Author: Li Xiaotian
My life also has an end, and knowledge has no end.
This is the opening sentence in Lao Tzu's "Health Lord", which says that an individual's life is limited, but knowledge has no boundaries. It is often printed in schools or libraries as inspirational quotes for learning. The original title Chinese of the film was "The Man Who Knew Infinity", which is a mathematical term referring to "infinity" and a mathematical symbol ∞. The title is easy for people who know English to understand, and it is roughly guessed that this is a story about mathematics. The translation is a bit difficult, and the literal translation should be "someone who understands ∞", but it is also weird. And the translation of "the one who knows no end" is very good, to achieve the letter Daya, but there is also trouble, Ya is Ya, and the consequent disadvantage is that it loses its connection with mathematics, can not make people look forward to the meaning of literature, some like falling into the clouds.
However, as already mentioned above, this is a story related to mathematics, in fact it is a biographical story about the life of a genius mathematician named Ramanujan, an Indian. "The Know-It-All" revolves around Ramanujan's legendary experience.
For non-mathematical Chinese, srinivasser Ramanujin (December 22, 1887 – April 26, 1920) may be little known, but for Indians, he was a prominent figure, on a par with Gandhi and Tagore, and was known as the "Son of India", a much higher status than Hua Luogeng and Chen Jingrun in China. At the turn of the millennium, Time magazine selected 100 of the most influential figures of the 20th century, including Ramanujan, and praised him as India's greatest mathematician in a thousand years. As far as the field of mathematics is concerned, in his short life (only 32 years old), he independently discovered nearly 3900 mathematical formulas and propositions, providing a good historical material for modern mathematicians to engage in mathematical research, and having an immeasurable impact on the development of modern mathematics. He has made important contributions to stack number theory, especially integer splitting, and has also made many achievements in the fields of elliptic functions, hypergeometric functions, divergent series and so on. Many of the mathematical propositions he foresaw were later confirmed. For example, the Belgian mathematician V. Deligne) proved a conjecture made by Ramanujan in 1916 in 1973 and won the Fields Medal in 1978 for it.
In addition to mathematics, several theorems he discovered played a fairly important role in different fields, including particle physics, statistical mechanics, computer science, cryptography, and space technology, and even the development of crystals and plastics was inspired by the theory of integer splitting he founded, and his research results on Riemann ζ functions have now been linked to advances in gear technology, and have also been used in thermometry and optimization of metallurgical blast furnaces. The last achievement of his life, mimicking the lambda function, powerfully propelled the study of the deterioration and spread of cancer cells and the motion of tsunamis using isolated wave theory; recently some experts believed that this function may well have been used to explain some of the mysteries of black holes in the universe, and surprisingly, when Ramanujan first proposed such a function, people did not yet know what a black hole was.
Didn't you understand the above paragraph? I didn't care, because I didn't understand, it was copied by me. But The Knower does mention Ramanujan's last groundbreaking discovery, the mathematical formula he listed, which was used a century later to explain the mysteries of black holes, a discovery of da Vinci's Tenth Symphony, to be hailed as important as Leonardo da Vinci's Tenth Symphony.
For the achievement of integer splitting, the film is even more heavily portrayed. To put it simply, take a chestnut: the number 4, if you split this number, there are five ways to split, which are:
1+1+1+1
2+1+1
3+1
2+2
4
This doesn't seem unusual, any one integer can be split. However, when an integer is enlarged to 100 bits, its split form reaches 204226. At the beginning of the 21st century, ramanujan's time, the famous British mathematician Hardy once intended to split the numbers and calculate them, but it turned out that it was impossible. McMahon, who was teaching at Cambridge university with Hardy at the time and was the dean of Trinity College, was also a mathematician, and he was particularly interested in integer splitting, and it took a few weeks and clumsy hand calculations to calculate 204226 split of hundreds of integers. Moreover, McMahon also believed that there was no formula that could easily calculate integer splitting. However, Ramanujan wrote out of thin air the asymptotic formula for the spin-off number p(n) of the positive integer n, which anyone who brings in a number according to the formula can easily calculate it. Ramanujan's first-of-its-kind discovery completely shocked McMahon and conquered him completely. As a result, Ramanujan was elected a Fellow of the Royal Society, and in the same year he became the first Indian to be elected a Fellow of Trinity College, at the age of 31 (1918).
Isn't it enough cattle? But what's even better is that Ramanujan had no formal mathematical education at all, knew nothing about the rigor of modern scholarship, and to some extent didn't know what proof was. He was completely from the wild road, in today's words, a folk science, a madman, and the 3900 mathematical formulas he wrote were basically written out of thin air by his own imagination. In his own words, he was able to write those formulas because they were originally in his mind, in a dream the goddess Namakal gave him a revelation and could write them down when he woke up in the morning.
Yes, Ramanujan believes in God, is a staunch Hindu, and has been a vegetarian all his life. He was born into the noble caste brahmins of India, but his family was in decline, and his family was not rich in economy from an early age. In order to support the family, his parents went to the charter wife and rented the space in the home to some students at a nearby university. At the age of 12, Ramanujan began dabbling in mathematics and developed a keen interest. At the age of 16, he obtained an English edition of the mathematics book Compendium of the Basic Results of Pure and Applied Mathematics from a college student who was staying at his home, which listed more than 5,000 equations, theorems, and formulas, and categorized them into algebra, trigonometry, calculus, analytic geometry, and differential equations, which were included in most of the mathematics known to mankind in the late 19th century. Amazingly, the book did not give detailed proofs, the book brought Ramanujan great interest and brought him directly into the world of mathematics, and the unproven formulas obviously influenced his research style, but also catered to his intuitive mathematical thinking.
What is intuitive mathematical thinking? To take another chestnut, when we were in junior high school, we studied geometry, and many people had a feeling that it was enough to prove that a problem could be done in one step, but the teacher said no, because our step still needed to be proved, and we felt that it should be like this. In the end, our intuition is right, and this is mathematical intuition. Truth be told, the process by which we are trained as tools is the process that kills our mathematical intuition. Chinese education, in particular, is constantly strangling more creative intuitions, not only in mathematics, but also in other subjects, and gradually educates people into tools.
Back in Ramanujan, he relies on intuition to learn and deduce mathematics in an unproven leap forward. He spent 5 years treating each equation in the book as a subject, trying to prove it in his own way, and further deducing some of the formulas. And every time he proves a mathematical formula, he will find several other formulas. Thus, his discoveries began to accumulate in the process. Later, he was expelled from college for getting too caught up in his own reasoning. Saying that it is purely based on mathematical intuition, in fact, she has made her own proof and deduction, once, he and his friend walked and chatted by the beach, saying you look at my elbow, my friend saw that his elbow skin was dark and thick. It turned out that he thought it would take too long to use rags to wipe the words on the stone slab, and he used his elbow to directly wipe the words on the stone slab every few minutes (no money to buy paper), and the time was so long that a thick cocoon grew on his elbow!
Later, in order to make a living, Ramanujan had the privilege of meeting with a tax collector and secretary of the Mathematical Society, Rao. When Rao learned that Ramanujan simply wanted a spare time to continue his mathematical research, he generously promised to fund him 25 rupees a month in his personal name. In this way, with Rao's funding, Ramanujan's first paper was published in the Journal of the Indian Mathematical Society, and has since officially entered the stage of mathematics. Rao, too, recommended Ramanujan to the Port authority of Madras and recommended him to work as a clerk in the Finance Section of the Trust Office so that he could have a job that was not too busy and stable. Here he met two more nobles, Sir Spring, an Irishman, chief engineer of the Port of Madras Authority, and Yeer, Chief Accountant of the Port Authority and a member of the Mathematical Society of India. Thanks to their appreciation, attention, and friendship, Ramanujan studied mathematics even when he was at work, and his colleagues and superiors turned a blind eye. More importantly, it was through Spring's relationship with Yale and his surroundings that Ramanujan entered "British India." Before that, he had too little contact with the British, and now it has finally changed. One consequence of this change was that Ramanujan had a yearning for his suzerainty, Britain. Based on the pursuit of mathematics, he began to write letters to famous mathematicians in Britain. (Minke loves to write letters, full of tears!) ）
In his letter, Ramanujan, in 1913, listed a long list of complex theorems for three Cambridge academics, H.F. Baker, E.W. Hobson, and G.H. Hardy. As a result, only the third mathematician, Hardy, wrote back to him. Well, it was Hardy, the famous mathematician Hardy, not the more familiar thomas Hardy who wrote Tess, but Godfrey Harold, who was 35 years old at the time. (Note that although both are translated as Hardy, the english names of the two men are actually spelled differently, and they are not related in the slightest.) Oh, yes, this mathematician Hardy is also the teacher of Hua Luogeng, the most famous mathematician in China.
At that time, Ramnugin's e-mails were accompanied by nine pieces of paper stating that his study of the distribution of prime numbers was tied with 120 formulas, covering many fields of mathematics. Most of these formulas have been proven by others, and some seem easy to prove but are actually difficult to prove. Hardy had never seen such a mathematical formula, like the sudden emergence of many new varieties of flowers in his familiar mathematical forest, which made people wonder if they were artificially patchwork forgeries. Hardy wanted to ignore them, but the more he thought about it, the more he felt that they could not be fake, because no one could have fabricated these formulas out of thin air. So he asked his colleague JE Littlewood to review the theorems and concluded that the little-known Ramanujan was a brilliant and creative mathematician.
Hardy describes his discovery of Ramanujan as a romantic episode of his life. When he decided that Ramanujan was a rare genius, he immediately invited him to England. But for Ramanujan and his family, although the family was in decline, because of religious concerns and cultural resistance, it should be known that Brahmins and canonical Hindus could not cross the sea, and that going to England was a kind of defilement to the family, which was as serious as the public abandonment of the holy scarf, the eating of beef or the marriage of widows. Nearly a quarter of a century ago, Gandhi was expelled from the caste by his family for studying in England. Although by ramanujan's time, the uneasiness of Indians' conscience because of going abroad had been alleviated a lot, but it was still a big problem for his family, which made him hesitate. However, Hardy continued to urge Ramanujan to go to Cambridge, and arranged a scholarship for him through many efforts. In April 1914, Ramanujan came to England and entered cambridge university, where he received a formal education while working with Hardy.
Hardy, who spent a lot of effort teaching Ramanujan modern European mathematics, found that the limits of Ramanujan's knowledge were as astonishing as its profundity. Ramanujan has only one vague concept of proof, is not familiar with the increment of variables, Cauchy's theorem, but has a deep understanding of the facts of values and combinations, even fractions, divergent series and integrals, the spin-off of numbers, Riemannξ functions, and various special series.
With the help of Hardy and Littlewood and others, Ramanujan made rapid progress, achieving many results in the fields of prime distribution, stack number theory, generalized hypergeometric series, elliptic functions, divergent series, and so on. He published 21 papers and 17 notes during his 5 years in Europe, several of which were in collaboration with Hardy. (Because Hardy sometimes couldn't help but help Ramanujan prove his formula directly, making it a formal formula that could be used directly, otherwise the unproven formulas would only be conjectures.) ）
In 1916, Ramanujan received his doctorate. In 1918, he reached the peak of his scholarship, was elected a fellow of the Royal Society, and was the youngest academician at the time, and in the same year he was elected a fellow of Trinity College, both of which were difficult for others to reach. However, those familiar with history know that this time coincided with the period of the First World War (August 1914 - November 1918). Moreover, Britain was a belligerent, and this war directly killed more than two thousand people in Cambridge and injured countless people. Ramanujan attended during this period and was undoubtedly going to be affected.
This effect was directly reflected in his body. Although Ramanujan was an adult at this time, he was always a minor psychologically, and while working with Hardy, he spent a lot of time indulging in nostalgia between classes. Moreover, as a devout Hindu and Brahmin caste, he adhered to the canon rules and did not eat the food made of meat oil in the Cambridge University canteen, but only cooked it himself in his dormitory. The food shortage caused by the war directly brought great trouble to his recipe. Lack of food, malnutrition, and the harsh climate of London brought him the discomfort of life. Finally, in the spring of the fourth year after reaching England, Ramanujan was overthrown. Hardy, as an arrogant English gentleman and an atheist, and Ramanujan, a devout Hindu, did not interact much in their lives except for their in-depth academic exchanges. Although Hardy brought ramanujan all kinds of academic conveniences, he was not strictly a "friend of life" for Ramanujan. Ramanujan fell, but for wartime reasons, he was unable to return home. At that time, the medical conditions could not confirm what Ramanujan had, first thought that he had a stomach ulcer, and then thought that he was poisoned by blood, (because he liked to put canned vegetables made of lead directly on the gas and heat it and eat it), and then directly treated him as tuberculosis. Ramanujan also wanted his wife in India to take care of himself, but his mother, who received his email, flatly refused the request and did not even pass on the message to his wife. At that time, the relationship between the mother-in-law and daughter-in-law who stayed in India also dropped to zero. On difficult days, Ramanujan even almost committed suicide by jumping off the rails in the subway station, but was saved.
In March 1919, after the end of the first stop, Ramanujan was able to return to India. When Ramanujan's earliest funder, the tax collector Rao, went to the train station to greet him, he saw a emaciated, gaunt, morbid man with a sick face, "I saw the ending," he later recalled. Still, local celebrities lined up to meet the genius, and the wealthy scrambled to pay for him medical and other expenses or give up their houses to him. In fact, no Indian in history has reached his scientific status and fame at that time. However, Ramanujan no longer had time to enjoy these trips and honors. In April of the following year, Ramanujan died at the age of 33.
Hardy lamented the untimely death of the Indian mathematical prodigy and was devastated to learn the information, as Ramanujan wrote to him in a cheerful tone two months before his death, reporting on his new research. Hardy is deeply saddened and regretful to say that he owes a lot to Ramanujan, and during the five years he worked with him, Ramanujan has always been a source of his creativity and inspiration. He co-ordinated Ramanujan's collected essays and authored Ramanujan (1940), which included 12 speeches on Ramanujan's life and work, which described Ramanujan's life and research results in more detail and made appropriate comments, which is an important document for understanding and studying Ramanujan. The relationship between Hardy and Ramanujan has also long been a good story in the mathematical community.
In terms of mathematical talent, the mathematical community classifies Ramanujan as a great mathematician, Gauss, and Euler. According to Hardy's assessment, he believes that if Ramanujan's talent is 100 points, Hardy himself is only 25%, and his collaborator Littlewood is 30%. Hardy also credits one of the greatest mathematicians of the 19th and 20th centuries, Hilbert of Germany, who scored 80 points, and that Hilbert was the founder and founder of many fields of mathematics, and many scholars became famous in the direction he guided. This shows that Hardy values Ramanujan. To compare with famous Chinese mathematicians, Hua Luogeng may have 20%, while Chen Jingrun has 15%. Hua Luogeng is equivalent to Ramanujan's miniature Chinese version.
A more famous passage about the relationship between Hardy and Ramanujan is the story of 1729. It is said that when Ramanujan was hospitalized, Hardy went to visit him. Hardy's taxi on the road had a license plate number of 1729, and Hardy kept wondering what the number meant, only to find it meaningless. When he walked into Ramanujan's hospital room, he hadn't even said hello, blurting out his disappointment with the number, which he said was boring and boring, and hoped it wasn't a bad sign. "Hardy, you're wrong," Ramanujan said, "that's a very interesting number." It is the smallest number that can be expressed in two different ways as the sum of two regular cubic numbers. "The sum of two positive cubic numbers, i.e. 1729 = 1^3 + 12^3 = 9^3 + 10^3, the next number with this characteristic is 4104, so 1729 is the first and the smallest. Later, such numbers were called taxi numbers, or Hardy Ramanujan numbers, and to date there are only 6 of them. Littlewood heard about it and said, "All the integers are Friends of Ramnukin!" ”
The film "The Knower" is Ramanujan's biography of life, and the above-mentioned life map is roughly presented in the film. In order to increase the drama, the story of the film has been appropriately expanded, and even the famous philosopher Russell can be seen in the film. The film stars Dave Patel, the male protagonist of "The Fantasy Drifting of The Young Pi" and "The Lion". (Can you see, I watched this film because of Dave Patel, and I've seen all the films he starred in so far.) Hardy is played by veteran Oscar-winning jeremy Irons, whose new work is to play the new "Batman" butler Afu in "Batman v Superman", which is also an important role in the great return to the public eye. Littlewood is played by veteran supporting actor Toby Jones. The performances of all three people are very good.
As a headline forerunner, since the topic of "genius died of vegetarianism" was mentioned, here is a few more words. Ramanujan was a Hindu and a member of the Brahmin caste. In fact, in Hinduism, in addition to avoiding beef, ordinary people can still eat meat, such as lamb, chicken and the like. But the caste system in India is equally strict, strictly speaking, only low-ranking people will eat meat, and high-ranking people will not eat meat, And those who are lamanu metal in your race, he strictly abides by the law and refuses to eat meat, in fact, it is precisely because of unhealthy diets and living customs such as malnutrition that his life span is harmed.
At present, we all believe that vegetarian food is more beneficial to health and is also a good deed of non-killing, especially Buddhists. As a disciple who officially took refuge in the Kyaw Nang school of Tibetan Buddhism, I am considered a Buddhist monk, but I have a different view of vegetarianism. How the teachings of Hinduism are, there is no study, only Buddhism is spoken of here. In fact, the Buddha never taught buddhists that they had to eat vegetarian food. It was after the introduction of Buddhism from the Western Han Dynasty to the Chinese mainland, and it was during the Liang Dynasty that Emperor Wu of Liang explicitly combined traditional Confucian culture with Buddhist culture, and issued the "Broken Wine meat text" as an emperor, gathering monks to make a vow in front of the Buddha and swearing an oath of "forever cutting off wine and meat", which made the precepts of inlandization. As a result of his strong advocacy, Chinese Buddhist monks and nuns changed their original eating habits, abstained from alcohol and vegetarianism, purified their mouths, and vegetarian food became a major tradition of Han Buddhism. Buddhists outside the interior still maintain the habit of eating "three pure meats", that is, they can eat meat, but they do not kill themselves, and try to eat only the meat of naturally dead animals.
At present, many vegetarians regard vegetarian food as fashion, and the specifications of major vegetarian restaurants are far more advanced than those of ordinary restaurants, and vegetarian food is not cheap at all, which actually deviates from the Buddha and also deviates from the original intention of Emperor Liangwu. Vegetarian food is to save life, to protect animals, but animals are life, and plants are inanimate. In the buddha's eyes, there was a world of sand, a leaf and a bodhi, and even dead plants were attached to other life. All beings are equal, life here is universal, and the equal status is more complete, not exclusively for animals.
On the basis of modern nutrition, you can go to the supermarket for 10 yuan to buy half a kilogram of meat, and then get enough protein nutrition to support the body's needs for many days. In order to achieve the same nutritional value, simple vegetarian food may cost 100 yuan and cannot be obtained. Therefore, from the perspective of input-output ratio, it is clear that meat has more economic value, while vegetarian food occupies food resources to a greater extent. In ancient times, the number of human beings on the earth was far less than it is now, the number of plants was far beyond the limits of human control, and more vegetarian food would be more beneficial to the ecological balance of the earth. At present, human life on Earth has exceeded the limit of 6 billion. In this case, any resource on Earth is limited and needs to be protected. Not only animals, but also plants need to be cherished. In order to have a full meal, the resources to be used for vegetarian food are far greater than the share of meat. Simple vegetarian diet has not achieved the purpose of sparing life and protecting life. Killing an animal and destroying a plant, that wastes more resources and needs to be recalculated. Now take vegetarian food as fashion, personal eating is also counted, but take this as a moral standard, vegetarian yourself and then look down on meat eaters, this is not right.
Cherishing the earth's resources should be indiscriminately cherished, whether animals or plants. The use of technical means, edible plants are artificially farmed, edible animal resources, but also need to use technical means, rely on scientific feeding, the damage control to the minimum, the effective use of control to the maximum, is a reasonable choice. As for wild animals, it is better not to touch them, and indiscriminate killing is even more unlikely to occur.
It is enough to strike a balance between meat and vegetarian recipes in individual recipes. For me, I usually have a relatively light side, eat less meat, eat more vegetarian, neither lack of nutrition, nor waste resources, you can, so I think it is very good.
7 .6
The Know-It-All (2015)