Pythagoras’s Transmigration Of The Soul: An Atheist’s Nightmare
Pythagoras is regarded as one of the very first philosophers, who founded a cult based on mathematics. He also incorporated spiritual beliefs into his teachings, however, although modern day atheist existentialists of the 21st century, who are partly his philosophical descendants, use a distilled form of numerology to contest that the world is only the material existence we know—and the spiritual is just a figment of our minds.
Pythagoras embraces irrational numbers, however, which have innumerable square roots—and so he falls onto the side of faith as well as fact, as does so much math, due to verifiability through extrapolation. According to Pythagoras, being an immaterial concept, math is well positioned to explain something that cannot be fully conceptualized—and the transmigration of the souls is as provable by his standards, as are the endless gamut of integers in the universe.. In his metaphysics of reincarnation, Pythagoras offers a spiritual side to his philosophic reasoning.
G. K. Chesteron recognizes this important spiritual component to Pythagoras, in The Everlasting Man: Another important tradition descends from Pythagoras; who is significant because he stands nearest to the Oriental mystics who must be considered in their turn. He taught a sort of mysticism of mathematics, that number is the ultimate reality; but he also seems to have taught the transmigration of souls like the Brahmins; and to have left to his followers certain traditional tricks of vegetarianism and water-drinking very common among the eastern sages.
Also, in Siren Land, Norman Douglas attributes Pythagoras with a more Asian approach to spirituality: “Pythagoras, strongly tainted with Orientalism, made his daimon perceptible to the senses, whereas the familiar of Socrates was invisible, the “divine voice” of reason”. So the atheist existentialist’s nightmare is to grapple with the argument that if they embrace the existence of irrational numbers, as Pythagoras did, they must then in turn accept the possibility of an irrational spirit—for what is uncountable in numbers could be roughly equated to what is objectively unprovable in the real world.
Ultimately, however, regardless of whether a spiritual plane exists, or transmigration of the soul is possible—or whether the atheist existentialists are right, and the human essence is all just a mock-up in our thoughts–the end result is still the same. If we cannot know the difference between what we perceive and what is real, then even the truth of the matter would not necessarily change our actions in daily life. It is too easy to forget the enlightenments discovered, in order to return to the uncritical thinking necessary to get through a day.
The most profound mathematical epiphanies are lost on the common person. Wise advances of thought may have serious and lasting consequences on all of human evolution, but for the common thinker, two of the most powerful gifts Pythagoras ever provided were simply a formula to find the lengths of a right-angled triangle’s smaller two sides—and an imminent mathematician’s conviction that the soul exists. Beside aiding carpenters and architects, and a myriad of other professions in their day-to-day applications—the Pythagorean theory also helps the normal human grasp how well the universe fits together.
Beside giving spiritualists cold hard facts for the evidences of their gods, Pythagoras also gave reincarnation credibility to the commoner. Certainly, it can be contested whether the beauty of math and that ofspirituality dovetail together—yet while some may prefer more focus on one or the other, Pythagoras found a balance between the two that served him and his followers well–and which will likely continue to help others who learn of his principles for countless future generations. The Pythagoreans were ruled by strict guidelines. In the cult, silence was primary, as talk was considered to be typically counter-productive.
Crossing this rule of keeping mum was punishable by death. The cult consisted of an inner circle of hard-core mathematicians, while an outer circle of followers were less involved with theoretical practices—and more rehearsed in superstitious stories and cryptic messages. This outer circle would eventually split off, before Pythagoras finally fled for his life from a Croton dissenter named Cylon. In his school, Pythagoras taught about the harmony of the spheres, and how numbers ruled all things. He also documented how music is composed of equally measured numbers. He is most famous, however, for the Pythagorean Theorem.
This theory can be verified by any objective party, to show that the square of the hypotenuse of a right-angle triangle is equal to the square of the other two sides. In From Hegel to Existentialism, Richard Solomon adequately describes the separation between Pythagoras and his theorem: Descriptive or objective truth has impersonal or at least suprapersonal criteria of ‘correctness. ‘ ‘The earth is more than ninety million miles from the sun’ is not true because I say it is, regardless of who I am, how firmly I believe it, or what I might have done to demonstrate it.
This proposition is true because it is a fact that the earth is more than ninety million miles from the sun. Similarly, the Pythagorean theorem is not true because Pythagoras proved it, but because the Pythagorean theorem is provable at any time and any place by anyone who has the ability to do so. It is true that the earth is so far from the sun, and the Pythagorean theorem is true. Particular individuals are irrelevant to descriptive truth. The distance from earth to sun is independent of astronomers. The Pythagorean theorem has no dependence upon Pythagoras (Solomon 80).
Furthermore, it is the right-angle of the triangle that gives rise to the pattern, and so the building blocks of the universe begin at ninety degree angle units. In other words, all of the world, and every world, could be broken down to right-angles. It is a very simple and seductive approach to analyzing the anatomy of existence, and it works to this very day to explain a great deal—however, math is ultimately as tenuous a concept as spirituality, when taken into the long-view, as Frederick Philip Grove points out in “It Needs To Be Said … ”:
Science, as far as it is that edifice of human thought by the help of which we try to _interpret_ physical reality, is in itself strangely unstable; it is in a state of everlasting flux; it changes almost from moment to moment; and certainly from year to year; which is only natural since the true function of science can never be interpretation; it is classification. Science is a search; art is necessarily a finding. It is characteristic that those works of science which have endured through the decades and the centuries deal almost exclusively with observed facts, not with attempts at explanation of no matter what.
In order to realize that, we have only to look back over a few centuries and think of Newton’s Principia or of Harvey’s Circulation of the Blood. Newton’s observations were wonderfully exact; and consequently his explanations held sway, almost unquestioned and untested, for centuries; but, while his observations, capable of being repeated by anyone who cares to repeat them, remain the marvel of posterity, his explanations are shown to be inadequate right now; and that by the very methods which he taught us.
It has been the same with Heraclitus, Thales, Democritus, or Pythagoras. So the strength of Pythagoras mathematics may overall pan out to be equally or even less strong than his views on spirituality—dependent on not just the truth of Pythagoras’s time, but more importantly, the ever-evolving truth of the future. Regardless, in recorded history, his mathematical theories were expanded on by the greatest minds alive, but the spiritual keys of the ancient Greek man’s thinking still receive less popular coverage—though they may be no less deserving to be heard.
Despite his heavy numerology, Pythagoras was as much an artist as a scientist. In The Dance Of Life, Havelock Ellis aptly characterizes the fine balance of the ancient thinker’s interests: That remark, with its reference to the laws and rhythm in the universe, calls to mind the great initiator, so far as our knowledge extends back, of scientific research in our European world. Pythagoras is a dim figure, and there is no need here to insist unduly on his significance.
But there is not the slightest doubt about the nature of that significance in its bearing on the point before us. Dim and legendary as he now appears to us, Pythagoras was no doubt a real person, born in the sixth century before Christ, at Samos, and by his association with that great shipping centre doubtless enabled to voyage afar and glean the wisdom of the ancient world. In antiquity he was regarded, Cicero remarks, as the inventor of philosophy, and still
to-day he is estimated to be one of the most original figures, not only of Greece, but the world. He is a figure full of interest from many points of view, however veiled in mist, but he only concerns us here because he represents the beginning of what we call “science”–that is to say, measurable knowledge at its growing point–and because he definitely represents it as arising out of what we all conventionally recognise as “art,” and as, indeed, associated with the spirit of art, even its most fantastic forms, all the way.
Pythagoras was a passionate lover of music, and it was thus that he came to make the enormously fruitful discovery that pitch of sound depends upon the length of the vibrating chord. Therein it became clear that law and spatial quantity ruled even in fields which had seemed most independent of quantitative order. The beginning of the great science of mechanics was firmly set up. The discovery was no accident. Even his rather hostile contemporary Heraclitus said of Pythagoras that he had “practised research and inquiry beyond all other men.
” He was certainly a brilliant mathematician; he was, also, not only an astronomer, but the first, so far as we know, to recognise that the earth is a sphere,–so setting up the ladder which was to reach at last to the Copernican conception,–while his followers took the further step of affirming that the earth was not the centre of our cosmic system, but concentrically related. So that Pythagoras may not only be called the Father of Philosophy, but, with better right the Father of Science in the modern exact sense. Yet he remained fundamentally an artist even in the conventional sense.
His free play of imagination and emotion, his delight in the ravishing charm of beauty and of harmony, however it may sometimes have led him astray,–and introduced the reverence for Number which so long entwined fancy too closely with science,–yet, as Gomperz puts it, gave soaring wings to the power of his severe reason. He was heavily influenced by Orphism, lending to his belief in the transmigration of souls. He taught that people repeated life-cycles death after death, until they learned to be more moral—through ascribing to ascetism, and therefore achieving communion with the gods.
There are no surviving texts written by Pythagoras himself, giving rise to valid questions about the verifiability of his authorship of his work. Whoever formulated the theories, however, it is clear that they are still objectively provable—and therefore, destined to remain in the human consciousness for a long time, being thoroughly intertwined with the very fabric of our existence. In St. Thomas Aquinas, G. K. Chesterton relates this point about how good philosophy transcends the ages, but he also points to a breakage in philosophic lineage that has left modernity without any more classical thinkers:
The great intellectual tradition that comes down to us from Pythagoras and Plato was never interrupted or lost through such trifles as the sack of Rome, the triumph of Attila or all the barbarian invasions of the Dark Ages. It was only lost after the introduction of printing, the discovery of America, the founding of the Royal Society and all the enlightenment of the Renaissance and the modern world. It was there, if anywhere, that there was lost or impatiently snapped the long thin delicate thread that had descended from distant antiquity; the thread of that unusual human hobby; the habit of thinking.
This is proved by the fact that the printed books of this later period largely had to wait for the eighteenth century, or the end of the seventeenth century, to find even the names of the new philosophers; who were at the best a new kind of philosophers. But the decline of the Empire, the Dark Ages and the early Middle Ages, though too much tempted to neglect what was opposed to Platonic philosophy, had never neglected philosophy. In that sense St. Thomas, like most other very original men, has a long and clear pedigree. He himself is constantly referring back to the authorities from St. Augustine to St. Anselm, and from St.
Anselm to St. Albert, and even when he differs, he also defers. This then highlights a central conceit of philosophy, which William James would shoulder in the 19th century Darwin era, which is that useful thoughts and theories are perpetually subject to the test of the survival of the fittest. Under this light then, it can be seen that not only do 21st century thinkers need to re-align with the burdens of proof and ancient authority that so defined the past, but that Pythagoras’s theories stood the test of time for a reason—they were well thought out, and based entirely on observable facts—while remaining true to a spiritual order.
Another of Pythagoras’s major ideas, which more fully fleshes out his connection between spirit and number, and how they are equally provable, is that because mathematics is an immaterial truth, other immaterial ideas can be proven by it—as it can meet them in that realm of thought where those in this world cannot go. This singular concept seems particularly striking in historical context, as all math and science are founded not only on facts and evidence—but also on leaps of faith into the spaces beyond, where our human eyes cannot see, but where our formulas can cast and illuminate.
This sort of measurement beyond the perceivable world echoes the order of irrational numbers—whose square roots do not repeat or terminate, casting imaginary lines of endless integers into eternity, causing the human mind to be able to see through the veil of the material world. This aspect of math is difficult to conceptualize, in opposition to the more concrete numbers of basic addition and subtraction. Grade school apples cannot be used to symbolize infinite numbers.
One cannot count to infinity on their ten digits, no matter how long they take. In effect, the uncountable sections of mathematics are almost akin to the immaterial forces of the world. Pythagoras’s souls transmigrating across the ages could be crudely correlated to those unending square roots which also unravel forever through time and space. Indeed, in hindsight, both seem precursors to our modern quantum physics, where string theorists posit essentially immaterial membranes woven of fine string make up the blanket of everything.
The most difficult understandings to arrive at, however, in contemplation of all of Pythagoras’s teachings, lie in the tedious details of the more involved and sophisticated equations that his inner circle once lived and breathed. His followers were called Pythagoreans, and they were early monks, devoted day and night to edification and enlightenment through the study of numbers. They believed that numbers ruled all things, so no other pursuit of knowledge was worthier. This stoic commitment to numbers is the hardest part of the Pythagorean path to grasp.
One cannot even come close to fully comprehending mathematics, unless one immerses oneself in math for life—and for this reason, most laypeople remain only superficially versed in the advances humankind has made since Pythagoras, toward the ultimate formula of existence. Subsequent thinkers to Pythagoras expanded the fields, even into psychology—expounding countless variations and extrapolations, all based on the basic right-angle building blocks of one early Greek thinker.
In the realm of modern philosophy even, Pythagoras’s estate of thought has its influences, wherein the atheist existentialists base their material view of life on basic numbers breaking the world down—leaving out the Greek thinker’s transmigration theory. Indeed, in general, Pythagoras was a spiritual man—leaving room for metaphysics in his teachings, while the modern atheist existentialists do not believe in the spirit, but just the basic flesh and bone of blood and mind that comprise what it is to be human.
The atheist existentialists see all fancies of apparition as merely contrived by the living mind, and doomed to die with the body when it goes. Atheist existentialism is a branch of the Pythagorean way of life, that is missing that rebirth aspect—which is key to the moral emancipation which Pythagoras espouses. Interestingly, alongside Existentialism, Buddhism is another philosophy that has recently soared in popularity—and the two of them together approximate the teachings of Pythagoras.
It could be then that, if Pythagoras were alive today, he would warn the existentialists of risking eternal fetters in the material world, by ignoring the truth of the transmigration of souls—while at the same time, he might remind those who trust too much in a higher order, that the reality of the day-to-day is ultimately the subject of math, and victim to the whims of a grid greater than us all. He would not warn that this existence is the last, but that it is bitterly everlasting, unless one learns the equation for getting out of the perpetual spin-cycle of life.
For Pythagoras, that escape was made through abstinence and asceticism, to reach a higher moral ground—but for many people, of his day even, it was too much to ask. Still, although he had his share of dissenters, in the end, his name trickled down into the history books—to where his teachings still instruct and inspire every new generation. In regards to my own relationship to math and Pythagoras, he has transcended over two millenium to tutor me—yet I, like most, still feel largely unversed in the game of equations.
Certainly, I learned as much as I could in school, but only the string theorists and other genuine geniuses are on the cutting edge of actually knowing how the numbers play out. Even the existentialists are mostly just dealing with philosophy when they contend that the earth is a cold, harsh place—but to commit your destiny to studying numbers, and to create a cult out of it, is beyond an amusing preoccupation, careening well into the realm of total obsession. For me, it would have been the simplicity that was the most attractive.
Pythagoreans would have found great peace of mind in knowing every question they every posed could be answered by ten numbers. They would have felt themselves to be important pioneers in a new world, where even the stars could be reduced to digits. But the outstanding debate about whether the spiritual aspects of life are in our own minds—or whether they can be proven to exist by math—is at once an open question for pondering, and also a pointless distinction to fret over, as either way the truth bends, the effects are still the same to those who will never know any different.
Pythagoras was not just a mathematician, but a spiritualist, who showed that, like in life itself, the numbers did not always play by the same rules—and they were not always fully countable or comprehensible. More than just laying the groundwork for the numerological sciences, Pythagoras was also leading the way for a composite religion that allowed room for both the spiritual and the existential to co-exist in one person’s paradigm. Moreover, he showed that, beyond bringing these two apparently polar opposites onto the same field—math proved that they actually originated together.
Indeed, in a modern world rife with cultures that may be accused of becoming overly spiritual—or overly existential, it might be prudent for us all to return to a more Pythagorean balance. Works Cited Chesterton, G. K.. St. Thomas Aquinas. Project Gutenberg. December 2001. March 24, 2009. <http://gutenberg. net. au/ebooks01/0100331. txt> Chesterton, G. K.. The Everlasting Man. Project Gutenberg. December 2001. March 24, 2009. <http://gutenberg. net. au/ebooks01/0100311. txt> Douglas, Norman. Siren Land.
First published 1911 NEW AND REVISED EDITION New York: Dodd, Mead & Company 1923 Printed in Great Britain Project Gutenberg. March 2003. March 24, 2009. <http://gutenberg. net. au/ebooks03/0300571. txt> Ellis, Havelock. The Dance of Life. 1923. Project Gutenberg. April 2003. March 24, 2009. <http://gutenberg. net. au/ebooks03/0300671. txt> Grove, Frederick Philip. It Needs to be Said… Project Gutenberg. April 2008. March 24, 2009. <http://gutenberg. net. au/ebooks08/0800451. txt> Solomon, Robert. From Hegel to Existentialism. Published by Oxford University Press US, 1989. ISBN 0195061829, 9780195061826 80.Sample Essay of Edusson.com