The Music of Pythagoras

by Kitty Ferguson

  While Russell and his colleagues recognized there were questions they could not answer, they preferred to leave them unanswered rather than cling to what they felt were foolish and misleading “answers,” or believe there are “higher” sources of answers:

  The pursuit of truth, when it is profound and genuine, requires also a kind of humility which has some affinity to submission to the will of God. The universe is what it is, not what I choose that it should be. Towards facts, submission is the only rational attitude, but in the realm of ideals there is nothing to which to submit.7

  Reading that, one cannot avoid the conclusion that Russell was far more ambivalent about the issue of “discovery” versus “invention” than he was willing to admit.

  Though he deplored the way mathematics had been “misused” in other areas, Russell believed that what he was insisting philosophy do—utilize logical analysis, adopt methods of science, and try to base its conclusions on impersonal, disinterested observations and inferences—should be applied in all spheres of human activity. This would bring about a decrease of fanaticism and an increase in sympathy and mutual understanding. He attempted, with scant success, to apply logical analysis to fields such as metaphysics, epistemology, ethics, and political theory, making (ironically) what was arguably a “Pythagorean” leap of faith that what seemed to be a good idea in one area of experience would be a good idea in all.

  Russell decried yet another aspect of the Pythagorean legacy: The Pythagoreans lived by an ethic that held the contemplative life in high esteem and had bequeathed to the future something he called “the contemplative ideal.” In the fable about the people at the Olympic Games, Pythagoras and his followers were in the third group, those who had come to watch. These “onlookers” celebrated not practical but “disinterested” science—in other words, they were disengaged from the world of buying, selling, and competing, able to view the whole scene with greater objectivity—thinking that their roles as independent observers placed them in a better position on the path of escape from the eternal circle of the transmigration of souls. Russell contrasted this view with a modern set of values that sees the players on the field as superior to mere spectators, and that admires politicians, financiers, and those who govern the state, the “competitors in the game,” above those who keep to the sidelines and watch and make wise observations.

  Nevertheless, said Russell, the elevated status of the “gentlemanly on-looker” who does not dirty his hands has endured, and this began in ancient Croton, was carried forward with the Greek idea of genius, then with the monks and scholars of the church, and later with the academic university life. He criticized all these, including “saints and sages,” who, except for a few activists, had lived on “slave labor,” “or at any rate upon the labor of men whose inferiority is unquestioned.” It is these “gentlemen,” these “spectators at the Games,” he lamented, who have given us pure mathematics, and that contribution has meant, for them, prestige and success in theology, ethics, and philosophy, because pure mathematics is generally regarded as a “useful activity.” Russell did not mention that he himself was one of these gentlemen he was criticizing—literally so, for he was born into the British nobility, studied at the University of Cambridge and became a fellow of Trinity College there, and spent most of his life as an academic and writer. However, he did, certainly, become one of the activists as well.

  Parodoxically, Russell believed passionately in some ideals that he could not have arrived at by confining himself to strict empiricism, deductive thinking, and the scientific method. Perhaps his intuitions about what is right and what is wrong were, indeed, self-evident. To judge from his writings, these ideals became for him a higher priority than his logical analysis. He was a pacifist during World War I, and this unpopular stand cost him his Cambridge fellowship and landed him in prison for a while, but in 1939, in the face of the Nazi threat, he renounced pacifism. He was a lifelong, outspoken opponent of Nazism, Soviet communism, and belief in God. He campaigned vigorously for nuclear disarmament and against the Vietnam War. In these causes he was superbly able to write essays for popular readers that often seemed to begin as polemics but ended with reasoned arguments.

  Russell was an impassioned and influential man, who recognized that there was a directionality built into human beings that makes us at least seem to be existing somewhere on a continuum from evil to good, ugliness to beauty, unfairness to justice, mediocrity to greatness, weakness to strength, with the ultimate in every case being off the scale, over the horizon of human comprehension or imagination. In his espousal of a mathematical philosophy that would soon be outdated, but still more in the positions he took against nuclear weapons, war, and what he saw as cruel dogmatisms, Russell, paradoxically, lived by this Platonic, perhaps Pythagorean-based view of the world. Ironically, it was the decisions he made on that foundation that ultimately made him memorable.

  ARTHUR KOESTLER’S PICTURE of Pythagoras was far more positive. Born in Budapest in 1905, Koestler was an author and journalist and probably the most widely read political novelist in the world in the 1940s and early 1950s. His writing highlighted the moral dilemmas caused by the rise of communism and the two world wars. Koestler, like Russell, spent time in prison. While serving as a foreign correspondent in Spain, he was captured by Franco’s troops and sentenced to death. The British government intervened and Koestler was able to return to London. As he aged, he took an increasing interest in science and the history of ideas and knowledge. His 1959 The Sleepwalkers was a masterpiece when it came to splendid writing and an ability to convey Koestler’s passion for science, scientists, and scientific ideas. It was the first in a trilogy that continued in 1964 with The Act of Creation and in 1967 with The Ghost in the Machine. Koestler died in 1983. He was suffering from leukemia and Parkinson’s disease, and he and his wife, both advocates of voluntary euthanasia, together took their own lives.

  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 Laotzu, 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 fervor had been channeled into intellectual fervor, “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 mathematization 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 n
ot mean a loss of “color, 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 marvelous, 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.

  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 realized that Science may become a hymn to the creator or a Pandora’s box, and that it should be trusted only to saints.”

  Arthur Koestler

  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 skeptical 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 practiced 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 labors, 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 analyzed 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 recognize 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 recognizing 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.