Founders Of Religions

"Nicomachus concludes his first book with a theorem that indicates that mathematics was not yet free from ethical and æsthetic mixture. From Pythagoras onward two ideas were widespread in Greek, especially Platonic, philosophy. These are that the beautiful and the definite are prior to the ugly and the indefinite, and that from them are formed all the parts and classes of the infinite and indefinite. Nicomachus aims to show that in mathematics the same principle holds good in that from equality may be derived all the species of inequality."

"Pythagoras, as everyone knows, said that "all things are numbers." This statement, interpreted in a modern way, is logical 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 or 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 calculi] (or as we would more naturally say, shot) required to make the shapes in question."

"Some fundamental unity was surely to be discerned either in the matter or the structure of things. The Ionic philosophers chose the former field: Pythagoras took the latter. ...The geometry which he had learnt in Egypt was merely practical. ...It was natural to nascent philosophy to draw, by false analogies, and the use of a brief and deceptive vocabulary,2 enormous conclusions from a very few observed facts: and it is not surprising if Pythagoras, having learnt in Egypt that number was essential to the exact description of forms and of the relations of forms, concluded that number was the cause of form and so of every other quality. Number, he inferred, is quantity and quantity is form and form is quality. Footnote2 Primitive men, on seeing a new thing, look out especially for some resemblance in it to a known thing, so that they may call both by the same name. This developes a habit of pressing small and partial analogies. It also causes many meanings to be at attached to the same word. Hasty and confused theories are the inevitable result."

"Aristotle was no trustworthy witness. He misrepresented Plato, and he almost caricatured the doctrines of Pythagoras. There is a canon of interpretation, which should guide us in our examinations of every philosophical opinion: The human mind has, under the necessary operation of its own laws, been compelled to entertain the same fundamental ideas, and the human heart to cherish the same feelings in all ages. It is certain that Pythagoras awakened the deepest intellectual sympathy of his age, and that his doctrines exerted a powerful influence upon the mind of Plato. His cardinal idea was that there existed a permanent principle of unity beneath the forms, changes, and other phenomena of the universe. Aristotle asserted that he taught that numbers are the first principles of all entities. Ritter has expressed the opinion that the formula of Pythagoras should be taken symbolically, which is doubtless correct."

"The laws of Manu are the doctrines of Plato, Philo, Zoroaster, Pythagoras, and of the Kabala. The esoterism of every religion may be solved by the latter. The kabalistic doctrine of the allegorical Father and Son, or Xlarrjp and Aoyos is identical with the groundwork of Buddhism. Moses could not reveal to the multitude the sublime secrets of religious speculation, nor the cosmogony of the universe ; the whole resting upon the Hindu Illusion, a clever mask veiling the Sanctum Sanctorum, and which has misled so many theological commentators. (p. 271)"

"Zoroaster, Pythagoras, Epicharmus, Empedocles, Kebes, Euripides, Plato, Euclid, Philo, Boethius, Virgil, Marcus Cicero, Plotinus, Iamblichus, Proclus, Psellus, Synesius, Origen, and, finally, Aristotle himself, far 'from denying our immortality, support it most emphatically. (p. 251)"

"Scholastic skeptics, as well as ignorant materialists, have greatly amused themselves for the last two centuries over the absurdities attributed to Pythagoras by his biographer, Iamblichus. The Samian philosopher is said to have persuaded a she-bear to give up eating human flesh; to have forced a white eagle to descend to him from the clouds, and to have subdued him by stroking him gently with the hand, and by talking to him. On another occasion, Pythagoras actually persuaded an ox to renounce eating beans, by merely whispering in the animal's ear! (Iamblichus: "De Vita Pythag.") Oh, ignorance and superstition of our forefathers, how ridiculous they appear in the eyes of our enlightened generations! Let us, however, analyze this absurdity. Every day we see unlettered men, proprietors of strolling menageries, taming and completely subduing the most ferocious animals, merely by the power of their irresistible will... Every one has either witnessed or heard of the seemingly magical power of some mesmerizers and psychologists. They are able to subjugate their patients for any length of time. Regazzoni, the mesmerist who excited such wonder in France and London, has achieved far more extraordinary feats than what is above attributed to Pythagoras. Why, then, accuse the ancient biographers of such men as Pythagoras and Apollonius of Tyana of either wilful misrepresentation or absurd superstition?"

"Pythagoras stands at the fountainhead of our culture. The ideas he set in motion were, according to Daniel Boorstin, "among the most potent in modern history," resulting directly in many of the pillars upon which the modern world is built. In particular, the very existence of science becomes possible only when it is realized that inner, purely subjective, mathematical forms have a resonance with the form and behavior of the external world — a Pythagorean perception. And a world at peace — that is to say, in a nuclear age, the survival of our planet — is predicated upon ideas of universal brotherhood to which Pythagoras, while not the sole author, made an enormous contribution. Even the seeming remoteness of Pythagorean teaching helps one to realize that the current world view, while it seems destined to dominate the planet, is fleeting and temporary and, like others before it, will pass."

"Nor need you question but that Pythagoras a long time be­fore he found the demonstration for which he offered the Heca­tomb, had been certain, that the square of the side subtending the right angle in a rectangle triangle, was equal to the square of the other two sides: and the certainty of the conclusion condu­ced not a little to the investigating of the demonstration, un­derstanding me alwayes to mean in demonstrative Sciences."

"Pythagoras was indeed the first man to call himself a philosopher. Others before had called themselves wise (sophos), but Pythagoras was the first to call himself a philosopher, literally a lover of wisdom. More importantly, for Pythagoras and his followers philosophy was not merely an intellectual pursuit, but a way of life, the aim of which was the assimilation to God."

"If someone associates with a true Pythagorean, what will he will get from him, and in what quantity? I would say: statesmanship, geometry, astronomy, arithmetic, harmonics, music, medicine, complete and god-given prophecy, and also the higher rewards — greatness of mind, of soul, and of manner, steadiness, piety, knowledge of the gods and not just supposition, familiarity with blessed spirits and not just faith, friendship with both gods and spirits, self-sufficiency, persistence, frugality, reduction of essential needs, ease of perception, of movement, and of breath, good color, health, cheerfulness, and immortality."

"It seems to me that they do well to study mathematics, and it is not at all strange that they have correct knowledge about each thing, what it is. For if they knew rightly the nature of the whole, they were also likely to see well what is the nature of the parts. About geometry, indeed, and arithmetic and astronomy, they have handed us down a clear understanding, and not least also about music. For these seem to be sister sciences; for they deal with sister subjects, the first two forms of being."

"The Ionians were optimistic, heathenly materialists... Every philosopher of the period seems to have had his own theory regarding the nature of the universe around him. ...The sixth century scene evokes the image of an orchestra expectantly 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, whose 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."

"We know that he (Pythagoras) went to India to be instructed; but the capacity of the learner determines his degree of proficiency, and if Pythagoras on his return had so little knowledge in geometry as to consider the forty-seventh of Euclid as a great discovery, he certainly was entirely incapable of acquiring the Indian method of calculation, through his deficiency of preparatory knowledge… each teacher, or head of sect that drew his knowledge from Indian sources, might conceal his instructions to be reckoned an inventor."

"Ionian philosophers... had sought to identify a first principle for all things. Thales had thought to find this in water, but others preferred to think of air or fire as the basic element. The Pythagoreans had taken a more abstract direction, postulating that number... was the basic stuff behind phenomena; this numerical atomism... had come under attack by the followers of Parmenides of Elea... The fundamental tenet of the was the unity and permanence of being... contrasted with the Pythagorean ideas of multiplicity and change. Of Parmenides' disciples the best known was Zeno the Eleatic... who propounded arguments to prove the inconsistency in the concepts of multiplicity and divisibility."

"Among the sages of this description, to whose useful labors the world is so much indebted, none held a more deservedly conspicuous rank than Pythagoras […] Quitting the land of his nativity […] his zeal for the acquisition of knowledge led him first to Egypt […] Having at this celebrated fountain of learning exhausted the supply without diminishing his thirst, he sought the further means of slaking it, in the then almost unexplored peninsula of India, whence he returned, bringing back with him the doctrine of Metempsychosis, the prejudices against animal diet, the mysterious notions respecting the powers of numbers, and other visionary and fanciful tenets of the East."

"Pythagoras, the son of Mnesarchus, was the most learned of all men of history; and having selected from these writings, he thus formed his own wisdom and extensive learning, and mischievous art."

"Let us suppose that we have set the problem of finding a solution to the equation \scriptstyle x^2=2. \, This is a problem for which the Babylonians around 1700 BC found the excellent approximation \scriptstyle \sqrt{2}. ...This is the identical problem which Pythagoras asserted had no fractional solution and in whose honor he was supposed to have sacrificed a hecatomb of oxen—the problem which caused the existentialist crisis in ancient Greek mathematics. The \scriptstyle \sqrt{2} exists (as the diagonal of the unit square); yet it does not exist (as a fraction)!"

"Pythagoras did not possess a proof of the theorem which bears his name... he was temperamentally uninterested in proofs of this nature, as may be gleaned from... his numerological deductions. ...the Pythagorean theorem was known to Thales. ...the hypotenuse theorem is a direct consequence of the principle of similitude, and... Thales was fully conversant with the theory of similar triangles. On the other hand, there is no doubt that Pythagoras fully appreciated the metaphysical implications. ...this relation ...was to Pythagoras and the Pythagoreans a basic law of nature, and... a brilliant confirmation of their number philosophy."

"A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines. With consistency a great soul has simply nothing to do. He may as well concern himself with his shadow on the wall. Speak what you think now in hard words, and to-morrow speak what to-morrow thinks in hard words again, though it contradict every thing you said to-day. — "Ah, so you shall be sure to be misunderstood." — Is it so bad, then, to be misunderstood? Pythagoras was misunderstood, and Socrates, and Jesus, and Luther, and Copernicus, and Galileo, and Newton, and every pure and wise spirit that ever took flesh. To be great is to be misunderstood."

"Koyré's exaltation of the "Platonic and Pythagorean" elements of the Scientific Revolution... was based on a demonstrably false understanding of how Galileo reached his conclusions. Koyré asserted that Galileo merely used experiments as a check on the theories he devised by mathematical reasoning. But later research has definitively established that Galileo's experiments preceded his attempts to give a mathematical account of their results."

"Pythagoras could not have been the discoverer of the relation, because... this property was known and used by scholars and artisans of Oriental lands thousands of years before Pythagoras... While deductive geometry is barely more than twenty-five hundred years old, empirical geometry is probably as old as civilization itself."

"But there was among them a man of prodigious knowledge who acquired the profoundest wealth of understanding and was the greatest master of skilled arts of every kind; for, whenever he willed with his whole heart, he could with ease discern each and every truth in his ten—nay, twenty—men's lives."

"There remains no firm basis for the belief that Pythagoras was a geometer and in any case no attestation of his having written anything."

"Pythagoras was said to have been the first man to call himself philosopher; in fact, the world is indebted to him for the word philosopher. Before that time the wise men called themselves sages, which was interpreted to mean those who know. Pythagoras was more modest. He coined the word philosopher, which he defined as one who is attempting to find out."

"The apparently ancient reports of the importance of Pythagoras and his pupils in laying the foundations of mathematics crumble on touch, and what we can get hold of is not authentic testimony by the efforts latecomers to paper over a crack, which they obviously found surprising, by the use of various kinds of reconstruction and reinterpretation. On the other hand, there are ancient and unassailable indications of a Greek mathematics antedating Pythagoras and quite outside his sphere of influence."

"I wished to show that Pythagoras, the first founder of the vegetable regimen, was at once a very great physicist and a very great physician; that there has been no one of a more cultured and discriminating humanity; that he was a man of wisdom and of experience; that his motive in commending and introducing the new mode of living was derived not from any extravagant superstition, but from the desire to improve the health and the manners of men."

"I have often admired the mystical way of Pythagoras, and the secret Magic of numbers."

"Pythagoras is the founder of European culture in the Western Mediterranean sphere."

"It is further interesting to remark that the finest characters among women with which ancient Greece presents us were formed in the school of Pythagoras, and the same is true of the men."

"The school of the Pythagoras and those of the Neo-Platonists kept up the tradition for Greece, and we know that Pythagoras gained some of his learning in India, while Plato studied, and was initiated in the schools of Egypt. More precise information has been published of the Grecian schools than of others; the Pythagorean had pledged disciples as well as an outer discipline, the inner circle passing through three degrees during five years of probation."

"The world is always ungrateful to its great men. Florence has built a statue to Galileo, but hardly even mentions Pythagoras. The former had a ready guide in the treatises of Copernicus, who had been obliged to contend against the universally established Ptolemaic system. But neither Galileo nor modern astronomy discovered the emplacement of the planetary bodies. Thousands of ages before, it was taught by the sages of Middle Asia, and brought thence by Pythagoras, not as a speculation, but as a demonstrated science. "The numerals of Pythagoras," says Porphyry, "were hieroglyphical symbols, by means whereof he explained all ideas concerning the nature of all things." Verily, then, to antiquity alone have we to look for the origin of all things. p. 31"

"It seems probable that the early Greeks were largely indebted to the Phoenicians for their knowledge of practical arithmetic or the art of calculation, and perhaps also learnt from them a few properties of numbers. It may be worthy of note that Pythagoras was a Phoenician; and according to Herodotus, but this is more doubtful, Thales was also of that race."

"But it is, however, in the teachings of Pythagoras that we find the closest and most frequent identities of teachings and argumentation [about as to the nature and position of the Gods], explained as due to Pythagoras himself having visited India and learned his philosophy there, as tradition asserts. In later centuries we find some peculiarly Sânkhyan and Buddhist ideas playing a prominent part in Gnostic thought."

"Pythagoras called his Gnosis “the knowledge of things that are,” or ἡ γνῶσις τῶν ὄντων, and preserved that knowledge for his pledged disciples only: for those who could digest such mental food and feel satisfied; and he pledged them to silence and secrecy. Occult alphabets and secret ciphers are the development of the old Egyptian hieratic writings, the secret of which was, in the days of old, in the possession only of the Hierogrammatists, or initiated Egyptian priests."

"Personal religion is derived from ecstasy, theology from mathematics, and both are to be found in Pythagoras."

"They thought they found in numbers, more than in fire, earth, or water, many resemblances to things which are and become; thus such and such an attribute of numbers is justice, another is soul and mind, another is opportunity, and so on; and again they saw in numbers the attributes and ratios of the musical scales. Since, then, all other things seemed in their whole nature to be assimilated to numbers, while numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number."

"Whenever he heard a person who was making use of his symbols, he immediately took him into his circle, and made him a friend."

"Pythagoras repeats our archaic doctrine when stating that the Ego (Nous) is eternal with Deity; that the soul only passed through various stages to arrive at divine excellence; while thumos returned to the earth, and even the phren, the lower Manas, was eliminated."

"The games which can be built up from the simple idea of dots and lines... can be a productive source of teaching material. After all, s provided the Pythagoreans and neo-Pythagoreans with important theorems about the summing of series."

"In this theater of man's life it is reserved only for God and angels to be lookers on."

"Concern should drive us into action and not into a depression."

"Ten is the very nature of number. All Greeks and all barbarians alike count up to ten, and having reached ten revert again to the unity. And again, Pythagoras maintains, the power of the number 10 lies in the number 4, the tetrad. This is the reason: if one starts at the unit (1) and adds the successive number up to 4, one will make up the number 10 (1+2+3+4 = 10). And if one exceeds the tetrad, one will exceed 10 too.... So that the number by the unit resides in the number 10, but potentially in the number 4. And so the Pythagoreans used to invoke the Tetrad as their most binding oath: "By him that gave to our generation the Tetractys, which contains the fount and root of eternal nature...""

"The oldest, shortest words— "yes" and "no"— are those which require the most thought."

"There is nothing so easy but that it becomes difficult when you do it reluctantly."

"Pythagoras... assumed as first principles the numbers and symmetries existing among them, which he calls harmonies, and the elements compounded of both, that are called geometrical. ...he says that the nature of Number is the Decad."

"Evil destroyeth itself."

"He is worst of all, that is malicious against his friends."

"Better be mute, than dispute with the Ignorant."

"Virtue is harmony."