate with the Russian Provisional Government because they feared the Social Democrats\' power would grow, resulting in radical reforms, such as equal suffrage in municipal elections, or a land reform. The majority had the completely opposite opinion. They did not accept the Provisional government\'s right to dissolve the Parliament.
The Social Democrats held on to the Power Act and opposed the promulgation of the decree of dissolution of the Parliament, whereas the non-Socialists voted for promulgating it. The disagreement over the Power Act led to the Social Democrats leaving the Senate. When the Parliament met again after the summer recess in August 1917, only the groups supporting the Power Act were present. Russian troops took possession of the chamber, the Parliament was dissolved, and new elections were held. The result was a (small) non-Socialist majority and a purely non-Socialist Senate. The suppression of the Power Act, and the cooperation between Finnish non-Socialists and Russia provoked great bitterness among the Socialists, and had resulted in dozens of politically motivated attacks and murders.
### Independence
The October Revolution of 1917 turned Finnish politics upside down. Now, the new non-Socialist majority of the Parliament desired total independence, and the Socialists came gradually to view Soviet Russia as an example to follow. On 15 November 1917, the Bolsheviks declared a general right of self-determination \"for the Peoples of Russia\", including the right of complete secession. On the same day the Finnish Parliament issued a declaration by which it temporarily took power in Finland.
Worried by developments in Russia and Finland, the non-Socialist Senate proposed that Parliament declare Finland\'s independence, which was voted by the Parliament on 6 December 1917. On 18 December (31 December N. S.) the Soviet government issued a Decree, recognizing Finland\'s independence, and on 22 December (4 January 1918 N. S.) it was approved by the highest Soviet executive body (VTsIK). Germany and the Scandinavian countries followed without delay.
### Civil war {#civil_war}
*Main article: Finnish Civil War* Finland after 1917 was bitterly divided along social lines. The Whites consisted of the Swedish-speaking middle and upper classes and the farmers and peasantry who dominated the northern two-thirds of the land. They had a conservative outlook and rejected socialism. The Socialist-Communist Reds comprised the Finnish-speaking urban workers and the landless rural cottagers. They had a radical outlook and rejected capitalism.
From January to May 1918, Finland experienced the brief but bitter Finnish Civil War. On one side there were the \"white\" civil guards, who fought for the anti-Socialists. On the other side were the Red Guards, which consisted of workers and tenant farmers. The latter proclaimed a Finnish Socialist Workers\' Republic. World War I was still underway and the defeat of the Red Guards was achieved with support from Imperial Germany, while Sweden remained neutral and Russia withdrew its forces. The Reds lost the war and the White peasantry rose to political leadership in the 1920s--1930s. About 37,000 men died, most of them in prisoner camps ravaged by influenza and other diseases.
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# History of Finland
## Finland in the inter-war era {#finland_in_the_inter_war_era}
After the civil war, the parliament controlled by the Whites voted to establish a constitutional monarchy to be called the *Kingdom of Finland*, with German prince Frederick Charles of Hesse as king. However, Germany\'s defeat in November 1918 made the plan impossible and Finland instead became a republic, with Kaarlo Juho Ståhlberg elected as its first President in 1919. Despite the bitter civil war, and repeated threats from fascist movements, Finland became and remained a capitalist democracy under the rule of law. By contrast, nearby Estonia, in similar circumstances but without a civil war, started as a democracy and was turned into a dictatorship in 1934.
### Agrarian reform {#agrarian_reform}
Large scale agrarian reform in the 1920s involved breaking up the large estates controlled by the old nobility and selling the land to ambitious peasants. The farmers became strong supporters of the government.
### Diplomacy
Finland became member of the League of Nations on 16 December 1920. The new republic faced a dispute over the Åland Islands, which were overwhelmingly Swedish-speaking and sought retrocession to Sweden. However, as Finland was not willing to cede the islands, they were offered an autonomous status. Nevertheless, the residents did not approve the offer, and the dispute over the islands was submitted to the League of Nations. The League decided that Finland should retain sovereignty over the Åland Islands, but they should be made an autonomous province. Thus Finland was under an obligation to ensure the residents of Åland a right to maintain the Swedish language, as well as their own culture and local traditions. At the same time, an international treaty was concluded on the neutral status of Åland, under which it was prohibited to place military headquarters or forces on the islands.
### Prohibition
Alcohol abuse had a long history, especially regarding binge drinking and public intoxication, which became a crime in 1733. In the 19th century the punishments became stiffer and stiffer, but the problem persisted. A strong abstinence movement emerged that cut consumption in half from the 1880s to the 1910s, and gave Finland the lowest drinking rate in Europe. Four attempts at instituting prohibition of alcohol during the Grand Duchy period were rejected by the czar; with the czar gone Finland enacted prohibition in 1919. Smuggling emerged and enforcement was slipshod. Criminal convictions for drunkenness went up by 500%, and violence and crime rates soared. Public opinion turned against the law, and a national plebiscite went 70% for repeal, so prohibition was ended in early 1932.
### Politics {#politics_1}
Nationalist sentiment remaining from the Civil War developed into the proto-Fascist Lapua Movement in 1929. Initially the movement gained widespread support among anti-Communist Finns, but following a failed coup attempt in 1932 it was banned and its leaders imprisoned.
### Relations with Soviet Union {#relations_with_soviet_union}
In the wake of the Civil War there were many incidents along the border between Finland and Soviet Russia, such as the Aunus expedition and the Pork mutiny. Relations with the Soviets were improved after the Treaty of Tartu in 1920, in which Finland gained Petsamo, but gave up its claims on East Karelia.
Tens of thousands of radical Finns---from Finland, the United States and Canada---took up Stalin\'s 1923 appeal to create a new Soviet society in the Karelian Autonomous Soviet Socialist Republic (KASSR), a part of Russia. Most were executed in the purges of the 1930s.
The Soviet Union started to tighten its policy against Finland in the 1930s, limiting the navigation of Finnish merchant ships between Lake Ladoga and the Gulf of Finland and blocking it totally in 1937.
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# History of Finland
## Finland in the Second World War {#finland_in_the_second_world_war}
In August 1939, Nazi Germany and the Soviet Union signed the Molotov--Ribbentrop Pact, where Finland and the Baltic states were allocated to the Soviet \"sphere of influence\". After invading Poland, the Soviet Union sent ultimatums to the Baltic countries, where it demanded military bases on their soil. The Baltic states accepted Soviet demands, and lost their independence in the summer of 1940. In October 1939, the Soviet Union sent a similar request to Finland, but the Finns refused these demands.
The Soviet Union invaded Finland on 30 November 1939, launching the Winter War, with the aim of annexing Finland into the Soviet Union. The Finnish Democratic Republic was established by Joseph Stalin at the beginning of the war with the purpose of governing Finland after Soviet conquest. The Red Army was defeated in numerous battles, notably at the Battle of Suomussalmi. After two months of negligible progress on the battlefield, as well as severe losses of men and materiel, the Soviets put an end to the Finnish Democratic Republic in late January 1940 and recognized the legal Finnish government as the legitimate government of Finland. Soviet forces began to make progress in February and reached Vyborg in March. Fighting came to an end on 13 March 1940 with the signing of the Moscow Peace Treaty. Finland had successfully defended its independence, but ceded 9% of its territory to the Soviet Union. The Soviet Union was expelled from the League of Nations as a result of the invasion.
After the Winter War the Finnish Army was exhausted and needed recovery and support as soon as possible. The United Kingdom declined to help, but in autumn 1940, Nazi Germany offered weapon deals to Finland if the Finnish government would allow German troops to travel through Finland to German-occupied Norway. Finland accepted, weapons deals were made, and military co-operation began in December 1940.
Hostilities resumed in June 1941 with the start of the Continuation War, when Finland aligned with Germany following Germany\'s invasion of the Soviet Union. Finland was involved with the Siege of Leningrad and occupied East Karelia from 1941 to 1944. This irredentist sentiment of a Greater Finland, whose inhabitants were culturally related to the Finnish people, although Eastern Orthodox by religion, resulted in other countries being considerably less sympathetic to the Finnish cause.
Finnish forces won several decisive battles during the Soviet Vyborg--Petrozavodsk offensive of 1944, including the Battle of Tali-Ihantala and the Battle of Ilomantsi. These victories helped ensure Finnish independence, and led to the Moscow Armistice with the Soviet Union. The armistice called for the expulsion of German troops residing in northern Finland, leading to the Lapland War whereby the Finns forced the Germans to withdraw into Norway (then under German occupation).
Finland was never occupied by Soviet forces. Its army of over 600,000 soldiers saw only 3,500 prisoners of war. About 96,000 Finns died, or 2.5% of a population of 3.8 million; civilian casualties were under 2,500. Finland managed to defend its democracy, contrary to most other countries within the Soviet sphere of influence, and suffered comparably limited losses in terms of civilian lives and property. It was, however, punished harsher than other German co-belligerents and allies, having to pay large reparations and resettle an eighth of its population after having lost an eighth of its territory, including the major city of Viipuri. After the war, the Soviet government settled these gained territories with people from many different regions of the USSR, for instance from Ukraine.
The Finnish government did not participate in the systematic killing of Jews, although the country remained a \"co-belligerent\", a *de facto* ally of Germany until 1944. In total, eight German Jewish refugees were handed over to the German authorities. In the Tehran Conference of 1942, the leaders of the Allies agreed that Finland was fighting a separate war against the Soviet Union, and that in no way was it hostile to the Western allies. The Soviet Union was the only Allied country against which Finland had conducted military operations. Unlike any of the Axis nations, Finland was a parliamentary democracy throughout the 1939--1945 period. The commander of Finnish armed forces during the Winter War and the Continuation War, Carl Gustaf Emil Mannerheim, became the President of Finland at the very end of the Continuation War. Finland made a separate armistice agreement with the Soviet Union on 19 September 1944, and was the only bordering country of USSR in Europe (alongside Norway, which gained a border with the Soviet Union only after the war) that kept its independence after the war.
During and in between the wars, approximately 80,000 Finnish war-children were evacuated abroad: 5% went to Norway, 10% to Denmark, and the rest to Sweden. Most of the children were sent back by 1948, but 15--20% remained abroad. The Moscow Armistice was signed between Finland on one side and the Soviet Union and Britain on the other side on 19 September 1944, ending the Continuation War. The armistice compelled Finland to drive German troops from its territory, leading to the Lapland War 1944--1945.
In 1947, Finland reluctantly declined Marshall aid in order to preserve good relations with the Soviets, ensuring Finnish autonomy. Nevertheless, the United States shipped secret development aid and financial aid to the non-communist SDP (Social Democratic Party). Establishing trade with the Western powers, such as Britain, and the reparations to the Soviet Union caused Finland to transform itself from a primarily agrarian economy to an industrialised one. After the reparations had been paid off, Finland continued to trade with the Soviet Union in the framework of bilateral trade.
Finland\'s role in the Second World War was unusual in several ways. Despite massive superiority in military strength, the Soviet Union was unable to conquer Finland when the former invaded in 1939. In late 1940, German-Finnish co-operation began; it took a form that was unique when compared to relations with the Axis. Finland signed the Anti-Comintern Pact, which made Finland an ally with Germany in the war against the Soviet Union. But, unlike all other Axis states, Finland never signed the Tripartite Pact, meaning that Finland was not *de jure* an Axis nation.
### Memorials
Although Finland lost territory in both of its wars with the Soviets, the memory of these wars was sharply etched in the national consciousness. Finland celebrates these wars as a victory for the Finnish national spirit, which survived against long odds and allowed Finland to maintain its independence. Many groups of Finns are commemorated`{{clarify|date=April 2021}}`{=mediawiki} today, including not just fallen soldiers and veterans, but also orphans, evacuees from Karelia, the children who were evacuated to Sweden, women who worked during the war at home or in factories, and the veterans of the women\'s defense unit Lotta Svärd.
Some of these groups could not be properly commemorated until long after the war ended in order to preserve good relations with the Soviet Union. However, after a long political campaign backed by survivors of what Finns call the Partisan War, the Finnish Parliament passed legislation establishing compensation for the war\'s victims.
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# History of Finland
## Post WW2 and Cold War {#post_ww2_and_cold_war}
### Neutrality in Cold War {#neutrality_in_cold_war}
Finland retained a democratic constitution and free economy during the Cold War era. Treaties signed in 1947 and 1948 with the Soviet Union included obligations and restraints on Finland, as well as territorial concessions. The Paris Peace Treaty (1947) limited the size and the nature of Finland\'s armed forces. Weapons were to be solely defensive. A deepening of postwar tensions led a year later to the Treaty of Friendship, Cooperation, and Mutual Assistance (1948) with the Soviet Union. The latter, in particular, was the foundation of Finno-Soviet relations in the postwar era. Under the terms of the treaty, Finland was bound to confer with the Soviets and perhaps to accept their aid if an attack from Germany, or countries allied with Germany, seemed likely. The treaty prescribed consultations between the two countries, but it had no mechanism for automatic Soviet intervention in a time of crisis. Both treaties have been abrogated by Finland since the 1991 dissolution of the Soviet Union, while leaving the borders untouched. Even though being a neighbor to the Soviet Union sometimes resulted in overcautious concern in foreign policy (\"Finlandization\"), Finland developed closer co-operation with the other Nordic countries and declared itself neutral in superpower politics.
The Finnish post-war president, Juho Kusti Paasikivi, a leading conservative politician, saw that an essential element of Finnish foreign policy must be a credible guarantee to the Soviet Union that it need not fear attack from, or through, Finnish territory. Because a policy of neutrality was a political component of this guarantee, Finland would ally itself with no one. Another aspect of the guarantee was that Finnish defenses had to be sufficiently strong to defend the nation\'s territory. This policy remained the core of Finland\'s foreign relations for the rest of the Cold War era.
In 1952, Finland and the countries of the Nordic Council entered into a passport union, allowing their citizens to cross borders without passports and soon also to apply for jobs and claim social security benefits in the other countries. Many from Finland used this opportunity to secure better-paying jobs in Sweden in the 1950s and 1960s, dominating Sweden\'s first wave of post-war labour immigrants. Although Finnish wages and standard of living could not compete with wealthy Sweden until the 1970s, the Finnish economy rose remarkably from the ashes of World War II, resulting in the buildup of another Nordic-style welfare state.
Despite the passport union with Sweden, Norway, Denmark, and Iceland, Finland could not join the Nordic Council until 1955 because of Soviet fears that Finland might become too close to the West. At that time the Soviet Union saw the Nordic Council as part of NATO of which Denmark, Norway and Iceland were members. That same year Finland joined the United Nations, though it had already been associated with a number of UN specialized organisations. The first Finnish ambassador to the UN was G.A. Gripenberg (1956--1959), followed by Ralph Enckell (1959--1965), Max Jakobson (1965--1972), Aarno Karhilo (1972--1977), Ilkka Pastinen (1977--1983), Keijo Korhonen (1983--1988), Klaus Törnudd (1988--1991), Wilhelm Breitenstein (1991--1998) and Marjatta Rasi (1998--2005). In 1972 Max Jakobson was a candidate for Secretary-General of the UN. In another remarkable event of 1955, the Soviet Union decided to return the Porkkala peninsula to Finland, which had been rented to the Soviet Union in 1948 for 50 years as a military base, a situation which somewhat endangered Finnish sovereignty and neutrality.
Officially claiming to be neutral, Finland lay in the grey zone between the Western countries and the Soviet Union, and it also developed into one of the centres of the East-West espionage, in which both the KGB and the CIA played their parts. The 1949 established Finnish Security Intelligence Service (*SUPO, Suojelupoliisi*), an operational security authority and a police unit under the Interior Ministry, whose core areas of activity are counter-Intelligence, counter-terrorism and national security, also participated in this activity in some places. The Finno-Soviet Treaty of 1948 (Finno-Soviet Pact of *Friendship, Cooperation, and Mutual Assistance*) gave the Soviet Union some leverage in Finnish domestic politics. However, Finland maintained capitalism unlike most other countries bordering the Soviet Union. Property rights were strong. While nationalization committees were set up in France and UK, Finland avoided nationalizations. After failed experiments with protectionism in the 1950s, Finland eased restrictions and committed to a series of international free trade agreements: first an associate membership in the European Free Trade Association in 1961, a full membership in 1986 and also an agreement with the European Community in 1973. Local education markets expanded and an increasing number of Finns also went abroad to study in the United States or Western Europe, bringing back advanced skills. There was a quite common, but pragmatic-minded, credit and investment cooperation by state and corporations, though it was considered with suspicion. Support for capitalism was widespread. Savings rate hovered among the world\'s highest, at around 8% until the 1980s. In the beginning of the 1970s, Finland\'s GDP per capita reached the level of Japan and the UK. Finland\'s economic development shared many aspects with export-led Asian countries.
Building on its status as western democratic country with friendly ties with the Soviet Union, Finland pushed to reduce the political and military tensions of cold war. Since the 1960s, Finland urged the formation of a Nordic Nuclear Weapons Free Zone (Nordic NWFZ), and in 1972--1973 was the host of the Conference on Security and Cooperation in Europe (CSCE), which culminated in the signing of the Helsinki Accords in 1975 and lead to the creation of the OSCE.
### Society and the welfare state {#society_and_the_welfare_state}
Before 1940 Finland was a poor rural nation of urban and rural workers and independent farmers. There was a small middle class, employed chiefly as civil servants and in small local businesses. As late as 1950 half of the workers were in agriculture and only a third lived in urban towns. The new jobs in manufacturing, services and trade quickly attracted people to the towns and cities. The average number of births per woman declined from a baby boom peak of 3.5 in 1947 to 1.5 in 1973. When baby boomers entered the workforce, the economy did not generate jobs fast enough and hundreds of thousands emigrated to the more industrialized Sweden, migration peaking in 1969 and 1970 (today 4.7 percent of Swedes speak Finnish).
By the 1990s, farm laborers had nearly all moved on, leaving owners of small farms. By 2000 the social structure included a politically active working class, a primarily clerical middle class, and an upper bracket consisting of managers, entrepreneurs, and professionals. The social boundaries between these groups were not distinct. Causes of change included the growth of a mass culture, international standards, social mobility, and acceptance of democracy and equality as typified by the welfare state.
The generous system of welfare benefits emerged from a long process of debate, negotiations and maneuvers between efficiency-oriented modernizers on the one hand and Social Democrats and labor unions. A compulsory system provides old-age and disability insurance. The national government provides unemployment insurance, maternity benefits, family allowances, and day-care centers. Health insurance covers most of the cost of outpatient care. The national health act of 1972 provided for the establishment of free health centers in every municipality. There were major cutbacks in the early 1990s, but they were distributed to minimize the harm to the vast majority of voters.
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# History of Finland
## Post WW2 and Cold War {#post_ww2_and_cold_war}
### Economy {#economy_1}
The post-war period was a time of rapid economic growth and increasing social and political stability for Finland. The five decades after the Second World War saw Finland turn from a war-ravaged agrarian society into one of the most technologically advanced countries in the world, with a sophisticated market economy and high standard of living.
In 1991, Finland fell into a depression caused by a combination of economic overheating, fixed currency, depressed Western, Soviet, and local markets. Stock market and housing prices declined by 50%. The growth in the 1980s was based on debt and defaults started rolling in. GDP declined by 15% and unemployment increased from a virtual full employment to one fifth of the workforce. The crisis was amplified by trade unions\' initial opposition to any reforms. Politicians struggled to cut spending and the public debt doubled to around 60% of GDP. Some 7--8% of GDP was needed to bail out failing banks and force banking sector consolidation. After devaluations the depression bottomed out in 1993.
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# History of Finland
## Post-Cold War history {#post_cold_war_history}
The GDP growth rate has since been one of the highest of OECD countries and Finland has topped many indicators of national performance.
Until 1991, President Mauno Koivisto and two of the three major parties, Center Party and the Social Democrats opposed the idea of European Union membership and preferred entering into the European Economic Area treaty. However, after Sweden had submitted its membership application in 1991 and the Soviet Union was dissolved at the end of the year, Finland submitted its own application to the EU in March 1992. The accession process was marked by heavy public debate, where the differences of opinion did not follow party lines. Officially, all three major parties were supporting the Union membership, but members of all parties participated in the campaign against the membership. Before the parliamentary decision to join the EU, a consultative referendum was held on 16 April 1994, in which 56.9% of the votes were in favour of joining. The process of accession was completed on 1 January 1995, when Finland joined the European Union along with Austria and Sweden. Leading Finland into the EU is held as the main achievement of the Centrist-Conservative government of Esko Aho then in power. In the economic policy, the EU membership brought with it many large changes. While politicians were previously involved in setting interest rates, the Bank of Finland was given an inflation-targeting mandate until Finland joined the eurozone. During Prime Minister Paavo Lipponen\'s two successive governments 1995--2003, several large state companies were privatized fully or partially. Matti Vanhanen\'s two cabinets followed suit until autumn 2008, when the state became a major shareholder in the Finnish telecom company Elisa with the intention to secure the Finnish ownership of a strategically important industry.
In 2000, Finland\'s first female president, Tarja Halonen, took office. The former President of Finland, Martti Ahtisaari, received the Nobel Peace Prize in 2008. President Halonen was succeeded by President Sauli Niinistö, holding office since 2012 until 2024.
In addition to fast integration with the European Union, safety against Russian leverage has been increased by building fully NATO-compatible military. 1000 troops (a high per-capita amount) are simultaneously committed in NATO and UN operations. Finland has also opposed energy projects that increase dependency on Russian imports. For a long time, Finland remained one of the last non-NATO members in Europe, without enough support for full membership unless Sweden joined first.
On 24 February 2022, the Russian president Vladimir Putin ordered the Russian Armed Forces to begin the invasion of Ukraine. On 25 February, a Russian Foreign Ministry spokesperson threatened Finland and Sweden with \"military and political consequences\" if they attempted to join NATO, which neither were actively seeking. After the invasion public support for membership rose significantly.
On 4 April 2023, the last NATO members ratified Finland\'s application to join the alliance, making Finland the 31st member. On 1 March 2024, Alexander Stubb, a staunch supporter of NATO, was sworn in as Finland's new president. In July 2024, Stubb approved a Defence Cooperation Agreement between Finland and the United States
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# Hamiltonian (quantum mechanics)
In quantum mechanics, the **Hamiltonian** of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy. Its spectrum, the system\'s *energy spectrum* or its set of *energy eigenvalues*, is the set of possible outcomes obtainable from a measurement of the system\'s total energy. Due to its close relation to the energy spectrum and time-evolution of a system, it is of fundamental importance in most formulations of quantum theory.
The Hamiltonian is named after William Rowan Hamilton, who developed a revolutionary reformulation of Newtonian mechanics, known as Hamiltonian mechanics, which was historically important to the development of quantum physics. Similar to vector notation, it is typically denoted by $\hat{H}$, where the hat indicates that it is an operator. It can also be written as $H$ or $\check{H}$.
## Introduction
The Hamiltonian of a system represents the total energy of the system; that is, the sum of the kinetic and potential energies of all particles associated with the system. The Hamiltonian takes different forms and can be simplified in some cases by taking into account the concrete characteristics of the system under analysis, such as single or several particles in the system, interaction between particles, kind of potential energy, time varying potential or time independent one.
## Schrödinger Hamiltonian {#schrödinger_hamiltonian}
### One particle {#one_particle}
By analogy with classical mechanics, the Hamiltonian is commonly expressed as the sum of operators corresponding to the kinetic and potential energies of a system in the form $\hat{H} = \hat{T} + \hat{V},$ where $\hat{V} = V = V(\mathbf{r},t) ,$ is the potential energy operator and $\hat{T} = \frac{\mathbf{\hat{p}}\cdot\mathbf{\hat{p}}}{2m} = \frac{\hat{p}^2}{2m} = -\frac{\hbar^2}{2m}\nabla^2,$ is the kinetic energy operator in which $m$ is the mass of the particle, the dot denotes the dot product of vectors, and $\hat{p} = -i\hbar\nabla ,$ is the momentum operator where a $\nabla$ is the del operator. The dot product of $\nabla$ with itself is the Laplacian $\nabla^2$. In three dimensions using Cartesian coordinates the Laplace operator is $\nabla^2 = \frac{\partial^2}{ {\partial x}^2} + \frac{\partial^2}{ {\partial y}^2} + \frac{\partial^2}{ {\partial z}^2}$
Although this is not the technical definition of the Hamiltonian in classical mechanics, it is the form it most commonly takes. Combining these yields the form used in the Schrödinger equation: $\begin{align}
\hat{H} & = \hat{T} + \hat{V} \\[6pt]
& = \frac{\mathbf{\hat{p}}\cdot\mathbf{\hat{p}}}{2m}+ V(\mathbf{r},t) \\[6pt]
& = -\frac{\hbar^2}{2m}\nabla^2+ V(\mathbf{r},t)
\end{align}$ which allows one to apply the Hamiltonian to systems described by a wave function $\Psi(\mathbf{r}, t)$. This is the approach commonly taken in introductory treatments of quantum mechanics, using the formalism of Schrödinger\'s wave mechanics.
One can also make substitutions to certain variables to fit specific cases, such as some involving electromagnetic fields.
#### Expectation value {#expectation_value}
It can be shown that the expectation value of the Hamiltonian which gives the energy expectation value will always be greater than or equal to the minimum potential of the system.
Consider computing the expectation value of kinetic energy: $\begin{align}
T &= -\frac{\hbar^2}{2m} \int_{-\infty}^{+\infty} \psi^* \frac{d^2\psi}{dx^2} \, dx \\[1ex]
&=-\frac{\hbar^2}{2m} \left( {\left[ \psi'(x) \psi^*(x) \right]}_{-\infty}^{+\infty} - \int_{-\infty}^{+\infty} \frac{d\psi}{dx} \frac{d\psi^*}{dx} \, dx \right) \\[1ex]
&= \frac{\hbar^2}{2m} \int_{-\infty}^{+\infty} \left|\frac{d\psi}{dx} \right|^2 \, dx \geq 0
\end{align}$
Hence the expectation value of kinetic energy is always non-negative. This result can be used to calculate the expectation value of the total energy which is given for a normalized wavefunction as: $E = T + \langle V(x) \rangle = T + \int_{-\infty}^{+\infty} V(x) |\psi(x)|^2 \, dx \geq V_{\text{min}}(x) \int_{-\infty}^{+\infty} |\psi(x)|^2 \, dx \geq V_{\text{min}}(x)$ which complete the proof. Similarly, the condition can be generalized to any higher dimensions using divergence theorem.
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# Hamiltonian (quantum mechanics)
## Schrödinger Hamiltonian {#schrödinger_hamiltonian}
### Many particles {#many_particles}
The formalism can be extended to $N$ particles: $\hat{H} = \sum_{n=1}^N \hat{T}_n + \hat{V}$ where $\hat{V} = V(\mathbf{r}_1,\mathbf{r}_2,\ldots, \mathbf{r}_N,t) ,$ is the potential energy function, now a function of the spatial configuration of the system and time (a particular set of spatial positions at some instant of time defines a configuration) and $\hat{T}_n = \frac{\mathbf{\hat{p}}_n\cdot\mathbf{\hat{p}}_n}{2m_n} = -\frac{\hbar^2}{2m_n}\nabla_n^2$ is the kinetic energy operator of particle $n$, $\nabla_n$ is the gradient for particle $n$, and $\nabla_n^2$ is the Laplacian for particle `{{mvar|n}}`{=mediawiki}: $\nabla_n^2 = \frac{\partial^2}{\partial x_n^2} + \frac{\partial^2}{\partial y_n^2} + \frac{\partial^2}{\partial z_n^2},$
Combining these yields the Schrödinger Hamiltonian for the $N$-particle case: $\begin{align}
\hat{H} & = \sum_{n=1}^N \hat{T}_n + \hat{V} \\[6pt]
& = \sum_{n=1}^N \frac{\mathbf{\hat{p}}_n\cdot\mathbf{\hat{p}}_n}{2m_n}+ V(\mathbf{r}_1,\mathbf{r}_2,\ldots,\mathbf{r}_N,t) \\[6pt]
& = -\frac{\hbar^2}{2}\sum_{n=1}^N \frac{1}{m_n}\nabla_n^2 + V(\mathbf{r}_1,\mathbf{r}_2,\ldots,\mathbf{r}_N,t)
\end{align}$
However, complications can arise in the many-body problem. Since the potential energy depends on the spatial arrangement of the particles, the kinetic energy will also depend on the spatial configuration to conserve energy. The motion due to any one particle will vary due to the motion of all the other particles in the system. For this reason cross terms for kinetic energy may appear in the Hamiltonian; a mix of the gradients for two particles: $-\frac{\hbar^2}{2M}\nabla_i\cdot\nabla_j$ where $M$ denotes the mass of the collection of particles resulting in this extra kinetic energy. Terms of this form are known as *mass polarization terms*, and appear in the Hamiltonian of many-electron atoms (see below).
For $N$ interacting particles, i.e. particles which interact mutually and constitute a many-body situation, the potential energy function $V$ is *not* simply a sum of the separate potentials (and certainly not a product, as this is dimensionally incorrect). The potential energy function can only be written as above: a function of all the spatial positions of each particle.
For non-interacting particles, i.e. particles which do not interact mutually and move independently, the potential of the system is the sum of the separate potential energy for each particle, that is $V = \sum_{i=1}^N V(\mathbf{r}_i,t) = V(\mathbf{r}_1,t) + V(\mathbf{r}_2,t) + \cdots + V(\mathbf{r}_N,t)$
The general form of the Hamiltonian in this case is: $\begin{align}
\hat{H} & = -\frac{\hbar^2}{2}\sum_{i=1}^N \frac{1}{m_i}\nabla_i^2 + \sum_{i=1}^N V_i \\[6pt]
& = \sum_{i=1}^N \left(-\frac{\hbar^2}{2m_i}\nabla_i^2 + V_i \right) \\[6pt]
& = \sum_{i=1}^N \hat{H}_i
\end{align}$ where the sum is taken over all particles and their corresponding potentials; the result is that the Hamiltonian of the system is the sum of the separate Hamiltonians for each particle. This is an idealized situation---in practice the particles are almost always influenced by some potential, and there are many-body interactions. One illustrative example of a two-body interaction where this form would not apply is for electrostatic potentials due to charged particles, because they interact with each other by Coulomb interaction (electrostatic force), as shown below.
## Schrödinger equation {#schrödinger_equation}
The Hamiltonian generates the time evolution of quantum states. If $\left| \psi (t) \right\rangle$ is the state of the system at time $t$, then $H \left| \psi (t) \right\rangle = i \hbar {d\over\ d t} \left| \psi (t) \right\rangle.$
This equation is the Schrödinger equation. It takes the same form as the Hamilton--Jacobi equation, which is one of the reasons $H$ is also called the Hamiltonian. Given the state at some initial time ($t = 0$), we can solve it to obtain the state at any subsequent time. In particular, if $H$ is independent of time, then $\left| \psi (t) \right\rangle = e^{-iHt/\hbar} \left| \psi (0) \right\rangle.$
The exponential operator on the right hand side of the Schrödinger equation is usually defined by the corresponding power series in $H$. One might notice that taking polynomials or power series of unbounded operators that are not defined everywhere may not make mathematical sense. Rigorously, to take functions of unbounded operators, a functional calculus is required. In the case of the exponential function, the continuous, or just the holomorphic functional calculus suffices. We note again, however, that for common calculations the physicists\' formulation is quite sufficient.
By the \*-homomorphism property of the functional calculus, the operator $U = e^{-iHt/\hbar}$ is a unitary operator. It is the *time evolution operator* or *propagator* of a closed quantum system. If the Hamiltonian is time-independent, $\{U(t)\}$ form a one parameter unitary group (more than a semigroup); this gives rise to the physical principle of detailed balance.
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# Hamiltonian (quantum mechanics)
## Dirac formalism {#dirac_formalism}
However, in the more general formalism of Dirac, the Hamiltonian is typically implemented as an operator on a Hilbert space in the following way:
The eigenkets of $H$, denoted $\left| a \right\rang$, provide an orthonormal basis for the Hilbert space. The spectrum of allowed energy levels of the system is given by the set of eigenvalues, denoted $\{ E_a \}$, solving the equation: $H \left| a \right\rangle = E_a \left| a \right\rangle.$
Since $H$ is a Hermitian operator, the energy is always a real number.
From a mathematically rigorous point of view, care must be taken with the above assumptions. Operators on infinite-dimensional Hilbert spaces need not have eigenvalues (the set of eigenvalues does not necessarily coincide with the spectrum of an operator). However, all routine quantum mechanical calculations can be done using the physical formulation.`{{clarify|date=December 2011}}`{=mediawiki}
## Expressions for the Hamiltonian {#expressions_for_the_hamiltonian}
Following are expressions for the Hamiltonian in a number of situations. Typical ways to classify the expressions are the number of particles, number of dimensions, and the nature of the potential energy function---importantly space and time dependence. Masses are denoted by $m$, and charges by $q$.
### Free particle {#free_particle}
The particle is not bound by any potential energy, so the potential is zero and this Hamiltonian is the simplest. For one dimension: $\hat{H} = -\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2}$ and in higher dimensions: $\hat{H} = -\frac{\hbar^2}{2m}\nabla^2$
### Constant-potential well {#constant_potential_well}
For a particle in a region of constant potential $V = V_0$ (no dependence on space or time), in one dimension, the Hamiltonian is: $\hat{H} = -\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2} + V_0$ in three dimensions $\hat{H} = -\frac{\hbar^2}{2m}\nabla^2 + V_0$
This applies to the elementary \"particle in a box\" problem, and step potentials.
### Simple harmonic oscillator {#simple_harmonic_oscillator}
For a simple harmonic oscillator in one dimension, the potential varies with position (but not time), according to: $V = \frac{k}{2}x^2 = \frac{m\omega^2}{2}x^2$ where the angular frequency $\omega$, effective spring constant $k$, and mass $m$ of the oscillator satisfy: $\omega^2 = \frac{k}{m}$ so the Hamiltonian is: $\hat{H} = -\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2} + \frac{m\omega^2}{2}x^2$
For three dimensions, this becomes $\hat{H} = -\frac{\hbar^2}{2m}\nabla^2 + \frac{m\omega^2}{2} r^2$ where the three-dimensional position vector $\mathbf{r}$ using Cartesian coordinates is $(x, y, z)$, its magnitude is $r^2 = \mathbf{r}\cdot\mathbf{r} = |\mathbf{r}|^2 = x^2+y^2+z^2$
Writing the Hamiltonian out in full shows it is simply the sum of the one-dimensional Hamiltonians in each direction: $\begin{align}
\hat{H} & = -\frac{\hbar^2}{2m}\left( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2} \right) + \frac{m\omega^2}{2} \left(x^2 + y^2 + z^2\right) \\[6pt]
& = \left(-\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2} + \frac{m\omega^2}{2}x^2\right) + \left(-\frac{\hbar^2}{2m} \frac{\partial^2}{\partial y^2} + \frac{m\omega^2}{2}y^2 \right ) + \left(- \frac{\hbar^2}{2m}\frac{\partial^2}{\partial z^2} +\frac{m\omega^2}{2}z^2 \right)
\end{align}$
### Rigid rotor {#rigid_rotor}
For a rigid rotor---i.e., system of particles which can rotate freely about any axes, not bound in any potential (such as free molecules with negligible vibrational degrees of freedom, say due to double or triple chemical bonds), the Hamiltonian is: $\hat{H} = -\frac{\hbar^2}{2I_{xx}}\hat{J}_x^2 -\frac{\hbar^2}{2I_{yy}}\hat{J}_y^2 -\frac{\hbar^2}{2I_{zz}}\hat{J}_z^2$ where $I_{xx}$, $I_{yy}$, and $I_{zz}$ are the moment of inertia components (technically the diagonal elements of the moment of inertia tensor), and `{{nowrap|<math> \hat{J}_x</math>,}}`{=mediawiki} `{{nowrap|<math> \hat{J}_y</math>,}}`{=mediawiki} and $\hat{J}_z$ are the total angular momentum operators (components), about the $x$, $y$, and $z$ axes respectively.
### Electrostatic (Coulomb) potential {#electrostatic_coulomb_potential}
The Coulomb potential energy for two point charges $q_1$ and $q_2$ (i.e., those that have no spatial extent independently), in three dimensions, is (in SI units---rather than Gaussian units which are frequently used in electromagnetism): $V = \frac{q_1q_2}{4\pi\varepsilon_0 |\mathbf{r}|}$
However, this is only the potential for one point charge due to another. If there are many charged particles, each charge has a potential energy due to every other point charge (except itself). For $N$ charges, the potential energy of charge $q_j$ due to all other charges is (see also Electrostatic potential energy stored in a configuration of discrete point charges): $V_j = \frac{1}{2}\sum_{i\neq j} q_i \phi(\mathbf{r}_i)=\frac{1}{8\pi\varepsilon_0}\sum_{i\neq j} \frac{q_iq_j}{|\mathbf{r}_i-\mathbf{r}_j|}$ where $\phi(\mathbf{r}_i)$ is the electrostatic potential of charge $q_j$ at $\mathbf{r}_i$. The total potential of the system is then the sum over $j$: $V = \frac{1}{8\pi\varepsilon_0}\sum_{j=1}^N\sum_{i\neq j} \frac{q_iq_j}{|\mathbf{r}_i-\mathbf{r}_j|}$ so the Hamiltonian is: $\begin{align}
\hat{H} & = -\frac{\hbar^2}{2}\sum_{j=1}^N\frac{1}{m_j}\nabla_j^2 + \frac{1}{8\pi\varepsilon_0}\sum_{j=1}^N\sum_{i\neq j} \frac{q_iq_j}{|\mathbf{r}_i-\mathbf{r}_j|} \\
& = \sum_{j=1}^N \left ( -\frac{\hbar^2}{2m_j}\nabla_j^2 + \frac{1}{8\pi\varepsilon_0}\sum_{i\neq j} \frac{q_iq_j}{|\mathbf{r}_i-\mathbf{r}_j|}\right) \\
\end{align}$
### Electric dipole in an electric field {#electric_dipole_in_an_electric_field}
For an electric dipole moment $\mathbf{d}$ constituting charges of magnitude $q$, in a uniform, electrostatic field (time-independent) $\mathbf{E}$, positioned in one place, the potential is: $V = -\mathbf{\hat{d}}\cdot\mathbf{E}$ the dipole moment itself is the operator $\mathbf{\hat{d}} = q\mathbf{\hat{r}}$
Since the particle is stationary, there is no translational kinetic energy of the dipole, so the Hamiltonian of the dipole is just the potential energy: $\hat{H} = -\mathbf{\hat{d}}\cdot\mathbf{E} = -q\mathbf{\hat{r}}\cdot\mathbf{E}$
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# Hamiltonian (quantum mechanics)
## Expressions for the Hamiltonian {#expressions_for_the_hamiltonian}
### Magnetic dipole in a magnetic field {#magnetic_dipole_in_a_magnetic_field}
For a magnetic dipole moment $\boldsymbol{\mu}$ in a uniform, magnetostatic field (time-independent) $\mathbf{B}$, positioned in one place, the potential is: $V = -\boldsymbol{\mu}\cdot\mathbf{B}$
Since the particle is stationary, there is no translational kinetic energy of the dipole, so the Hamiltonian of the dipole is just the potential energy: $\hat{H} = -\boldsymbol{\mu}\cdot\mathbf{B}$
For a spin-`{{frac|1|2}}`{=mediawiki} particle, the corresponding spin magnetic moment is: $\boldsymbol{\mu}_S = \frac{g_s e}{2m} \mathbf{S}$ where $g_s$ is the \"spin g-factor\" (not to be confused with the gyromagnetic ratio), $e$ is the electron charge, $\mathbf{S}$ is the spin operator vector, whose components are the Pauli matrices, hence $\hat{H} = \frac{g_s e}{2m} \mathbf{S} \cdot\mathbf{B}$
### Charged particle in an electromagnetic field {#charged_particle_in_an_electromagnetic_field}
For a particle with mass $m$ and charge $q$ in an electromagnetic field, described by the scalar potential $\phi$ and vector potential $\mathbf{A}$, there are two parts to the Hamiltonian to substitute for. The canonical momentum operator $\mathbf{\hat{p}}$, which includes a contribution from the $\mathbf{A}$ field and fulfils the canonical commutation relation, must be quantized; $\mathbf{\hat{p}} = m\dot{\mathbf{r}} + q\mathbf{A} ,$ where $m\dot{\mathbf{r}}$ is the kinetic momentum. The quantization prescription reads $\mathbf{\hat{p}} = -i\hbar\nabla ,$ so the corresponding kinetic energy operator is $\hat{T} = \frac{1}{2} m\dot{\mathbf{r}}\cdot\dot{\mathbf{r}} = \frac{1}{2m} \left ( \mathbf{\hat{p}} - q\mathbf{A} \right)^2$ and the potential energy, which is due to the $\phi$ field, is given by $\hat{V} = q\phi .$
Casting all of these into the Hamiltonian gives $\hat{H} = \frac{1}{2m} \left ( -i\hbar\nabla - q\mathbf{A} \right)^2 + q\phi .$
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# Hamiltonian (quantum mechanics)
## Energy eigenket degeneracy, symmetry, and conservation laws {#energy_eigenket_degeneracy_symmetry_and_conservation_laws}
In many systems, two or more energy eigenstates have the same energy. A simple example of this is a free particle, whose energy eigenstates have wavefunctions that are propagating plane waves. The energy of each of these plane waves is inversely proportional to the square of its wavelength. A wave propagating in the $x$ direction is a different state from one propagating in the $y$ direction, but if they have the same wavelength, then their energies will be the same. When this happens, the states are said to be *degenerate*.
It turns out that degeneracy occurs whenever a nontrivial unitary operator $U$ commutes with the Hamiltonian. To see this, suppose that $|a\rang$ is an energy eigenket. Then $U|a\rang$ is an energy eigenket with the same eigenvalue, since $UH |a\rangle = U E_a|a\rangle = E_a (U|a\rangle) = H \; (U|a\rangle).$
Since $U$ is nontrivial, at least one pair of $|a\rang$ and $U|a\rang$ must represent distinct states. Therefore, $H$ has at least one pair of degenerate energy eigenkets. In the case of the free particle, the unitary operator which produces the symmetry is the rotation operator, which rotates the wavefunctions by some angle while otherwise preserving their shape.
The existence of a symmetry operator implies the existence of a conserved observable. Let $G$ be the Hermitian generator of $U$: $U = I - i \varepsilon G + O(\varepsilon^2)$
It is straightforward to show that if $U$ commutes with $H$, then so does $G$: $[H, G] = 0$
Therefore, $\frac{\partial}{\partial t} \langle\psi(t)|G|\psi(t)\rangle
= \frac{1}{i\hbar} \langle\psi(t)|[G,H]|\psi(t)\rangle
= 0.$
In obtaining this result, we have used the Schrödinger equation, as well as its dual, $\langle\psi (t)|H = - i \hbar {d\over\ d t} \langle\psi(t)|.$
Thus, the expected value of the observable $G$ is conserved for any state of the system. In the case of the free particle, the conserved quantity is the angular momentum.
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# Hamiltonian (quantum mechanics)
## Hamilton\'s equations {#hamiltons_equations}
Hamilton\'s equations in classical Hamiltonian mechanics have a direct analogy in quantum mechanics. Suppose we have a set of basis states $\left\{\left| n \right\rangle\right\}$, which need not necessarily be eigenstates of the energy. For simplicity, we assume that they are discrete, and that they are orthonormal, i.e., $\langle n' | n \rangle = \delta_{nn'}$
Note that these basis states are assumed to be independent of time. We will assume that the Hamiltonian is also independent of time.
The instantaneous state of the system at time $t$, $\left| \psi\left(t\right) \right\rangle$, can be expanded in terms of these basis states: $|\psi (t)\rangle = \sum_{n} a_n(t) |n\rangle$ where $a_n(t) = \langle n | \psi(t) \rangle.$
The coefficients $a_n(t)$ are complex variables. We can treat them as coordinates which specify the state of the system, like the position and momentum coordinates which specify a classical system. Like classical coordinates, they are generally not constant in time, and their time dependence gives rise to the time dependence of the system as a whole.
The expectation value of the Hamiltonian of this state, which is also the mean energy, is $\langle H(t) \rangle \mathrel\stackrel{\mathrm{def}}{=} \langle\psi(t)|H|\psi(t)\rangle
= \sum_{nn'} a_{n'}^* a_n \langle n'|H|n \rangle$ where the last step was obtained by expanding $\left| \psi\left(t\right) \right\rangle$ in terms of the basis states.
Each $a_n(t)$ actually corresponds to *two* independent degrees of freedom, since the variable has a real part and an imaginary part. We now perform the following trick: instead of using the real and imaginary parts as the independent variables, we use $a_n(t)$ and its complex conjugate $a_n^*(t)$. With this choice of independent variables, we can calculate the partial derivative $\frac{\partial \langle H \rangle}{\partial a_{n'}^{*}}
= \sum_{n} a_n \langle n'|H|n \rangle
= \langle n'|H|\psi\rangle$
By applying the Schrödinger equation and using the orthonormality of the basis states, this further reduces to $\frac{\partial \langle H \rangle}{\partial a_{n'}^{*}}
= i \hbar \frac{\partial a_{n'}}{\partial t}$
Similarly, one can show that $\frac{\partial \langle H \rangle}{\partial a_n}
= - i \hbar \frac{\partial a_{n}^{*}}{\partial t}$
If we define \"conjugate momentum\" variables $\pi_n$ by $\pi_{n}(t) = i \hbar a_n^*(t)$ then the above equations become $\frac{\partial \langle H \rangle}{\partial \pi_n} = \frac{\partial a_n}{\partial t},\quad \frac{\partial \langle H \rangle}{\partial a_n} = - \frac{\partial \pi_n}{\partial t}$ which is precisely the form of Hamilton\'s equations, with the $a_n$s as the generalized coordinates, the $\pi_n$s as the conjugate momenta, and $\langle H\rangle$ taking the place of the classical Hamiltonian
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# Hi-hat
High hat}} `{{More citations needed|date=April 2021}}`{=mediawiki} `{{TOC_Right}}`{=mediawiki} A **hi-hat** (**hihat**, **high-hat**, etc.) is a combination of two cymbals and a pedal, all mounted on a metal stand. It is a part of the standard drum kit used by drummers in many styles of music including rock, pop, jazz, and blues. Hi-hats consist of a matching pair of small to medium-sized cymbals mounted on a stand, with the two cymbals facing each other. The bottom cymbal is fixed and the top is mounted on a rod which moves the top cymbal toward the bottom one when the pedal is depressed (a hi-hat that is in this position is said to be \"closed\" or \"closed hi-hats\").
The hi-hat evolved from a \"sock cymbal\", a pair of similar cymbals mounted at ground level on a hinged, spring-loaded foot apparatus. Drummers invented the first sock cymbals to enable one drummer to play multiple percussion instruments at the same time. Over time these became mounted on short stands---also known as \"low-boys\"---and activated by pedals similar to those used in modern hi-hats. When extended upward roughly 3 feet (76 cm) they were originally known as \"high sock\" cymbals, which evolved over time to the familiar \"high-hat\" term.
The cymbals may be played by closing them together with the pedal, which creates a \"chck\" sound or striking them with a stick, which may be done with them open, closed, open and then closed after striking to dampen the ring, or closed and then opened to create a shimmering effect at the end of the note. Depending on how hard a hi-hat is struck and whether it is \"open\" (i.e., pedal not pressed, so the two cymbals are not closed together), a hi-hat can produce a range of dynamics, from very quiet \"chck\" (or \"chick\") sounds, done with merely gently pressing the pedal---this is suitable for soft accompaniment during a ballad or the start of a guitar solo---to very loud (e.g. striking fully open hats hard with sticks, a technique used in loud heavy metal music songs).
While the term *hi-hat* normally refers to the entire setup (two cymbals, stand, pedal, rod mechanism), in some cases, drummers use it to refer exclusively to the two cymbals themselves.
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# Hi-hat
## History
Initial versions of the hi-hat were called clangers, which were small cymbals mounted onto a bass drum rim and struck with an arm on the bass drum pedal. Then came shoes, which were two hinged boards with cymbals on the ends that were clashed together. Next was the low-sock, low-boy or low-hat,`{{clarify |date=September 2023 |reason=The original sentence is unclear. Here is a suggested edit/rewording to allow for clarity: “Lowboys (also referred to as “low boys” or “sock cymbals”) were a type of cymbal setup used in early drum kits, especially the 1920s. They consisted of a pair of cymbals mounted on a stand, similar to a hi-hat stand. The lowboy setup allowed drummers to incorporate subtle cymbal accents into their performances. However, as the lowboy stand was close to the ground, sticks and brushes could not be used. Instead, an additional set of cymbals such as Gladstone cymbals could be used to add stick work.”}}`{=mediawiki} pedal-activated cymbals employing an ankle-high apparatus similar to a modern hi-hat stand. A standard size was 10 in, some with heavy bells up to 5 in wide.
Hi-hats that were raised and could be played by hand as well as foot may have been developed around 1926 by Barney Walberg of the drum accessory company Walberg and Auge. The first recognized master of the new instrument was \"Papa\" Jo Jones, whose playing of timekeeping \"ride\" rhythms while striking the hi-hat as it opened and closed inspired the innovation of the ride cymbal. Another claim, published in Jazz Profiles Blogspot on 8 August 2008, to the invention of the hi-hat is attributed to drummer William \"O\'Neil\" Spencer (b.1909-d.1944). Legendary Jazz drummer \"Philly Joe Jones\" (born as Joseph Rudolph Jones, b.1923-d.1985) was quoted describing his understanding of the hi-hat\'s history. Jones said, \"I really dug O\'Neil. He came to a club in Philadelphia where I was working in 1943, I think it was, and talked to me about the hi-hat. I was using a foot cymbal, the low-hat. O\'Neil was the one who invented the hi-hat. I believe that, man. He suggested I close the hat on \'2\' and \'4\' when playing 4/4 time. The idea seemed so right hadn\'t heard anyone do that before.\" The editor of the 2008 Jazz Profiles article made specific mention of others who are thought to have invented the hi-hat, including Papa Jo Jones and Kaiser Marshall. A 2013 *Modern Drummer* article credits Papa Jo Jones with being the first to use brushes on drums and shifting time keeping from the bass drum to the hi-hat (providing a \"swing-pulse focus\").
Until the late 1960s, standard hi-hats were 14 in, with 13 in available as a less-common alternative in professional cymbal ranges, and smaller sizes down to 12 in restricted to children\'s kits. In the early 1970s, hard rock drummers (including Led Zeppelin\'s John Bonham) began to use 15 in hi-hats, such as the Paiste Giant Beat. In the late 1980s, Zildjian released its revolutionary 12 in Special Recording hats, which were small, heavy hi-hat cymbals intended for close miking either live or recording, and other manufacturers quickly followed suit, Sabian for example with their 10 in mini hats. In the early to mid-1990s, Paiste offered 8 in mini hi-hats as part of its Visions series, which were among the world\'s smallest hi-hats. Starting in the 1980s, a number of manufacturers also experimented with rivets in the lower cymbal. But by the end of the 1990s, the standard size was again 14 in, with 13 in a less-common alternative, and smaller hats mainly used for special sounds. Rivets in hi-hats failed to catch on.
Modern hi-hat cymbals are much heavier than modern crash cymbals, reflecting the trend to lighter and thinner crash cymbals as well as to heavier hi-hats. Another evolution is that a pair of hi-hat cymbals may not be identical, with the bottom often heavier than the top, and possibly vented. Some examples are Sabian\'s Fusion Hats with holes in the bottom cymbal, and the Sabian X-cellerator, Zildjian Master Sound and Zildjian Quick Beats, Paiste Sound Edge, and Meinl Soundwave. Some drummers even use completely mismatched hi-hats from different cymbal ranges (Zildjian\'s K/Z hats), of different manufacturers, and even of different sizes (similar to the K Custom Session Hats where the top hat is a 1/16 in smaller than the bottom). Max Roach was particularly known for using a 15 in top with a 14 in bottom.`{{dubious|date=October 2012}}`{=mediawiki}
Other recent developments include the X-hat (fixed, closed, or half-open hi-hats) and cable-controlled or remote hi-hats. Sabian introduced the Triple Hi-Hat, designed by Peter Kuppers. In this variation of the hi-hat, the top cymbal moves down and the bottom cymbal moves up simultaneously while the middle cymbal remains stationary.
Drop-clutches are also used to lock and release hi-hats while both feet are in use playing double bass drums.
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