The Future of Everything: The Science of Prediction
Page 3
The oracular ceremonies were held once per month, except during the three-month winter break, when Delphi was often covered in snow. Suppose you are a theoprope, a supplicant. You arrive by boat at the harbour of Kirrha, in the Gulf of Corinth, then make the journey up into the mountains, reaching Delphi as night falls.
You have with you two things: a written question and, for reasons that will become obvious, a young goat (which you purchased from a goatherd outside the town). You spend the night at a crowded inn, then get up early the next morning to join the long line of people outside the temple. In your mind is the question you have carried all this way. Perhaps it relates to a marriage, or treatment of an illness, or a business concern.
Your growing anxiety isn’t helped when you notice that some people appear to be jumping the queue, after offering the priests extravagant bribes. But finally it is your turn. A priest beckons you to climb the steps of the temple. In your arms is the small, warm goat. You feel it trembling with fear. You hand it to the priest, who takes it towards a blood-stained altar. Another priest has at the ready a long bronze blade. On the walls, you notice, are inscribed rather bland motivational messages. Know thyself. Avoid excess. A single letter E. What can that mean? While the first two priests busy themselves with the poor struggling animal, another leads you to the spring near the temple. You have to shower before they will let you into the pool. As you wash, you try to close your ears to the goat’s plaintive bleats, which are soon followed by silence. You hope that Apollo is satisfied by the humble sacrifice.
Once purified, you are led by a high priest to the inner sanctum. And there she is: the Pythia, the oracle. She sits on a threelegged bronze stool, the tripod. The room, you notice, has a peculiar sweetish smell—some strange vapour that seems to be emanating from the earth itself.5 The Pythia is a middle-aged woman. Her hair is thin and grey, her eyes appear glazed. She doesn’t seem to notice you come in. Suddenly, you feel very afraid of this person.
Before you can back out of the room, the high priest reads your question aloud. Again, the Pythia fails to react. She sways slowly back and forth on her tripod. You wonder if she has heard.But then she starts to make a noise. Not exactly speech or singing, but s nonsense. You listen, but it is like tryiomething in between, on the edge of sense andng to make sense of the call of birds or the rustling of leaves in a storm.
After some time, you’re not sure how long, the Pythia falls silent. It is as if a switch in her head just turned off. You notice how drained she looks. The high priest steps forward. Whatever language she was speaking, he must understand it, because he reads out a neat response in hexameter verse. You’re trying to figure out what it means as they lead you down the steps of the temple. And you’re still trying to figure it out days later, when you eventually get home. But when you announce your decision to your waiting family, it feels like you knew it all along.
According to the philosopher Heraclitus, the Pythia never gave a straight answer, but only hinted at the truth. King Croesus of Lydia famously asked the Pythia if he should invade Persian territory. The oracle told him that if he did, a mighty empire would be destroyed. He took this as a green light, but unfortunately, the empire she was referring to was his own.6
Despite the equivocal nature of the prophecies, the oracle played an enormously important role in Greek culture, especially in the Archaic period (the eighth to sixth centuries B.C.). Most major decisions about war or politics were made in consultation with it. The oracle retained its power for almost a thousand years, gradually falling into decline with the rise of Christianity, and in the third century A.D., it made its final prediction: the gods would no longer speak at Delphi.
APOLLO’S ARROW
The poet Iamblichus relates a tale about the oracle when it was still at the height of its powers. A gem engraver called Mnesarchus visits to ask whether a journey he is about to undertake will be profitable. The oracle replies that it will; furthermore, the man is told, his wife, who unknown to him is pregnant at the time, will give birth to a son “surpassing in beauty and wisdom all that had ever lived.”7 Mnesarchus realizes that the child has been sent by the gods. When he is born, he is named Pythagoras, “signifying that such an offspring had been predicted by the Pythian Apollo.”8
Mathematician, philosopher, even Olympic trainer, Pythagoras would go on to found a new system of prediction based not on oracles but on the power of numbers. He was literally a demigod to the Greeks—some said he had been fathered by Apollo.9 This was a story that his many followers never denied. A proof of Pythagoras’s divinity was thought to be his golden thigh, a description that perhaps referred to a birthmark. Iamblichus tells of Abaris, a Hyperborean priest or druid, who was returning to his home in the north after a fundraising mission for his temple. The Hyperboreans were the ancestors of Celtic tribes and worshippers of Apollo. On his way through Italy, Abaris saw Pythagoras and became convinced by his appearance that he was none other than Apollo himself. He offered Pythagoras the most precious thing in his possession, a sacred arrow said to have belonged to Apollo, like the ones that killed Python. The arrow, Abaris claimed, had magical powers: whenever he had encountered obstacles on his travels, such as impassable rivers or mountains, the arrow had enabled him to fly across. He had used it also to stop epidemics and to purify Sparta of a mysterious toxin that was poisoning the city (perhaps toxic gases rising from Mount Taygetus).
Pythagoras accepted this magical arrow without any hint of surprise, “as if he was in reality a God himself.”10 He took Abaris aside, showed him his golden thigh to prove that Abaris was not mistaken, and explained that “he had come for the purpose of remedying and benefiting the condition of mankind, and that on this account he had assumed a human form, lest men being disturbed by the novelty of his transcendency, should avoid the discipline which he possessed.”11
No written works by Pythagoras have survived. We know that he was born on the island of Samos, in the Aegean Sea, sometime in the sixth century B.C. In his life, he travelled and studied extensively: with the mathematician Thales of Ionia (who forecast the yields of harvests, and predicted an eclipse of the sun in 585 B.C.), the Phoenician sages of Syria, and the high priests of Egypt. He stayed in Egypt until the Persians invaded and he was taken to Babylon. He spent a further several years in the capital of Mesopotamia before finally returning to Samos.
In Samos he set up a school, known as the semicircle, to study philosophy and hold political meetings. He lived outside the city in a secluded cave, where he carried out his mathematical research. As his popularity and reputation grew, the citizens of Samos began to draw on his help with city affairs, intruding on the privacy and calm that he required for his studies. At about the age of forty, Pythagoras left Samos and went to Croton, in southern Italy. There he formed a new, secretive society.
THE MOST PERFECT NUMBER
As both teacher and spiritual leader, Pythagoras attracted hundreds of students. Those in his inner circle, both men and women, were known as mathematikoi. To join the commune, they had to give up all personal possessions, follow a strict vegetarian diet and ascetic lifestyle, and study five years under a vow of silence. Pythagoras explained that the aim of these privations was to train the applicant’s power of reason: “Excess brings lust, intoxication and uncontrolled emotions, which drive men and women into the abyss. Greed brings envy, theft and exploitation. These thickets, which choke the soul, must be cleared out by systematic discipline, as if with fire and sword. Only when reason is liberated from such evils are we able to implant what is useful and good within the soul.”12
The mathematikoi were the hard-core Pythagoreans, the true priests of Apollo. They could quit the arduous program whenever they wanted, and recover all the material goods they had donated, times two. But if they did, a monument was constructed to them as for a burial, and they were regarded as dead; every time a Pythagorean passed them in the street, he would act as if they had never met.
The outer circle were know
n as akousmatics. They lived in their own houses, kept their possessions, were allowed to eat meat, and visited the society only during the day. However, they were not allowed to see Pythagoras, and were not taught the cult’s inner secrets. When the akousmatics attended lectures, they sat in the back, separated from the master by a screen. They were never shown mathematical proofs, and instead had to accept the results ipse dixit, because Pythagoras said they were so.
Life in the commune adhered to a strict routine. Solitary or group walks were followed by lectures on astronomy, music, or mathematics; corrective counselling; and exercise sessions similar perhaps to Tai Chi or yoga. Some of the exercises might have been of Pythagoras’s own devising; while in Samos, he had turned the athlete Eurymenes into an Olympic champion by making him follow an arduous training regimen. Lunch was bread and honey or honeycomb; dinner was vegetarian. In the evenings, Pythagoras would give lectures. These were typically attended by at least 600 people, with the mathematikoi at front and everyone else shielded by the screen.
One of the topics for the evening lectures was no doubt foretelling the future. Pythagoras had studied under Thales and was said to have surpassed his mentor in the art of prognostication. Like Thales, he is said to have been able to predict eclipses, harvests, and earthquakes, and perhaps through his influence with Apollo, could halt epidemics and calm storms. He taught many systems of prediction, such as the reading of entrails or listening to oracles. But for him, the highest form of prediction was divination through numbers, which Pythagoras thought connected more closely with the “celestial numbers of the gods” than other methods.13 One of his students, Empedocles, became known as Alexanamos, or “Averter of Winds,” for being able to predict and control the weather. (His modern counterpart is the U.S. evangelist Pat Robertson, who claims to have used the power of prayer to steer the course of hurricanes.) Just as Apollo’s arrow had enabled Arabis to dart across landscapes without needing to traverse mountains or rivers, so the magic of numbers allowed the Pythagoreans to dart through time and foresee future events without having to wait for them to happen.
The details of how this system of numerical prediction worked remain unknown, since the group was obsessed with secrecy. According to Iamblichus, “Their writings and all the books which they published were not composed in a popular and vulgar diction, so as to be immediately understood, but in such a way as to conceal, after an arcane mode, divine mysteries from the uninitiated.”14 Rather than rely on written records, the Pythagoreans were trained to improve their powers of memory; each morning before arising, for example, they would recount to themselves the exact events of the previous day. We would know little of Pythagoras’s teachings if it weren’t for the writings of subsequent philosophers, such as Plato and Aristotle. This secrecy certainly also added to Pythagoras’s mystique.
For the Pythagoreans, numbers were much more than a tool for prognostication. Rather, they were what united the reason of man with the workings of nature. Each number was a kind of mystical entity with its own special properties. By understanding these properties, man could gain insight into the workings of the world, see into the future, and become closer to the gods.
The monad represented the initial unified state from which the universe was created, and was associated with divine intelligence. The division of the monad into the dyad, the number two, symbolized polarization: unity became duality. The dyad therefore signified mutability, or the ability to change appearances, and also unlimited excess, conflict, and indeterminacy—all negative qualities in a commune where applicants were selected for their ability to control anger and passion. “Lamentations, weepings, supplications, entreaties were considered abject and effeminate and neither gain, desire, anger, ambition nor anything of a similar nature became the cause of dissension among them.”15 The number three, the triad, enabled all things with a beginning, a middle, and an end, or a past, a present, and a future. It was the number associated with prophecy, as in the tripod at Delphi. Number four, the tetrad, represented completion, as in the four seasons that make up a year. The greatest and most perfect of all numbers was the decad, ten. Just as the first four numbers sum to ten, the decad was also the sum of the laws of nature. The following arrowhead arrangement of ten dots, known as the tetractys, was used by the Pythagoreans as a sacred symbol:
RIGHT VS LEFT
The dyad represented the division of the universe into two groups. Table1.1, a list of ten pairs of antitheses, was compiled by the Pythagoreans in reference to the decad and documented in Aristotle’s Metaphysics. These antitheses were believed to represent fundamental organizing principles of the universe.
TABLE 1.1
Limited Unlimited
Odd Even
One Plurality
Right Left
Male Female
At Rest In Morion
Straight Crooked
Light Darkness
Square Oblong
Good Evil
Pythagoras believed in reincarnation and claimed to be able to remember his past lives. He once rescued a dog from being beaten on the street and told the owner that he could tell by the animal’s cries that it was the soul of his late friend Abides. Through repeated incarnations, the Pythagoreans believed that they could choose limited over unlimited, light over darkness—the first column over the second—and thus achieve divinity.16
Why the Pythagoreans chose these particular items for their list of opposites is unclear (though we explore some possible reasons later). It is interesting to compare it with the following lists (on page 30), which are from very different sources.
TABLE 1.2
Left Brain/Right Side Right Brain/Left Side
Intellect Intuition
Abstract Concrete
Analytic Holistic
Rational Intuitive
Objective Subjective
TABLE 1.3
Yang Yin
Odd Even
Conscious Unconscious
Right Side Left Side
Masculine Feminine
Aggressive Melding
Light Darkness
Reason Emotion
TABLE 1.4
Physical Science The Humanities
Hard Soft
Determinism Free Will
Reason Feeling, Emotion
Objective Subjective
Quantity Quality
Specialism Holism
Prose Poetry
Male Female
Clarity Mystery
The list in table 1.2 was the result of so-called split brain studies, conducted with patients who had been disabled by extremely severe epileptic seizures.17 The human brain is divided into two hemispheres, with the left controlling the right side of the body and vice versa. In a last attempt at therapy, connections between the two hemispheres were severed to stop the seizures spreading across the brain. While the treatment succeeded in controlling the seizures, it effectively isolated the two sides. Through a series of experiments, the researchers attempted to determine the functions of each hemisphere. The left brain, they came to believe, is associated with abstract, rational thinking, and the right brain with holistic and intuitive modes of thought. In a healthy brain, the two sides work in concert, so it is never possible to cleanly separate their functions.
Table 1.3 is from the I Ching, or Book of Changes.18 From these tables, one might deduce that Pythagoras was a left-brain (right-hand) kind of guy, more yang than yin. As Iamblichus wrote, “The right hand he called the principle of the odd number and is divine, but the left hand is the symbol of the even number and of that which is dissolved.”19 Apollo was the god of reason, and one of the commune’s aims was to elevate rational, objective reasoning over subjective, emotional behaviour. (The preference for the right hand has continued in our language—the word “sinister” is from the Latin for left.) Table 1.4 is from a longer list compiled by the philosopher Mary Midgley, who wrote in 1985 that the instruction to keep with the items in the first column “has fo
r the last century usually been issued to English-speaking scientists with their first test-tube and has often gone with them to the grave.”20
Science has changed a great deal since the time of Pythagoras, but the emphasis on using reason and analysis to provide hard, fixed solutions for particular, specialized problems has remained the same. The development of quantum physics, which revealed the wavelike properties of matter, along with attempts to adopt a rounder, more holistic perspective, as in systems biology, has softened this distinction. But scientists on the whole are still squares, not oblongs, and the idea, so prevalent in science, that complex phenomena should be reduced to simple ones is Pythagorean. As we will see, this tendency to drive on the right has been both the strength and the weakness of scientific forecasting.
MUSIC OF THE SPHERES
Like Apollo, who was frequently portrayed with a lyre, Pythagoras was a musician. He believed that music had healing powers and could be used to calm the soul. A powerful proof of the importance of numbers was the discovery, attributed to him, of their role in music. A string on a lyre, when plucked, will give a particular note. Fretting the string at a position halfway down gives a note differing by an octave; a third of the length down gives a musical fifth; and one quarter the length a musical fourth. Use a different string, or an electric guitar, and the same relationship holds.
Pythagoras realized that the relationship between pleasing notes was all a question of numbers. And if music, one of the most expressive art forms, could be reduced to numbers, then so perhaps could everything else. In the Pythagorean cosmos (a word he invented), the stars, planets, moon, and sun were contained in nested, concentric, transparent spheres, all of which rotated around the earth according to a cosmic harmony, which Pythagoras called the Music of the Spheres. He argued correctly that the earth itself was a sphere that caused night and day by its revolution, and that the seasons were the result of the angle of the earth’s axis with the sun. Even time itself was cyclical, repeating itself once every Great Year. This was the period it took the sun, moon, and planets to return to the same configuration, estimated by ancient astronomers to be around 10,800 years.21