Pythagoras Philosophy Quotes

It is the act of an ill-instructed man to blame others for his own bad condition; it is the act of one who has begun to be instructed, to lay blame on himself; and of one whose instruction is completed, neither to blame another, nor himself.

For Pythagoras as for Kepler, the two kinds of contemplation were twins; for them philosophy and religion were motivated by the same longing : to catch glimpses of eternity through the window of time.

Wonder acts upon a man like a shock, he is "moved" and "shaken", and in the dislocation that succeeds all that he had taken for granted as being natural or self-evident loses its compact solidity and obviousness; he is literally dislocated and no longer knows where he is. If this were only to involve the man of action in all of us, so that a man only lost his sense of certainty of everyday life, it would be relatively harmless; but the ground quakes beneath his feet in a far more dangerous sense, and it is his whole spiritual nature, his capacity to know, that is threatened. It is an extremely curious fact that this is the only aspect of wonder, or almost the only aspect, that comes to evidence in modern philosohpy, and the old view that wonder was the beginning of philosophy takes on a new meaning: doubt is the beginning of philosophy. . . . The innermost meaning of wonder is fulfilled in a deepened sense of mystery. It does not end in doubt, but is the awakening of the knowledge that being, qua being, is mysterious and inconceivable, and that it is a mystery in the full sense of the word: neither a dead end, nor a contradiction, nor even something impenetrable and dark. Rather, mystery means that a reality cannot be comprehended because its light is ever-flowing, unfathomable, and inexhaustible. And that is what the wonderer really experiences. . . . Since the very beginning philosophy has always been characterized by hope. Philosophy never claimed to be a superior form of knowledge but, on the contrary, a form of humility, and restrained, and conscious of this restraint and humility in relation to knowledge. The words philosopher and philosophy were coined, according to legend--and the legend is of great antiquity--by Pythagoras in explicit contrast to the words sophia and sophos: no man is wise, and no man "knows"; God alone is wise and all-knowing. At the very most a man might call himself a lover of wisdom and a seeker after knowledge--a philosopher. --from The Philosophical Act, Chapter III

From Pythagoras (whether by way of Socrates or not) Plato derived the Orphic elements in his philosophy: the religious trend, the belief in immortality, the other-worldliness, the priestly tone, and all that is involved in the simile of the cave; also his respect for mathematics, and his intimate intermingling of intellect and mysticism.

It is fair to say that those who make Zeno, Pythagoras, Democritus and other giants of philosophy their daily companions will be more fully engaged in a rewarding life. None of these friends will be too busy to welcome you inside their home, none will fail to leave his caller feeling refreshed after an appointment. Any man can spend time with them day or night.

Whereas Socrates would walk up to people in the marketplace and harass them by asking them to define virtue, Pythagoras and his young students in Croton supposedly observed a code of silence, to prevent their secret teachings from being divulged to the uninitiated.

Philosophers and psychiatrists should explain why it is that we mathematicians are in the habit of systematically erasing our footsteps. Scientists have always looked askance at this strange habit of mathematicians, which has changed little from Pythagoras to our day.

There was not a philosopher of any notoriety who did not hold to this doctrine of metempsychosis, as taught by the Brahmans, Buddhists, and later by the Pythagoreans, in its esoteric sense, whether he expressed it more or less intelligibly. Origen and Clemens Alexandrinus, Synesius and Chalcidius, all believed in it; and the Gnostics, who are unhesitatingly proclaimed by history as a body of the most refined, learned, and enlightened men, * were all believers in metempsychosis. Socrates entertained opinions identical with those of Pythagoras; and both, as the penalty of their divine philosophy, were put to a violent death. The rabble has been the same in all ages. Materialism has been, and will ever be blind to spiritual truths. These philosophers held, with the Hindus, that God had infused into matter a portion of his own Divine Spirit, which animates and moves every particle. They

The greatest thinkers of Greece — Pythagoras, Plato, Aristotle, and later Plutarch and Plotinus — derived their ideas from ancient tradition, and further on from divine revelation.

There is geometry in the humming of the strings, there is music in the spacing of the spheres." Pythagoras

Ask not that events should happen as you will, but let your will be that events should happen as they do, and you shall have peace.

Pythagoras’s Theorem showed that shapes and ratios are governed by principles that can be discovered. This suggested that it might be possible, in time, to work out the structure of the entire cosmos.

There is in fact also something more recent that Greek philosophy may regard only as an imported plant, something that is actually indigenous to Asia and Egypt; we must conclude that philosophy of this sort essentially only ruined the Greeks, that they declined because of it (Heraclitus, because of Zoroaster [Zarathustra of Iran]; Pythagoras, because of the Chinese; the Eleatics, because of the Indians; Empedocles, because of the Egyptians; Anaxagoras, because of the Jews).

[Pythagoras] is one of the most interesting and puzzling men in history. Not only are the traditions concerning him an almost inextricable mixture of truth and falsehood, but even in their...least disputable form they present us with a very curious psychology...He founded a religion, of which the main tenets were the transmigration of souls and the sinfulness of eating beans...His religion...acquired control of the State and established a rule of the saints. But the unregenerate hankered after beans, and sooner or later rebelled.

Generalizations in biology are almost invariably of a probabilistic nature. As one wit has formulated it, there is only one universal law in biology: 'All biological laws have exceptions.' This probabilistic conceptualization contrasts strikingly with the view during the early period of the scientific revolution that causation in nature is regulated by laws that can be stated in mathematical terms. Actually, this idea occurred apparently first to Pythagoras. It has remained a dominant idea, particularly in the physical sciences, up to the present day. Again and again it was made the basis of some comprehensive philosophy, but taking very different forms in the hands of various authors. With Plato it gave rise to essentialism, with Galileo to a mechanistic world picture, and with Descartes to the deductive method. All three philosophies had a fundamental impact on biology.

Can you tell us about Ama: Playing the Glass Bead Game with Pythagoras? Sunday Times Interview "Both Hesse and Tolstoy were my first spiritual gurus. Through their deep insights and soulful messages, for the first time I experienced the world of spiritual growth and deep contemplation. Many artists have inspired my writings, the likes of Leonardo da Vinci, Lao Tzu and Giordano Bruno. Pythagoras lived on the crossroads of civilisations, as I see us, and he has given us his fascinating research into music and numbers. With my deep respect towards ancient worlds, Pythagoras with his ancient Egyptian mystical knowledge had to be my protagonist.

Pythagoras also established the principle of deductive reasoning, which is the step-by-step process of starting with self-evident axioms (such as “2 + 2 = 4”) to build toward a new conclusion or fact. Deductive reasoning was later refined by Euclid, and it formed the basis of mathematical thinking into medieval times and beyond.

Finally, the dishonesty in the movement of the publication of a Greek philosophy, becomes very glaring, when we refer to the fact, purposely that by calling the theorem of the Square on the Hypotenuse, the Pythagorean theorem, it has concealed the truth for centuries from the world, who ought to know that the Egyptians taught Pythagoras and the Greeks, what mathematics they knew.

Pythagoras was born around 570 B.C. in the island of Samos in the Aegean Sea (off Asia Minor), and he emigrated sometime between 530 and 510 to Croton in the Dorian colony in southern Italy (then known as Magna Graecia). Pythagoras apparently left Samos to escape the stifling tyranny of Polycrates (died ca. 522 B.C.), who established Samian naval supremacy in the Aegean Sea. Perhaps following the advice of his presumed teacher, the mathematician Thales of Miletus, Pythagoras probably lived for some time (as long as twenty-two years, according to some accounts) in Egypt, where he would have learned mathematics, philosophy, and religious themes from the Egyptian priests. After Egypt was overwhelmed by Persian armies, Pythagoras may have been taken to Babylon, together with members of the Egyptian priesthood. There he would have encountered the Mesopotamian mathematical lore. Nevertheless, the Egyptian and Babylonian mathematics would prove insufficient for Pythagoras' inquisitive mind. To both of these peoples, mathematics provided practical tools in the form of "recipes" designed for specific calculations. Pythagoras, on the other hand, was one of the first to grasp numbers as abstract entities that exist in their own right.

Even though it is almost impossible to attribute with certainty any specific mathematical achievements either to Pythagoras himself or to his followers, there is no question that they have been responsible for a mingling of mathematics, philosophy of life, and religion unparalleled in history. In this respect it is perhaps interesting to note the historical coincidence that Pythagoras was a contemporary of Buddha and Confucius.

now I want to speak about the word ‘theory’. This was originally an Orphic word, which Cornford interprets as ‘passionate sympathetic contemplation’. In this state, he says, ‘The spectator is identified with the suffering God, dies in his death, and rises again in his new birth.’ for Pythagoras, the ‘passionate sympathetic contemplation’ was intellectual, and issued in mathematical knowledge. In this way, through Pythagoreanism, ‘theory’ gradually acquired its modern meaning; but for all who were inspired by Pythagoras it retained an element of ecstatic revelation. To those who have reluctantly learnt a little mathematics in school this may seem strange; but to those who have experienced the intoxicating delight of sudden understanding that mathematics gives, from time to time, to those who love it, the Pythagorean view will seem completely natural even if untrue.

What is man? and what difference is there between him and other plants, between him and all the other animals of the world? None, obviously. Fortuitously placed, like them, upon this globe, he is born like them; like them, he reproduces, rises, and falls; like them he arrives at old age and sinks like them into nothingness at the close of the life span Nature assigns each species of animal, in accordance with its organic construction. Since the parallels are so exact that the inquiring eye of philosophy is absolutely unable to perceive any grounds for discrimination, there is then just as much evil in killing animals as men, or just as little, and whatever be the distinctions we make, they will be found to stem from our pride's prejudices, than which, unhappily, nothing is more absurd. If all individuals were possessed of eternal life, would it not become impossible for Nature to create any new ones? If Nature denies eternity to beings, it follows that their destruction is one of her laws. Now, once we observe that destruction is so useful to her that she absolutely cannot dispense with it, and that she cannot achieve her creations without drawing from the store of destruction which death prepares for her, from this moment onward the idea of annihilation which we attach to death ceases to be real; there is no more veritable annihilation; what we call the end of the living animal is no longer a true finis, but a simple transformation, a transmutation of matter, what every modern philosopher acknowledges as one of Nature's fundamental laws. According to these irrefutable principles, death is hence no more than a change of form, an imperceptible passage from one existence into another, and that is what Pythagoras called metempsychosis

If you want to know the secrets of existence, do the math. There is no other way. There is only one truth, the truth of mathematics. It is the infallible, absolute truth. All truth-seekers come in the end to mathematics. Pythagoras got there first. It’s time for everyone else to join him and hear the Music of the Spheres. Are your ears attuned to the perfect notes of the universe? Only the gods can hear the divine music. Are you one of them?

Pythagoras is in fact credited with having coined the words "philosophy" ("love of wisdom") and "mathematics" ("that which is learned"). To him, a "philosopher" was someone who "gives himself up to discovering the meaning and purpose of life itself...to uncover the secrets of nature." Pythagoras emphasized the importance of learning above all other activities, because, in his words, "most men and women, by birth or nature, lack the means to advance in wealth and power, but all have the ability to advance in knowledge.

theory'. This was originally an Orphic word, which Cornford interprets as 'passionate sympathetic contemplation'. In this state, he says, 'The spectator is identified with the suffering God, dies in his death, and rises again in his new birth.' For Pythagoras, the 'passionate sympathetic contemplation' was intellectual, and issued in mathematical knowledge. In this way, through Pythagoreanism, 'theory' gradually acquired its modern meaning; but for all who were inspired by Pythagoras it retained an element of ecstatic revelation.

All things were ready for us at our birth; it is we that have made everything difficult for ourselves, through our disdain for what is easy.” –Seneca, c. 4 BC–65 AD “Philosophy consists in avoiding excess in everything.” –Pythagoras, c. 570 BC–c. 495 BC “It is better for you to be free of fear lying upon a bed of straw, than to have a golden couch and a lavish table and be full of trouble.” –Epicurus, c. 341 BC–c. 270 BC “Very little is needed to make a happy life; it is all within yourself, in your way of thinking.” –Marcus Aurelius, 121–180 AD

[I]t has been eagerly pointed out how much the Greeks could find and learn abroad, in the Orient, and how many different things they may easily have brought from there. Of course an odd spectacle resulted, when certain scholars brought together the alleged masters from the Orient and the possible disciples from Greece, and exhibited Zarathustra near Heraclitus, the Hindoos near the Eleates, the Egyptians near Empedocles, or even Anaxagoras among the Jews and Pythagoras among the Chinese. In detail little has been determined; but we should in no way object to the general idea, if people did not burden us with the conclusion that therefore Philosophy had only been imported into Greece and was not indigenous to the soil, yea, that she, as something foreign, had possibly ruined rather than improved the Greek. Nothing is more foolish than to swear by the fact that the Greeks had an aboriginal culture; no, they rather absorbed all the culture flourishing among other nations, and they advanced so far, just because they understood how to hurl the spear further from the very spot where another nation had let it rest.

So I came back to philosophy, but differently; feeling it in myself, and in those I met in talk, a fever of the blood. I had come to it as a boy from wonder at the visible world; to know the causes of things; and to feel the sinews of my mind, as one feels one’s muscles in the palaestra. But now we searched the nature of the universe, and our own souls, more like physicians in time of sickness. It was not that we were in love with the past. We were of an age to feel the present our own, and to suppose it would never outstrip us. In painting and sculpture and verse, the names we grew passionate over looked to us as big as those of Perikles’ day, and it still half surprises me when I find them unknown to my sons. But we seldom stood to enjoy good work, as one stands before a fine view or a flower, in simple gladness that it is. As we hailed each new artist we grew angry with the former ones, as with false guides we had caught out; we hastened, though we knew not where. To freedom, we said; the sculptors no longer proportioned their forms by the Golden Number of Pythagoras, as Pheidias and Polykleitos did; and art would do great things, we said, now it had cast off its chains.

On the question of whether mathematics was discovered or invented, Pythagoras and the Pythagoreans had no doubt-mathematics was real, immutable, omnipresent, and more sublime than anything that could conceivably emerge from the feeble human mind. The Pythagoreans literally embedded the universe into mathematics. In fact, to the Pythagoreans, God was not a mathematician-mathematics was God! The importance of the Pythagorean philosophy lies not only in its actual, intrinsic value. By setting the stage, and to some extent the agenda, for the next generation of philosophers-Plato in particular-the Pythagoreans established a commanding position in Western thought.

Mathematical knowledge appeared to be certain, exact, and applicable to the real world; moreover it was obtained by mere thinking, without the need of observation. Consequently, it was thought to supply an ideal, from which every-day empirical knowledge fell short. It was supposed, on the basis of mathematics, that thought is superior to sense, intuition to observation. If the world of sense does not fit mathematics, so much the worse for the world of sense. In various ways, methods of approaching nearer to the mathematician's ideal were sought, and the resulting suggestions were the source of much that was mistaken in metaphysics and theory of knowledge. This form of philosophy begins with Pythagoras.

Philosophy begins when one learns to doubt—particularly to doubt one’s cherished beliefs, one’s dogmas and one’s axioms. Who knows how these cherished beliefs became certainties with us, and whether some secret wish did not furtively beget them, clothing desire in the dress of thought? There is no real philosophy until the mind turns round and examines itself. Gnothi seauton, said Socrates: Know thyself. There had been philosophers before him, of course: strong men like Thales and Heraclitus, subtle men like Parmenides and Zeno of Elea, seers like Pythagoras and Empedocles; but for the most part they had been physical philosophers; they had sought for the physis or nature of external things, the laws and constituents of the material and measurable world. That is very good, said Socrates; but there is an infinitely worthier subject for philosophers than all these trees and stones, and even all those stars; there is the mind of man. What is man, and what can he become? So he went about prying into the human soul, uncovering assumptions and questioning certainties. If men discoursed too readily of justice, he asked them, quietly, tò tí?—what is it? What do you mean by these abstract words with which you so easily settle the problems of life and death? What do you mean by honor, virtue, morality, patriotism? What do you mean by yourself? It was with such moral and psychological questions that Socrates loved to deal. Some

But what seemed to me most shocking, Philosophy, was this, that if people saw any of these fellows engaged in any wicked or unseemly or indecent practice, every man of them at once laid t he blame upon Philosophy herself, and upon Chrysippus, or Plato, or Pythagoras or whichever one of you furnished that sinner with a name for himself and a model for his harangues; and from him, because he was leading an evil life, they drew sorry conclusions about you others, who died long ago. For as you were not alive, he could not be compared with you. You were not there, and they all clearly saw him following dreadful and discreditable practices, so that you suffered judgment by default along with him and became involved in the same scandal.

Great mathematical geniuses such as Pythagoras, Plato, Descartes, Leibniz, Fourier and Gödel all recognized that mathematics is ontological. ‘Real’ mathematics is ontological mathematics that tells us about reality; it’s not abstract mathematics that has no connection with reality, as most professional mathematicians seem to believe. Reality is 100% mathematical. Above all, Fourier mathematics is the key to the mystery of the universe because it’s the answer to the mystery of mind and matter and how they interact. Mind is the Fourier frequency domain and matter is the inverse Fourier spacetime domain, and the two domains are absolutely tied together in feedback loop. The universe, finally, is a hologram and holography is all about Fourier mathematics.

The outsiders stood always in awe in front of what they had surnamed the Celestial City with Mighty Walls. The great mystery that cloaked its very foundations kept impelling the youth of Crotona, as well as those of the adjacent cities, to seek admittance. In spite of the difficult rules of the Master, curiosity goaded many to venture inside its secrecy, with a passionate aspiration to discover the unknown. Yet, to enroll, young men and women should be introduced by their parents. Sometimes, it was one of the assigned Masters of the Pythagorean Society who assumed the introduction. At the massive wooden gated entrance, one could admire the marble statue of Hermes-Enoch, the father of the spiritual laws. A cubical stone formed its stall where a skillful hand had carved the words: No entry to the vulgar

The life of man is a story; an adventure story; and in our vision the same is true even of the story of God. The Catholic faith is the reconciliation because it is the realisation both of mythology and philosophy. It is a story and in that sense one of a hundred stories; only it is a true story. It is a philosophy and in that sense one of a hundred philosophies; only it is a philosophy that is like life. But above all, it is a reconciliation because it is something that can only be called the philosophy of stories. That normal narrative instinct which produced all the fairy tales is something that is neglected by all the philosophies—except one. The Faith is the justification of that popular instinct; the finding of a philosophy for it or the analysis of the philosophy in it. Exactly as a man in an adventure story has to pass various tests to save his life, so the man in this philosophy has to pass several tests and save his soul. In both there is an idea of free will operating under conditions of design; in other words, there is an aim and it is the business of a man to aim at it; we therefore watch to see whether he will hit it. Now this deep and democratic and dramatic instinct is derided and dismissed in all the other philosophies. For all the other philosophies avowedly end where they begin; and it is the definition of a story that it ends differently; that it begins in one place and ends in another. From Buddha and his wheel to Akhen Aten and his disc, from Pythagoras with his abstraction of number to Confucius with his religion of routine, there is not one of them that does not in some way sin against the soul of a story. There is none of them that really grasps this human notion of the tale, the test, the adventure; the ordeal of the free man. Each of them starves the story-telling instinct, so to speak, and does something to spoil human life considered as a romance; either by fatalism (pessimist or optimist) and that destiny that is the death of adventure; or by indifference and that detachment that is the death of drama; or by a fundamental scepticism that dissolves the actors into atoms; or by a materialistic limitation blocking the vista of moral consequences; or a mechanical recurrence making even moral tests monotonous; or a bottomless relativity making even practical tests insecure. There is such a thing as a human story; and there is such a thing as the divine story which is also a human story; but there is no such thing as a Hegelian story or a Monist story or a relativist story or a determinist story; for every story, yes, even a penny dreadful or a cheap novelette, has something in it that belongs to our universe and not theirs. Every short story does truly begin with creation and end with a last judgement.

Pythagoras, as everyone knows, said that 'all things are numbers'. This statement, interpreted in a modern way, is logically nonsense, but what he meant was not exactly nonsense. He discovered the importance of numbers in music, and the connection which he established between music and arithmetic survives in the mathematical terms 'harmonic mean' and 'harmonic progression'. He thought of numbers as shapes, as they appear on dice or playing cards. We still speak of squares and cubes of numbers, which are terms that we owe to him. He also spoke of oblong numbers, triangular numbers, pyramidal numbers, and so on. These were the numbers of pebbles (or, as we should more naturally say, shot) required to make the shapes in question. He presumably thought of the world as atomic, and of bodies as built up of molecules composed of atoms arranged in various shapes. In this way he hoped to make arithmetic the fundamental study in physics as in aesthetics.

But it seems to have eluded all these philosophers in what way each of us is truly two fold and composite. For that other two fold nature of ours they have not discerned, but merely the more obvious one, the blend of soul and body. But that there is some element of composition, some two fold nature and dissimilarity of the very soul within itself, since the irrational, as though it were another substance, is mingled and joined with reason by some compulsion of Nature — E this, it is likely, was not unknown even to Pythagoras, if we may judge by the man’s enthusiasm for the study of music, which he introduced to enchant and assuage the soul, perceiving that the soul has not every part of itself in subjection to discipline and study, and that not every part can be changed from vice by reason, but that the several parts have need of some other kind of persuasion to co operate with them, to mould them, and to tame them, if they are not to be utterly intractable and obstinate to the teaching of philosophy.

Mathematics is, I believe, the chief source of the belief in eternal and exact truth, as well as in a super-sensible intelligible world. Geometry deals with exact circles, but no sensible object is exactly circular; however carefully we may use our compasses, there will be some imperfections and irregularities. This suggests the view that all exact reasoning applies to ideal as opposed to sensible objects; it is natural to go further, and to argue that thought is nobler than sense, and the objects of thought more real than those of sense-perception. Mystical doctrines as to the relation of time to eternity are also reinforced by pure mathematics, for mathematical objects, such as numbers, if real at all, are eternal and not in time. Such eternal objects can be conceived as God's thoughts. Hence Plato's doctrine that God is a geometer, and Sir James Jeans' belief that He is addicted to arithmetic. Rationalistic as opposed to apocalyptic religion has been, ever since Pythagoras, and notably ever since Plato, very completely dominated by mathematics and mathematical method.

The influence of geometry upon philosophy and scientific method has been profound. Geometry, as established by the Greeks, starts with axioms which are (or are deemed to be) self-evident, and proceeds, by deductive reasoning, to arrive at theorems that are very far from self-evident. The axioms and theorems are held to be true of actual space, which is something given in experience. It thus appeared to be possible to discover things about the actual world by first noticing what is self-evident and then using deduction. This view influenced Plato and Kant, and most of the intermediate philosophers. When the Declaration of Independence says 'we hold these truths to be self-evident', it is modelling itself on Euclid. The eighteenth-century doctrine of natural rights is a search for Euclidean axioms in politics.8 The form of Newton's Principia, in spite of its admittedly empirical material, is entirely dominated by Euclid. Theology, in its exact scholastic forms, takes its style from the same source. Personal religion is derived from ecstasy, theology from mathematics; and both are to be found in Pythagoras.

The purely philosophical influences on Plato were also such as to pre-dispose him in favour of Sparta. These influences, speaking broadly, were: Pythagoras, Parmenides, Heraclitus, and Socrates. From Pythagoras (whether by way of Socrates or not) Plato derived the Orphic elements in his philosophy: the religious trend, the belief in immortality, the other-worldliness, the priestly tone, and all that is involved in the simile of the cave; also his respect for mathematics, and his intimate intermingling of intellect and mysticism. From Parmenides he derived the belief that reality is eternal and timeless, and that, on logical grounds, all change must be illusory. From Heraclitus he derived the negative doctrine that there is nothing permanent in the sensible world. This, combined with the doctrine of Parmenides, led to the conclusion that knowledge is not to be derived from the senses, but is only to be achieved by the intellect. This, in turn, fitted in well with Pythagoreanism. From Socrates he probably learnt his preoccupation with ethical problems, and his tendency to seek teleological rather than mechanical explanations of the world. 'The Good' dominated his thought more than that of the pre-Socratics, and it is difficult not to attribute this fact to the influence of Socrates.

But we may fairly say that they alone are engaged in the true duties of life who shall wish to have Zeno, Pythagoras, Democritus, and all the other high priests of liberal studies, and Aristotle and Theophrastus, as their most intimate friends every day. No one of these will be "not at home," no one of these will fail to have his visitor leave more happy and more devoted to himself than when he came, no one of these will allow anyone to leave him with empty hands; all mortals can meet with them by night or by day. No one of these will force you to die, but all will teach you how to die; no one of these will wear out your years, but each will add his own years to yours; conversations with no one of these will bring you peril, the friendship of none will endanger your life, the courting of none will tax your purse. From them you will take whatever you wish; it will be no fault of theirs if you do not draw the utmost that you can desire. What happiness, what a fair old age awaits him who has offered himself as a client to these! He will have friends from whom he may seek counsel on matters great and small, whom he may consult every day about himself, from whom he may hear truth without insult, praise without flattery, and after whose likeness he may fashion himself. We are wont to say that it was not in our power to choose the parents who fell to our lot, that they have been given to men by chance; yet we may be the sons of whomsoever we will. Households there are of noblest intellects; choose the one into which you wish to be adopted; you will inherit not merely their name, but even their property, which there will be no need to guard in a mean or niggardly spirit; the more persons you share it with, the greater it will become. These will open to you the path to immortality, and will raise you to a height from which no one is cast down. This is the only way of prolonging mortality—nay, of turning it into immortality. Honours, monuments, all that ambition has commanded by decrees or reared in works of stone, quickly sink to ruin; there is nothing that the lapse of time does not tear down and remove. But the works which philosophy has consecrated cannot be harmed; no age will destroy them, no age reduce them; the following and each succeeding age will but increase the reverence for them, since envy works upon what is close at hand, and things that are far off we are more free to admire. The life of the philosopher, therefore, has wide range, and he is not confined by the same bounds that shut others in. He alone is freed from the limitations of the human race; all ages serve him as if a god. Has some time passed by? This he embraces by recollection. Is time present? This he uses. Is it still to come? This he anticipates. He makes his life long by combining all times into one. But those who forget the past, neglect the present, and fear for the future have a life that is very brief and troubled; when they have reached the end of it, the poor wretches perceive too late that for such a long while they have been busied in doing nothing.

Well, there are all sorts of formulas in junior high school math: Pythagoras’s theorem, the quadratic equation, that sort of thing … Memorizing formulas enables you to solve a whole variety of problems. If, however, you memorize a formula wrongly to start with, you’ll end up getting things wrong over and over again. That can happen, can’t it? … Make sure to get your students to memorize all the formulas correctly.

All things were ready for us at our birth; it is we that have made everything difficult for ourselves, through our disdain for what is easy.” –Seneca, c. 4 BC–65 AD “Philosophy consists in avoiding excess in everything.” –Pythagoras, c. 570 BC–c. 495 BC “It is better for you to be free of fear lying upon a bed of straw, than to have a golden couch and a lavish table and be full of trouble.” –Epicurus, c. 341 BC–c. 270 BC “Very little is needed to make a happy life; it is all within yourself, in your way of thinking.” –Marcus Aurelius, 121–180 AD “I threw my cup away when I saw a child drinking from his hands at the trough.” –Diogenes, c. 412 BC–323 BC “Money, which ever since it began to be regarded with respect, has caused the ruin

It must not be thought that gold can be injured by rust, or virtue by baseness.

And then there is Pythagoras. The legend is that the founder of theoretical mathematics was so outraged when one of his students, the haplessly gifted Hippasus, discovered irrational numbers21 that he sent the poor fellow out on a raft to drown, initiating a venerable tradition of professors mistreating their graduate students.

To find the origin of the stream of intellectualism we must go back further than the Middle Ages. The epoch of the birth of human intellect, the period when this transformation took place, lies about a thousand years before the Christian era. It is the epoch of Thales, Pythagoras, Buddha. Then for the first time arose philosophy and science, that is to say truth presented to the reason in the form of logic. Before this age, truth presented itself in the form of religion, of revelation received by the teachers and accepted by the masses. In our times, truth passes into the individual intelligence and would fain be proved by argument, would like to have its own wings clipped.

It is a remarkable fact that the Greeks, who were so inquisitive about nature, and so quick to pick up foreign technology and artistic skills, were quite incurious about alien languages. They were in Egypt for a millennium but never bothered to learn anything except trading demotic; Pythagoras was apparently the only Greek scholar who understood hieroglyphics. They had exactly the same blindness towards Hebrew, Hebrew literature and Jewish religious philosophy. They ignored it and knew of it only from inaccurate hearsay. This culture-contempt on the Greek side, and the love-hate which some educated Jews had for Greek culture, were sources of constant tension.

The vital roles that schema and pattern play in Archaic art can be considered symptoms of a larger Greek demand for regularity and order which extends beyond the realms of representational art into architecture, poetry, and philosophy and beyond the limits of the Archaic period itself. The language of Homer is highly ordered: its formulae were originally patterns for the ear. Hesiod's Theogony imposes patterns on gods and heroes by putting each in his genealogical place, and his Works and Days moves from a particular instance of injustice to universal truths and patterns of human activity. Archaic poetry in general is full of literary schemata or conventions, and Archaic poets express thought and meaning through the harmony of opposites. Archilochos detected a rhysmos (pattern) even in the rise and fall of human fortunes. The philosophers of Miletos attempted to fit nature to preconceived patterns and so to extract order from apparent chaos. Pythagoras (or his followers) ordered the world through number. The urge to impose kosmos (order) on the nature of things is not peculiar to the Archaic mind – in Xenophon's Oikonomikos Sokrates reports that all things, even pots and pans, look more beautiful when they are kept in order, and even the space between them looks beautiful – but is nonetheless particularly characteristic of it.

Saint John Chrysostom commented on St. Paul’s distinction between the spiritual man and the natural man and what it means to have the mind of Christ. His preference for spiritual insight over the application of human reasoning is completely consistent with the patristic (and thus, Orthodox) view of the use of human wisdom and philosophy in theology. “The natural man does not receive the things of the Spirit.” For he is “a natural man,” who attributes everything to reasonings of the mind and considers not that he needs help from above; which is a mark of sheer folly. For God bestowed it that it might learn and receive help from Him, not that it should consider itself sufficient unto itself. . . . For the mind which we have about these things we have of Christ; that is, the knowledge which we have concerning the things of the faith is spiritual; so that with reason we are “judged of no man.” For it is not possible that a natural man should know divine things. . . . For reason was absolutely made of no effect by our inability to apprehend through Gentile wisdom the things above us. You may observe, too, that it was more advantageous to learn in this way from the Spirit. For that is the easiest and clearest of all teaching. . . . “But we have the mind of Christ” (1 Cor. 2:16), that is, spiritual, divine, that which has nothing human. For it is not of Plato, nor of Pythagoras, but it is Christ Himself, putting His own things into our mind.9

Emerson was learning now to regard Pythagoras as the father of philosophy, “the first who called himself a ‘philosopher’ or lover of wisdom.” Plato was to be seen as “the most genuine and best of all his disciples.” Giordano Bruno was a modern Pythagoras, the “second Pythagoras.

Here’s another way to think of atoms. They are numbers. Numbers are the true atoms of existence, and all things are compounded from numbers. When you break up all compounds, you return to the ultimate, simple, indivisible parts: eternal, necessary numbers. Numbers and their mathematical relations are all there are. Numbers, ontologically, are not pencil strokes on paper. Rather, they are energy-frequencies that exist as sinusoidal waves, and reality is nothing but how these eternal waves interact, and enter into temporal, contingent wavefunctions. In other words, the answer to existence is simply to correctly define what numbers are ontologically, and what laws dictate their interactions. This is what Pythagoras first attempted two and a half thousand years ago. He conceived of numbers as living, dynamic things ruled by harmony (and discord). Isn’t that a far more powerful notion of reality than Feynman’s?

Here’s another way to think of atoms. They are numbers. Numbers are the true atoms of existence, and all things are compounded from numbers. When you break up all compounds, you return to the ultimate, simple, indivisible parts: eternal, necessary numbers. Numbers and their mathematical relations are all there are. Numbers, ontologically, are not pencil strokes on paper. Rather, they are energy-frequencies that exist as sinusoidal waves, and reality is nothing but how these eternal waves interact, and enter into temporal, contingent wavefunctions. In other words, the answer to existence is simply to correctly define what numbers are ontologically, and what laws dictate their interactions. This is what Pythagoras first attempted two and a half thousand years ago. He conceived of numbers as living, dynamic things ruled by harmony (and discord). Isn’t that a far more powerful notion of reality than Feynman’s?

Here’s another way to think of atoms. They are numbers. Numbers are the true atoms of existence, and all things are compounded from numbers. When you break up all compounds, you return to the ultimate, simple, indivisible parts: eternal, necessary numbers. Numbers and their mathematical relations are all there are. Numbers, ontologically, are not pencil strokes on paper. Rather, they are energy-frequencies that exist as sinusoidal waves, and reality is nothing but how these eternal waves interact, and enter into temporal, contingent wavefunctions. In other words, the answer to existence is simply to correctly define what numbers are ontologically, and what laws dictate their interactions. This is what Pythagoras first attempted two and a half thousand years ago. He conceived of numbers as living, dynamic things ruled by harmony (and discord). Isn’t that a far more powerful notion of reality than Feynman’s?

The only religion that could ever be taken seriously is rationalism religion. The likes of Pythagoras, Plato, Aristotle, Descartes, Leibniz, Hegel, and Godel have done the hard work necessary to make such a religion viable. Wouldn't you want a religion that every logician, mathematician, philosopher, and scientist on earth could embrace? In fact, that religion already exists. It's called ontological mathematics, predicated on the principle of sufficient reason and Occam's razor. It constitutes a coherent, holistic, a priori, rationalist, analytic, deductive religion, metaphysics and physics. Ontological mathematics explains all.

Only a brief study of history is necessary to show that Greek philosophers were undesirable citizens, who throughout the period of their investigations were victims of relentless persecution, at the hands of the Athenian government. Anaxagoras was imprisoned and exiled; Socrates was executed; Plato was sold into slavery and Aristotle was indicted and exiled; while the earliest of them all, Pythagoras, was expelled from Croton in Italy. Can we imagine the Greeks making such an about turn, as to claim the very teachings which they had at first persecuted and openly rejected?

However, no one will deny that the soul of Pythagoras was sent to mankind from Apollo’s domain, having either been one of his attendants, or more intimate associates, which may be inferred both from his birth and his versatile wisdom....

Ancient philosophy is traditionally held to begin in the sixth century BC, in the Greek cities of coastal Asia Minor. A large number of philosophers are generally grouped as ‘Presocratics’; their activities cover the sixth and fifth centuries. Thales, Anaximander and Anaximenes are early cosmologists, giving ambitious accounts of the world as a whole. Pythagoras began a tradition emphasizing mysticism and authority. Heraclitus produced notoriously obscure aphorisms. Xenophanes begins a long concern with knowledge and its grounds.

In a sense, Pythagoras exemplified Heracles (Melqart of the Phoenicians), i.e., as being an archetype of the spiritual hero who practiced the rites of incubation, oracular dreams, and was immortalized through the theurgic (or alchemical) fire. He joins the company of the gods in Heaven, thus following certain Phoenician and Hittitian cultic patterns.

The school of Pythagoras was thus a religious society centered around the Muses and their leader Apollo, the solar Intellect. Following the lead of Apollo and Pythagoras, one thereby became aware of the divine order and unity.

The Pythagorean strain survived in Neoplatonism. For Porphyry and other Neoplatonists, Pythagoras was a member of a great chain of ancient prophets, theologians, and sages, essentially a Platonic philosopher whose many doctrines could be traced to their Eastern prototypes.

15. It was Pythagoras who first called heaven kosmos, because it is perfect, and “adorned” with infinite beauty and living beings.

Porphyry the Phoenician regarded Pythagoras as essentially a Platonic philosopher whose views could be corroborated by reference to the divinely revealed teachings of the Egyptian priesthood. The Life of Pythagoras was initially part of the first book of a Philosophical History in four books. This history, now lost, covered Hellenic philosophy from Homer to Plato.

Pythagoras was the first among the Greeks to call himself a lover of wisdom, philosophos. He regarded philosophia as a form of purification, a way of life aimed at assimilation to God and the gaining of immortality.

According to the Hellenic tradition, Pythagoras restricted the use of the word wisdom (sophia) so as to make it refer only to the science of immaterial realities treated as true Being, against the fluid material world of becoming whose very flow imitates the archetypes of true Being and derives from them. Before him wise men in Greece called themselves sages (sophoi, tantamount to those “exceeding in wisdom” who bear the attributes of the god Ea in Mesopotamia), but Pythagoras was the first among the Greeks to call himself a lover of wisdom, philosophos. He regarded philosophia as a form of purification, a way of life aimed at assimilation to God and the gaining of immortality.

Plutarch on eating flesh Plutarch would have spoilt many a traditional Christmas Dinner . . . imagine him there, grim faced as the turkey is brought out: It all began the same way that tyrants began to slaughter men. At Athens the first man they put to death was the worst of their informers, who everyone said deserved it. The second was the same sort of man, and so was the third. But after that, the Athenians were accustomed to bloodshed and looked on passively when Niceratus, son of Nicias, and the general Thramenes, and Polemarchus the philosopher were executed. In the same way the first animal was killed and eaten was a wild and mischievous beast, and then a bird and a fish were caught. And murder, being thus tried and practised upon creatures like these, arrived at the labouring ox, and the sheep that clothes us, and the cock that guards our house. And little by little, our desires hardening, we proceeded to the slaughter of men, wars and massacres. Can you really ask what reason Pythagoras had for abstaining from flesh? For my part I rather wonder both by what accident and in what state of soul or mind the first man did so, touched his mouth to gore and brought his lips to the flesh of a dead creature, he who set forth tables of dead, stale bodies and ventured to call food and nourishment the parts that had a little before bellowed and cried, moved and lived. How could his eyes endure the slaughter when throats were slit and hides flayed and limbs torn from limb? How could his nose endure the stench? How was it that the pollution did not turn away his taste, which made contact with the sores of others and sucked juices and serums from mortal wounds . .

…The just man does not allow the several elements in his soul to usurp one another's functions; he is indeed one who sets his house in order, by self-mastery and discipline coming to be at peace with himself, and bringing into tune those three parts, tike the terms in the proportion of a musical scale, the highest and lowest notes and the mean between them, with all the intermediate intervals. Only when he has linked these parts together in well-tempered harmony and has made himself one man instead of many, will he be ready to go about whatever he may have to do, whether it be making money and satisfying bodily wants, or business transactions, or the affairs of state. In all these fields when he speaks of just and honorable conduct, he will mean the behavior that helps to produce and preserve this habit of mind; and by wisdom he will mean the knowledge which presides over such conduct. Any action which tends to break down this habit will be for him unjust; and the notions governing it he will call ignorance and folly. (My emphasis.)

German teachers have shown how the very plays of children can be made instrumental in conveying to the childish mind some concrete knowledge in both geometry and mathematics. The children who have made the squires of the theorem of Pythagoras out of pieces of coloured cardboard, will not look at the theorem, when it comes in geometry, as on a mere instrument of torture devised by the teachers; and the less so if they apply it as the carpenters do. Complicated problems of arithmetic, which so much harassed us in our boyhood, are easily solved by children seven and eight years old if they are put in the shape of interesting puzzles. And if the Kindergarten — German teachers often make of it a kind of barrack in which each movement of the child is regulated beforehand — has often become a small prison for the little ones, the idea which presided at its foundation is nevertheless true. In fact, it is almost impossible to imagine, without having tried it, how many sound notions of nature, habits of classification, and taste for natural sciences can be conveyed to the children’s minds; and, if a series of concentric courses adapted to the various phases of development of the human being were generally accepted in education, the first series in all sciences, save sociology, could be taught before the age of ten or twelve, so as to give a general idea of the universe, the earth and its inhabitants, the chief physical, chemical, zoological, and botanical phenomena, leaving the discovery of the laws of those phenomena to the next series of deeper and more specialised studies.

As for the other aspect, creative or signed enunciation, it is clear that scientific propositions and their correlates are just as signed or created as philosophical concepts: we speak of Pythagoras’s theorem, Cartesian coordinates, Hamiltonian number, and Lagrangian function just as we speak of the Platonic Idea or Descartes’s cogito and the like. But however much the use of proper names clarifies and confirms the historical nature of their link to these enunciations, these proper names are masks for other becomings and serve only as pseudonyms for more secret singular entities

In the immortal parable of the Cave, where men stand in their chains backs to the light , perceiving only the play of shadows on the wall, unaware that these are but shadows, unaware of the luminous reality outside the Cave-in this allegory of the human condition, Plato hit an archetypal chord as pregnant with echoes as Pythagoras' Harmony of the Spheres. But when we think of Neoplatonism and scholasticism as concrete philosophies and precepts of life, we may be tempted to reverse the game, and to paint a picture of the founders of the Academy and the Lyceum as two frightened men standing in the self-same Cave, facing the wall, chained to their places in a catastrophic age, turning their back on the flame of Greece's heroic era, and throwing grotesque shadows which are to haunt mankind for a thousand years and more.

The PSR is reflected in points traveling in complex-numbered Euler circles where no point is privileged over any other. From this motion, we get sine and cosine waves, even and odd functions, symmetry and antisymmetry, orthogonality and non-orthogonality, phase, straight-line radii, right-angled triangles, Pythagoras’ theorem, the speed of mathematics (c), π, e, i, Fourier mathematics … and from all of that we get the whole of mathematics (eternal, necessary and mental; Being), and thus the whole of science (temporal, contingent and material; Becoming). And that is the whole universe explained. Nothing else is required. The PSR gives us mathematics, mathematics gives us science, and that’s all we need for the universe: science with a mathematical and rational core rather than with a material and observable core. What could be more rational and logical?

Pythagoras, should he want to continue on for a degree in modern-day mathematics, would have to learn to abide far more counterintuitive results than numbers that cannot be written as ratios between whole numbers. From the square root of −1, to Georg Cantor’s revelation of infinite domains infinitely more infinite than other infinite domains, to Kurt Gödel’s incompleteness theorems, mathematics has constantly displaced the borders between the conceivable and the inconceivable, and Pythagoras would be in for some long hours of awesome mind-blowing.

In fact, by founding the Academy in the year 387 BC, Plato was envisaging a practical pattern of life in retreat that he had encountered shortly before on his first Sicilian journey. Near the city of Kroton (now called Crotone) in southern Italy, he had come upon a commune of hermits doing theory who were followers of the savant Pythagoras, a man of whom it was not known whether he was still a shaman or had already become a mathematician or was both at once.

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

Pythagoras (550 BCE), with his theory of numbers, had been a source of inspiration for those who sought harmony in the Universe. His aim was to show in his philosophy that there was a high, structural, divine order to the Universe. This was a natural habitat for the souls. Mathematics was the tool to investigate this order.

right man to prepare the citizens of his country, who were facing disempowerment, for the benefits of the vita contemplativa. The transition to reflective existence was worth an error in reasoning: Cicero unhesitatingly created a lofty nimbus for the future Roman spectator by portraying Pythagoras making the many in the stadium into the few in study.