Dünya Avrupa'dan İbaret (Mi?)

Kopernik modern astronomiyi kuran kitabını ölüm döşeğindeyken yayınladı.
Ondan üç asır önce, Arap bilim adamları Müeyyeddin el-Urdi ve Nasreddin el-Tusi bu eserin oluşumunda büyük önem taşıyan teoremleri ortaya koymuşlardı. Kopernik onları kullandı, ama hiçbir kaynak göstermedi.

Avrupa aynaya baktığında dünyayı gördüğünü sanıyordu.
Onun ötesi, bir hiçlik.

Rönesans’ı mümkün kılan üç icat, pusula, barut ve matbaa Çin’den geliyordu. Babilliler, gerçeği Pisagor’a bin beş yüz yıl önce söylemişlerdi. Hindular herkesten çok önce dünyanın yuvarlak olduğunu öğrenmişler ve yaşını hesaplamışlardı. Ve Mayalar yıldızları, yani gecenin gözlerini ve zamanın gizemlerini herkesten çok daha iyi tanımışlardı.

Ancak bu küçük ayrıntılar dikkat çekmeye layık değillerdi. 

Pythagoreans and the Irrationality

Modern people would say “the square root of 2 is irrational”—that is, it is not the ratio of any two whole numbers. But the Pythagoreans would not have said that. How could they? Their notion of quantity was built on the idea of proportions between whole numbers. To them, the length of that hypotenuse had been revealed to be not a number at all.

This caused a fuss. The Pythagoreans, you have to remember, were extremely weird. Their philosophy was a chunky stew of things we’d now call mathematics, things we’d now call religion, and things we’d now call mental illness. They believed that odd numbers were good and even numbers evil; that a planet identical to our own, the Antichthon, lay on the other side of the sun; and that it was wrong to eat beans, by some accounts because they were the repository of dead people’s souls. Pythagoras himself was said to have had the ability to talk to cattle (he told them not to eat beans) and to have been one of the very few ancient Greeks to wear pants.

The mathematics of the Pythagoreans was inseparably bound up with their ideology. The story (probably not really true, but it gives the right impression of the Pythagorean style) is that the Pythagorean who discovered the irrationality of the square root of 2 was a man named Hippasus, whose reward for proving such a nauseating theorem was to be tossed into the sea by his colleagues, to his death.

Numerology and Pythagorean BrotherHood

This, he explained, showed which numbers corresponded to which letters. He took his fingers to the first column: ‘Letters that equal one are A, J, S. Allah, Jehovah, Jesus, Saviour, Salvation. Two is the number of diplomats, ambassadors. Two gives good advice, two you love, you’re a team player, that’s B, K and T, that’s why if you go to a Burger King you can have it your way. Number three controls radio, TV, entertainment and numerology. C, L, U. Of course, you go into radio and television, you don’t have a clue.’ He gave me an ironic wink. ‘But if you learn numerology, it will open you up to the clue of life. Number four: D, M, V. How many wheels on a car? Where do you get the licence? The Department of Motor Vehicles. Five is halfway between 1 and 10: E, N and W. Five is the number of change. If you scramble the letters you get “new”. Six is the number of Venus, love, family, community. When you see a beautiful woman, what do you see? A FOX. Seven is the number of spirituality. Jesus was born on the twenty-fifth, 2 and 5 equals 7. Eight is the number of business, finance, commerce, money. Where do you keep the money? In the headquarters. Nine is the only one that has two letters. I and R. You ever talked to a Jamaican? Everything is irie, man.’

On conclusion he put down his pen and looked me full in the face: ‘This,’ he said, ‘is Jerome Carter’s method of the Pythagorean system.’

Pythagoras is the most famous name in mathematics, entirely due to his theorem about triangles. (More about that later.) He is credited with other contributions, though, such as the discovery of ‘square numbers’.

**

Pythagoras was entranced by the numerical patterns he found in nature, believing that the secrets of the universe could be understood only through mathematics. Yet rather than seeing maths merely as a tool to describe nature, he saw numbers as somehow the essence of nature—and he tutored his flock to revere them. For Pythagoras was not just a scholar. He was the charismatic leader of a mystical sect devoted to philosophical and mathematical contemplation, the Pythagorean Brotherhood, which was a combination of health farm, boot camp and ashram. Disciples had to obey strict rules, such as never urinating towards the sun, never marrying a woman who wears gold jewellery, and never passing an ass lying in the street. So select was the group that those wishing to join the Brotherhood had to go through a five-year probationary period, during which they were allowed to see Pythagoras only from behind a curtain.

In the Pythagorean spiritual cosmos, ten was divine not for any reason to do with fingers or toes, but because it was the sum of the first four numbers (1 + 2 + 3 + 4 = 10), each of which symbolized one of the four elements: fire, air, water and earth. The number 2 was female, 3 was male, and 5 – their union—was sacred. The crest of the Brotherhood was the pentagram, or five-pointed star. While the idea of worshipping numbers may now seem bizarre, it perhaps reflects the scale of wonderment at the discovery of the first fragments of abstract mathematical knowledge. The excitement of learning that there is order in nature, when previously you were not aware that there was any at all, must have felt like a religious awakening.

Pythagoras’s spiritual teachings were more than just numerological. They included a belief in reincarnation, and he was probably a vegetarian. In fact, his dietary requirements have been hotly debated for more than 2000 years. The Brotherhood famously forbade ingestion of the small, round, black fava bean, and one account of Pythagoras’s death has him fleeing attackers when he came to a field of fava beans. As the story goes, he preferred to be captured and killed rather than tread on them. The reason the beans were sacred, according to one ancient source, was that they sprouted from the same primordial muck as humans did. Pythagoras had proved this by showing that if you chew up a bean, crush it with your teeth, and then put it for a short while in the sun, it will begin to smell like semen. A more recent hypothesis was that the Brotherhood was just a colony for those with hereditary fava-bean allergies.

Pythagoras lived in the sixth century BC. He did not write any books. All we know about him was written many years after he died. Though the Brotherhood was lampooned in ancient Athenian comic theatre, by the beginning of the Christian Era Pythagoras himself was seen in a rather favourable light, viewed as being a unique genius; his mathematical insights making him the intellectual forefather of the great Greek philosophers. Miracles were attributed to him, and some authors, rather oddly, claimed that he had a thigh made of gold. Others wrote that he once walked across a river, and the river called out to him, loud enough for all to hear, ‘Greetings, Pythagoras’. This posthumous myth-making has parallels with the story of another Mediterranean spiritual leader and, in fact, Pythagoras and Jesus were temporarily religious rivals. As Christianity was taking root in Rome in the second century CE, the empress Julia Domna encouraged her citizens to worship Apollonius of Tyna, who claimed he was Pythagoras reincarnated.

Pythagoras has a dual and contradictory legacy: his mathematics and his anti-mathematics. Maybe, in fact, as some academics now suggest, the only ideas that can be correctly attributed to him are the mystical ones. Pythagorean esotericism has been a constant presence in Western thought since antiquity, but was especially in vogue during the Renaissance, thanks to the rediscovery of a poem of ‘self-help’ maxims written around the fourth century BC called The Golden Verses of Pythagoras. The Pythagorean Brotherhood was the model for many occult secret societies and influenced the creation of freemasonry, a fraternal organization with elaborate rituals that is believed to have almost half a million members in the UK alone. Pythagoras also inspired the ‘founding mother’ of Western numerology, Mrs L. Dow Balliett, an Atlantic City housewife who wrote the book The Philosophy of Numbers in 1908. ‘Pythagoras said the Heavens and Earth vibrate to the single numbers or digits of numbers,’ she wrote, and she proposed a system of fortune-telling in which each letter of the alphabet corresponded with a number from 1 to 9. By adding up the numbers of the letters in a name, she asserted, personality traits could be divined. I tested this idea on myself. ‘Alex’ is 1 + 3 + 5 + 6 = 15. I completed the process by adding the two digits of the answer, getting 1 + 5 = 6. This gives me a name vibration of six, which means that I ‘should always be dressed with care and precision; be fond of dainty effects and colors, lifting your especial colors of orange, scarlet and heliotrope into their lighter shades, yet always keeping their true tones’. My gems are topaz, diamond, onyx and jasper, while my mineral is borax, and my flowers are tuberose, laurel and chrysanthemum. My odour is japonica.

Numerology, of course, is now an established dish on the buffet of modern mysticism, with no shortage of gurus willing to advise on lottery numbers or speculate on the portent of a prospective date. It sounds like harmless fun—and I enjoyed my conversation with Jerome Carter immensely—yet giving numbers spiritual significance can also have sinister consequences. In 1987, for example, the military government in Burma issued new banknotes with a face value divisible by nine—for the sole reason that nine was the ruling general’s favourite number. The new notes helped precipitate an economic crisis, which led to an uprising on 8 August 1988 – the eighth of the eighth of ’88. (Eight was the anti-dictatorship movement’s favourite number.) The protest was violently put down, however, on 18 September: in the ninth month, on a day divisible by nine.

**

In some commentaries about Pythagoras it is said that before he founded the Brotherhood he travelled on a fact-finding mission to Egypt. If he had spent any time on an Egyptian building site he would have seen that the labourers used a trick to create a right angle that was an application of the theorem that would later gain his name. A rope was marked with knots spread out at a distance of 3, 4 and 5 units. Since 32 + 42 = 52, when the rope was stretched around three posts, with a knot at each post, it formed a triangle with one right angle.

**

Rope-stretching was the most convenient way to achieve right angles, which were needed so that bricks, or giant stone blocks such as those used to construct the Pyramids, could be stacked next to and on top of each other. (The word hypotenuse comes from the Greek for ‘stretched against’.) The Egyptians could have used many other numbers in addition to 3, 4 and 5 to get real right angles. In fact, there is an infinite number of numbers a, b and c such that a² + b² = c². They could have marked out their rope into sections of 5, 12 and 13, for example since 25 + 144 = 169, or 8, 15 and 17, since 64 + 225 = 289, or even 2772, 9605 and 9997 (7,683,984 + 92,256,025 = 99,940,009) though that would hardly have been practical. The numbers 3, 4, 5 are best suited to the task. As well as being the triple with the lowest value, it is also the only one whose digits are consecutive integers. Due to its rope-stretching heritage, the right-angled triangle with sides that are in the ratio 3:4:5 is known as an Egyptian triangle.

Mathematics Does Not Age

Unlike the humanities, which are in a permanent state of reinvention, as new ideas or fashions replace old ones, and unlike applied science, where theories are undergoing continual refinement, mathematics does not age. The theorems of Pythagoras and Euclid are as valid now as they always were—which is why Pythagoras and Euclid are the oldest names we study at school. The GCSE syllabus contains almost no maths beyond what was already known in the mid seventeenth century, and likewise A-level with the mid eighteenth century. (In my degree the most modern maths I studied was from the 1920s.)

Dünyanın Yuvarlaklığı

“Herhalde en çok kendi adını taşıyan matematik kuramıyla tanınan Pisagor, Dünya'nın yuvarlak olabileceğini öne süren ilk kişiydi. Kuramı destekleyecek sağlam kanıta sahip değildi, fakat tanrıların dünyayı en mantıklı ve en güzel şekilde, yani bir küre olarak yarattıklarına inanıyordu. Yaklaşık yüzyıl sonra Platon bu düşünceyi destekleyerek, bizi dengelemek için dünyanın diğer tarafında başka bir kara kütlesinin olması gerektiğini savundu, ama bu düşünce de felsefi bir varsayımdan öteye geçmiyordu.

Dünya'nın yuvarlak olduğuna dair bilimsel kanıt öne sürmek, Platon'un öğrencilerinden Yunan filozof Aristo'ya düştü. "O zamanlar sağduyu sahibi herkes Dünya'nın düz olduğunu görebiliyordu," diyor Nurse. "Ama Aristo işin doğrusunu biliyordu. Zira takımyıldızların gökyüzünde güneye doğru giden bir yolcu gibi gözüktüğünü ve ay tutulması sırasında Dünya'nın Ay'a düşen gölgesinin yuvarlak olduğunu gözlemlemişti. Bu iki gerçek Dünya'nın aslında yuvarlak olduğunu kanıtlıyordu.”

“1966 yılında nadide bir mamut dişi günümüz Ukrayna'sı içinde Mezhiriç'te bulundu. Böyle bir dişin bulunması ilginç olmakla birlikte, özellikle heyecan verici değildi. Buluşu özel yapan, dişin üzerine çizilen haritanın yaklaşık 12.000 yıl öncesine dayanan, bilinen en eski harita olmasıydı. Bu buluşu gölgede bırakabilecek tek harita ise Kerkük yakınlarında bir kil tablet üzerinde bulunan ve 27.000 yıl eskiye uzanan harita olsa gerekti. Kesin olan şu ki, binlerce yıldır evlerinden uzaklara giden insanlar yazılı bir rehbere ihtiyaç duyuyorlar.

MÖ yaklaşık 610 ile 547 yılları arasında yaşayan Yunan filozof Anaximander ilk bilimsel coğrafyacı ve haritacı sayılmaktadır. Onun dünya haritası sadece bildiği karaları içeriyordu ve düz bir tepesi olan silindir bir dünya gösteriyordu. Düz Dünya fikri, Pisagor'un Dünya'nın yuvarlak olabileceğini söylediği MÖ 500 civarına kadar doğru kabul ediliyordu. Pisagor'dan birkaç asır sonra Aristo, Dünya'nın Ay'a düşen gölgesinin yuvarlak olması ve seyyahların güneye yolculuklarında tespit ettikleri yıldızların kuzey yarıkürede görülememesi gerçeğinden hareketle Dünya'nın yuvarlaklığını kanıtladı.”