Pythagorus (44 page)

In
The Sleepwalkers
, Koestler wrote of Pythagoras: ‘His influence on the ideas, and thereby on the destiny, of the human race was probably greater than that of any single man before or after him.' Koestler called the sixth century B.C. a ‘turning point for the human species', a ‘miraculous century'. It was also the century of Buddha, Confucius, and Lao-tzu, and in the Greek world, Thales and Anaximander. Still, it was, in a sense, like an orchestra tuning up,

each player absorbed in his own instrument only, deaf to the caterwaulings of the others. Then there is a dramatic silence, the conductor enters the stage, raps three times with his baton, and harmony emerges from the chaos. The maestro is Pythagoras of Samos.

For Koestler, the power of the Pythagorean vision came from its ‘all-embracing, unifying character; it unites religion and science, mathematics and music, medicine and cosmology, body, mind, and spirit in an inspired and luminous synthesis'. ‘Cosmic wonder and aesthetic delight no longer live apart from the exercise of reason', and the intuitions of religion had also been joined to the whole in the concept of a scientific/philosophical search for God. Religious fervour had been channelled into intellectual fervour, ‘religious ecstasy into the ecstasy of discovery'. Koestler concluded that although one cannot know which specific discoveries to attribute to what person or to what date, it is clear that the ‘basic features were conceived by a single mind', making Pythagoras the founder of ‘a new religious philosophy and of science as the word is understood today'. In fact, the transmigration of souls itself was not a new religious philosophy, and Koestler gave a long description of Orphic religion. As for founding science, the discovery of the ratios of musical harmony was, Koestler said, the ‘first successful reduction of quality to quantity, the first step towards the mathematisation of human experience'.

According to Koestler, the reduction of experience to a straitjacket of numbers rightly arouses misgivings in the modern world, but for the Pythagoreans it did not diminish or impoverish anything. It enriched them. Because numbers were sacred to the Pythagoreans, reduction to numbers did not mean a loss of ‘colour, warmth, meaning, and value'. Instead, marrying music to numbers ennobled music. Koestler may be correct, but one could also reasonably believe that the Pythagoreans did not think numbers were sacred until they had made the discovery of their connection with music. Possibly only after that did numbers seem to them to have the marvellous, immortal qualities that Koestler ecstatically described, and come to be regarded as a link between humans and the divine mind. Koestler probably would have liked either interpretation equally well.

Arthur Koestler

Koestler also singled out the idea that ‘disinterested science leads to purification of the soul and its ultimate liberation' as a major contribution of the Pythagoreans, and wrote about the enormous historical importance of this idea. ‘Harnessing science to the contemplation of the eternal, entered, via Plato and Aristotle, into the spirit of Christianity and became a decisive factor in the making of the Western world.' Indeed it did keep the feeble flame of something resembling science alive during the Middle Ages and caused scholar-clerics to welcome with immense thirst and enthusiasm the rediscovery of ancient knowledge. Through the time of Kepler and Galileo, the scientific quest and the quest for the knowledge of God were considered to be the same quest.

As for Pythagorean secrecy, Koestler wrote that ‘even a lesser genius than Pythagoras might have realised that Science may become a hymn to the creator or a Pandora's box, and that it should be trusted only to saints'.

Koestler seductively clothed the bare skeletal outline of Pythagoras with the garments of creative hindsight and beautiful prose, and fashioned a legend for the twentieth century. But, remembering the little ancient community, trapped in many ways in the thinking of that time, able – except for the great discovery of rationality in the ratios of musical harmony – to make only feeble attempts to link numbers with nature and the cosmos and creation, believing in a unity of all being that there was no way to demonstrate, one is forced to conclude that he was looking through the glasses of his own ideals. Nevertheless, his interpretation makes wonderful reading. He was truly the master of the magnificent overstatement that sounds so beautiful and convincing that we long for it to be correct. His is an ‘ode to Pythagoras', or an orchestral variation on a brief, sketchy ‘theme of Pythagoras', but it resonates better than any other existing account with the awe with which the modern world – hardly knowing Pythagoras at all – nevertheless regards his name. Koestler's retelling is not quite the truth about Pythagoras, and it is also more than the truth. In any case, it is Koestler's truth.

At the end of Koestler's chapter about Pythagoras, there are two statements with which not even the most sceptical scholars would disagree. The first is that Pythagoreanism had the ‘elastic' quality of all truly great systems of ideas, the ‘self-regenerating power of a growing crystal or a living organism'. The second is that the Pythagoreans were probably the first to believe that mathematical relations hold the secrets of the universe. The world, concluded Koestler, ‘is still blessed and cursed with this heritage'. By ‘cursed' he meant that the modern age should rightly have misgivings about the reduction of experience to a straitjacket of numbers. The Pythagorean conviction that numbers hold the secrets of the universe had carried us magnificently to the edges of time and space, but ‘our hypnotic enslavement to the numerical aspects of reality has dulled our perception of non-quantitative moral values; the resultant end-justifies-the-means ethics may be a major factor in our undoing'.

CHAPTER 19

The Labyrinths of Simplicity

Twentieth and Twenty-first Centuries

The ‘scientific method'
as it is taught in science classrooms and practised by scientists all over the world is not very old when compared with the spans of time covered in this book. It emerged in the seventeenth century. No committee put it together, not even one so august as the Royal Society of London for Improving Natural Knowledge or the French Academy. ‘Emerged' is the correct word. In their day-to-day labours, Tycho Brahe, Galileo, and Johannes Kepler knew no ‘scientific method'. They were working out, by trial and error, employing common sense and genius, how science from their time forward was going to operate. But their procedure for systematically separating what is true from what is not had not yet been assigned a name or analysed precisely. Little if any consideration was given to the fact that it incorporated and rested on unproved articles of faith that are not even self-evident – principles that were much older and already so embedded in the European worldview that no one thought to debate whether they were valid. Bertrand Russell might lament that the practice of building on some truths without questioning them was being employed in other areas besides geometry, but with regard to science, G. K. Chesterton was on target when he wrote, ‘You can only find truth with logic if you have already found truth without it.'

From a twentieth- or twenty-first-century vantage point – with hindsight and knowledge of what has happened since the seventeenth century – it is easier to recognise what an essential role the Pythagorean legacy played in providing this basic foothold for the scientific method and how much it came into its own in that method. The conviction that the universe is rational, the belief in underlying order and harmony, the confidence that truth is accessible by way of numbers, and the assumption that there is unity to the universe have become the pillars undergirding science. In the twentieth century, challenge after challenge was hurled at this list, by investigators and by nature itself, but the scientist who gets up and goes to work in the morning does so largely assuming that these articles of faith do hold true. An essentially Pythagorean faith remains as instrumental in driving science as the Aristotelian insistence on observation and experiment. Indeed, if the universe is not rational and ordered, if numbers are not a reliable guide, if there is no unity to the universe, observation and experiment are shortsighted and futile and there is little possibility of doing science at all. The conclusion is inevitable: Either the Pythagoreans in the sixth century B.C. brilliantly and prophetically uncovered truths that have not failed to hold in two thousand, five hundred years . . . or their persuasive philosophy has for all these centuries pulled the wool over our eyes so effectively that we are incapable of recognising and following up on evidence that would expose their worldview as a mirage . . . or (a third possibility) when Arthur Koestler wrote of a truly great system of ideas, with the ‘self-regenerating power of a growing crystal or a living organism', he was only clothing a group of self-evident ideas, erroneously traced to an ancient cult, in beautiful language.

It was not only the ancient assumptions underlying modern cutting-edge science that made the twentieth century a Pythagorean century. There were also discoveries that caused crises of faith in the power of numbers and the rationality of the universe.

One of the most dramatic, successful stories of trusting numbers and mathematics as guides into the unknown in a scientific search was the discovery of black holes. The physicist Stephen Hawking commented, ‘I do not know any other example in science where such a great extrapolation was successfully made solely on the basis of thought.'
1
The ‘thought' was mathematical thought. By the mid-1960s physicists had discovered solutions to Albert Einstein's equations that made it difficult not to conclude that there must be black holes in the universe, even though there was no observational evidence for them. By the mid-1980s, confidence ran high that black holes did indeed exist, and there were several ‘candidates', but still no unequivocal evidence. It was not until the 1990s that there was convincing observational evidence of the presence of several black holes and reason to conclude that there are many, many more. Still, the evidence was indirect, circumstantial. The discovery of a black hole was an ingenious collaboration of theory, mathematics, and observational astronomy. But there is now little question that black holes do exist, and old candidates and new ones are not difficult to evaluate.

The nonexpert public, though intrigued by such discoveries as black holes and eager to read about Stephen Hawking, has not been so entirely convinced by the power of mathematical thinking as the scientists, nor by the travelogues into the wilds of physics theory that these experts have provided for those who cannot follow the equations. In 1988, Hawking's first wife, Jane Hawking, told an interviewer, ‘There's one aspect of his thought that I find increasingly upsetting and difficult to live with. It's the feeling that, because everything is reduced to a rational, mathematical formula, that must be the truth.'
2
One could well imagine the wife of Pythagoras saying something like that. Jane Hawking was not the only one who had trouble sharing the faith in mathematics that leads the thinking of theoretical physicists. Arthur Koestler deplored ‘our hypnotic enslavement to the numerical aspects of reality'.

Writers like myself who explain science for nonexpert readers are often approached by intelligent people who have read of such things as the extra dimensions of physics theory – sometimes more dimensions, sometimes fewer, but hardly ever just the three of space and one of time that humans experience – and who say, ‘I can picture it easily enough the way you describe it, the dimensions rolled up into little hose-like tubes, but how does it actually link with reality? Is it only a mathematical reality?' That ‘only' betrays a suspicion that mathematicians and physicists immersed in their own Pythagorean universe are at a loss to explain away. In the sixth century B.C., no one could see ten bodies in the heavens. In the twenty-first century, not only can no one see the extra dimensions, no one can even
imagine
them. Hawking has admitted that anyone who thinks he or she can imagine what the extra dimensions would be like has either made a large evolutionary leap in mental capacity or is mistaken. But that has not kept theoretical physicists from following eagerly the paths of the equations in which such things do make sense.

Scientists are not the only ones who adopt a Pythagorean view of numbers as the strongest vehicles on the avenue to truth and progress. Pythagorean faith in mathematics shows up at nearly all school curriculum meetings. Though no one proposes resurrecting the quadrivium, educators seem to have decided that a child who can talk and read and calculate holds the essential keys to all knowledge, and many would argue that the third – ‘calculate' – is potentially the most powerful by far. Music has, however, tended to fall by the wayside.

When Hawking wrote in the late twentieth century about his high hopes that he and others would find the Theory of Everything that would unify all of physics, and when he brought that quest into the public mind in his
Brief History of Time
– even for those who only read
about
that book – he was expressing another Pythagorean theme. Many physicists were hoping, indeed expecting, complete knowledge of the universe to turn out, ultimately, to be unified, harmonious, and simple. This hope was not based only on wishful thinking. Listen, for example, to the way the physicist Richard Feynman traced its history.

There was a time, wrote Feynman, when we had something we called motion and something else called heat and something else again called sound,

but it was soon discovered, after Sir Isaac Newton explained the laws of motion, that some of these apparently different things were aspects of the same thing. For example, the phenomena of sound could be completely understood as the motion of atoms in the air. So sound was no longer considered something in addition to motion. It was also discovered that heat phenomena are easily understandable from the laws of motion. In this way, great globs of physics theory were synthesised into a simplified theory.
3

In the early twentieth century, physics seemed to be coming together in a thoroughly Pythagorean unity. Einstein unified space and time and explained gravity in a way that the physicist John Archibald Wheeler could encapsulate in one short sentence: ‘Spacetime grips mass, telling it how to move; mass grips spacetime, telling it how to curve.'
4
Einstein's theory of special relativity could be summarised in an equation on a T-shirt: E=mc
2
. The Russian mathematician Alexander Friedmann predicted that anywhere we might stand in the universe we would see the other galaxies receding from us, just as we do from Earth, and better understanding of the expansion of the universe has shown he was undoubtedly right, although no one has been able to try it yet. Just as Nicholas of Cusa thought in the fifteenth century, the universe is homogenous.

Two of four forces of nature known to underlie everything that happens in the universe – the electromagnetic force (already a unification) and the weak nuclear force – were combined by the ‘electroweak theory' in the early 1980s. There was also work going on that promised to show that, if we could observe the extremely early universe, it would be obvious that all four forces were originally united and that nature was composed of symmetries well concealed in our own era of the universe's history. James Watson and Francis Crick and their colleagues discovered the simple pattern of the structure of DNA, the double helix. Those who were insisting that Darwin's nineteenth-century theory of evolution was no threat to religious faith were pointing out that it was difficult to imagine anything that could more eloquently support the conviction that there was a brilliant and unified (and some would add, pitiless) rationality behind the universe. John Archibald Wheeler wrote his essentially Pythagorean poem:

Behind it all

is surely an idea so simple,

so beautiful,

so compelling that when –

in a decade, a century,

or a millennium –

we grasp it,

we will all say to each other,

how could it have been otherwise?

How could we have been so stupid

for so long?

All was not, however, a story of undiluted success for the Pythagorean vision of a ‘unity of all being'. Einstein, a firm believer in the unity of nature, spent thirty years trying to construct a theory that would explain electromagnetism in terms of space-time, as he had explained gravity. He never succeeded, and many physicists would blame his failure in part on the fact that he so stubbornly refused to admit quantum mechanics into the picture. But a new theory, called string theory, that saw the elementary particles as tiny strings or loops of string and that certainly had no qualms about accepting quantum mechanics, was gaining supporters in the 1980s. It offered hope of doing what Einstein had failed to do: gathering into the fold the most rebellious of the four forces (when it came to unification) – gravity. As the first decade of the twenty-first century progressed, however, physicists were becoming impatient with string theory. It had been able to come up with no prediction that could be tested in a way that would show whether the theory was correct. Aristotle would have been happier with this development than Pythagoras or Plato, not because Aristotle wanted to tear down theories, but because twenty-first-century mathematical physicists were clearly not out of touch with the need for truth to be linked with the perceptible world. However, even with string theory looking less promising than it had, no one really questioned the essential unity of the universe.

Such faith is hard to lose, especially when no evidence definitively shows that it is wrong. However, some serious mathematical and scientific blows to Pythagorean convictions have occurred during the past one hundred years. Humans seem fated to discover again and again that the universe is not so rational after all – at least, not by the best current human standards of rationality. Such discoveries have challenged and stretched scientists to dig deeper in search of a level of reality where the Pythagorean principles still hold. One of the greatest manifestations of symmetry, harmony, unity and rationality in the universe is the fact that, although drastic changes do occur over time and from situation to situation, and although things can look dramatically different in different parts of the universe – and act in what even seem contradictory ways – the underlying laws that govern how change occurs apparently do not change. Maybe this is convincing evidence that our Pythagorean assumption of unity is correct, or it might be that our assumption is leading us to a false impression. We can only answer by pointing to past experience.

The search for a more fundamental law often begins with the discovery that something that has seemed fundamental and unchanging fails to hold under some circumstances. When that happens, the Pythagorean assumption of unity and symmetry kicks in and compels everyone to conclude that whatever it is they have been regarding as bedrock is not that at all. It is merely an approximation. Researchers put their noses back to the grindstone and explore for a deeper underlying law that does not change.