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de2398f
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All that was required to measure the planet was a man with a stick and a brain. In other words, couple an intellect with some experimental apparatus and almost anything seems achievable.
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Simon Singh |
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819bdc4
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An astronomer, a physicist, and a mathematician (it is said) were holidaying in Scotland. Glancing from a train window, they observed a black sheep in the middle of a field. "How interesting," observed the astronomer, "all Scottish sheep are black!" To which the physicist responded, "No, no! Some Scottish sheep are black!" The mathematician gazed heavenward in supplication, and then intoned, "In Scotland there exists at least one field, con..
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Simon Singh |
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45fbcd2
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God exists since mathematics is consistent, and the Devil exists since we cannot prove it.
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Simon Singh |
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a887a3a
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Similarly, if you're trying to prove something mathematically, it's possible that no proof exists.
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Simon Singh |
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c207f0b
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Pascal was even convinced that he could use his theories to justify a belief in God. He stated that 'the excitement that a gambler feels when making a bet is equal to the amount he might win multiplied by the probability of winning it'. He then argued that the possible prize of eternal happiness has an infinite value and that the probability of entering heaven by leading a virtuous life, no matter how small, is certainly finite. Therefore, ..
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Simon Singh |
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f11370c
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A mathematician is a machine for turning coffee into theorems.
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Simon Singh |
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04da204
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The first known European book to describe the use of cryptography was written in the thirteenth century by the English Franciscan monk and polymath Roger Bacon. Epistle on the Secret Works of Art and the Nullity of Magic included seven methods for keeping messages secret, and cautioned: "A man is crazy who writes a secret in any other way than one which will conceal it from the vulgar."
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Simon Singh |
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3ee4d69
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if N is large enough, it is virtually impossible to deduce p and q from N, and this is perhaps the most beautiful and elegant aspect of the RSA asymmetric cipher.
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Simon Singh |
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f257a07
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like Turing and the cryptanalysts at Bletchley Park, the Navajo were ignored for decades. Eventually, in 1968, the Navajo code was declassified, and the following year the code talkers held their first reunion.
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Simon Singh |
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ec2a53e
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Ron Rivest, one of the inventors of RSA, thinks that restricting cryptography would be foolhardy: It is poor policy to clamp down indiscriminately on a technology just because some criminals might be able to use it to their advantage. For example, any U.S. citizen can freely buy a pair of gloves, even though a burglar might use them to ransack a house without leaving fingerprints. Cryptography is a data-protection technology, just as gloves..
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Simon Singh |
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e750728
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Propose to an Englishman any principle, or any instrument, however admirable, and you will observe that the whole effort of the English mind is directed to find a difficulty, a defect, or an impossibility in it. If you speak to him of a machine for peeling a potato, he will pronounce it impossible: if you peel a potato with it before his eyes, he will declare it useless, because it will not slice a pineapple.
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Simon Singh |
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e934ed2
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The NSA employs more mathematicians, buys more computer hardware, and intercepts more messages than any other organization in the world.
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Simon Singh |
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881802e
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if a message protected by quantum cryptography were ever to be deciphered, it would mean that quantum theory is flawed,
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Simon Singh |
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66d7676
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The nineteenth-century mathematician Leopold Kronecker said, "God made the integers; all the rest is the work of man."
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Simon Singh |
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65eab2d
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Enigma was considered invulnerable, until the Poles revealed its weaknesses.
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Simon Singh |
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8a0dae3
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This apparently innocuous observation would lead to the first great breakthrough in cryptanalysis.
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Simon Singh |
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5f76dcd
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Florence) Nightingale's passion for statistics enabled her to persuade the government of the importance of a whole series of health reforms. for example, many people had argued that training nurses was a waste of time, because patients cared for by trained nurses actually had a higher mortality rate than those treated by untrained staff. Nightingale, however, pointed out that this was only because more serious cases were being sent to those..
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science
nursing
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Simon Singh |
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e739473
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Maths is one of the purest forms of thought, and to outsiders mathematicians may seem almost other-worldly.
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Simon Singh |
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a3cc3b8
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Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. 'Immortality' may be a silly word, but probably a mathematician has the best chance of whatever it may mean. G.H. Hardy 23
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Simon Singh |
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777d876
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Although this may seem a paradox, all exact science is dominated by the idea of approximation.
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Simon Singh |
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4516b07
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The Last Theorem is at the heart of an intriguing saga of courage, skulduggery, cunning, and tragedy, involving all the greatest heroes of mathematics.
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Simon Singh |
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606252a
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The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.
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world
infinity
intellect
question
math
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Simon Singh |
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ffeffcf
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Previous experience, however, tells us that every so-called unbreakable cipher has, sooner or later, succumbed to cryptanalysis
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Simon Singh |
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fdd5c80
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Quantum cryptography would mark the end of the battle between codemakers and codebreakers, the codemakers emerging victorious, because quantum cryptography is a truly unbreakable system of encryption.
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Simon Singh |
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6e9a162
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In fact, Britain had captured thousands of Enigma machines, and distributed them among its former colonies, who believed that the cipher was as secure as it had seemed to the Germans. The British did nothing to disabuse them of this belief, and routinely deciphered their secret communications in the years that followed. Meanwhile,
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Simon Singh |
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01f37c7
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Had the Arabs merely been familiar with the use of the mono-alphabetic substitution cipher, they would not warrant a significant mention in any history of cryptography. However, in addition to employing ciphers, the Arab scholars were also capable of destroying ciphers. They in fact invented cryptanalysis, the science of unscrambling a message without knowledge of the key. While the cryptographer develops new methods of secret writing, it i..
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Simon Singh |
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9eb9c5d
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Pascal was even convinced that he could use his theories to justify a belief in God. He stated that 'the excitement that a gambler feels when making a bet is equal to the amount he might win multiplied by the probability of winning it'.
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Simon Singh |
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055c51c
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Cryptanalysis could not be invented until a civilization had reached a sufficiently sophisticated level of scholarship in several disciplines, including mathematics, statistics, and linguistics. The Muslim civilization provided an ideal cradle for cryptanalysis, because Islam demands justice in all spheres of human activity, and achieving this requires knowledge, or ilm. Every Muslim is obliged to pursue knowledge in all its forms, and the ..
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Simon Singh |
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bfebd4d
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At the same time as acquiring knowledge, the Islamic civilization was able to disperse it, because it had procured the art of paper-making from the Chinese. The manufacture of paper gave rise to the profession of warraqin, or 'those who handle paper,' human photocopying machines who copied manuscripts and supplied the burgeoning publishing industry. At its peak, tens of thousands of books were published every year, and in just one suburb of..
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Simon Singh |
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e642707
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impenetrability of the Navajo code was all down to the fact that Navajo belongs to the Na-Dene family of languages, which has no link with any Asian or European language.
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Simon Singh |
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d01c41b
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He took the messages to a local brewer, who wrapped them in a leather packet, which was then hidden inside a hollow bung used to seal a barrel of beer. The brewer would deliver the barrel to Chartley Hall, whereupon one of Mary's servants would open the bung and take the contents to the Queen of Scots. The process worked equally well for getting messages out of Chartley Hall.
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Simon Singh |
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2c65a90
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In addition to a greater understanding of secular subjects, the invention of cryptanalysis aslo depended on the growth of religious sholarship. Major theological schools were established in Basra, Kufa and Baghdad, where thelogians scrutinized the revelations of Muhammad as contained in the Koran. The theologians were interested in establishing the chronology of the revelations, which they did by counting the frequencies of words contained ..
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Simon Singh |
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92578ce
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The core principle of the trial is simple and can be traced back as far as the 13th century, when the Holy Roman Emperor Frederick II conducted an experiment to find out the effects of exercise on digestion. Two knights consumed identical meals, and then one went hunting while the other rested in bed. Several hours later, both knights were killed and the contents of their alimentary canals were examined. This revealed that digestion had pro..
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Simon Singh |
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3f565e5
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In April 1977, Rivest, Shamir and Adleman spent Passover at the house of a student, and had consumed significant amounts of Manischewitz wine before returning to their respective homes some time around midnight. Rivest, unable to sleep, lay on his couch reading a mathematics textbook. He began mulling over the question that had been puzzling him for weeks--is it possible to build an asymmetric cipher? Is it possible to find a one-way functi..
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Simon Singh |
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27647c1
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Al-Kindi's technique, known as frequency analysis, shows that it is unnecessary to check each of the billions of potential keys. Instead, it is possible to reveal the contents of a scrambled message simply by analysing the frequency of the characters in the ciphertext.
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Simon Singh |
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439acb1
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I am a liar!
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Simon Singh |
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0ebbd27
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The mathematical life of a mathematician is short. Work rarely improves after the age of twenty-five or thirty. If little has been accomplished by then, little will ever be accomplished.
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Simon Singh |
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4370290
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I had written this paper on pancake numbers with help from my adviser, Manuel Blum, who's a well-known computer scientist, and we submitted it to a journal called . I subsequently left graduate school to come and write for . After the paper was accepted, there was an extremely long lag between it being submitted, revised, and published. So, by the time the paper was published, I had been working at for a while, and Ken Keeler had also b..
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Simon Singh |
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f54f231
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I had this very rare privilege of being able to pursue in my life what had been my childhood dream. I know it's a rare privilege, but if you can tackle something in adult life that means that much to you, then it's more rewarding than anything imaginable." - Andrew Wiles"
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Simon Singh |
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30c53b5
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Codebreakers are linguistic alchemists, a mystical tribe attempting to conjure sensible words out of meaningless symbols.
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Simon Singh |
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1267456
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Vigenere's work culminated in his Traicte des Chiffres ("A Treatise on Secret Writing"), published in 1586. Ironically, this was the same year that Thomas Phelippes was breaking the cipher of Mary Queen of Scots. If only Mary's secretary had read this treatise, he would have known about the Vigenere cipher, Mary's messages to Babington would have baffled Phelippes, and her life might have been spared." --
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Simon Singh |
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b0e068a
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As a society, we rightly adore our great musicians and novelists, yet we seldom hear any mention of the humble mathematician. It is clear that mathematics is not considered part of our culture. Instead, mathematics is generally feared and mathematicians are often mocked.
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Simon Singh |
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ba8676f
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many shipwrecks and engineering disasters were blamed on faulty tables. These mathematical tables were calculated by hand, and the mistakes were simply the result of human error. This caused Babbage to exclaim, "I wish to God these calculations had been executed by steam!" This marked the beginning of an extraordinary endeavor to build a machine capable of faultlessly calculating the tables to a high degree of accuracy. In 1823 Babbage desi..
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Simon Singh |
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40c1f85
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a Navajo verb is conjugated not solely according to its subject, but also according to its object. The verb ending depends on which category the object belongs to: long (e.g., pipe, pencil), slender and flexible (e.g., snake, thong), granular (e.g., sugar, salt), bundled (e.g., hay), viscous (e.g., mud, feces) and many others. The verb will also incorporate adverbs, and will reflect whether or not the speaker has experienced what he or she ..
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Simon Singh |