The Pythagorean Sourcebook and Library

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The Pythagorean Sourcebook and Library

Postby admin » Tue Nov 12, 2013 9:09 pm

The Pythagorean Sourcebook and Library
An Anthology of Ancient Writings Which Relate to Pythagoras and Pythagorean Philosophy
Compiled and Translated by Kenneth Sylvan Guthrie, with additional translations by Thomas Taylor and Arthur Fairbanks, Jr.
Edited and Introduced by David Fideler
With a foreword by Joscelyn Godwin
© 1987, 1988 by Phanes Press




Table of Contents:

Foreword by Joscelyn Godwin
Preface to the Original Edition by Kenneth Sylvan Guthrie
Preface to the New Edition
Introduction by David Fideler
o Introductory Remarks
o Pythagoras
o Number, Kosmos, Harmonia
o The Monochord: The Mathematics of Harmonic Mediation
o The Tetraktys: Number as Paradigm
o The Way of Philosophy and the Three Lives
o The Soul, its Nature and Care
o Pythagorean Educational Theory
o Pythagorean Political and Ethical Theory
o The Pythagorean Tradition and its Development
o A Philosophy of Whole Systems
o Notes to the Introduction
• The Life of Pythagoras by Iamblichus of Chalcis
o 1. The Importance of the Subject
o 2. His Youth, Education and Travels
o 3. His Journey to Egypt
o 4. His Studies in Egypt and Babylonia
o 5. Travels in Greece; Settlement at Croton
o 6. The Pythagorean Community
o 7. Italian Political Achievements
o 8. His Intuition, Reverence, Temperance and Studiousness
o 9. Community and Chastity
o 10. His Advice to youths
o 11. His Advice to Women
o 12. Why he Called himself a Philosopher
o 13. How he Shared Orpheus' Control over Animals
o 14. On Pythagoras' Preexistence
o 15. How Pythagoras Cured by Medicine and Music
o 16. Pythagorean Asceticism
o 17. The Tests of Pythagorean Initiation
o 18. The Organization of the Pythagorean School
o 19. His Relations with Abaris the Hyperborean
o 20. Psychological Requirements
o 21. The Pythagorean Daily Program
o 22. On Pythagorean Friendship
o 23. The Use of Parables in Instruction
o 24. His Dietary Suggestions
o 25. The Pythagorean Use of Music and Poetry
o 26. His Study of Musical Harmonics
o 27. Political and Social Achievements of the Pythagoreans
o 28. Concerning the Divinity of Pythagoras
o 29. Pythagorean Sciences and Maxims
o 30. His Theory of Justice and Political Philosophy
o 31. Pythagorean Temperance and Self-Control
o 32. Courage or Fortitude
o 33. Universal Friendship
o 34. Miscellaneous Topics
o 35. The Attack on Pythagoreanism
o 36. The Pythagorean Succession
The Life of Pythagoras by Porphyry of Tyre
The Anonymous Life of Pythagoras Preserved by Photius
The Life of Pythagoras by Diogenes Laertius
o 1. Early Life
o 2. Studies
o 3. Initiations
o 4. Transmigration
o 5. Works of Pythagoras
o 6. General Views of Life
o 7. Ages of Life
o 8. Social Customs
o 9. Distinguished Appearance
o 10. Women Deified by Marriage
o 11. Scientific Culture
o 12. Diet and Sacrifices
o 13. Measures and Weights
o 14. Hesperus as Phosphorus
o 15. Students and Reputation
o 16. Friendship Founded on Symbols
o 17. Symbols or Maxims
o 18. Personal Habits
o 19. Various Teachings
o 20. Poetic Testimonies
o 21. Death of Pythagoras
o 22. Pythagoras' Family
o 23. Jesting Epigrams
o 24. The Last Pythagoreans
o 25. Various Pythagorases
o 26. Pythagoras' Letter
o 27. Empedocles a Pythagorean
• The Pythagorean Symbols or Maxims
The Golden Verses of Pythagoras
The Fragments of Philolaus
The Fragments of Archytas
Ocellus Lucanus: On the Nature of the Universe
o A Fragment on Laws
Hippodamus the Thurian: On Felicity
o On a Republic
Diotogenes: On Sanctity
o Concerning a Kingdom
Theages: On the Virtues
The Preface to the Laws of Zaleucus the Locrian
The Preface to the Laws of Charondas the Catanean
Callicratidas: On the Felicity of Families
Perictyone: On the Duties and Harmony of a Woman
Aristoxenus of Tarentum: Apothegms
Euryphamus: Concerning Human Life
Hipparchus: On Tranquility
Metopus: Concerning Virtue
Crito: On Prudence and Prosperity
Polus: On Justice
Sthenidas the Locrian: On a Kingdom
Ecphantus the Crotonian: On Kings
Pempelus: On Parents
Phyntis, Daughter of Callicrates: On Woman's Temperance
A Fragment of Clinias
Select Sentences of Sextus the Pythagorean
Select Pythagorean Sentences
1. From The Exhortation to Philosophy of lamblichus
2. From Stobaeus
3. From Clement of Alexandria
The Ethical Fragments of Hierocles
0. On Conduct Towards the Gods
1. On Conduct Towards our Country
2. On Conduct Towards the Parents
3. On Fraternal Love
4. On Marriage
5. On Conduct Towards our Relatives
6. On Economics
Timaeus of Locri: On the World and the Soul
Passages from the Church Fathers
Passages from Plato and Aristotle
Passages from the Doxographers
Appendix I: How Many Tetraktys are There?
Appendix II: Pythagorean Titles of the First Ten Numbers
Appendix III: The Formation and Ratios of the Pythagorean Scale
Appendix IV: Pythagorean Mathematical Discoveries
Glossary of Select Pythagorean Terms
Index of Proper Names
Index of Select Topics
o Frontispiece. PYTHAGORAS (From Stanley's History of Philosophy, 1687)
o 10. IAMBLICHUS (From Taylor's Life of Pythagoras, 1818)
o 11. COIN FROM CROTON (From Stanley's History of Philosophy, 1687)
o 12. THE PYTHAGOREAN Y (From Geoffroy Tory's Champfleury, 1529)
o 13. THE MUSIC OF THE SPHERES (From Stanley's History of Philosophy, 1687)
o 14. THE MUSIC OF THE SPHERES (From Gafurius' Practica musice, 1496)
o 18. THE DIVINE MONOCHORD (From Robert Fludd's History of the Macrocosm and Microcosm, 1617)
Back Cover
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Re: The Pythagorean Sourcebook and Library

Postby admin » Tue Nov 12, 2013 9:11 pm



IF WESTERN CIVILIZATION has taken, as it seems, not one but several wrong turnings between the time of Pythagoras (sixth century B.C.E.) and the present, it is because it has been unfaithful to him who should by rights have been its tutelary genius. Pythagoras is the very midwife of our epoch, ushering it to birth from the dusky, mythic past, sowing the seeds of a new consciousness, a new possibility for growth after the plan laid up in Heaven. His own story, accordingly, is part myth, part ascertainable history. Such divine figures as he inhabit both realms. His achievement is a prophetic one, for in his life and work he set forth the perfect framework for the unfoldment not only of Classical Greek culture but of the whole coming age up to our own time. The Pythagorean synthesis of religion with spiritual and natural philosophy would have been the ideal guide for a civilization whose destiny was to come to terms with the material world.

Pythagoras set the stage for this development with a careful system of checks and balances. In his emphasis on Number -- the keystone of his doctrine -- he revealed the secret without which modern technology would have been impossible. It is applied mathematics, after all, that has led to the so- called conquest of Nature. But at the same time, and much more importantly, Pythagoras taught the metaphysical and sacred aspect of Number as reflecting the One and its emanations. In this respect the Numbers, especially those from 1 to 10, are archetypal beings. To approach them as quantity alone is a denial of their nature verging on blasphemy. It is not the fault of Christianity that the idea of sacred number and geometry has vanished, along with any viable science based thereon: nowhere are these things more evident than in the scriptures and rituals of the Churches. It is the error of those who have forgotten the Pythagorean (and Christian) precept, to "honor first the Immortal Gods" -- themselves Numbers -- before embarking on any enterprise. Consequently number today carries not meaning and wisdom, but only information and power of a very dubious character.

The Pythagorean world view is a graduated, hierarchical one, with every stage filled by appropriate beings: Divinities, lesser Gods, daimons, heroes, geniuses. etc. It is in no way contrary to the Jewish, early Christian, and Islamic vision of rank upon rank of angels standing between God and the earth. Angels are unfashionable nowadays, and while in some respects it has been an advantage to bring the Absolute closer to man, it has lost most of its absoluteness in becoming a personal God. Far better to worship the One within, but to recognize and cooperate with those beings who have to maintain the world against mankind's best efforts to spoil it. Given this orderly hierarchical universe, Pythagoreanism has no need to blandly oppose spirit to matter: things are more subtle than that. Neither does it need to invent a Fall of angels or of man that violates the divine order. The Golden Verses say: "Men are children of the Gods, and sacred Nature all things hid reveals. " Everything proceeds according to a law that renders perfect justice to each, as surely as every physical action provokes an equal and opposite reaction. The One has no personality to make its favor or anger our concern. Since there is no Fall except the periodic one of soul into body, there is no vicarious salvation. Only one's own efforts and acquired wisdom can free one from this migration around the states of being. Nevertheless, there is every reason for piety towards the Gods, and for gratitude to Pythagoras and those others who have taught the means to attain freedom through rational conduct and the philosophic life.

Pythagoras' metaphysics enables the Intellect to approach and know the ultimate TRUTH. His moral precepts ensure conformity with the perfect GOODNESS. To complete the trinity, he also adored the supreme BEAUTY which inspires the Muses as they do our Arts. In the first place he seems to have used Music, both for the intellectual benefits of its speculative side and for the effects of practical music on psycho-physical health. Music is the art in which the Numbers penetrate directly to the heart; in Mathematics they occupy the brain. But it is not music alone that incarnates the transcendent virtues of Number. As it does so in time, so the visual arts do in space, depending no less for their beauty on harmony and correct proportion. It was this knowledge that enabled Classical Greek architecture and sculpture to attain such heights in the century after Pythagoras. Ever since then the high-points of Western and Islamic architecture have followed on the reapplication of harmonic principles, as one can prove by measurement of Gothic cathedrals, early Renaissance churches, and the masterpieces of Islamic architecture. Disobedience to harmonic laws leads to ugliness, which is a sin against the Muses and a denial of the divinely beautiful order of the cosmos. Obedience to them, on the other hand, presupposes a state of soul open also to Intelligible Beauty; music and architecture open our souls in the same way.

When he came to teach, Pythagoras recognized that people, too, are arranged in a hierarchy, and that they vary enormously in their receptivity to philosophy. Some are little more than animals, and require the same loving attentions, while others are little short of Gods. Consequently he reserved different degrees of teaching for the different levels. Much has been said about the secrecy of the most esoteric branch of his school, but like Plato and Jesus he also involved himself in public life, often to his cost. As a political reformer and giver of laws to several cities, he provided a field for the improvement of all, even of the lowest types -- for that is what politics should be about. Within his school he went against contemporary custom in giving equal status to women, and his biographers are careful to record the names of his female disciples. I am sure that much evil would have been avoided had Western civilization not indulged in such parodies of the hierarchical principle as the simplistic division into Saved and Damned, and the restriction of public office and education to men alone.

Naturally Pythagoras did not invent his philosophy: it was not original except in the brilliance of his synthesis. Since Truth is perennial and invariable, to create an "original" philosophy is merely to hatch another untruth. Pythagoras' unique advantage was that he studied in every available school, philosophic and religious alike. Orphic by temperament, he also knew the early natural philosophers Thales and Anaximenes, but far from stopping with Greece he investigated the mysteries of Egypt, the science of Babylon, even the wisdom of the Hyperboreans (presumably the Ancient Britons). When he was in his fifties he began to teach the distillation of what he had learnt. Some of it, such as his mystery initiations, he could not pass on. He retained, in fact, only what would be useful to a coming age in which those mysteries would decline and disappear. The discovery of the Divine within oneself (the "Kingdom of Heaven within you") was to be its goal, aided by contemplation of that which "sacred Nature" reveals. There is no reason why this could not have been adapted to make an exoteric religion to serve the whole civilization. This actually seems to have been happening in the time of Caeser and the early Roman Empire, scene of so many religious might-have-beens. As it was, the Pythagorean strain survived only in its more esoteric cultivation by the Neoplatonic philosophers. Neoplatonism is to a very large degree Neopythagorean: it shares the typical interests in theosophy, cosmology, arithmology, speculative music, and exotic religion. In fact, just as Platonists regard Aristotle as a rather limited successor to their master, so Pythagoreans may well regard the Divine Plato.

Since the end of the Roman Empire Pythagoreans have periodically found shelter in the esoteric schools of Christianity and Islam. From time to time their presence has manifested, especially in architecture and the other arts. While I do not believe, as some do, that these schools can have been the motive force behind a history as disappointing as that of the West, one should mention some of those who have publicly carried the torch. Marsilio Ficino in the fifteenth century cast Pythagoras as a link in his genealogy of "prisci theologi": Hermes Trismegistus, Orpheus, Aglaophamus, Pythagoras, Philolaus, Plato. The astronomers Copernicus, Galileo and Kepler invoked the Pythagorean school as a precedent for their heliocentric astronomy; in Kepler's case there was much more, including his researches into the geometry and harmony of the spheres. Later there were two great "romantic" Pythagoreans, Thomas Taylor (1758-1835) and Fabre d'Olivet (1767-1825), perhaps the only ones up to their time who were not also Christians. Fabre published the Golden Verses in French, with his remarkable commentary, in 1813; Taylor published his Theoretic Arithmetic in 1816, his translation of Iamblichus's Life of Pythagoras, the basis of Guthrie's version, in 1818. Largely as a consequence of the work of these two men, the nineteenth century swarms with semi-Pythagoreans, great and small, but all of rather limited effect on the world in general. A stronger impetus was given by the Theosophical Society at the end of the nineteenth century, and by the various esoteric groups that surrounded and derived from it. Kenneth Sylvan Guthrie's work belongs in this context, as does the better-known achievement of Manly Palmer Hall.

Our civilization is now, quite unconsciously, more imbued with Pythagorean influences than it has ever been. The evidence is plain to see wherever one looks, in phenomena as various as vegetarianism and the whole-food movement; postmodernist architecture; the synthesis of religions; travelers in search of Oriental wisdom; researches into ancient Egypt and Babylon; the revivals of sacred geometry, arithmology and speculative music; reprints of Pythagorean literature; meditation; music therapy; the speculations of modern physicists; communes and spiritual communities; the widespread belief in reincarnation. Pythagoras is the center towards which all these scattered impulses point. If he failed as the avatar of the passing age, perhaps he is coming into his own as a new one dawns.

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Re: The Pythagorean Sourcebook and Library

Postby admin » Tue Nov 12, 2013 9:12 pm


THE REASON THAT PYTHAGOREANISM has been neglected, and often treated mythically, is that until this edition all the Pythagorean fragments have never been collected, in text or any translation. This book therefore marks an era in the study of philosophy, and is needed by every university and general library in the world, not to mention those of the students of philosophy.

But there is yet a wider group of people who will welcome it, the lovers of wisdom in general, who will be charmed by Hierocles' modern views about the family, inspired by Iamblichus' beautiful Life of Pythagoras, which has been inaccessible for over a century, and strengthened by the maxims of Sextus, which represent the religious facts of the future more perfectly than can easily be found elsewhere.

The universal culture of Pythagoras is faithfully portrayed by the manifold aspects of the teachings of Archytas, and Philolaus, and of many other Pythagoreans, among whose fragments we find dissertations on every possible subject: metaphysics, psychology, ethics, sociology, science, and art. Men of general culture, therefore, will feel the need of this encyclopedic information and study; and conversely, there is neither scientist, metaphysician, clergyman, litterateur or sociologist who will fail to discover herein something to his taste.

The Pythagorean fragments have been gathered from various sources. On Philolaus, the authority is Boeckh. The Archytas fragments have been taken from Chaignet; the minor works from Gale and Taylor, and the Maxims and Golden Verses from Dacier. The work by Timaeus was taken from Plato's works, among which it has been preserved.

This work was undertaken because of the great significance of these writings in the history of philosophy, which has been elsewhere more definitely been pointed out, and for the sake of which, no doubt, the book will be procured by all students, philosophers, and general lovers of wisdom. It was undertaken for no purpose other than the benefit of humanity that had for so long been deprived of this its precious heritage, and the editor will be satisfied if he succeeds in restoring these treasures of thought and inspiration to his day and generation.

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Re: The Pythagorean Sourcebook and Library

Postby admin » Tue Nov 12, 2013 9:13 pm


THIS ANTHOLOGY is based on Kenneth Sylvan Guthrie's Pythagoras Source Book and Library, issued in a very small printing by the Platonist Press between 1919 and 1920. Guthrie's edition contained his own translations of ancient Greek writings in addition to edited versions of writings initially translated by Thomas Taylor. In editing Taylor's translations, Guthrie carefully adhered to Taylor's renditions but greatly improved the readability of the style. Guthrie's original translations include Porphyry's Life of Pythagoras, the anonymous Life of Pythagoras from Photius, the biography from Diogenes Laeritus, and the fragments of Philolaus and Archytas. Most of the remaining works were translated by Taylor, and their sources are noted in the bibliography under "Pythagorean Texts." In editing this work I have repaired some awkward phrasings and have checked all of Guthrie's renditions against other translations including those of Taylor.

In addition to containing all the texts of Guthrie's original edition, much new material has been added as well: additional translations by Arthur Fairbanks, four new appendixes, illustrations, an index, a large bibliography, and a new foreword and introduction.

Throughout the production process a number of individuals have graciously provided assistance to whom thanks is due: Joscelyn Godwin, Steve Miller, Henry Morren, and Arthur Versluis were instrumental in helping with the proofreading, and Bob Tarte provided assistance with typography. I would also like to acknowledge the assistance of my father, Raymond E. Fideler (1912-1986), without whose help and generosity this project might not have been completed; unfortunately, he passed away before he could view the final results, so I would like to dedicate my introductory essay, with gratitude and affection, to his memory.

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Re: The Pythagorean Sourcebook and Library

Postby admin » Tue Nov 12, 2013 9:19 pm



IT HAS BEEN SUGGESTED, by Alfred North Whitehead, that "the safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato. " If such be the case, what might then be said of Pythagoras, to whose philosophy Plato was so greatly indebted? While no definitive answer will be attempted here, it might do well to note that not only did Pythagoras first employ the term philosophy, and define the discipline thereof in the classic sense, but that he bequeathed to his followers, and to the whole of Western civilization, many important studies and sciences which he was instrumental in either formulating or systematizing.

True as this may be, much mystery surrounds the figure of Pythagoras, despite the significant influence of Pythagorean thought in antiquity. Of course, many things can be precisely stated. He was both a natural philosopher and a spiritual philosopher, a scientist and a religious thinker. He was a political theorist, and was even involved in local government. While he may not have been the first to discover the ratios of the musical scale, with which he is credited, there can be no doubt that he did conduct extensive research into musical harmonics and tuning systems. Pythagoras is well known as a mathematician, but few realize that he was also a music therapist having, in fact, founded the discipline. Pythagoras taught the kinship of all living things; hence, he and his followers were vegetarians. Yet, while all these things may be safely stated, quite a bit of mystery still remains. [1] This is due in large part to the fact that Pythagoras left no writings, although it is said that he wrote some poems under the name of Orpheus [2]. Pythagoras' teaching was of an oral nature. While he seems to have made some speeches upon his arrival in southern Italy to the populace, the true fruits of his philosophic inquiries were presented only to those students who were equipped to assimilate them. Pythagoras no doubt felt, like his later admirer Plato, that philosophic doctrines of ultimate concern should never be published, seeing that philosophy is a process, and that books can never answer questions, nor engage in philosophical enquiry. [3]

Yet, despite the lack of first-hand writings by Pythagoras himself, we need not be deterred. There is an immense amount of material in the biographies of Pythagoras which goes back to a very early date, and it is certainly possible to sketch an accurate if not complete picture of early Pythagorean philosophy, even being quite specific on many points. [4] Let us then begin with Pythagoras himself.


THE PRIMARY SOURCES of information about the life of Pythagoras are to be found in this anthology. In addition to containing quite a bit of information about Pythagoras which goes back to an early date, these four biographies also demonstrate in an admirable fashion the high esteem in which the philosopher was held.

Pythagoras was born around 570 B.C.E. to Mnesarchus of Samos, a gemengraver, and his wife, Pythais.

The biographies of Pythagoras are unanimous that at an early age he travelled widely to assimilate the wisdom of the ancients wherever it might be found. He is said by Iamblichus to have spent some 22 years in Egypt studying there with the priests, and is also said to have studied the wisdom of the Chaldeans firsthand. These accounts are generally accepted by most scholars -- as indeed they should be, owing to the high degree of contact between Asia Minor and other cultures -- although it is doubtful, while not impossible, that he travelled to Persia to study the teachings of Zoroaster. In these distant lands Pythagoras not only studied the sciences there cultivated, including mathematical sciences we may safely presume, but was also initiated into the religious mysteries of the "barbarians." As Porphyry succinctly observes, "It was from his stay among these foreigners that Pythagoras acquired the greater part of his wisdom." [5]

After his studies abroad, Pythagoras returned home to the island of Samos, where he continued his philosophical researches. It is said that he outfitted a cave especially designed for the study of philosophy, and it was there that he made his home. About this time Pythagoras opened his first school, as we are told by Porphyry, yet it probably was not long-lived, as Pythagoras decided to leave Samos at the age of 40, owing to the tyranny of Poly crates which was then flourishing.

From Samos Pythagoras journeyed to South Italy, arriving at Croton, "conceiving that his real fatherland must be the country containing the greatest number of the most scholarly men." [6]

It would seem that his reputation preceded the philosopher, for he was shortly asked to speak to the populace of Croton -- men, women, and children -- on the proper conduct of life. The essence of these speeches is to be found in the biography by Iamblichus. While obviously not recorded verbatim, it seems quite likely that the content of these talks is genuinely Pythagorean and goes back to Pythagoras himself. [7] According to the biographies, the populace was enthralled by the wisdom of this man, owing to which he was invited to become involved in local government.

Number, Kosmos, Harmonia

... and the ancients, who were superior to us and dwelt nearer to the Gods, have handed down a tradition that all things that are said to exist consist of a One and a Many and contain in themselves the connate principles of Limit and Unlimitedness.
-- Plato, Philebus 16c

WHERE PYTHAGORAS DEVELOPED his interest in Number we do not know, although it is likely that he was not the first to be concerned with its sacred or metaphysical dimension. What we do know is that a metaphysical philosophy of Number lay at the heart of his thought and teaching, permeating, as we shall see, even the domains of psychology, ethics and political philosophy.

The Pythagorean understanding of Number is quite different from the predominately quantitative understanding of today. For the Pythagoreans, Number is a living, qualitative reality which must be approached in an experiential manner. Whereas the typical modern usage of number is as a sign, to denote a specific quantity or amount, the Pythagorean usage is not, in a sense, even a usage at all: Number is not something to be used; rather, its nature is to be discovered. In other words, we use numbers as tokens to represent things, but for Pythagoreans Number is a universal principle, as real as light (electromagnetism) or sound. As modern physics has demonstrated, it is precisely the numeric, vibrational frequency of electromagnetic energy -- the "wavelength" -- which determines its particular manifestation. Pythagoras, of course, had already determined this in the case of sound.

Because Pythagorean science possessed a sacred dimension, Number is seen not only as a universal principle, it is a divine principle as well. The two, in fact, are synonymous: because Number is universal it is divine; but one could as easily say that because it is divine, it is universal. Hence, the aim of Pythagorean and later Platonic science is different from that of modern "Aristotelian" science: it is not so much involved with the investigation of things, as the investigation of principles. It should be very firmly emphasized, however, that for Pythagoras the scientific and religious dimensions of number were never at odds with each other. Moreover, the Pythagorean approach to Number, for the first time in Greece, elevated mathematics to a study worth pursuing above any purely utilitarian ends for which it had previously been employed.

The Pythagoreans believed that Number is "the principle, the source and the root of all things." [8] But to make things more explicit: the Monad, or Unity, is the principle of Number. In other words, the Pythagoreans did not see One as a number at all, but as the principle underlying number, which is to say that numbers -- especially the first ten -- may be seen as manifestations of diversity in a unified continuum [9] To quote Theon of Smyrna:

Unity is the principle of all things and the most dominant of all that is: all things emanate from it and it emanates from nothing. It is indivisible and it is everything in power. It is immutable and never departs from its own nature through multiplication (lxl=1). Everything that is intelligible and not yet created exists in it; the nature of ideas, God himself, the soul, the beautiful and the good, and every intelligible essence, such as beauty itself, justice itself, equality itself, for we conceive each of these things as being one and as existing in itself. [10]

If One represents the principle of Unity from which all things arise, then Two, the Dyad, represents Duality, the beginning of multiplicity, the beginning of strife, yet also the possibility of logos, the relation of one thing to another:

The first increase. the first change from unity is made by the doubling of unity which becomes 2, in which are seen matter and all this is perceptible, the generation of motion, multiplication and addition, composition and the relationship of one thing to another. [11]

With the Dyad arises the duality of subject and object, the knower and the known. With the advent of the Triad, however, the gulf of dualism is bridged, for it is through the third term that a Relation or Harmonia ("joining together") is obtained between the two extremes. While Two represents the first possibility of logos, the relation of one thing to another, the Triad achieves that relation in actuality. If this process of emergence is represented graphically as in figure I, we can see that the Triad not only binds together the Two, but also, in the process, centrally reflects the nature of the One in a "microcosmic" and balanced fashion. (See figure 1.)


What we have seen in this example of Pythagorean paradigm, based on the universal principles of pure Number and Form, is the emergence of Duality out of Unity, and the subsequent unification of duality, which in turn results in a dynamic, differentiated image of the One in three parts-a continuum of beginning, middle and end, or of two extremes bound together with a mean term. This process, in fact, is the archaic and archetypal paradigm of cosmogenesis, the pattern of creation which results in the world. As F.M. Corn ford has observed:

The abstract formula which is common to the early cosmogonies is as follows: (1) There is an undifferentiated unity. (2) From this unity two opposite powers are separated out to form the world order. (3) The two opposites unite again to generate life. [12]

Cornford goes on to demonstrate how this universal pattern underlies not only the cosmogonies of Greek myth, but also those of the early Ionian scientific tradition. [13] It also underlies, as one may suspect, the Pythagorean view of the kosmos, literally "world-order" or "ordered-world," a term that Pythagoras is credited with first applying to the universe. The word kosmos, in addition to its primary meaning of order, also means ornament. The world, according to Pythagoras, is ornamented with order. This is another way of saying that the universe is beautifully ordered.

The idea of order is intimately connected with Limit (peras), the opposite of which is the Unlimited (apeiron), and these are the two most basic, and hence most universal, principles of Pythagorean cosmology. According to the Pythagoreans, the world or cosmos is compounded of these elements, summarized in the famous "Table of Opposites" which has been preserved by Aristotle in his Metaphysics (i. 5 986 a 23):


Limit is a definite boundary; the Unlimited is indefinite and is therefore in need of Limit. Apeiron also may be translated as Infinite, but it is infinite in a negative sense: that is, it is infinitely or indefinitely divisible, and hence weak, rather than the modern "positive" usage of the term, which is often synonymous with "powerful." To avoid any confusion between the ancient and modern meanings, Apeiron has been translated as either Indefinite or Unlimited in the writings which appear in this book, unless the context suggests otherwise.

Aristotle stated that the Pythagoreans made everything out to be created of numbers; what he means to say is that everything is created out of the elements of number, which include the Limited and the Indefinite, the Odd and the Even.

The Pythagoreans were in the habit of representing arithmetical numbers as geometrical forms, through which they arrived at some interesting insights. In fact, Aristotle makes reference to this very practice:

The Pythagoreans identify the Unlimited with the Even. For this. they say, when it is enclosed and limited by the Odd provides things with the element of unlimitedness. An indication of this is what happens in numbers: if gnomons are placed around the unit and apart from the unit, in the latter case the resulting figure is always other, in the former it is always one. [14]

Aristotle is referring to the following figures:



The Greek word gnomon signifies a "carpenter's square." In figure 3 gnomons have been placed around the One, in figure 4 around the Dyad. From this arrangement several patterns arise. In the case of figure 3, each gnomon or band of points is odd, in figure 4 each gnomon is even. From the above diagrams, we can easily see why the Pythagoreans, in the Table of Opposites, identified the Odd and Even with the Square and Oblong respectively. Moreover, the principles of Limit and the Unlimited are also most manifest in these representations, for figure 3 is limited by the stable form of the square, while figure 4 is infinitely variable: with each successive gnomon, the shape and its corresponding lateral to horizontal ratio changes each time, for it is the nature of the Unlimited to be eternally variable and multifarious.

According to the paradigms of ancient cosmology, Matter (the Indefinite) receives and is shaped by Form (Limit); hence, these two principles of peras and apeiron may be seen at the two most universal and essential elements which are absolutely necessary for the manifestation of phenomenal reality. From this perspective it becomes easy to see the logic behind the Pythagorean sentiment that the cosmos is created out of the elements of Number, namely the Limited and the Indefinite. Plato, in fact, takes over this Pythagorean cosmology to the letter. His only change, and a minor one at that, is that he referred to Limit as the One, the Unlimited as the Indefinite Dyad, terms which have even more Pythagorean implications than the originals.

In the Pythagorean and Platonic cosmology, Limit and the Indefinite, Form and Matter, are woven together through numerical harmony: their offspring, existing in the indefinite receptacle of space, is the phenomenal universe, in which every being is composed of universal constants and local variables. Hence, in his Pythagorean cosmogony of the Timaeus, Plato shows how the fabricator of the cosmos parcels out the stuff of the World Soul according to the numerical proportions of the musical scale. [15]

The Monochord: The Mathematics of Harmonic Mediation

The musical proportions seem to me to be particularly correct natural proportions.
- Novalis

PYTHAGORAS IS SAID to have discovered the musical intervals. While the story of the musical smithy is probably a Middle Eastern folk tale, [16] there can be no doubt that Pythagoras experimented with the monochord (figure 5), a one-stringed musical instrument with a moveable bridge, used to investigate the principles and problems of tuning theory.

FIGURE 5. THE MONOCHORD. String, sounding box and moveable bridge.

The monochord affords an excellent example of how the primary principles of peras and apeiron underlie the realm of acoustic phenomena. Of course, the fact that numerical proportions underlie musical harmony has become a commonplace since the days of Pythagoras; yet there is something about the perfect beauty of these proportions, and their manifestations in the realm of sound, which will exercise a curious fascination over anyone who chooses to actually investigate them on the monochord.

The problem which the monochord presents is that the string can be divided at any point. The string represents an Indefinite continuum of tonal flux which may be infinitely divided. How, then, is it possible to "create" a musical scale at all? The solution, of course, resides in the limiting power of Number.

A curious phenomenon occurs when a string is plucked. First, the string vibrates as a unit. Then, in two parts, then in three parts, four, and so on. As the string vibrates in smaller parts higher tones are produced, this being the so-called harmonic overtone series. [17] While they are not as loud as the fundamental tone of the entire string vibrating, with practice the overtones can nonetheless be heard.

Through the power of Limit, the most formal manifestation of which is Number, harmonic nodal points naturally and innately exist on the string, dividing its length in halves, thirds, fourths, and so on, as shown in figure 6. Plucking the string at one end, and simultaneously touching one of the nodal points without the bridge, will produce the corresponding overtone vibration. In this fashion, one can play out the overtone series, as far as is practical. However, dampening the string at any other point will just deaden out the string. (See figure 6.)

The overtone series provides, as it were, the architectural foundation of the musical scale, the basic "field" of which is the octave, 1:2, or the doubling of the vibrational frequency, which inversely correlates with a halving of the string. Returning again to the basic question of how one bridges the tonal flux, we know the answer to be Number, but now we can see more clearly that the problem itself is one of mediation or harmonia, through the medium of numerical proportion or logos. The solution, in fact, can be seen as performing a marriage of opposites, linking together the upper and the lower (I :2), in a truly cosmic fashion, which is to say in a manner partaking of both order and beauty.

While the complete ratios of the scale are set out in Appendix IV, "The Ratios and Formation of the Pythagorean Scale," we shall here note the essentials.

In order to arrive at whole number solutions, we will use the octave of 6:12.

1) The first step is one of arithmetic mediation. To find the arithmetic mean we take the two extremes, add them together, and divide by 2. The result is a vibration of 9, which, in relation to 6, is in the ratio of 2: 3. This is the perfect fifth, the most powerful musical relationship.

2) The second form of mediation is harmonic. It is arrived at by multiplying together the two extremes, doubling the sum, and dividing that result by the sum of the two extremes (i.e., 2AB / A+B). The harmonic mean linking together 6 and 12 then is 8. This proportion, 6:8 or 3:4, is the perfect fourth, which is actually the inverse of the perfect fifth.

3) Through only two operations we have arrived at the foundation of the musical scale, the so-called "musical" or "harmonic" proportion, 6:8 :: 9:12, the discovery of which was attributed to Pythagoras. (See figure 7.)

FIGURE 6. THE HARMONIC NODAL POINTS AND OVERTONE SERIES ON THE MONOCHORD. The above figure illustrates the reciprocal relation which exists between string length and vibrational frequency. By stopping the string at the geometrical nodal points the harmonic overtones may be individually emphasized.


This arrangement of the perfect consonances of the octave, fifth and fourth needs to be played out, preferably on the monochord, in order to fully appreciate its significance. While we have not "created" a complete musical scale, we have arrived at the architectural foundation on which it is based. By carefully observing the above arrangement, however, we shall discover enough information to complete the scale.

First of all, it would be well to notice the peculiar form of musical and mathematical "dialectic" which is occurring. That is to say, not only is 6:9 a perfect fifth, but 8: 12 is as well; i.e., 6:9 :: 8: 12. Nor is that all, for while 6:8 is a fourth, so too is 9:12; or, 6:8 :: 9:12. Again, the significance of this harmonic symmetry will be fully realized by playing these relations out. [18] However, not only are the fourth and fifth manifested in these multiple ways, but the ratio of 8:9 defines the whole tone as well.

The tone having been defined, the final creation of the scale is quite simple. The vibration of the tonic C is increased by the ratio 8:9 to arrive at D. D is increased by 8:9 to arrive at E. Now, if E were increased by that ratio, it would overshoot F; hence there we must stop. The ratio between E and F ends up being 243:256, called in Greek the leimma, or "left over," corresponding to our semi-tone. [19] Ascending from G, the same 8:9 ratio is used to fill up the remaining intervals. Likewise, the interval between B and C is the leimma.

While the fourth and fifth mediate between the two extremes via harmonic and arithmetic proportion, the scale is filled up through the continued geometrical proportion of 8:9; hence, the geometric mean between C and E would be D. All these forms of proportion interpenetrate, cooperate and harmonize with one another to produce the musical scale.

In summary, we can see the paramount importance of the musical scale and its formation in Pythagorean thought. First of all, the experiments conducted by the Pythagoreans on the monochord confirmed the importance of numerical peras as the limiting factor in the otherwise indefinite realm of manifestation. It also suggested for the first time that if a mathematical harmony underlies the realm of tone and music, that Number may account for other phenomena in the cosmic order -- for example, planetary motion, which was also thought of being related to the mathematical harmonia of the scale, this being the famous "Music of the Spheres." [20] Moreover, the world is full of beings and phenomena which reflect the harmonic principle of dynamic symmetry present in the musical proportion as well. Through their investigation of musical harmony, the Pythagoreans shifted philosophic inquiry away from the materialistic cosmologies of the earlier Ionic tradition to the consideration of Form, which was now to be seen as constituting the world of First Principles. In addition to shifting emphasis from Matter to Form, the Pythagoreans also discovered the principle of harmonia, the fitting together of the high and the low, the hot and the cold, the moist and the dry. From then on, Health was seen as the perfect harmony of the elements comprising the body, disease as that state in which one of the elements becomes too weak or strong, destroying the proper symmetry of the arrangement. Indeed, it was Alcmaeon of Croton, a young man when Pythagoras was old, who first defined health as "the harmonious mixture of the qualities." [21] This had an inestimable effect on Hippocratic medicine. As is so apparent in their various cultural achievements, the ancient Greeks had a very special affinity with the principles of Form, Symmetry, and Harmony. The Pythagoreans were the inheritors of this affinity, and helped to articulate these principles in new, important ways which have profoundly influenced the arts and sciences of Western civilization.

The Tetraktys: Number as Paradigm

I swear by the discoverer of the Tetraktys
Which is the spring of all our wisdom
The perennial fount and root of Nature.
-- Pythagorean Oath

THE PYTHAGOREANS PERCEIVED another principle of Number, in addition to seeing it as a formative agent active in nature. This is perhaps best exemplified in the figure of the Tetraktys which, as we might say in the present century, stood as a numerical paradigm of whole systems.

As we have observed, the Pythagoreans were accustomed to arranging numbers in geometrical shapes, and there are a variety of descriptions which have come down to us from antiquity of triangular, square, pentagonal, and other figured numbers and their properties. [22] This way of representing numbers may have well resulted in the discovery of geometrical theorems. Moreover, the observation that the relations between different types of "geometrical numbers" follow certain definite patterns surely furthered the Pythagorean contention that mathematical study is an important route leading, to the perception of universal laws.

The most well known example of such a "figured number" is the famous Pythagorean Tetraktys ("Quaternary"), consisting of the first four integers arranged in a triangle of ten points:


For the Pythagoreans the Tetraktys symbolized the perfection of Number and the elements which comprise it. In one sense it would be proper to say that the Tetraktys symbolize, like the musical scale, a differentiated image of Unity; in the case of the Tetraktys, it is an image of unity starting at One, proceeding through four levels of manifestation, and returning to unity, i.e., Ten. In the sphere of geometry, One represents the point Image, Two represents the line Image, Three represents the surface Image, and Four the tetrahedron Image, the first three-dimensional form. Hence, in the realm of space the Tetraktys represent the continuity linking the dimensionless point with the manifestation of the first body; the figure of the Tetraktys itself also represents the vertical hierarchy of relation between Unity and emerging Multiplicity. In the realm of music, it will be seen that the Tetraktys also contains the symphonic ratios which underlie the mathematical harmony of the musical scale: 1:2, the octave; 2:3, the perfect fifth; and 3:4, the perfect fourth. [23]

We might further note that the Tetraktys, being a Triangular number, is composed of consecutive integers, incorporating both the Odd and Even, whereas Square number (Limited) is composed of consecutive odd integers, and Oblong number of consecutive even integers (Indefinite). Since the universe is comprised of peras and apeiron woven together through mathematical harmonia, it is easy to see from these considerations why the Tetraktys, or the Decad, was called Kosmos (world-order), Ouranos (heaven), and Pan (the All). In Pythagorean thought the Tetraktys came to represent an inclusive paradigm of the four-fold pattern which underlies different classes of phenomena, as exemplified by Theon of Smyrna in Appendix 1. Not only does a four-fold pattern underlie each class, but each level is in a certain fashion analogous or proportionately similar with that same level in every other class of phenomena. In many respects Pythagorean philosophy is a philosophy of analogia.

The Pythagoreans, then, were the first to use numerical and geometrical diagrams as models of cosmic wholeness and the celestial order. This use of arithmetic and geometrical paradigms of whole systems has a long and interesting history, extending from antiquity through Medieval times, through the Renaissance, up until the modern era. [24] If geometrical principles actually shape the phenomena of nature, why not use those same geometrical forms to illustrate the harmonies and symmetries which exist between natural phenomena? This is no doubt the reasoning behind this symbolic usage of number and geometry, and its appeal seems firmly rooted in the human imagination. In fact, it might be argued that such paradigms possess greater merit than more arbitrary typologies insofar that, being based on the principles of natural order, "Pythagorean" models have more intrinsically in common with the phenomena they seek to classify than other typologies which are of merely human invention. Whereas other models sometimes fail, Pythagorean cosmological symbolism seems particularly well suited in showing how parts relate to a larger whole, thus illustrating the principle of unity underlying diversity.

The Way of Philosophy and the Three Lives

ACCORDING TO A BEAUTIFUL and well known account, Pythagoras likened the entrance of men into the present life to the progression of a crowd to some public spectacle. There assemble men of all descriptions and views. One hastens to sell his wares for money and gain; another exhibits his bodily strength for renown; but the most liberal assemble to observe the landscape, the beautiful works of art, the specimens of valor, and the customary literary productions. So also in the present life men of manifold pursuits are assembled. Some are influenced by the desire of riches and luxury; others, by the love of power and dominion, or by insane ambition for glory. But the purest and most genuine character is that of the man who devotes himself to the contemplation of the most beautiful things, and he may properly be called a philosopher. [25]

Likewise, the story is told of how 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. Even in the days of Plato the surviving Pythagoreans were noted for their distinctive bios Pythagorikos, or Pythagorean way of life, as Plato puts it in the Republic (600a-b).

The school of Pythagoras in Croton appears to have been a religious society centered around the Muses, the goddesses of learning and culture, and their leader Apollo. [26] Iamblichus' description of the school gives it something of a monastic flavor, and there was indeed a "rule" of life, but while the Pythagoreans gathered together at certain times of the day, most of them did not live together.

Apparently there were different levels within the school. One group, the akousmatikoi or "auditors" (from the verb akouo, to hear), went through a three year probationary period and were limited mainly to hearing lectures. A more advanced group, the mathematikoi or "students," went through a five year period of "silence," [27] and held their property in common whereas the akousmatikoi did not; there is, however, nothing to indicate that the mathematikoi took anything like a vow of poverty. Rather, their property was managed by certain members of the society -- the politikoi -- and they received an adequate subsistence in return for its use. [28]

Pythagoras himself was heavily influenced by Orphism, an esoteric, private religion of ancient Greece, named after the legendary musician Orpheus, "the founder of initiations," which also featured a distinctive way of life. According to Orphism, the soul, a divine spark of Dionysus, is bound to the body (soma) as to a tomb (sema). Mankind is in a state of forgetfulness of its true, spiritual nature. The soul is immortal, but descends into the realm of generation, being bound to the "hard and deeply- grievous circle" of incarnations, [29] until it is released through a series of purifications and rites, regaining its true nature as a divine being.

Pythagoras fully accepted the Orphic belief in transmigration or "reincarnation" -- in fact, he is said to have possessed the power to remember his previous lives, and the ability to remind his associates of theirs as well. Yet while Pythagoreanism remains closely related to the Orphic thought of the period, [30] the clearly distinguishing factor between the two is that for the Pythagoreans liberation from the wheel is obtained not through religious rite, but through philosophy, the contemplation of first principles. Hence, philosophia is a form of purification, a way to immortality. As others have observed, whereas the Eleusinian mysteries offered a single revelation, and Orphism a religious way of life, Pythagoras offered a way of life based on philosophy. Burnett notes that this conception lies at the heart of Plato's Phaedo. itself "dedicated, as it were, to a Pythagorean community at Phlious"; [31] moreover, "This way of regarding philosophy is henceforth characteristic of the best Greek thought." [32]

One may well ask how assimilation to God is possible through philosophy. The answer is to be found in the nature of man:

Pythagoras said that man is a microcosm, which means a compendium of the universe; not because, like other animals, even the least, he is constituted by the four elements, but because he contains all the powers of the cosmos. For the universe contains Gods, the four elements, animals and plants. All of these powers are contained in man. He has reason. which is a divine power; he has the nature of the elements, and the powers of moving, growing, and reproduction. [33]

Man, by comprising a world-order in miniature, contains all of those principles constituting the greater cosmos, of which he is a reflection, including the powers of divinity. The problem is not so much of becoming divine as becoming aware of the divine, universal principles within. It is this end, primarily, toward which the Pythagorean curriculum was focused. Plato alludes to the Pythagorean theory of philosophy in the Republic (500c) when he observes:

a man should come to resemble that with which it delights him to associate... Hence the philosopher through the association with what is divine and orderly (kosmios) becomes divine and orderly (kosmios) insofar as a man may.

Man realizes the divine by knowing the universal and divine principles which constitute the cosmos -- i.e., for the Pythagoreans, Number. To know the cosmos is to seek and know the divine element within, and one must become divine and harmonized since only like can know like. From this perspective it also becomes obvious that philosophy is nothing other, at least in one respect, than the care of the soul.

The Soul, its Nature and Care

ACCORDING TO SEVERAL ancient sources, it was from the Pythagoreans that Plato received his doctrine of the tripartite soul, a doctrine which underlies Pythagoras' parable of the three lives: one group of humanity is covetous, another ambitious, and the other curious. As J.L. Stocks has pointed out, "What the division specifies is the three typical motives of human action, and all three motives will be found in operation at different times in every normal human soul." [34] These motives are the desire for profit, honor, and knowledge.

Plato, apparently in line with the Pythagorean tradition, divides the soul into three parts: one part is reasoning, another part is "spirited," and the last desires the pleasures of nutrition and generation. Unlike certain schools of modern psychology, the Platonic division of the soul is hierarchical: the reasoning part is superior to the other two, and deserves more attention, for it is this dimension of the soul which makes us uniquely human. We might summarize the relation between the levels of the soul and their attendant virtues, or forms of excellence, as shown in figure 9.


Seen in this perspective, it becomes plain that psychic health must result when the three "parts" of the soul are brought into a state of harmony, which is not to say a state of equality. Rather, this state of balance could be seen as a state of attunement, where each part receives what it is due. Psychic disturbance results when each part of the soul tries to go its own separate way; the psyche then becomes a house divided, resulting in dissociation and fragmentation, as opposed to the realization of psychic wholeness.

The grand project behind Plato's Republic is to define the nature of justice. We know that the Pythagoreans identified justice with proportion, especially geometrical proportion, because it is through proportion that "each part receives what it is due." [35] Following the Pythagorean tradition, Plato observes that in the realm of society justice exists when each part of society receives its due, and is able to achieve the function for which it is truly best suited. Justice, as a universal principle, operates in exactly the same fashion in the realm of the soul. There, "justice is produced in the soul, like health in the body, by establishing the elements concerned in their natural relations of control and subordination, whereas injustice is like disease and means that this natural order is inverted." [36] As Plato notes, in a magnificently Pythagorean passage:

... 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, like 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.) [37]

If Pythagorean philosophy, then, constitutes a care of the soul, of what precisely is that care comprised? The answer to this is to be found in the ethical and educational conceptions of the Pythagoreans, as well as in those special pursuits and studies for which they were renowned.

Pythagorean Educational Theory

WE HAVE SEEN that for Pythagoras philosophy represents a "purification," the aim of which is the assimilation to God. The universe is divine because of its order (kosmos), and the harmonies and symmetries which it contains and reflects. These principles make the universe divine for they are the characteristics of divinity, and they also innately subsist within the human soul. The Pythagoreans taught that the soul is a harmony. [38] If we are to become like God, then according to Pythagorean philosophy the soul must become aware of its harmonic origin, structure and content. Since the source of all harmony and order is the divine principle of Number, we can perhaps come to understand the initially enigmatic statement of Heracleides that, according to Pythagoras, true "happiness consists in knowledge of the perfection of the numbers of the soul." [39]

In the realm of epistemology the presence of Number is most evident: progress in rational thought depends on a fundamentally dyadic relationship between knower and known, subject and object. Moreover, as certainly as the principle of polarity underlies the world of phenomenal manifestation, so too does the mind depend on dualistic typologies, such as the Table of Opposites, in order to make intellectual progress. [40] Knowledge itself is the third, harmonic element which conjoins the two poles of subject and object. Knowledge then is unifying, much like the harmonic ratios of the musical scale or the central circle in figure 1. Moreover, as we shall see, to the Pythagoreans the knowledge of divine harmony can be either abstract or experiential or, indeed, both.

Even more immediately evident is the undeniable influence of Number on our psychic state through the medium of music, depending as it does on numerical proportion. Certain musical proportions express a sense of cheerfulness; others, such as the minor third, possess a bittersweet quality that can make us sad. The fact that Number can influence a person's emotional state is indeed mysterious and points toward a dimension of qualitative Number which transcends the merely quantitative.

Related to the question of music and harmony is the principle of resonance: two strings, tuned to the same frequency, will both vibrate if only one is plucked, the unplucked string resonating in sympathy with the first. This, of course, is accomplished through the medium of the vibrating air, but the principle underlying the phenomenon is one of harmonic attunement. If, as the Pythagoreans held, man is a microcosm, and the soul is a harmony, perhaps it is through a form of resonance that we relate so intensely to the archetypal ratios of musical proportion. [41] Moreover, by experientially investigating and employing the principles of harmony in the external world, one comes to understand and activate those same principles within. This idea in fact underlies the Pythagorean approach to mathematical study.

The Pythagoreans divided the study of Number into four branches which may be analyzed in the following fashion:

Arithmetic = Number in itself.
Geometry = Number in space.
Music or Harmonics = Number in time.
Astronomy = Number in space and time.

Plato, of course, was heavily influenced by the Pythagorean study of number and incorporates the above quadrivium into his own educational curriculum set out in the Republic, adding another branch of study, Stereometry, the investigation of Number in three-dimensional space, which probably relates to the regular "Platonic" solids and other polyhedra. For Plato -- who believed that God geometrizes always [42] -- "geometry is the knowledge of the eternally existent," [43] and the emphasis that he placed on the study is well known from the legendary inscription above the Academy door, "Let no one ignorant of geometry enter here. " [44]

Within the Platonic curriculum, the purpose of mathematical studies is to purify the eye of the intellect, for mathematical studies have the propensity "to draw the soul towards truth and to direct upwards the philosophic intelligence which is now wrongly turned earthwards." [45] Number, for Plato, is a transcendent Form to which we must intellectually ascend. For the earlier Pythagoreans, however, the emphasis was clearly on the immanence of Number.

While the Pythagoreans moved the direction of philosophical inquiry from the realm of matter to that of Form and principles, Plato took this movement even further than his predecessors. For Plato mathematical studies are a preparation for the contemplation of divine principles; for the Pythagoreans, mathematical studies are the contemplation of divine principles. As Cornelia de Vogel has lucidly observed, for the Pythagoreans.

The contemplation of divine Law, which was the content of the study of mathematics, was a direct contact with a divine Reality: Divinity immanent in the cosmos.

It was different for Plato. He adopts the Pythagorean notion that number is the principle of order in the cosmos and life, but number as such to him is not yet a theion [divinity]. It points at a purely intelligible Number which is a 'Form' (eidos) -- no immanent principle of order within the objects, but a transcendent Example. This is the basic difference between the Pythagorean doctrine of number and Plato's Theory of Forms. Plato's philosophy is a metaphysic of the transcendent; the Pythagorean philosophy is a metaphysic of the immanent order. [46]

This particular difference between the earlier Pythagoreans and Plato must have manifested itself in the sphere of praxis. For Plato it was, in a sense, best to pursue mathematical contemplation with as little reference to physical objects as possible: truth must be approached through intellect, and through intellect alone. For the Pythagoreans, truth manifests itself through the world of physical phenomena; for example, the Pythagoreans no doubt felt that through experimentation on the monochord one could experience the divine principles of harmony which underlie the structure of the cosmos.

The differing views between Plato and the earlier Pythagoreans can also be seen in the realm of music. Plato refers to different musical modes throughout his writings, and to the negative effects that some forms of music can have on the soul and on society. The Pythagoreans, however, actually used certain forms of music to pacify and harmonize the psychic state. In the same way that the music of Orpheus enchanted the wild beasts of the field, so too did the Pythagoreans use music to quell and harmonize the irrational passions.

While the Pythagoreans placed emphasis on the immanence of divine Number and Harmonia, they certainly did not ignore the transcendental dimension. This is made clear by their emphasis on peras and apeiron, the elements of Number, which they obviously took to be universal principles of the first order. It seems that, rather than focusing exclusively on either the immanent or transcendent levels of being, the Pythagoreans were intent on unifying all levels of human experience through the principles of harmony. The divine harmony can be grasped through the mind, yet can also be perceived through the senses. The experiential perception of harmony through the senses can lead to its intellectual apprehension. By means of theoria or contemplation the universal and abstract principles of harmony may be perceived, but through praxis they may be felt in the soul, itself a harmonic entity. Yet there is another level, that of therapeia, where harmonic principles can be used to effect changes in the psychic disposition.

Through the use of proper music, diet, and exercise, the early Pythagoreans sought to nurture and maintain the natural harmony of the psychic and somatic faculties. According to Iamblichus, "They took solitary morning walks to places which happened to be appropriately quiet, to temples or groves, or other suitable places. They thought it inadvisable to converse with anyone until they had gained inner serenity, focusing their reasoning powers. They considered it turbulent to mingle in a crowd as soon as they rose from bed, and that is the reason why these Pythagoreans always selected the most sacred spots to walk." [47] All of these practices can be seen as a form of philosophic "purification" (catharsis) or "practice"(praxis), designed to regulate the body and the emotions. On the intellectual and psychic levels, through their study of mathematics and the natural world, the Pythagoreans approached the principles of harmony experientially through the study of harmonics on the monochord and through geometrical constructions. The Pythagoreans also pursued the study of purely abstract mathematics.

Recalling that the end of all of these pursuits was to follow God, it is interesting to briefly contrast the Pythagorean approach to divinisation with the Christian mysticism of the late Hellenistic period and thereafter. The first stage of "the mystical ascent" consists of the ethical purification of the soul commonly known as praxis. The second stage is contemplation or theoria; in Christianity, however, the contemplation of Nature and universal principles, so characteristic of the Greek philosophic tradition, is replaced predominately by the contemplation of scripture. The final stage, theosis, is the union of the mystic with God. In Hellenistic Christian mysticism of the late antique world, however, the first two stages lose virtually all significance when the final stage is reached. Catharsis and theoria are merely the steps of a ladder; when the summit is reached, the ladder is oftentimes kicked away.

The ancient Pythagorean approach to divinisation would have never sanctioned kicking away the ladder. In early Pythagorean thought there nowhere appears an earnest desire to escape from the world. True, like the Orphics, the Pythagoreans believed in reincarnation, and looked upon the body as limiting the soul. But even so, there is no firm evidence that, like the Orphics, the Pythagoreans sought exemption from the Wheel of Generation. Rather than transcend the world, Pythagorean religiosity held as its goal to exist within the cosmos in a state of emotional repose and intellectual acuteness. Man, while possessing a soul which clearly transcends the limitations of the body, the realm of time and space, is nonetheless a reflection of the entire universe, a microcosm, and is linked together with nature, other living beings, and the Gods through harmony, justice, and proportion. The Pythagorean goal is not to leave the divinely beautiful cosmos behind for a realm of transcendent harmony, but rather to become aware of, and enhance the function of, transcendent harmony in the natural, psychological and social orders. [48]

Pythagorean Political and Ethical Theory

THE CENTRAL INSIGHTS of the Pythagoreans concerning the significance of harmonia were applied to political theory as well: in the same way that harmonic proportion underlies the health of the balanced soul, so too does the principle of justice underlie the living structure of a healthy state. In this regard Plato's Republic, which is a study of justice in both the psychic and social realms, appears to be firmly based on earlier Pythagorean conceptions. Plato, via analogia, identifies the three parts of the soul with three different parts of society, and shows how both the soul and society attain their peak of excellence when "each part receives its due" and when each of the three parts fulfils the particular function for which it is best adapted. It is not possible to say whether Plato's tripartite division of society corresponds precisely with an earlier Pythagorean division, although it is known that the Pythagoreans identified justice with proportion, of which they viewed geometrical proportion as being the most perfect. Like Plato the early Pythagoreans were aristocrats, in the authentic sense of the word, believing that the best government will be composed of those best qualified to govern, as opposed to other political systems in which leadership is based on wealth, on power, or on the choice of the populace. Finally, it should be noted that the Pythagoreans were the first philosophical school to concern themselves with such social and political questions, which fell outside the natural philosophy of the earlier Ionian tradition.

As for Pythagorean ethics, little needs to be said, as the entire idea of "proper action" is tied up with the ideas of philosophy as a way of life, and the nature of the soul and the cosmos. As one discovers the structure and nature of the soul, and experiences and begins to understand the principles of harmony, it seems inevitable that such insight will leave a mark on one's personal conduct and dealings with others. Nonetheless, as the writings in this volume demonstrate, the Pythagoreans did not hesitate to make use of aphorisms and other explicit ethical teachings. At all events, however, it will be seen that these teachings reflect and spring from the more universal insights of Pythagorean thought. In short, because each part is linked to the whole through harmonia, every action has its repercussions, either beneficial or not, for which the individual is supremely responsible.
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Re: The Pythagorean Sourcebook and Library

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The Pythagorean Tradition and its Development

TO SURVEY THE INFLUENCE of Pythagorean thought would expand this introductory essay beyond reasonable boundaries, insofar as the basic conceptions of the Pythagoreans have influenced a long line of thinkers from antiquity reaching up until the present day. Nonetheless, something should be said about the thought of the early Pythagoreans and the Neopythagoreans of the first centuries B.C.E. and C.E., thus helping to place some of the writings here assembled into their proper context.
As the biographical accounts in this volume show, the downfall of the original Pythagorean school had much to do with anti-aristocratic sentiments amongst the populace of south Italy. A revolt was led against the Pythagoreans by Cylon in 500 B.C.E. -- some say because he was rejected admission into the school -- and a period of unrest followed. During the revolt led by Cylon, or during another revolt which followed, various meeting houses were attacked and a good number of Pythagoreans may have perished in the flames. This final attack seems to have been rather successful, and those Pythagoreans that remained alive seem to have migrated to mainland Greece with the exception of Archytas at Tarentum.

Unfortunately, the details concerning the attack on the school are sketchy and little more can be said than the above. The Pythagoreans did, however, carry on in mainland Greece where centers were established at Phlious and Thebes. Echecrates went to Phlious, Xenophilus went to Athens, and the names of Lysis and Philolaus are associated with Thebes, and it was there that Philolaus taught Simmias and Cebes who appear as characters in Plato's Phaedo. Philolaus, who was born around 474 B.C.E., was the first Pythagorean to actually record the teachings of the school in writing; hence his fragments, which are collected in this volume, possess an exceptional value.

Archytas (first half of the fourth century B.C.E.), who was the general of Tarentum and one of the Pythagorean mathematikoi like Philolaus, made contributions to mathematics, geometry, and harmonic theory. He was visited by Plato in 388 B.C.E. and it is possible that Archytas was Plato's model for the so-called "philosopher king."

This brings us to a discussion of Plato himself (428-348 B.C.E.) which is not a topic of minor significance for, as W.K.C. Guthrie has observed, "In general the separation of early Pythagoreanism from the teaching of Plato is one of the historian's most difficult tasks, to which he can scarcely avoid bringing a subjective bias of his own. If later Pythagoreanism was coloured by Platonic influences, it is equally undeniable that Plato himself was deeply affected by earlier Pythagorean belief." [49]

Many important Pythagorean influences have already been noted on the thought of Plato and perhaps it would be fair to view Plato as the most important Pythagorean thinker in the history of the West. There was quite a bit of interest in Pythagorean thought in the early Academy as well, and it has been suggested that the idea of the Academy was in part due to the inspiration of the earlier Pythagorean school. Whatever the case, some points of contact include the tripartite division of the soul; [50] Plato's usage of the One and the Indefinite Dyad; [51] the theory of education in the Republic; [52] the identification of the One and the Good in "the unwritten doctrine" referred to by Aristotle; [53] the Pythagorean character of Plato's lecture "On the Good" reported on by Aristotle;[54] the idea that the soul of the philosopher attains order by contemplating those things which possess order in nature; [55] the idea that "the goodness of anything is due to order and arrangement"; [56] the idea that various beings are linked together through geometrical equality; [57] a doctrine of idea-numbers in the dogmata agrapha reported by Aristotle; [58] and various examples of Pythagorean musical symbolism. [59]

Following Plato in the leadership of the Academy was his nephew Speusippus (407-339 B.C.E.) who was also quite interested in Pythagorean thought: he suggested that there exists a One above being (an important teaching of later Neopythagorean and Neoplatonic thought), and also wrote a work On Pythagorean Numbers about the Tetraktys and numbers comprising the Decad. [60] This treatise was based on the writings of Philolaus and an interesting fragment of it survives.

Aristotle showed an interest in the Pythagorean school and even wrote an essay On the Pythagoreans which does not survive. One of his students, Aristoxenus of Tarentum, was a music theorist and was in touch with the last surviving generation of Pythagoreans at Phlious. Aristoxenus, who might have been one of the Pythagorean mathematikoi, possessed an antiquarian interest in the school and wrote a biography of Pythagoras which is quoted from by Porphyry, Iamblichus and Diogenes Laertius.

After the time of Aristotle we are left with an uncomfortable gap in the history of Pythagorean thought until the Neopythagorean revival commencing in the first century B.CE. Yet it is precisely during this period that most of the Pythagorean ethical and political tractates contained in the second section of this volume were probably composed. But the question remains, by whom were they written? And why?

Unfortunately, no one is certain even about the date or location of their composition. There now exists a tendency to see these writings as being somewhat earlier than previously thought, and Holger Thesleff suggests that the bulk of them were composed around the third century B.C.E. It will be noted that these writings are attributed to original members of the Pythagorean school, which in fact is actually not the case. This does not mean that these writings are "forgeries" in the modern sense of the word, for it was a fairly common practice in antiquity to publish writings as pseudepigrapha, attributing them to earlier, more-renowned individuals. It was probably out of reverence for their master -- and also perhaps because they were discussing authoritative school traditions -- that certain Pythagoreans who published writings attributed them directly to Pythagoras himself. Even Pythagoras is said to have attributed some poems of his to Orpheus. Other examples which might be cited include the many Jewish pseudepigrapha of the time, Orphic fragments, the Hermetic writings, and even a number of Pauline epistles from the New Testament.

A careful study of these writings will show that they are deeply imbued with many Pythagorean ideas - what, in fact, could be more Pythagorean than comparing the structure of the family or society to a well-tuned lyre? -- a particularly beautiful and useful simile which appears more than once in the Pythagorica here collected. Yet, alongside the central Pythagorean core of these writings are found strong Academic and Peripatetic influences as well. Thesleff is probably correct in suggesting that these writings were composed as philosophical textbooks for laymen, [61] but it is unlikely that the exact date or locale of their composition will ever be decisively settled. However, as has been suggested, a careful study of these texts might well provide for some valuable insights into the thought of the early Academy.

The next phase of Pythagorean thought involves the so-called Neopythagorean revival at the beginning of the common era. Due to the Hellenization of the ancient world stemming from the conquests of Alexander the Great, interest in Greek philosophy was no longer limited to one small part of the world. This was especially true of the interest in Pythagorean and Platonic thought, and the names of many Pythagorean philosophers are known from the Hellenistic age. Unfortunately, for some of the most important thinkers the information concerning them is quite fragmentary, which is perhaps one reason why no one has attempted the kind of full scale study that the topic deserves: the study of the Neopythagorean thought of this period is not only significant for its own sake, but also for understanding the thought of Plotinus and the later Neoplatonists who were influenced by a range of Neopythagorean ideas. Actually, as John Dillon has succinctly observed, during this period "Middle Platonism" and "Neopythagoreanism" existed as something of a continuous tradition, with Neopythagoreanism representing "an attitude that might be taken up within Platonism." [62] Keeping this in mind, it might be useful to mention some of the thinkers during this period who were influenced by Pythagorean thought, for it is only through such a listing that one can get a true feeling for the creative ferment of this period.

The first word that we have concerning a renewed interest in Pythagorean thought comes from Cicero, regarding his friend Nigidius Figulus (98-45 B.C.E.), who was attempting to revive Neopythagoreanism in Rome. It appears however that Nigidius was less interested in abstract philosophy than in integrating astrological, ritual and a variety of occultist beliefs.

Eudorus of Alexandria (fl. 30 B.C.E.) appears to have been influenced by Pythagorean thought, and attempted to show that the Pythagoreans held that a Supreme Principle, the One, existed above the Monad and the Dyad. Whether or not the earlier Pythagoreans actually held such a belief is another question altogether, but the notion of a transcendent One surpassing the principles of Limited and Unlimited is important for the history of later philosophy.

Philo of Alexandria (20 B.C.E.-40 C.E.), a Hellenized Jew who interpreted Jewish scripture in light of Greek philosophy, shows a deep interest in Pythagorean thought, especially arithmology, in his voluminous writings. Philo was primarily a Platonist who subscribed to a emanationist cosmology which he tried to reconcile with Jewish thought, but it is interesting to note that he was referred to by Clement of Alexandria, an early church father, simply as "Philo the Pythagorean." [63]

We should not fail to mention Apollonius of Tyana, a colorful figure who flourished during the first half of the first century C.E. Apollonius was perhaps more of a Pythagorean wonderworking ascetic than a philosopher, who travelled through the ancient world as something of a pagan missionary, meeting with priests, performing marvels, and restituting cults of worship to their former purity. His life and exploits are chronicled in an entertaining historical novel by Philostratus. Whether or not this biography gives a well-rounded picture of Apollonius remains uncertain. It does seem, however, that Apollonius saw himself as a reincarnation of Pythagoras and also possessed much information on the life of the sage, which he used in compiling a biography, subsequently used by Porphyry and Iamblichus. In addition to the Life of Philostratus, several letters attributed to Apollonius are extant. [64]

Often overlooked as an important witness to Pythagorean thought is Plutarch of Chaeronea (45-125 C.E.), well known for his famous Lives. What is not so generally well known is that Plutarch was a Platonist with Neopythagorean leanings and was also a priest of Apollo at Delphi. In certain writings of his Moralia he displays a keen interest in the interpretation of myth, the religio-philosophical esoterism of the time, and various bits of Neopythagorean lore, including arithmology. His writings remain a vital resource for understanding the profound, inner dimensions of the contemporary spiritual universe and, like Plotinus, he refers to the Pythagorean interpretation of the name Apollo, which equates Apollo with the One (a = not; pollon = of many). [65]

About the same time as Plutarch we have Moderatus of Gades (fl. second half of the first century) who has been termed an "aggressive Pythagorean" for the severe criticism he applied to Plato, accusing him of using ideas of Pythagoras without giving proper credit where credit was due. In his cosmology Moderatus taught the existence of three unities: the first and highest, the One above being which he identified with the Good; secondly, a unified, active logos, identified with the intelligible realm; and thirdly, the realm of soul. Needless to say, the resemblance between these ideas and those of Plotinus are quite striking.

Theon of Smyrna brings us into the second century (fl. circa 125 C.E.). He was a Platonist and wrote a work Mathematics Useful for Understanding Plato, of which a good English translation exists, and which is equally useful for understanding aspects of Pythagorean thought. [66] In addition to discussing the principles of arithmetic, harmonics and astronomy, Theon also treats the symbolism of the first ten integers and various forms of the Tetraktys (see Appendix I). The work also dealt with the principles of geometry, but this section no longer survives.

Working in a similar vein, and not much later, was Nicomachus of Gerasa (active 140-150 C.E.), whose Introduction to Arithmetic, [67] translated into Latin by Apuleius and Boethius, remained a definitive handbook up until the Renaissance. Also surviving is Nichomachus' Manual of Harmonics, and fragments of his Theology of Arithmetic, a work on Pythagorean arithmology. He also wrote a Life of Pythagoras which was used by the later biographers and an Introduction to Geometry which did not survive. He is known to have been familiar with the practice of gematria, [68] and it has been suggested that Iamblichus' "Pythagorean encyclopedia" found its inspiration in the wide-ranging works of this scholar.

Numenius of Apamea in Syria (fl. 160 C.E.) was also a Platonist with Neopythagorean leanings. Some fragments of his works remain, but the majority have perished. He wrote On the Good; On the Indestructibility of the Soul; On the Secret Doctrines of Plato; a work called Hoopoe, after the bird of the same name; On Numbers (perhaps a work on arithmology); On Place; and On the Divergence of the Academics from Plato. He had an associate, Cronius, who flourished about the same date and wrote a work On Reincarnation.

With Numenius, the mixture of Middle Platonic and Neopythagorean thought begins to transform itself into Neoplatonism, of which philosophy the most brilliant and beautiful expositor was Plotinus. Plotinus seems to have been influenced to a certain extent by the thought of Numenius, and John Dillon sees Plotinus' direct teacher Ammonius Saccas (fl. circa 230 C.E.) as a being a Platonist of a strongly Neopythagorean cast.

The main feature which differentiates Neoplatonism from Middle Platonism is the Neoplatonic doctrine of the transcendent absolute, the One, which exists above the realm of Being. However, as we have seen, Plato's nephew Speusippus, Eudorus of Alexandria, and Maderatus of Gades all posited the existence of such a transcendent principle; even Plato himself, in the Republic, suggests that the Good. which he identified with the One, exists above being. [69] As is typical, the "clear cut" distinctions between various schools and periods are not always so sharp as one has been led to believe. This is especially true of the distinctions between Middle Platonism and Neopythagoreanism in the period outlined above.

In addition to the doctrine of the One above being, Plotinus (204-269 CE.) also held that the intelligible realm, which he identified with nous or Mind, exists as a unity-diversity, as a differentiated "image" of the One. Hence, this world of Forms, which contains all the laws and principles of the universe, can be seen as the living union of the Monad and the Indefinite Dyad, with the Monad acting as the limiting and form-giving principle in the realm of nous, while the Indefinite Dyad acts as the "intelligible matter" upon which the Monad acts. The Indefinite Dyad also provides for the element of Infinity which allows for the existence of an unlimited number of forms and souls in the realm of Mind.

Henceforward, Pythagorean ideas played an important role in subsequent Neoplatonic thought. Porphyry (233-305 C.E.), Plotinus' successor, wrote a biography of Pythagoras which was part of his History of Philosophy in Ten Books. Iamblichus (d. circa 330), who was a student of Porphyry and thought of himself as something of a full-fledged Pythagorean, undertook the task of writing a multivolume "Pythagorean encyclopedia" which included The life of Pythagoras here reproduced and a number of other works: The Exhortation to Philosophy, On the Common Mathematical Science, Commentary on Nichomachus' Introduction to Arithmetic, three books On the Natural, Ethical and Divine Conceptions which are Perceived in the Science of Numbers (of which the anonymous Theology of Arithmetic is based on the third book); and three lost works on Pythagorean harmonies, geometry and astronomy, bringing the total number of volumes up to 10, the Pythagorean Perfect Number.

The Neopythagorean component of Neoplatonism did not end with Iamblichus but rather continued through to the closing of the school in Athens, only to resurface in Renaissance Florence with the thinkers associated with the Cosimo de' Medici's Platonic Academy, of which Marsilio Ficino was the head.

This is not to imply that only pagan thinkers were followers of Pythagorean thought. On the contrary, many of the early church fathers held Pythagoras and his teachings in high esteem. Not only that, it became quite fashionable, after the manner of Philo, to enlist the help of Pythagorean number symbolism in the interpretation of scripture. Justin Martyr (100-164 C.E.) was rejected by a Pythagorean teacher on account of his inadequate mathematical knowledge (recalling the words engraved above the Academy door); he turned to Platonism, and then to Christianity, but never gave up his admiration for the Greek sages. Clement of Alexandria (fl. circa 200 CE.) was also an admirer of Hellenistic thought and even applied the ratios of the Harmonic Proportion to the exegesis of the holy writ. [70] Augustine (354-430), heavily influenced by Neoplatonism, also loved to indulge in numerical exegesis, and he was instrumental in helping to transmit an interest in number symbolism to the Middle Ages.

Also important in the transmission of the Pythagorean ideas to the following age were the pagan encyclopediasts of the late antique world. Macrobius (first part of the fifth century) discussed Pythagorean thought in his Commentary on the Dream of Scipio, and Martianus Capella (fl. 410-429) in his allegorical work on the seven liberal arts, The Marriage of Philology and Mercury, discussed arithmology in Book VII. Another important source for the medievals was Boethius (480-525), especially his works On Arithmetic and On Music.

Having arrived at the close of the ancient world we have also arrived at the end of our survey. Pythagorean ideas continued to be transmitted in the work of Christian thinkers and applied in the realm of sacred architecture by groups of medieval masons. Insofar as Pythagorean thought had been Christianized, it had been changed, yet nonetheless many important conceptions -- such as the ideas of celestial harmony and the significance of Number as a cosmic paradigm -- remained unaltered. There was a brief and beautiful Renaissance of Pythagorean thought at the cathedral school of Chartres in France during the 12th century, due in part to a Latin translation of Plato's Timaeus, and of course there was a renewed interest in Pythagorean thought with the rediscovery of classical writings during the rebirth of learning in Renaissance Italy.

A Philosophy of Whole Systems

IT SHOULD COME AS NO SURPRISE that the figure of Pythagoras appealed strongly to those scholars of Renaissance Italy, as he has invariably appealed to the more universal thinkers of every age. The appeal lies in his important and influential conceptions, which in many ways seem to directly reveal important principles existing at the sacred "root of Nature's fount," but also in the man's character, for Pythagoras himself seems to well represent the possibility of an integrated approach to the study of Nature as a philosophical way of life.

As we have seen, the central focus of Pythagorean thought is in many respects placed on the principle of harmonia. The Universe is One, but the phenomenal realm is a differentiated image of this unity -- the world is a unity in multiplicity. What maintains the unity of the whole, even though it consists of many parts, is the hierarchical principle of harmony, the logos of relation, which enables every part to have its place in the fabric of the all.

Because of Pythagoras' approach, integrating mathematics, psychology, ethics, and political philosophy into one comprehensive whole, it would be quite inappropriate to end this essay without devoting a few words to the contemporary significance of the Pythagorean approach. Pythagoras would have never wished that his insights remain the focus of a merely antiquarian interest, and so we shall honor his intentions by inquiring into what value Pythagorean thought might possess in the contemporary world, addressing these matters in quite general terms.

Pythagoras, no doubt, would have disapproved of the radical split which occurred between the sciences and philosophy during the 17th century "enlightenment" and which haunts the intellectual and social fabric of Western civilization to this day. In retrospect perhaps we can see that man is most happily at home in the universe as long as he can relate his experiences to both the universal and the particular, the eternal and the temporal levels of being.

Natural science takes an Aristotelian approach to the universe, delighting in the multiplicity of the phenomenal web. It is concerned with the individual parts as opposed to the whole, and its method is one of particularizing the universal. Natural science attempts to quantify the universal, through the reduction of living form and qualitative relations to mathematical and statistical formulations based on the classification of material artifacts.

By contrast, natural philosophy is primarily Platonic in that it is concerned with the whole as opposed to the part. Realizing that all things are essentially related to certain eternal forms and principles, the approach of the natural philosopher strives to understand the relation that the particular has with the universal. Through the language of natural philosophy, and through the Pythagorean approach to whole systems, it is possible to relate the temporal with the eternal and to know the organic relation between multiplicity and unity.

If the scientific spirit is seen as a desire to study the universe in its totality, it will be seen that both approaches are complementary and necessary in scientific inquiry, for an inclusive cosmology must be equally at home in dealing with the part or the whole. The great scientists of Western civilization -- Kepler, Copernicus, Newton, Einstein, and those before and after -- were able to combine both approaches in a valuable and fruitful way.

It is interesting that the split between science and philosophy coincides roughly with the industrial revolution -- for once freed from the philosophical element, which anchors scientific inquiry to the whole of life and human values, science ceases to be science in a traditional sense, and is transformed into a servile nursemaid of technology, the development and employment of mechanization. Now machines are quite useful as long as they are subservient to human good, in all the ramifications of that word -- but as it turned out, the industrial revolution also coincided with a mechanistic conceptualization of the natural order, which sought to increase material profit at the expense of the human spirit. This era, which gave rise to the nightmare of the modern factory -- William Blake's "dark satanic mills" -- gained its strength through the naive premise that the human spirit might be elevated and perfected through the agency of the machine.

Today, in many circles, to a large part fueled by the desire for economic reward, science has nearly become confused with and subservient to technology, and from this perspective it might be said that the ideal of a universal or inclusive science has been lost. This is because the ideal scientist is also a natural philosopher who is interested in relating his discoveries to a larger universal framework, whereas the dull-minded technologist, if he has any interest in universal principles at all, limits that interest to their specific mechanistic applications rather than their intrinsic worth of study. Yet, those who study universal principles as principles-in-themselves, often find that these principles have many applications in a wide variety of fields.

While Pythagoras would have taken a dim view of this artificial and dangerous split between science and philosophy, the negative consequences of this rupture have not gone unnoticed. Yet with his emphasis on the unity of all life, Pythagoras would have been in an excellent position to foresee the negative consequences: ecological imbalance, materialism, the varied effects of personal greed, the disintegration of human values, the decline of the arts, a lack of interest in personal excellence and achievement. In a sense these problems, not necessarily unique to this age, result from a lack of balance and an ability to see the parts in relation to the whole. As the poet Francis Thompson said, "You cannot move a flower without troubling a star," and so it is with every individual and collective action. Pythagoras correctly observed that all things are linked together proportionately, by justice, harmony -- call it what you will. By cultivating an awareness of harmonic forming principles and working within the bounds set by necessity, mankind possesses the potential to become a sacred steward of the earth and co-creator with Nature; but the inevitable corollary is that humanity also has every power to create and inhabit a hell of its own making. The simple fact remains that the scales of justice are inexorable -- it is a principle of Nature, and not merely of human morals, that each should receive his due. If we poison our rivers, we poison ourselves; if we act in stupidity, it is only appropriate that we suffer the consequences. If there is a moral to the story it is simply that individuals and societies are far less likely to run into trouble should they possess an awareness of these principles and relationships. And if one would like to cultivate the innate human ability to see things as they are, in whole-part relations, there is scarcely a better guide than the Pythagorean sciences. There has been much talk among the avant garde of "whole systems," the "philosophy of holism," etc., but few have realized that it is actually Pythagoras who is the tutelary genius and founder of the philosophy of whole systems.

We have mentioned the split between science and philosophy because it is an easy and self-evident example. Yet Pythagoras would also have something to say about the structure of our educational system as well. It has become fashionable to create ever more specialized disciplines -- a Ph.D. thesis is considered proportionately better the fewer the number of people that can understand it. This is not to imply that specialized knowledge lacks value, but rather to say that a danger exists in the self- inflicted alienation of academia and the sciences. Great things cannot fail to happen when minds get together and one mind fertilizes another -- when disciplines inspire one another. Pythagoras would say that, from the standpoint of natural philosophy, a superfluous multiplicity of facts and compartmentalized data is useless in a higher sense unless one can determine their relation to the whole, or the universal patterns which underlie all creation.

Interestingly, it is the modern-day physicists who have come most closely to approximating Pythagorean conceptions. Hell-bent on proving the mechanistic notions of 18th-century materialism, physicists have discovered that the deeper they push into matter the more it looks like the cosmos of the Pythagoreans and Platonists. Each atom is a Pythagorean universe, the sight of eternity in a grain of sand, consisting of an arithmetic number of particles, geometrically distributed in space, dancing and vibrating like a miniature solar system to the music of the spheres. A modern physicist would have little difficulty comprehending the teaching of the Orphic theologians that "the essence of the Gods" -- that is to say the formative principles -- "is defined by Number." [71]

Matter and energy are but different aspects of one, underlying continuum. Advancing to the subatomic level, quantity becomes quality, energy becomes information. Many physicists, proceeding from particulars to universals, are now on the verge of recognizing the essential truth of the statement, common to all spiritual traditions, that "Through consciousness the universe is but one single thing; all is interdependent with all." [72] The science of physics, proceeding from matter to energy, from energy to intelligence (i.e., pattern, logos), and from intelligence to Nous, has all but discovered the deus absconditus of the alchemists, the God hidden in matter. If the alchemical poeticism be allowed, even matter, if properly tortured, slain and resurrected, contains the innate potentiality of revealing the Hermetic mercury of eternal being. With the atomic accelerator at their disposal, modern physicists indeed have the capability to change lead into gold. They have taught the world that flesh, coal and diamond are made of the same basic stuff (carbon), driving home the reality that soul and Form is the essential component of all things.

One important Pythagorean insight which possesses ramifications for both the sciences and human behavior is the observation that the phenomenal universe is a mixture, a synthesis of Limited and Unlimited elements. Plato, drawing upon this notion in the Timaeus, compares the limited world of the Forms to a father, and the unlimited Receptacle of Space to a mother, the "nurse of becoming" as he puts it. [73] From their conjunction is born an offspring: the visible, phenomenal universe, the world of eternal principles manifesting in time and space.

The significance of this observation lies in the fact that it paints a picture of the phenomenal realm existing as a manifestation of what might be called "ordered chaos" -- we exist in an intermediate realm. Platonism, which posits the existence of an extratemporal and extraspatial world of perfect form, recognizes that the universe in which we live mirrors this perfection in an imperfect way. Hence Plato notes in the Timaeus that the receptacle of becoming, which we inhabit, was initially "filled with powers that were neither alike nor evenly balanced." [74] The receptacle might be compared to a sea, in which various currents provide for an ambient randomness. Stated in the terms of contemporary physics, one might observe that in the intelligible realm light, as principle, travels in a perfectly straight line, while in the realm of manifestation its path -- and the fabric of space itself -- is warped to a degree by gravitational mass.

While the Pythagoreans identified the principle of Limit with the Good, it should also be observed that without the principle of the Unlimited all manifestation would be impossible. [75] Moreover, working in conjunction with its partner, the principle of Unlimitedness is equally responsible for the organic beauty of the phenomenal realm. All trees of the same species more-or-less follow the same laws of growth, but at each juncture of growth there exists an indefinite number of possibilities. It is precisely the unlimited element which makes for the beauty of a forest, which would be much less beautiful if each tree were exactly the same. A musical composition also relies on order and randomness (change); should either element come to predominate it ceases to be beautiful.

Whereas the Platonism before the Renaissance possessed a tendency to focus on the transcendent world of forms, the first Pythagoreans seemed to concentrate more on the incarnate manifestations of universal principles. After all, not only did they study harmonia as a universal principle, seeing it reflected on all levels of the beautiful cosmos, they incorporated the principle into the fabric of their daily lives as well. But already with Aristotle we find a lack of insight into the Pythagorean view -- he cannot understand how the Pythagoreans view Number as possessing "magnitude." [16] This could well represent a misunderstanding of the incarnationalist dimension of Pythagorean thought, and perhaps reveals an overly literalist interpretation on Aristotle's part as well.

The Pythagorean view of the universe as a living, harmonic mixture is not only indispensable as a scientific concept, but it beautifully articulates the position of man in the cosmos as well. If, along with Plato, we view time as a moving image of eternity, [77] then each generation of humanity stands poised between the present moment and the timeless immensity of the eternal. Rather than being a worthless speck meaninglessly situated in the infinite expanse of space, each person, according to the Pythagorean view, is a microcosm, a complete image of the entire cosmos, with one foot located in the realm of eternal principles and the other foot rooted in a particular world of manifestation. Poised as he is between time and eternity, matter and spirit, man possesses an incredible freedom to learn, create and know, limited only by those principles on which creation is based. From this vantage point, humanity is engaged in a never-ceasing dialectic between time and eternity, possessing the ability to incarnate eternal principles in time (and in this sense mirror the creative work of Nature), yet also possessing the ability to elevate the particular to the universal through conscious understanding.

In relation to this theme, one final observation is in order: the creative endeavors of humanity seem to attain their peak of excellence precisely at that point when the intermediate nature of humanity is actively recognized. For with this recognition comes the realization that one must actively integrate the particular and universal aspects of being. Hence, the best science will once again embrace its sister, philosophia: both deal with universal principles and particular phenomena -- and together they will not attempt to build up a system of thought either from "the top down," deduced from purely a priori formulations, nor will they dare to start exclusively from "the bottom up" abstracting observations only from particular phenomena while ignoring universal principles. This approach I believe is fundamentally Pythagorean: the harmonic proportion, according to legend discovered by Pythagoras, exists as a purely universal principle, but it would have never been discovered without empirical experimentation on the monochord. The value of the harmonic proportion lies in both its universal nature as well as the significance and usefulness of its particular applications. Through the creative dialectic between the temporal and the eternal, there necessarily occurs a form of integration between otherwise purely theoretic and pragmatic approaches. Another benefit of this realization -- the realization that all things are composed of constants and variables -- is that, if seriously embraced, it actively encourages honest inquiry, rendering the twin dangers of Fundamentalism and Relativism equally impotent, for universal justice has its own means of dealing with individuals who mistakenly believe that they possess the Absolute Truth, or, conversely, think that "everything is relative."

One final point needs to be made about the Pythagorean approach, and that concerns the topic of value. There are many occasions where it is useful to take a divisive approach to Nature for the purposes of abstract analysis, yet there are also times when it becomes expedient to stress the unity of all being. For Aristotle Number was merely an abstraction as opposed to an innately existing a priori principle, so it is easy to see how he might become confused. by the notion that abstract number possesses "magnitude." Yet, if Number acts as a geometrical forming principle in the sphere of natural phenomena, as some of the studies cited in the bibliography abundantly demonstrate, it seems unwise to deny its immanent efficacy. Likewise, Aristotle was equally bewildered by the Pythagorean symbolism which equated certain archetypal number forms with principles such as "justice." Yet the truth of the matter is that it is precisely through the Pythagorean approach that quantity (number) and quality are discovered to be integrally related. As Ernst Levy has pointed out in an important article, "The Pythagorean Concept of Measure," this is shown to be especially true in the realm of music where each tone is actually a number, yet also a qualitative phenomenon possessing value. [78] It is particularly true in the realms of music and what has been called "sacred geometry" that one can gain insight into the Pythagorean conception of Number as both creative paradigm and qualitative relation. Levy suggests that in order to once again benefit from a unified scientific and philosophical synthesis that "a new mental attitude is required which many among us will be reluctant to assume, because it is contrary to the scientifically determined mind. The definition of that attitude is simple enough. It consists in this, that we must be willing to ascribe equal reality and equal importance to quality and quantity." [79] It is worth observing that the Pythagorean approach, while realizing the necessity of employing antithetical pairs of opposites in a conceptual sense, always arrives at a position which emphasizes the unity of the all.

To conclude that Number, in the most Pythagorean sense of the term, and the cosmos itself possesses a dimension of meaning is, within the context of mechanistic "science" or modern reductionistic "philosophy," perhaps the ultimate heresy; yet, for the traditional scientist and philosopher such a realization is only the starting point. If Pythagoras had but one imperative for the present age -- or any age -- it would be, as F.M. Cornford has suggested, this:

Seek truth and beauty together; you will never find them apart. [80]



References to writings appearing in this volume follow Guthrie's chapter divisions.

1) It will not be my intention in this introductory essay to attempt to pierce through the various mysteries surrounding the figure of Pythagoras or to embark on the overwhelming task of textual criticism. Nor do I desire to write much about the life of Pythagoras, seeing that all of the primary source material is presented in this volume. Rather, I will attempt to briefly sketch out the history of the Pythagorean school and its influence, discussing those doctrines which are generally agreed upon, and to provide some type of context into which the writings of this sourcebook may be placed by the general reader. Indeed, I have tried to keep the general reader in mind throughout the introduction, and have limited more specialized comments to these notes, which also include references for further reading on topics which can only be touched upon here.

2) The source for this is Ion of Chios, quoted by Diogenes Laertius, Life of Pythagoras, chapter 5. For a discussion of Pythagorean Orphica see West, The Orphic Poems, Oxford University Press, 1984, 7- 15.

3) For Plato's views on writing about matters of ultimate concern see his Seventh Letter.

4) Since Pythagoras left no writings, this presents the historian with some difficulties. What, in fact, can safely be attributed to Pythagoras? Moreover, what do we know about his life? At a very early date a body of legends grew up around Pythagoras; many of these beautiful and amusing stories are recorded in the biographies, which constitute the first part of this book. For a long time, due to the nearly miraculous accounts, certain scholars dismissed the biographies as "late" and "unreliable." However, Aristotle in his lost monograph On the Pythagoreans emphasized how Pythagoras was seen at two places at once, how he showed his golden thigh, how he was thought to be the Hyperborean Apollo, and how he was addressed by a certain river. Obviously these stories are not "late Neopythagorean inventions" but go back to the time of Plato or before. Another source of these accounts was The Tripod of Andron of Ephesus, who was roughly contemporary with Aristotle. While the interpretive dimension of Iamblichus' biography is certainly colored by later Neopythagorean and Neoplatonic influence, it is now taken for granted that the biographies contain a great deal of early information about Pythagoras and his school, and much of the information is taken from older authorities whose work has since perished. Some of the ealiest authorities include Timaeus of Tauromenium (circa 352-256 B.C.E.) who wrote a History of Sicily which contained information of the Pythagoreans and the speeches of Pythagoras, and Dicaearchus of Messina (fourth century B.C.E.), a pupil of Aristotle who wrote a comprehensive study of Greek history which also treated the Pythagoreans. Another student of Aristotle, Aristoxenus of Tarentum, wrote several works on the Pythagoreans, used by the later biographers, which drew on early sources and his first-hand contact with members of the Pythagorean school.

5) Porphyry, Life of Pythagoras, chapter 12.

6) Iamblichus, Life of Pythagoras, chapter 5. For all we know, Pythagoras may have been invited to go to Croton. While this, to my knowledge, has not been previously suggested, it seems unlikely that he would have moved his teaching activities to a distant city without having some contact with and knowledge of the inhabitants. If this is correct, it would help explain his rapid acceptance by the populace.

7) See Vogel, Pythagoras and Early Pythagoreanism, for an analysis of these speeches. Iamblichus' source for these is Timaeus of Tauromenium.

8) Theon of Smyrna, Mathematics Useful for Understanding Plato, 12.

9) This concept -- that the One or principle of unity is the source of all numbers -- is easily grasped if one envisions "the One" as a circle in which various polygons are inscribed; the polygons, or numbers contained within the circle, may then be seen as various manifest aspects of the underlying unity. Another analogy is found in Pythagorean harmonics: the monochord, symbolizing unity (1/1), innately contains the entire overtone series (2/1, 3/1, 4/1, 5/1, etc.), which is manifested when the string is plucked.

10) Theon of Smyrna, Mathematics Useful for Understanding Plato, 66.

11) Ibid, 66.

12) Cornford, "Science and Mysticism in the Pythagorean Tradition," part 2, 3.

13) Ibid.

14) Aristotle, Physics 203 a 10.

15) Plato, Timaeus 35b f.

16) See Levin, The Harmonics of Nichomachus and the Pythagorean Tradition, chapter 6.

17) Different musical instruments emphasize different overtones. For example, the clarinet emphasizes the odd numbered overtones, thus accounting for its peculiar timbre.

18) This relation has been defined by Flora R. Levin in her Harmonics of Nicomachus and the Pythagorean Tradition, 1, as the "metaphysical octave," the characteristic feature of which is "a perfect fusion of parts (3:4 and 2:3) into a whole (2: 1)." Richard L. Crocker in his article "Pythagorean Mathematics and Music," 330, observes: "This construction, dividing as it does the first consonance by the second and third in a curious, interlocking way, has every right to be called the harmony. Here the inner affinity of whole-number arithmetic and music finds its most congenial expression."

19) The leimma is the excess of the fourth over the double tone: 4/3 : 9/8 x 9/8 = 4/3 x 64/81 = 256/243.

20) Needless to say, the "Music of the Spheres" is one of the most influential conceptions of Pythagoras. For a complete discussion which deals with its long and interesting history, as well as the significance of the concept as a poetic fact, see Joscelyn Godwin's The Harmonies of Heaven and Earth.

21) Alcmaeon of Croton in Freeman, Ancilla to the Pre-Socratic Philosophers, 41 (24 DK 4).

22) For more on figured numbers and their properties, see Heath, A History of Greek Mathematics, vol. 1, chapter 3, "Pythagorean Arithmetic." Also see the first volume of Ivor Thomas' Greek Mathematical Fragments.

23) Relating to the musical ratios of the Tetraktys is the Pythagorean saying "What is the Oracle at Delphi?" The answer is: "The Tetraktys, the very thing which is the Harmony of the Sirens" (Iamblichus, Life of Pythagoras, chapter 18). Nicomachus of Gerasa also identifies the harmonic ratio of 6:8: :9: 12 as a version of the Tetraktys in his Manual of Harmonics, vii, 10.

24) One modern proponent of this approach was Buckrninster Fuller. Some important sources for the study of this approach and geometrical forming principles include Keith Critchlow's Order in Space and Islamic Patterns, Ghyka's The Geometry of Art and Life, and The Geometrical Basis of Natural Structure by Robert Williams.

25) Iamblichus, The Life of Pythagoras, chapter 12.

26) Pythagoras was thought to be associated in some way with the God Apollo. This is only natural since Apollo is related to the celestial principles of harmonic order and logos, these being also the principles with which Pythagoras was most concerned. This connection is even made plain by the name of the philosopher -- for Pythios is the name of Apollo at Delphi, his most sacred shrine from which his oracles were delivered. This obvious etymological connection led Diogenes Laertius to interpret the name as meaning that he spoke (agoreuein) the truth no less than Apollo (Pythios) at Delphi.

27) This period of silence may have only been a ritual matter required during the religious ceremonies of the society, not during everyday life. "The ceremonies are conducted by Pythagoras behind a veil or curtain. Those who have passed this five-year test may pass behind the curtain and see him face to face during the ceremonies; the others must merely listen." Minar, "Pythagorean Communism," 39.

28) This is Minar's analysis in "Pythagorean Communism."

29) From an Orphic gold funerary plate, translated in Freeman, Ancilla to the Pre-Socratic Philosophers, 5. (l DK 18)

30) A fragment quoted by Iamblichus maintains that the nature of the Gods is related to Number (Iamblichus, Life of Pythagoras, chapter 28), and there was even an Orphic "Hymn to Number," portions of which are found in Kern, Orphicorum Fragmenta, Berlin, Weidemann, 1922.

Cameron, in his important study of Pythagorean thought observes that harmonia in Pythagorean thought inevitably possesses a religious dimension. He goes on to note that both harmonia -- there is no "h" in the Greek spelling -- and arithmos appear to be descended from the single root ar. This seems to "indicate that somewhere in the unrecorded past, the Number religion, which dealt in concepts of harmony or attunement, made itself felt in Greek lands. And it is probable that the religious element belonged to the arithmos-harmonia combination in prehistoric times, for we find that ritus in Latin comes from the same Indo-European root." (Alister Cameron, The Pythagorean Background of Recollection, 26.)

31) Burnet, Early Greek Philosophy, 83.

32) Ibid.

33) The Life of Pythagoras preserved by Photius, chapter 15.

34) Stocks, "Plato and the Tripartite Soul," 210-11.

35) For a good discussion of the Pythagorean view of justice as proportion see John Robinson, An Introduction to Early Greek Philosophy, 81-83.

36) Plato, Republic 444d (Comford translation, 143).

37) Plato, Republic 443d f. (Cornford translation, 141-2).

38) For sources and a discussion of the soul as a harmonia see Guthrie, A History of Early Greek Philosophy, vol. 1, 307 f.

39) Quoted by Clement of Alexandria, Stromateis ii, 84.

40) Certain scholars, appealing primarily to the "Table of Opposites," have argued that the orientation of Pythagoreanism was essentially dualistic. Such a simplistic view overlooks the fact that every philosophical system employs dualistic typologies and that "as a religious philosophy, Pythagoreanism unquestionably attached central importance to the idea of unity, in particular the unity of all life, divine, human, and animal, implied in the scheme of transmigration." (F.M. Cornford, Plato and Parmenides, 4.)

41) After writing this section I came across the observation of Vilctor Goldschmidt: "Our capacity to apprehend the outside world may be explained thus, that there are processes in our mind (microcosm) which are analogous to those in nature. These psychological processes we call natural laws. " (Quoted by Ernst Levy, "The Pythagorean Concept of Measure," 53.)

42) Heath, A History of Greek Mathematics, vol. 1, 10.

43) Plato, Republic 527b (Cornford translation, p. 244).

44) Tzetzes, Chiliad, viii. 972.

45) Plato, Republic 527b (Cornford translation, p. 244).

46) Vogel, Pythagoras and Early Pythagoreanism, 197.

47) Iamblichus, Life of Pythagoras, chapter 21.

48) Within this context it might be noted that Pythagorean metaphysics has, from ancient Greece to the present day, had an influence on the arts. The lesser can lead to the greater, and natural beauty, which is relative, can lead to the apprehension of transcendent Beauty which is absolute. This is, of course, a Platonic sentiment, but it is foreshadowed in the structure of Pythagorean thought. Perhaps, however, it would be more accurate in Pythagorean thought, with its immanent metaphysics, to suggest that the universal is realized through the particular. The use of mathematical and geometrical harmonies in sacred architecture, for example, can lead to the perception of, and resonance with, universal harmony. For example, through the medium of "Pythagorean geometry," a sacred edifice has the potential to become a celestial mediator: through the harmonic nature of its structure, the heavenly principles of harmonic form are reflected on earth; yet through the effect that this harmony has on those that are receptive to its beauty, the particular may be exalted to perceive the universal. This two- fold principle is applicable not only in architecture, however, but indeed in all the arts.

49) Guthrie, A History of Early Greek Philosophy, vol. 1, 170.

50) Plato, Republic 434d -44lc; also see J.L. Stocks, "Plato's Tripartite Soul."

51) Aristotle, Metaphysics i 6, 987 a 29 f.

52) Plato, Republic, particularly 398c -403c and 52lc -531c.

53) This was stated in Plato's lecture "On the Good." See the note below.

54) Aristotle enjoyed telling a story about Plato's lecture "On the Good": "Everyone went there with the idea that he would be put in the way of getting one or other of the things in human life which are usually accounted good, such as Riches, Health, Strength, or, generally, any extraordinary gift of fortune. But when they found that Plato discoursed about mathematics, arithmetic, geometry, and astronomy, and finally declared the One to be the Good, no wonder they were altogether taken by surprise; insomuch that in the end some of the audience were inclined to scoff at the whole thing, while others objected to it altogether." (Aristoxenus, Harmonica ii ad init., quoted by Heath, A History of Greek Mathematics, vol. 1, 24.)

55) Republic 500c.

56) Gorgias 506e.

57) Gorgias 508a.

58) Aristotle, Metaphysics xiii 7; see also the discussion in Dillon and Vogel (below).

59) For Pythagorean musical symbolism in Plato see Ernest McClain, The Pythagorean Plato. For more on similarities and differences between Plato and the Pythagoreans, and the characteristics of post-Platonic Pythagoreanism, see the valuable discussion in chapter 8 of Vogel's Pythagoras and Early Pythagoreanism. For a brief discussion of the dogmata agrapha and the early Academy see Dillon, The Middle Platonists, chapter 1.

60) A translation of the fragment appears in volume I of Ivor Thomas' Greek Mathematical Fragments. Dillon gives a succinct overview of the thought of Speusippus in chapter 1 of The Middle Platonists; Taran's Speusippus of Athens is a comprehensive study of the remaining Greek fragments and the thought of Speusippus.

61) Holger Thesleff, An Introduction to the Pythagorean Writings of the Hellenistic Period, 72.

62) Dillon in A.H. Armstrong, ed., Classical Mediterranean Spirituality, NY. Crossroad, 1987. 226.

63) Clement of Alexandria, Stromateis, i, 15.

64) Philostratus' Life of Apollonius of Tyana, which includes the letters, appears in the Loeb Classical Library.

65) For the equation of Apollo with the One see Plutarch, Moralia 270f, 393c and 436b. For his Pythagorizing tendencies see "On the Mysteries of Isis and Osiris" and his Delphic essays, collected in volume 5 of Plutarch's Moralia, Harvard. 1936.

66) Theon of Smyrna, Mathematics Useful for Understanding Plato, translated by Robert and Deborah Lawlor, San Diego, Wizards Bookshelf, 1979.

67) Nicomachus of Gerasa, Introduction to Arithmetic, translated by M.L. D'Ooge. New York, MacMillan, 1926.

68) Dillon, The Middle Platonists, 359. Each letter of the Greek alphabet possesses a numerical value and hence each word may also be represented as a number. The science of gematria involves the conscious use of this numerical symbolism and is not to be confused with either arithmology or numerology. A well known example is found in the name of the Gnostic divinity Abraxas, the numerical value of which is 365, the number of days in a solar year. The Babylonian divinities were represented by whole numbers and a Babylonian clay tablet indicates that Sargon II (fl. 720 B.C.E.) ordered that the wall of Khorsabad be constructed to have a length of 16,283 cubits, the numerical value of his name. The present writer has researched the history of gematria in some depth and has discovered an extremely strong body of evidence that gematria was utilized in Greece prior to the Hellenistic period.

69) Plato, Republic 509b.

70) In book ix, chapter II of the Stromateis, which deals with "The Mystical Meanings in the Proportions of Number, Geometrical Ratios, and Music." Clement also refers to the sage from Samos as "Pythagoras the great." (Stromateis i, 21.)

71) Iamblichus, The Life of Pythagoras, chapter 28.

72) R.A. Schwaller de Lubicz, Nature Word, West Stockbridge, MA, Lindisfarne Press, 1982, 99.

73) Plato, Timaeus 49.

74) Plato, Timaeus 52e.

75) Plato's nephew Speusippus thought that it was inappropriate to apply ethical values to the principles of peras and apeiron.

76) Aristotle, Metaphysics 1080 b 16; 1080 b 31; 1083 b 9; and 1090 a 20.

77) Plato, Timaeus 37d. Plato adds that time is a moving image of eternity "according to number."

78) Ernest Levy, "The Pythagorean Concept of Measure," 53.

79) Ibid.

80) Francis M. Cornford, "The Harmony of the Spheres." 27.
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Re: The Pythagorean Sourcebook and Library

Postby admin » Wed Nov 13, 2013 3:08 am







IAMBLICHUS (c. 250-c. 325 C.E.) was an important Neoplatonic philosopher and a student of Porphyry, whose Life of Pythagoras also appears in this volume. Iamblichus was very interested in the philosophical dimension of then current religious practices which he interpreted in light of Neoplatonism. He was also quite an original thinker and highly influenced later Neoplatonism with his triadic metaphysics. In addition to being a Platonist, Iamblichus thought of himself as a Pythagorean philosopher.

Iamblichus attempted to write a ten volume 'encyclopedia' of Pythagorean thought, the first volume of which is his Life of Pythagoras. The second volume of this work was entitled Concerning Pythagorean Explanations, Including an Exhortation to Philosophy, often called simply the Exhortation to Philosophy. The Exhortation, in addition to outlining the benefits of the philosophic life, contains a detailed commentary on the 39 Pythagorean Symbols. Other volumes in Iamblichus' Pythagorean corpus of works include On the Common Mathematical Science, On the Introduction to the Arithmetic of Nichomachus, and The Theology of Numbers.

Iamblichus saw Pythagoras as the Father of Philosophy who revealed to his disciples the principles of the philosophic life as well as all those studies which lead to the purification of the intellect. While Iamblichus has a tendency to personally interpret Pythagoras through the eyes of Neoplatonism, many of the sources on which he draws, which are often quoted verbatim, are quite ancient. Actually, Neoplatonism was in many ways heavily influenced by Pythagorean and Neopythagorean thought.

For a complete biography of Iamblichus and a listing of his various writings see the introduction to the Exhortation to Philosophy, Phanes Press, 1988.


1. The Importance of the Subject

SINCE WISE PEOPLE are in the habit of invoking the divinities at the beginning of any philosophic consideration, this is all the more necessary on studying that one which is justly named after the divine Pythagoras. Inasmuch as it emanated from the divinities it could not be apprehended without their inspiration and assistance. Besides, its beauty and majesty so surpasses human capacity, that it cannot be comprehended in one glance. Gradually only can some details of it be mastered when, under divine guidance we approach the subject with a quiet mind. Having therefore invoked the divine guidance, and adapted ourselves and our style to the divine circumstances, we shall acquiesce in all the suggestions that come to us. Therefore we shall not begin with any excuses for the long neglect of this sect, nor by any explanations about its having been concealed by foreign disciplines, or mystic symbols, nor insist that it has been obscured by false and spurious writings, nor make apologies for any special hindrances to its progress. For us it is sufficient that this is the will of the Gods, which all enable us to undertake tasks even more arduous than these. Having thus acknowledged our primary submission to the divinities, our secondary devotion shall be to the prince and father of this philosophy as a leader. We shall, however have to begin by a study of his descent and nationality.

2. Youth, Education, Travels

IT IS REPORTED that Ancaeus, who dwelt in Samos in Cephallenia, was descended from Zeus, the fame of which honorable descent might have been derived from his virtue, or from a certain magnanimity in any case, he surpassed the remainder of the Cephallenians in wisdom and renown. This Ancaeus was, by the Pythian oracle, bidden to form a colony from Arcadia and Thessaly; and besides leading with him some inhabitants of Athens, Epidaurus, and Chalcis, he was to render habitable an island, which, from the virtue of the soil and vegetation was to be called Black-leaved (Melamphyllos), while the city was to be called Samos, after Same, in Cephallenia. The oracle ran thus: "I bid you, Ancaeus, to colonize the maritime island of Same, and to call it Phyllas." That the colony originated from these places is proved first from the divinities, and their sacrifices, which were imported by the inhabitants, second by the relationships of the families, and by their Samian gatherings.

From the family and alliance of this Ancaeus, founder of the colony, were therefore descended Pythagoras' parents Mnesarchus and Pythais. That Pythagoras was the son of Apollo is a legend due to a certain Samian poet, who thus described the popular recognition of his noble birth. Sang he,

Pythais, the fairest of the Samian race
From the embraces of the God Apollo
Bore Pythagoras, the friend of Zeus.

It might be worthwhile to relate the circumstances of this prevalent report. Mnesarchus had gone to Delphi on a business trip, leaving his wife without any signs of pregnancy. He enquired of the oracle about the event of his return voyage to Syria, and he was informed that his trip would be lucrative, and most conformable to his wishes but that his wife was new with child, and would present him with a son who would surpass all others who had ever lived in beauty and wisdom, and that he would be of the greatest benefit to the human race in everything pertaining to human achievements. But when Mnesarchus realized that the God, without waiting for any question about a son, had by an oracle informed him that he would possess an illustrious prerogative, and a truly divine gift, he immediately changed his wife's former name Parthenis to one reminiscent of the Delphic prophet and her son, naming her Pythais, and the infant, who was soon after born at Sidon in Phoenicia, Pythagoras, by this name commemorating that such an offspring had been promised him by the Pythian Apollo. The assertions of Epimenides, Eudoxus and Xenocrates, that Apollo having at that time already had actual connection with Parthenis, causing her pregnancy, had regularized that fact by predicting the birth of Pythagoras, are by no means to be admitted. 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.

After Mnesarchus had returned from Syria to Samos, with great wealth derived from a favorable sea-voyage, he built a temple to Apollo, inscribed to Pythius. He took care that his son should enjoy the best possible education, studying under Creophilus, then under Pherecydes the Syrian, and then under almost all who presided over sacred concerns, to whom he especially recommended his son, that he might be as expert as possible in divinity. Thus by education and good fortune he became the most beautiful and godlike of all those who have been celebrated in the annals of history. After his father's death, though he was still but a youth, his aspect was so venerable, and his habits so temperate that he was honored and even reverenced by elderly men, attracting the attention of all who saw and heard him speak, creating the most profound impression. That is the reason that many plausibly asserted that he was a child of the divinity. Enjoying the privilege of such a renown, of an education so thorough from infancy, and of so impressive a natural appearance he showed that he deserved all these advantages, by the adornment of piety and discipline, by exquisite habits, by firmness of soul, and by a body duly subjected to the mandates of reason. An inimitable quiet and serenity marked all his words and actions, soaring above all laughter, emulation, contention, or any other irregularity or eccentricity; his influence at Samos was that of some beneficent divinity. His great renown, while yet a youth, reached not only men as illustrious for their wisdom as Thales at Miletus, and Bias at Priene, but also extended to the neighboring cities. He was celebrated everywhere as the "long-haired Samian," and by the multitude was given credit for being under divine inspiration.

When he had attained his eighteenth year, there arose the tyranny of Polycrates; and Pythagoras foresaw that under such a government his studies might be impeded, as they engrossed the whole of his attention. So by night he privately departed with one Hermodamas -- who was surnamed Creophilus, and was the grandson of the host, friend and general preceptor of the poet Homer -- going to Pherecydes, to Anaximander the natural philosopher, and to Thales at Miletus. He successively associated with each of these philosophers in a manner such that they all loved him, admired his natural endowments, and admitted him to the best of their doctrines, Thales especially, on gladly admitting him to the intimacies of his confidence, admired the great difference between him and other young men, who were in every accomplishment surpassed by Pythagoras. After increasing the reputation Pythagoras had already acquired, by communicating to him the utmost he was able to impart to him, Thales, laying stress on his advanced age and the infirmities of his body, advised him to go to Egypt, to get in touch with the priests of Memphis and Zeus. Thales confessed that the instruction of these priests was the source of his own reputation for wisdom, while neither his own endowments nor achievements equalled those which were so evident in Pythagoras. Thales insisted that, in view of all this, if Pythagoras should study with those priests, he was certain of becoming the wisest and most divine of men.

3. Journey to Egypt

PYTHAGORAS HAD BENEFITED by the instruction of Thales in many respects, but his greatest lesson had been to learn the value of saving time, which led him to abstain entirely from wine and animal food, avoiding greediness, confining himself to nutriments of easy preparation and digestion. As a result, his sleep was short, his soul pure and vigilant, and the general health of his body was invariable.

Enjoying such advantages, therefore, he sailed to Sidon, both because it was his native country, and because it was on his way to Egypt. In Phoenicia he conversed with the prophets who were the descendents of Moschus the physiologist, [1] and with many others, as well as with the local hierophants. He was also initiated into all the mysteries of Byblos and Tyre, and in the sacred function performed in many parts of Syria. He was led to all this not from any hankering after superstition as might easily be supposed, but rather from a desire and love for contemplation, and from an anxiety to miss nothing of the mysteries of the divinities which deserved to be learned.

After gaining all he could from the Phoenician mysteries, he found that they had originated from the sacred rites of Egypt, forming as it were an Egyptian colony. This led him to hope that in Egypt itself he might find monuments of erudition still more genuine, beautiful, and divine. Therefore following the advice of his teacher Thales, he left, as soon as possible, through the agency of some Egyptian sailors, who very opportunely happened to land on the Phoenician coast under Mount Carmel where, in the temple on the peak Pythagoras for the most part had dwelt in solitude. He was gladly received by the sailors who intended to make a great profit by selling him into slavery. But they changed their mind in his favor during the voyage, when they perceived the chastened venerability of the mode of life he had undertaken. They began to reflect that there was something supernatural in the youth's modesty, and in the manner in which he had unexpectedly appeared to them on their landing, when from the summit of Mount Carmel, which they knew to be more sacred than other mountains, and quite inaccessible to the vulgar, he had leisurely descended without looking back, avoiding all delay from precipices or difficult rocks and that when he came to the boat, he said nothing more than, "Are you bound for Egypt?" What is more, on their answering affirmatively, he had gone aboard, and had, during the whole trip sat silent where he would be least likely to inconvenience them at their tasks.

For two nights and three days Pythagoras had remained in the same unmoved position, without food, drink, or sleep, except that, unnoticed by the sailors, he might have dozed while sitting upright. Moreover the sailors considered that, contrary to their expectations, their voyage had proceeded without interruptions, as if some deity had been on board. From all these circumstances they concluded that a veritable divinity had passed over with them from Syria into Egypt. Addressing Pythagoras and each other with a gentleness and propriety that was uncommon, they completed the remainder of their voyage through a halcyon sea, and at length happily landed on the Egyptian coast. Reverently the sailors here assisted him to disembark; and after they had seen him safe onto a firm beach, they raised before him a temporary altar, heaped on it the now abundant fruits of trees, as if these were the first-fruits of their freight, presented them to him and departed hastily to their destination. Pythagoras, however, whose body had become emaciated through the severity of so long a fast, did not refuse the sailors' help on landing, and as soon as they had left partook as much of the fruits as was requisite to restore his physical vigor. Then he went inland, in entire safety preserving his usual tranquillity and modesty.

4. Studies in Egypt and Babylonia

HERE IN EGYPT he frequented all the temples with the greatest diligence, and most studious research, during which time he won the esteem and admiration of all the priests and prophets with whom he associated. Having most solicitously familiarized himself with every detail, he did not, nevertheless, neglect any contemporary celebrity, whether a sage renowned for wisdom, or a peculiarly performed mystery. He did not fail to visit any place where he thought he might discover something worthwhile. That is how he visited all of the Egyptian priests, acquiring all the wisdom each possessed. He thus passed twenty-two years in the sanctuaries of temples, studying astronomy and geometry, and being initiated in no casual or superficial manner in all the mysteries of the Gods. At length, however, he was taken captive by the soldiers of Cambyses, and carried off to Babylon. Here he was overjoyed to be associated with the Magi, who instructed him in their venerable knowledge, and in the most perfect worship of the Gods. Through their assistance, likewise, he studied and completed arithmetic, music, and all the other sciences. After twelve years, about the fifty-sixth year of his age, he returned to Samos.

5. Travels in Greece; Settlement at Croton

ON HIS RETURN to Samos he was recognized by some of the older inhabitants, who found that he had gained in beauty and wisdom, and had achieved a divine graciousness; wherefore they admired him all the more. He was officially invited to benefit all men by imparting his knowledge publicly. To this he was not averse; but the method of teaching he wished to introduce was the symbolical one, in a manner similar to that in which he had been instructed in Egypt. This mode of teaching, however did not please the Samians, whose attention lacked perseverance. Not one proved genuinely desirous of those mathematical disciplines which he was so anxious to introduce among the Greeks; and soon he was left entirely alone. This however did not embitter him to the point of neglecting or despising Samos. Because it was his home town; he desired to give his fellow-citizens a taste of the sweetness of the mathematical disciplines, in spite of their refusal to learn. To overcome this he devised and executed the following strategem. In the gymnasium he happened to observe the unusually skillful and masterful ball-playing of a youth who was greatly devoted to physical culture, but financially lacking and in difficult circumstances. Pythagoras wondered whether this youth if supplied with the necessities of life, and freed from the anxiety of supplying them, could be induced to study with him. Pythagoras therefore called the youth, as he was leaving the bath, and proposed furnishing him the means to continue his physical training, on the condition that he would study with him easily and gradually, but continuously so as to avoid confusion and distraction, certain disciplines which he claimed to have learned from the Barbarians in his youth, but which were now beginning to desert him in consequence of the inroads of the forgetfulness of old age. Moved by hopes of financial support, the youth took up the proposition without delay. Pythagoras then introduced him to the rudiments of arithmetic and geometry, illustrating them objectively on an abacus, paying him three oboli as fee for the learning of every figure. This was continued for a long time, the youth being incited to the study of geometry by the desire for honor, with diligence, and in the best order. But when the sage observed that the youth had become so captivated by the logic, ingeniousness and style of those demonstrations to which he had been led in an orderly way, that he would no longer neglect their pursuit merely because of the sufferings of poverty, Pythagoras pretended poverty, and consequent inability to continue payment of the three oboli fee. On hearing this, the youth replied, that even without the fee he could go on learning and receiving this instruction. Then Pythagoras said, "But even I myself am lacking the means to procure food!" As he would have to work to earn his living, he ought not to be distracted by the abacus and other trifling occupations. The youth, however, loath to discontinue his studies, replied, "In the future, it is I who will provide for you, and repay your kindness in a way resembling that of the stork; for in my turn, I will give you three oboli for every figure. From this time on he was so captivated by these disciplines, that, of all the Samians, he alone elected to leave home to follow Pythagoras, being a namesake of his, though differing in patronymic, being the son of Eratocles. It is probably to him that should be ascribed three books On Athletics, in which he recommends a diet of flesh, instead of dry figs, which of course would hardly have been written by the Mnesarchian Pythagoras.

About this time Pythagoras went to Delos where he was much admired as he approached the so-called bloodless altar of Father Apollo, and worshipped at it. Then Pythagoras visited all the oracles. He dwelt for some time in Crete and Sparta, to learn their laws; and on acquiring proficiency therein he returned home to complete his former omissions.

On his arrival in Samos, he first established a school, which is even now called, the Semicircle of Pythagoras, in which the Samians now consult about public affairs, feeling the fitness of dispensing justice and promoting profit in the place constructed by him who promoted the welfare of all mankind. Outside of the city he fashioned a cave adapted to the practices of his philosophy, in which he spent the greater part of day and night, ever busied with scientific research, and meditating as did Minos, the son of Zeus. Indeed he surpassed those who later practiced his disciplines chiefly in this, that they advertised themselves for the knowledge of theorems of minute importance, while Pythagoras unfolded a complete science of the celestial orbs, founding it on arithmetical and geometrical demonstrations.

Still more than for all this, he is to be admired for what he accomplished later. His philosophy now gained great importance, and his fame spread to all Greece so that the best students visited Samos on his account, to share in his erudition. But his fellow-citizens insisted on employing him in all their embassies, and compelling him to take part in the administration of public affairs. Pythagoras began to realize the impossibility of complying with the claims of his country while remaining at home to advance his philosophy, and observing that all earlier philosophers had passed their lives in foreign countries, he was determined to resign all political occupations. Besides, according to contemporary testimony, he was disgusted at the Samians' scorn for education.

Therefore, he went to Italy, conceiving that his real fatherland must be the country containing the greatest number of the most scholarly men. Such was the success of his journey that on his arrival at Croton, the noblest city in Italy, that he gathered as many as six-hundred followers, who by his discourses were moved, not only to philosophical study, but to an amicable sharing of their worldly goods, whence they derived the name of Cenobites. [2]

6. The Pythagorean Community

THE CENOBITES were students that philosophized; but the greater part of his followers were called Hearers (akousmatikoi) of whom, according to Nicomachus there were two thousand that had been captivated by a single oration on his arrival in Italy. These, with their wives and children, gathered into one immense auditory, called the Auditorium (Homacoion), which was so great as to resemble a city, thus founding a place universally called Greater Greece (Magna Graecia). This great multitude of people, receiving from Pythagoras laws and mandates as so many divine precepts, without which they declined to engage in any occupation, dwelt together in the greatest general concord, estimated and celebrated by their neighbors as among the number of the blessed, who, as was already observed, shared all their possessions.

Such was their reverence for Pythagoras, that they ranked him with the Gods, as a genial beneficent divinity. While some celebrated him as the Pythian, others called him the Hyperborean Apollo. Others considered him Paeon, [3] others, one of the divinities that inhabit the moon; yet others considered that he was one of the Olympian Gods, who, in order to correct and improve terrestrial existence appeared to their contemporaries in human form, to extend to them the salutary light of philosophy and felicity. Never indeed came, nor, for the matter of that, ever will come to mankind a greater good than that which was imparted to the Greeks through this Pythagoras. Hence, even now, the nickname of "long-haired Samian" is still applied to the most venerable among men.

In his treatise On the Pythagoric Philosophy, Aristotle relates that among the principle arcana of the Pythagoreans was preserved this distinction among rational animals: Gods, men, and beings like Pythagoras. Well indeed may they have done so, inasmuch as he introduced so just and apt a generalization as Gods, heroes and daimons; of the world, of the manifold notions of the spheres and stars, their oppositions, eclipses, inequalities, eccentricites and epicycles; and of all the natures contained in heaven and earth, together with the intermediate ones, whether apparent or occult. Nor was there, in all this variety of information, anything contrary to the phenomena, or to the conceptions of the mind. Besides all this, Pythagoras unfolded to the Greeks all the disciplines, theories and researches that would purify the intellect from the blindness introduced by studies of a different kind, so as to enable it to perceive the true principles and causes of the universe.

In addition, the best polity, popular concord, community of possessions among friends, worship of the Gods, piety to the dead, legislation, erudition, silence, abstinence from eating the flesh of animals, continence, temperance, sagacity, divinity, and in brief, whatever is anxiously desired by the scholarly, was brought to light by Pythagoras.

It was, on account of all this, as we have already observed, that Pythagoras was so much admired.

7. Italian Political Achievements

NOW WE MUST RELATE HOW HE TRAVELLED, what places he first visited, and what discourses he made, on what subjects, and to whom addressed, for this would illustrate his contemporary relations. His first task, on arriving in Italy and Sicily, was to inspire with a love of liberty those cities which he understood had more or less recently oppressed each other with slavery. Then, by means of his auditors, he liberated and restored to independence Croton, Sybaris, Catanes, Rhegium, Himaera, Agrigentum, Tauromenas and some other cities. Through Charondas the Catanaean, and Zaleucus the Locrian, he established laws which caused the cities to flourish, and become models for others in their proximity. Partisanship, discord and sedition, and that for several generations, he entirely rooted out, as history testifies, from all the Italian and Sicilian lands, which at that time were disturbed by inner and outer contentions. Everywhere, in private and in public, he would repeat, as an epitome of his own opinions, and as a persuasive oracle of divinity, that by any whatsoever, strategem, fire, or sword, we should amputate from the body, disease; from the soul, ignorance; from a household, discord; and from all things whatsoever, lack of moderation; through which he brought home to his disciples the quintessence of all teachings, and that with a most paternal affection.

For the sake of accuracy, we may state that the year of his arrival in Italy was that one of the Olympic victory in the stadium of Eryxidas of Chalcis, in the sixty-second Olympiad. He became conspicuous and celebrated as soon as he arrived, just as formerly he achieved instant recognition at Delos, when he performed his adorations at the bloodless altar of Father Apollo.

8. Intuition, Reverence, Temperance and Studiousness

ONE DAY, during a trip from Sybaris to Croton, by the sea-shore, he happened to meet some fishermen engaged in drawing up from the deep their heavily-laden fish-nets. He told them he knew the exact number of fish they had caught. The surprised fishermen declared that if he was right they would do anything he said. He then ordered them, after counting the fish accurately, to return them alive to the sea, and what is more wonderful, while he stood on the shore, not one of them died, though they had remained out of their natural element quite a little while. Pythagoras then paid the fishermen the price of their fish, and departed for Croton. The fishermen divulged the occurrence, and on discovering his name from some children, spread it abroad publicly. Everybody wanted to see the stranger, which was easy enough to do. They were deeply impressed on beholding his countenance, which indeed betrayed his real nature.

A few days later, on entering in the gymnasium, he was surrounded by a crowd of young men, and he embraced this opportunity to address them, exhorting them to attend to their elders, pointing out to them the general preeminence of the early over the late. He instanced that the east was more important than the west, the morning than the evening, the beginning than the end, growth than decay; natives than strangers, city-planners than city-builders; and in general that Gods were more worthy of honor than daimons, daimons than demigods, and heroes than men; and that among these the authors of birth in importance excelled their progeny. All this, however, he said only to prove by induction, that children should honor their parents to whom, he asserted, they were as much indebted for gratitude as would be a dead man to him who should bring him back to life, and light. He continued to observe that it was no more than just to avoid paining, and to love preeminently those who had benefitted us first and most. Prior to the children's birth, these are benefitted by their parents exclusively, being the springs of their offspring's righteous conduct. In any case, it is impossible for children to err by not allowing themselves to be outdistanced in reciprocation of benefits towards their parents. Besides, since from our parents we learn to honor divinity, no doubt the Gods will pardon those who honor their parents no less than those who honor the Gods, (thus making common cause with them). Homer even applied the paternal name to the King of the Gods, calling him the father of Gods and men. Many other mythologists informed us that the chiefs of the Gods even were anxious to claim for themselves that superlative affection which, through marriage, binds children to their parents. That is why they introduced among the Gods the terms father and mother, Zeus begetting Athena, while Hera produced Hephaestus, the nature of which offspring is contrary so as to unite the most remote through friendship.

As this argument about the immortals proved convincing to the Crotonians, Pythagoras continued to enforce voluntary obedience to the parental wishes, by the example of Hercules, who had been the founder of the Crotonian colony. Tradition indeed informs us that that divinity had undertaken labors so great out of obedience to the commands of a senior, and that after his victories therein, he instituted the Olympic games in honor of his father. Their mutual association should never result in hostility to friends, but in transforming their own hostility into friendship. Their benevolent filial disposition should manifest as modesty, while their universal philanthropy should take the form of fraternal consideration and affection.

Temperance was the next topic of his discourses. Since the desires are most flourishing during youth, this is the time when control must be effective. While temperance alone is universal in its application to all ages, boy, virgin, woman, or the aged, yet this special virtue is particularly applicable to youth. Moreover, this virtue alone applies universally to all goods, those of body and soul, preserving both the health, and studiousness. This may be proved conversely. When the Greeks and Barbarians warred over Troy, each of them feel into the most dreadful calamities, both during the war, and the return home, and all this through the incontinence of a single individual. Moreover, the divinity ordained that the punishment of this single injustice should last over a thousand and ten years, by an oracle predicting the capture of Troy, and ordering that annually the Locrians should send virgins into the Temple of Athena in Troy.

Cultivation of learning was the next topic Pythagoras urged upon the young men. He invited them to observe how absurd it would be to rate the reasoning power as the chief of their faculties, and indeed consult about all other things by its means, and yet bestow no time or labor on its exercise. Attention to the body might be compared to fostering unworthy friends, and is liable to rapid failure; while erudition lasts till death, and for some procures post-mortem renown, and may be likened to good, reliable friends. Pythagoras continued to draw illustrations from history and philosophy, demonstrating that erudition enables a naturally excellent disposition to share in the achievements of the leaders of the race. For others share in their discoveries by erudition.

[Erudition possesses four great advantages over all other goods.] First, some advantages, such as strength, beauty, health and fortitude, cannot be exercised except by the cooperation of somebody else. Moreover, wealth, dominion, and many other goods do not remain with him who imparts them to somebody else. Third, some kinds of goods cannot be possessed by some men, but all are susceptible to instruction, according to their individual choice. Moreover, an instructed man will naturally, and without any impudence, be led to take part in the administration of the affairs of his home country, (as does not occur with more wealth). One great advantage of erudition is that it may be imparted to another person without in the least diminishing the store of the giver. For it is education which makes the difference between a man and a wild beast, a Greek and a Barbarian, a free man and a slave, and a philosopher and a boor. In short, erudition has so great an advantage over those who do not possess it, that in one whole city and during one whole Olympiad seven men only were found to be eminent winners in racing, and that in the whole habitable globe those that excelled in wisdom amounted to no more than seven. But in subsequent times it was generally agreed that Pythagoras alone surpassed all others in philosophy; for instead of calling himself a wise man he called himself a philosopher (a lover of wisdom).

9. Community and Chastity

WHAT PYTHAGORAS said to the youths in the gymnasium, these reported to their elders. Hereupon these latter, a thousand strong, called him into the senate-house, praised him for what he had said to their sons, and desired him to unfold to the public administration any thoughts which he might have advantageous to the Crotonians.

His first advice was to build a temple to the Muses, which would preserve the already existing concord. He observed to them that all of these divinities were grouped together by their common names, that they subsisted only in conjunction with each other, that they specially rejoiced in social honors, and that [in spite of all changes] the choir of the Muses subsisted always one and the same. They comprehended symphony, harmony, rhythm, and all things breeding concord. Not only to beautiful theorems does their power extend, but to the general symphonious harmony.

Justice was the next desideratum. Their common country was [not to be victimized selfishly, but] to be received as a common deposit from the multitude of citizens. They should therefore govern it in a manner such that, as a hereditary possession they might transmit it to their posterity. This could best be effected if the members of the administration realized their equality with the citizens, with the only supereminence of justice. From the common recognition that justice is required in every place, came the fables that Themis seated in the same order with Zeus, and that Dike, or justice, is seated by Hades, and that Law is established in all cities, so that whoever is unjust in things required of him by his position in society, may concurrently appear unjust towards the whole world. Moreover, senators should not make use of any of the Gods for the purpose of an oath, inasmuch as their language should make them credible even without any oaths.

As to their domestic affairs, their government should be the object of deliberate choice. They should show genuine affection to their own offspring, remembering that those, from among all creatures, were the only ones who could appreciate this affection. Their associations with their partners in life, their wives, should be such as to be mindful that while other compacts are engraved on tables and pillars, the marital ones are incarnated in children. They should moreover make an effort to win the affection of their children, not merely in a natural, involuntary manner, but through deliberate choice, which alone constitutes beneficence.

He further besought them to avoid connexion with any but their wives; lest, angered by their husbands' neglect and vice, these should not get even by adulterating the race. They should also consider that they received their wives from the Vestal hearth with libations, and brought them home in the presence of the Gods themselves as suppliants would have done. By orderly conduct and temperance they should become models not only for their family, but also for their community.

Again, they should minimize public vice, lest offenders indulge in secret sins to escape the punishment of the laws, but should, rather be impelled to justice from reverence for beauty and propriety. Procrastination also should be ended, inasmuch as opportuneness is the best part of any deed. The separation of parents from their children Pythagoras considered the greatest of evils. While he who is able to discern what is advantageous to himself may be considered the best man, next to him in excellence should be ranked he who can see the utility in what happens to others, while the worst man is he who waits till he himself is afflicted before understanding where true advantage lies. Seekers of honor might well imitate racers, who do not injure their antagonists, but limit themselves to trying to achieve the victory themselves. Administrators of public affairs should not betray offense at being contradicted, but on the other hand benefit those they lead. Seekers of true glory should strive really to become what they wished to seem; for counsel is not as sacred as praise, the former being useful only among men, while the latter mostly refers to the divinities.

In closing, he reminded them that their city happened to have been founded by Hercules, at a time when, having been injured by Lacinius, he drove the oxen through Italy; when, rendering assistance to Croton by night, mistaking him for an enemy he slew him unintentionally. Wherefore Hercules promised that a city should be built over the sepulchre of Croton, from him the city derives its name, thus endowing him with immortality. Therefore, said Pythagoras to the rulers of the city, those should justly render thanks for the benefits they had received.

The Crotonians, on hearing his words built a temple to the Muses, and drove away their concubines, and requested Pythagoras to address the young men in the temple of Pythian Apollo, and the women in the temple of Hera.

10. Advice to Youths

TO BOYS PYTHAGORAS, complying with their parents' request, gave the following advice. They should neither revile anyone nor revenge themselves on those who did. They should devote themselves diligently to learning, which in Greek derives its name from their age. [4] A youth who started out modestly would find it easy to preserve probity for the remainder of his life, which would be a difficult task for one who at that age was not well disposed; nay, for one who begins his course from a bad impulse to run well to the end is almost impossible.

Pythagoras pointed out that boys were most dear to the divinities; and he pointed out that, in times of great drought, cities would send boys as ambassadors to implore rain from the Gods, in the persuasion that divinity is especially attentive to children, although such as are permitted to take part in sacred ceremonies continuously hardly ever arrive at perfect purification. That is also the reason why the most philanthropic of the Gods, Apollo and Love, are, in pictures, universally represented as having the ages of boys. It is similarly recognized that some of the [athletic] games in which the victors are crowned were instituted for the behoof of boys; the Pythian, in consequence of the serpent Python having been slain by a boy, and the Nemean and Isthmian, because of the death of Archemorus and Nelicerta. Moreover, while the city of Croton, was building, Apollo promised to the founder that he would give him a progeny, if he brought a colony into Italy, inferring therefrom that Apollo presided over their development, and that inasmuch as all the divinities protected their age, it was no more than fair that they should render themselves worthy of their friendship.

He added that they should practice hearing, so that they might learn to speak. Further, he said that as soon as they had entered on the path along which they intended to proceed for the remainder of their existence, they should imitate their predecessors, never contradicting those who were their seniors. For later on, when they themselves will have grown, they will justly expect not to be injured by their juniors. Because of these moral teachings, Pythagoras deserved no longer to be called by his own name, but deserved to be called divine.

11. Advice to Women

TO THE WOMEN Pythagoras spoke as follows about sacrifices. To begin with, inasmuch as it was no more than natural that they would wish that some other person who intended to pray for them should be worthy, nay, excellent, because the Gods attend to these particularly, so also it is advisable that they themselves should most highly esteem equity and modesty, so that the divinities may be the more inclined to grant their requests.

Further, they should offer to the divinities such things as they themselves have with their own hands produced, such as cakes, honey-combs, and perfumes, and should bring them to the altars without the assistance of servants. They should not worship divinities with blood and dead bodies, nor offer so many things at one time that it might seem they meant never to sacrifice again.

Concerning their association with men, they, should remember that their female nature had by their parents been granted the license to love their husbands more excessively than even the authors of their existence. Consequently they should take care neither to oppose their husbands, nor consider that they have subjected their husbands should these latter yield to them in any detail.

It was in the same assembly that Pythagoras is said to have made the celebrated suggestion that, after a woman has had congress with her husband, it is holy for her to perform sacred rites on the same day, which would be inadmissible, had the connection been with any man other than her husband.

He also advised the women that their conversation should always be cheerful, and to endeavor that others may speak good things of them. He further admonished them to care for their good reputation, and to try not to blame the fablewriter who, observing the justice of women, accused three women of using a single eye in common, so great is their mutual willingness to accommodate each other with the loan of garments and ornaments, without a witness, when some one of them has special need thereof, returning them without arguments or obligation.

Further, Pythagoras observed that he who is called the wisest of all (i.e., Hermes), [5] who arranged the human voice, and in short, was the inventor of names, whether he was a God or a divinity, or a certain divine man, or in special animals such as the ibis, ape, or dogs, perceiving that the female sex was most given to devotion, gave to each of their ages the name of one divinity. So an unmarried woman was called Kore (maiden), or Persephone, a bride, Nympha; a matron, Mother; and a grandmother, in the Doric dialect, Maia. Consequently, the oracles at Dodona and Delphi are brought to light by a woman.

By this praise of female piety Pythagoras is said to have affected so great a change in popular female attire, that some no longer dared to dress up in costly raiment, consecrating thousands of their garments in the temple of Hera.

This discourse had effect also on marital fidelity, to an extent such that in the Crotonian region connubial faithfulness became proverbial; [thus imitating] Ulysses who, rather than abandon Penelope, considered immortality well lost. Pythagoras encouraged the Crotonian women to also emulate Ulysses, by exhibiting their probity to their husbands.

In short, through these discourses Pythagoras acquired great fame both in Croton, and in the rest of Italy.

12. Why Pythagoras Called Himself a Philosopher

PYTHAGORAS is said to have been the first to call himself a philosopher, a word which heretofore had not been an appellation, but a description. He likened the entrance of men into the present life to the progression of a crowd to some public spectacle. There assemble men of all descriptions and views. One hastens to sell his wares for money and gain; another exhibits his bodily strength for renown; but the most liberal assemble to observe the landscape, the beautiful works of art, the specimens of valor, and the customary literary productions. So also in the present life men of manifold pursuits are assembled. Some are influenced by the desire of riches and luxury; others by the love of power and dominion, or by insane ambition for glory. But the purest and most genuine character is that of the man who devotes himself to the contemplation of the most beautiful things, and he may properly be called a philosopher.

Pythagoras adds that the survey of the whole heaven, and of the stars that revolve therein, is indeed beautiful, when we consider their order, which is derived from participation in the first and intelligible essence. But that first essence is the nature of Number and "reasons" [6] which pervades everything, and according to which all those [celestial] bodies are arranged elegantly, and adorned fittingly. Now veritable wisdom is a science conversant with the first beautiful objects which subsist in invariable sameness, being undecaying and divine, by the participation in which other things also may well be called beautiful. The desire for something like this is philosophy. Similarly beautiful is devotion to erudition, and this notion Pythagoras extended, in order to effect the improvement of the human race.

13. How He Shared Orpheus' Control Over Animals

ACCORDING TO CREDIBLE HISTORIANS, his words possessed an admonitory quality that prevailed even with animals, which confirms that, in intelligent men learning tames even wild or irrational beasts. The Daunian bear, who had severely injured the inhabitants, was by Pythagoras detained. After long stroking it gently, feeding it on maize and acorns, and compelling it by an oath to leave alone living beings, he sent it away. It hid itself in the mountains and forest, and was never since known to injure any irrational animal.

At Tarentum he saw an ox feeding in a pasture, where he ate green beans. He advised the herdsman to tell the ox to abstain from this food. The herdsman laughed at him, remarking he did not know the language of oxen; but that if Pythagoras did, he had better tell him so himself. Pythagoras approached the ox's ear and whispered into it for a long time, whereafter the ox not only refrained from them, but never even tasted them. This ox lived a long while at Tarentum, near the temple of Hera, and was fed on human food by visitors till very old, being considered sacred.

Once happening to be talking to his intimates about birds, symbols and prodigies, and observing that all these are messengers of the Gods, sent by them to men truly dear to them, he brought down an eagle flying over Olympia, which he gently stroked and dismissed.

Through such and similar occurrences, Pythagoras demonstrated that he possessed the same dominion as Orpheus over savage animals, and that he allured and detained them by the power of his voice.

14. On Pythagoras' Preexistence

PYTHAGORAS used to make the very best possible approach to men by teaching them what would prepare them to learn the truth in other matters. For by the clearest and surest indications he would remind many of his intimates of the former life lived by their soul before it was bound to their body. He would demonstrate by indubitable arguments that he had once been Euphorbus, son of Panthus, conqueror of Patroclus. He would especially praise the following funeral Homeric verses pertaining to himself, which he would sing to the lyre most elegantly, frequently repeating them.

The shining circlets of his golden hair,
Which even the Graces might be proud to wear,
Instarred with gems and gold, bestrew the shore
With dust dishonored, and deformed with gore.
As the young olive, in some sylvan scene,
Crowned by fresh fountains with eternal green,
Lifts the gay head, in snowy flowerets fair,
And plays and dances to the gentle air;
When lo, a whirlwind from high heaven invades
The tender plant and withers all its shades;
It lies uprooted from its genial bed,
A lovely ruin now defaced and dead; Thus young, thus beautiful Euphorbus lay,
While the fierce Spartan tore his arms away.
-- (Homer, Iliad, 17, Pope's translation.)

We shall, however, omit the reports about the shield of this Phrygian Euphorbus, which, among other Trojan spoils, was dedicated to Hera of Argive, as being too popular in nature. What Pythagoras, however, wished to indicate by all these particulars was that he knew the former lives he had lived which enabled him to originate his providential attention to others, in which he reminded them of their former existences.

15. How Pythagoras Cured by Music

PYTHAGORAS CONCEIVED that the first attention that should be given to men should be addressed to the senses, as when one perceives beautiful figures and forms, or hears beautiful rhythms and melodies. Consequently he laid down that the first erudition was that which subsists through music's melodies and rhythms, and from these he obtained remedies of human manners and passions, and restored the pristine harmony of the faculties of the soul. Moreover, he devised medicines calculated to repress and cure the diseases of both bodies and souls. Here is also, by Zeus, something which deserves to be mentioned above all: namely, that for his disciples he arranged and adjusted what might be called "preparations" and "touchings," divinely contriving mingling of certain diatonic, chromatic and enharmonic melodies through which he easily switched and circulated the passions of the soul in a contrary direction, whenever they had accumulated recently, irrationally, or clandestinely -- such as sorrow, rage, pity, over-emulation, fear, manifold desires, angers, appetites, pride, collapse, or spasms. Each of these he corrected by the use of virtue, attempering them through appropriate melodies, as through some salutary medicine.

In the evening, likewise, when his disciples were retiring to sleep, he would thus liberate them from the day's perturbations and tumults, purifying their intellective powers from the influxive and effluxive waves of corporeal nature, quieting their sleep, and rendering their dreams pleasing and prophetic. But when they arose again in the morning, he would free them from the night's heaviness, coma and torpor through certain peculiar chords and modulations, produced by either simply striking the lyre, or adapting the voice. Not through instruments or physical voice organs did Pythagoras effect this; but by the employment of a certain indescribable divinity, difficult of apprehension, through which he extended his powers of hearing, fixing his intellect on the sublime symphonies of the world, he alone apparently hearing and grasping the universal harmony and consonance of the spheres, and the stars that are moved through them, producing a melody fuller and more intense than anything effected by mortal sounds.

This melody was also the result of dissimilar and varying sounds, speeds, magnitudes and intervals arranged with reference to each other in a certain musical ratio, producing a convoluted motion most musical and gentle. Irrigated therefore with this melody, his intellect ordered and exercised thereby, he would, to the best of his ability exhibit certain symbols of these things to his disciples, especially through imitations thereof through instruments or the physical organs of voice. For he conceived that, of all the inhabitants of earth, by him alone were these celestial sounds understood and heard, as if coming from the central spring and root of nature. He therefore thought himself worthy to be taught, and to learn something about the celestial orbs, and to be assimilated to them by desire and imitation, inasmuch as his body alone had been well enough conformed thereto by the divinity who had given birth to him. As to other men, he thought they should be satisfied with looking to him and the gifts he possessed, and in being benefited and corrected through images and examples, in consequence of their inability truly to comprehend the first and genuine archetypes of things. Just as to those who are unable to look intently at the sun we contrive to show its eclipses in either the reflections of some still water, or in melted pitch, or some smoked glass, or well brazen mirror, so we spare the weakness of their eyes devising a method of representing light that is reflective, though less intense than its archetype, to those who are interested in this sort of thing.

This peculiar organization of 'Pythagoras' body, far finer than that of any other man, seems to be what Empedocles was obscurely driving at in his enigmatical verses:

Among the Pythagoreans was a man transcendent in knowledge;
Who possessed the most ample stores of intellectual wealth,
And in the most eminent degree assisted in the works of the wise.
When he extended all the powers of his intellect,
He easily beheld everything,
As far as ten or twenty ages of the human race!

These words "transcendent," he beheld every detail of all beings, "and the wealth of intellect," and so on, describe as accurately as possible his peculiar, and exceptionally accurate method of hearing, seeing and understanding.

16. Pythagorean Asceticism

MUSIC THEREFORE performed this Pythagorean soul-adjustment. But another kind of purification of the discursive reason, and also of the whole soul, through various studies, was effected [by asceticism]. He had a general notion that disciplines and studies should imply some form of labor; and therefore, like a legislator, he decreed trials of the most varied nature, punishments, and restraints by fire and sword, for innate intemperance, or an ineradicable desire for possessions, which the depraved should neither suffer nor sustain. Moreover, his intimates were ordered to abstain from all animal food, and any others that are hostile to the reasoning power by impeding its genuine energies. On them he likewise enjoined suppression of speech, and perfect silence, exercising them for years at a time in the subjugation of the tongue, while strenuously and assiduously investigating and ruminating over the most difficult theorems. Hence also he ordered them to abstain from wine, to be sparing in their food, to sleep little, and to cultivate an unstudied contempt of and hostility to fame, wealth, and the like; unfeignedly to reverence those to whom reverence is due, genuinely to exercise democratic assimilation and benevolence towards their fellows in age, and towards their juniors courtesy and encouragement without envy.

Moreover Pythagoras is generally acknowledged to have been the inventor and legislator of friendship, under its many various forms, such as universal amity of all towards all, of God towards men through their piety and scientific theories, or of the mutual interrelation of teachings, or universally of the soul towards the body and of the rational to the rational part, through philosophy and its underlying theories; or whether it be that of men towards each other, of citizens indeed through sound legislation, but of strangers through a correct physiology; or of the husband to the wife, or of brothers and kindred, through unperverted communion; or whether, in short, it be of all things towards all, and still farther, of certain irrational animals through justice, and a physical connexion and association; or whether it be the pacification and conciliation of the body which of itself is mortal, and of its latent conflicting powers, through health, and a temperate diet conformable to this, in imitation of the salubrious condition of the mundane elements.

In short, Pythagoras procured his disciples the most appropriate converse with the Gods, both waking and sleeping; something which never occurs in a soul disturbed by anger, pain, or pleasure, and surely, all the more, by any base desire, or defiled by ignorance, which is the most noxious and unholy of all the rest. By all these inventions, therefore, he divinely purified and healed the soul, resuscitating and saving its divine part, and directing to the intelligible its divine eye, which, as Plato says, is more worth saving than ten thousand corporeal eyes, for when it is strengthened and clarified by appropriate aids, when we look through this, we perceive the truth about all being. [7] In this particular respect, therefore, Pythagoras purified the discursive power of the soul. This is the [practical] form that erudition took with him, and such were the objects of his interest.
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17. Tests of Pythagorean Initiation

AS HE THEREFORE thus prepared his disciples for culture, he did not immediately receive as an associate any who came to him for that purpose until he had tested them and examined them judiciously. To begin with he inquired about their relation to their parents and kinsfolk. Next he surveyed their laughter, speech or silence, as to whether it was unseasonable; further, about their desires, their associates, their conversation, how they employed their leisure, and what were the subjects of their joy or grief. He observed their form, their gait, and the whole motions of their body. He considered their frame's natural indications physiognomically, rating them as visible exponents of the invisible tendencies of the soul.

After subjecting a candidate to such trials, he allowed him to be neglected for three years, still covertly observing his disposition towards stability, and genuine studiousness, and whether he was sufficiently averse to glory, and ready to despise popular honors.

After, this the candidate was compelled to observe silence for five years, so as to have made definite experiments in continence of speech, inasmuch as the subjugation of the tongue is the most difficult of all victories, as has indeed been unfolded by those who have instituted the mysteries.

During this probation, however, the property of each was disposed of in common, being committed to trustees, who were called politicians, economizers or legislators. Of these probationers, after the five-year silence, those who by modest dignity had won his approval as worthy to share in his doctrines, then became esoterics, and within the veil both heard and saw Pythagoras. Prior to this they participated in his words through the hearing alone, without seeing him who remained within the veil, and themselves offering to him a specimen of their manners.

If rejected, they were given the double of the wealth they had brought, but the homacoi raised to them a tomb, as if they were dead; the disciples being generally called Hearers. Should these later happen to meet the rejected candidate, they would treat him as a stranger, declaring that he whom they had by education modelled had died, inasmuch as the object of these disciplines had been to turn out good and honest men.

Those who were slow in the acquisition of knowledge were considered to be badly organized or, we may say, deficient, and sterile.

If, however, after Pythagoras had studied them physiognomically, their gait, motions and state of health, he conceived good hopes of them; and if, after the five years' silence, and the emotions and initiations from so many disciplines together with the ablutions of the soul, and so many and so great purifications produced by such various theorems, through which sagacity and sanctity is ingrained into the soul -- if, after all this even, some one was found to be still sluggish and dull, they would raise to such a candidate within the school a pillar or monument, such as was said to have been done to Perialus the Thurian, and Cylon the prince of the Sybarites, who were rejected. They expelled them from the auditorium, loading them down with silver and gold. This wealth had by them been deposited in common, in the care of certain custodians, aptly called Economics. Should any of the Pythagoreans later meet with the reject, they did not recognize him who they accounted dead. Hence, also Lysis, blaming a certain Hipparchus for having revealed the Pythagorean doctrines to the profane, and to such as accepted them without disciplines or theory, said: "It is reported that you philosophize indiscriminately and publicly, which is opposed to the customs of Pythagoras. With assiduity you did indeed learn them, O Hipparchus; but you have not preserved them. My dear fellow, you have tasted Sicilian tidbits, which you should not have repeated. If you give them up, I shall be delighted; but if you do not, you will to me be dead. For it would be pious to recall the human and divine precepts of Pythagoras, and not to communicate the treasures of wisdom to those who have not purified their souls, even in a dream. It is unlawful to give away things obtained with labors so great, and with assiduity so diligent to the first person you meet, quite as much as to divulge the mysteries of the Eleusinian goddesses to the profane. Either thing would be unjust and impious. We should consider how long a time was needed to efface the stains that had insinuated themselves in our breasts, before we became worthy to receive the doctrines of Pythagoras. Unless the dyers previously purified the garments in which the desired colors were to be fixed, the dye would either fade, or be washed away entirely. Similarly, that divine man prepared the souls of lovers of philosophy, so that they might not disappoint him in any of these beautiful qualities which he hoped they would possess. He did not impart spurious doctrines, nor stratagems, in which most of the Sophists, who are at leisure for no good purpose, entangle young men; but his knowledge of things human and divine was scientific. These Sophists, however, use his doctrines as a mere pretext to commit dreadful atrocities, sweeping the youths away as in a dragnet most disgracefully, making their auditors become rash nuisances. They infuse theorems and divine doctrines into hearts whose manners are confused and agitated, just as if pure, clear water should be poured into a deep well full of mud, which would stir up the sediment and destroy the clearness of the water. Such a mutual misfortune occurs between such teachers and disciples. The intellect and heart of those whose initiation has not proceeded by disciplines, are surrounded by thickets dense and thorny, which obscure the mild, tranquil and reasoning power of the soul, and impede the development and elevation of the intellective part. These thickets are produced by intemperance and avarice, both of which are prolific.

"Intemperance produces lawless marriages, lusts, intoxications, unnatural enjoyments, and passionate impulsions which drive headlong into pits and abysses. The unbridling of desires has removed the barriers against incest with even mothers or daughters, and just as a tyrant would violate city regulations, or a country's laws, with their hands bound behind them, like slaves, they have been dragged to the depths of degradation. On the other hand, avarice produces rapine, robbery, parricide, sacrilege, sorcery, and kindred evils. Such being the case, these surrounding thickets, infested with passions, will have to be cleared out with systematic disciplines, as if with fire and sword; and when the reason will have been liberated from so many and great evils, we are in a position to offer to it, and implant within it something useful and good."

So great and necessary was the attention which, according to Pythagoras, should be paid to disciplines as introductions to philosophy.

Moreover, inasmuch as he devoted so much care to the examination of the mental attitudes of prospective disciples, he insisted that the teaching and communication of his doctrines should be distinguished by great honor.

18. Organization of the Pythagorean School

THE NEXT STEP is to set forth how, after admission to discipleship followed distribution into several classes according to individual merit. As the disciples were naturally dissimilar, it was impractical for them to participate in all things equally, nor would it have been fair for some to share in the deepest revelations, while others might get excluded therefrom, or others from everything; such discrimination would be unjust. While he communicated some suitable portion of his discourses to all, he sought to benefit everybody, preserving the proportion of justice. By making every man's merit the index of the extent of his teachings. He carried this method so far as to call some Pythagoreans, and others Pythagorists, just as we discriminate poets from versifiers. According to this distinction of names, some of his disciples he considered genuine, and to be models of the others. The Pythagoreans' possessions were to be shared in common inasmuch as they were to live together, while Pythagorists should continue to manage their own property, though by assembling frequently they might all be at leisure to pursue the same activities. These two modes of life which originated from Pythagoras, were transmitted to his successors.

Among the Pythagoreans there were also two forms of philosophy, pursued by two classes, the Hearers (akousmatikoi) and the Students (mathematikoi). The latter were universally recognized as Pythagoreans by all the rest, though the Students did not admit as much for the Hearers, insisting that these derived their instructions not from Pythagoras, but from Hippasus, who was variously described as either a Crotonian or Metapontine.

The philosophy of the Hearers consisted in lectures without demonstrations or conferences or arguments merely directing something to be done in a certain way, unquestioningly preserving them as so many divine dogmas, non discussable, and which they promised not to reveal, esteeming as most wise those who more than others retained them.

Of the lectures there were three kinds: the first merely announced certain facts, others expressed what it was especially, and the third, what should, or should not be done about it. The objective lectures studied such questions as:

What are the islands of the Blessed?
The sun and moon?

What is the oracle at Delphi?
The Tetraktys, the very thing which is the Harmony of the Sirens.

The subjective lectures studied the special nature of an object, such as:

What is the most just thing?
To sacrifice.

What is the wisest thing?
Number. The next wisest is the naming power.

What is the wisest human thing?

What is the most beautiful?

What is the most powerful?
Mental decision.

What is the most excellent?

Which is the most unquestioned proposition?
That all men are depraved.

That is why Pythagoras was said to have praised the Salaminian poet Hippodomas, for singing:

Tell, O ye Gods, the source from whence ye came,
And ye, O Men, how evil ye became.

Such were these subjective lectures, which taught the distinctive nature of everything.

This sort of study really constitutes the wisdom of the so-called Seven Sages. For these also did not investigate what was simply good, but especially good, nor what is difficult, but what is particularly so -- namely, for a man to know himself. So also they considered not what was easy, but what was most so, namely, to continue following out your habits. Such studies resembled and followed those of the sages who preceded Pythagoras.

The practice lectures, which studied what should or should not be done, considered questions such as the necessity of begetting children, inasmuch as we must leave after us successors who may worship the divinities; or whether we should put the shoe on the right foot first; or whether it is proper or not to parade on the public streets, or to dip into a sprinkling vessel, or to wash in a public bath, for in all these cases the cleanliness of the agents is uncertain.

Other maxims include the following: Do not assist a man in laying down a burden, which encourages him to loiter, but to assist him in undertaking something. Do not hope to beget children from a woman who is rich. Speak not about Pythagoric affairs without light. Perform libations to the Gods from the handle of the cup, to make the omen auspicious and to avoid drinking from the same part [from which the liquor was poured out]. Wear not the image of a God on a ring, for fear of defiling it, as such resemblances should be protected in a house. Use no woman ill, for she is a suppliant; wherefore, indeed, we bring her from the Vestal hearth, and take her by the right hand. Nor is it proper to sacrifice a white cock, who also is a suppliant, being sacred to the moon and announces the hours. To him who asks for counsel, give none but the best, for counsel is a sacrament. The most laborious path is the best, just as the pleasurable one is mostly the worst, inasmuch as we entered into the present life for the sake of education, which best proceeds by chastening. It is proper to sacrifice, and to take off one's shoes on entering into a temple. In going to a temple, one should not turn out of the way; for divinity should not be worshipped carelessly. It is well to sustain, and show wounds, if they are in the breast, but not if they are behind. The soul of man incarnates in the bodies of all animals, except in those which it is lawful to kill; hence we should eat none but those whom it is proper to slay. Such were the subjects of these ethical lectures.

The most extended lectures, however, were those concerning sacrifices, both at the time when migrating from the present life, and at other times; also about the proper manner of sepulture.

For some of these propositions the reason is assigned -- such as for instance that we must beget children to leave successors to worship the Gods. But no justification is assigned for the others, although in some cases they are implied proximately or remotely, such as that bread is not to be broken, because it contributes to the judgment of Hades. Such merely probable reasons, that are additional, are not Pythagoric, but were devised by non-Pythagoreans who wished to add weight to the statement. Thus, for instance, in respect to the last statement, that bread is not to be broken, some add the reason that we should not [unnecessarily] distribute what has been assembled, inasmuch as in barbarian times a whole friendly group would together pounce upon a single piece. Others again explain that precept on the grounds that it is inauspicious, at the beginning of an undertaking, to make an omen of fracture or diminution. Moreover, all these precepts are based on one single underlying principle, the end of divinity, so that the whole of every life may result in following God, which is the principle and doctrine of philosophy. For it is absurd to search for good in any direction other than from the Gods. Those who do so resemble a man who, in a country governed by a king, should do honor to one of his fellow-citizens who is a magistrate, while neglecting him who is the ruler of them all. Indeed, this is what the Pythagoreans thought of people who searched for good elsewhere than from God. For since He exists as the lord of all things, it must be self-evident that good must be requested of Him alone. For even men impart good to those they love and enjoy, and do the opposite to those they dislike. Such indeed was the wisdom of those precepts.

There, was, however, a certain Aegean named Hippomedon, one of the Pythagorean Hearers, who insisted that Pythagoras himself gave the reasons for, and demonstrations of these precepts himself; but that in consequence of their being delivered to many, some of whom were slow, the demonstrations were removed, leaving the bare propositions. The Pythagorean Students, however, insist that the reasons and demonstrations were added by Pythagoras himself, explaining that the difference arose [between the Students and Hearers] as follows. According to them, Pythagoras hailed from Ionia and Samos, to Italy then flourishing under the tyranny of Polycrates, and he attracted as associates the very most prominent men of the city. But the more elderly of these who were busied with politics, and therefore had no leisure, needed the discourses of Pythagoras dissociated from reasonings, as they would have found it difficult to follow his meanings through disciplines and demonstrations, while nevertheless Pythagoras realized that they would be benefited by knowing what ought to be done, even though lacking the underlying reason, just as physicians' patients obtain their health without hearing the reasons of every detail of the treatment. But Pythagoras conversed through disciplines and demonstrations with the younger associates, who were able both to act and learn. Such then are the differing explanations of the Hearers and Students.

As to Hippasus, however, they acknowledge that he was one of the Pythagoreans, but that he met the doom of the impious in the sea in consequence of having divulged and explained the method of forming a sphere from twelve pentagons; but nevertheless he [unjustly] obtained the renown of having made the discovery. In reality, however, this just as everything else pertaining to geometry, was the invention of that man as they referred to Pythagoras. But the Pythagoreans say that geometry was divulged under the following circumstance: A certain Pythagorean happened to lose his fortune to recoup which he was permitted to teach that science which, by Pythagoras, was called historia [or inquiry].

So much then concerning the difference of each mode of philosophizing, and the classes of Pythagoras' disciples. For those who heard him either within or without the veil, and those who heard him accompanied with seeing, or without seeing him, and who are classified as internal or external auditors, were none other than these. Under these can be classified the Political, Economic, and Legislative Pythagoreans.

19. Abaris the Hyperborean

GENERALLY, however, it should be known, that Pythagoras discovered many paths of erudition, but that he communicated to each only that part of wisdom which was appropriate to the recipients' nature and power, of which the following is an appropriate striking illustration. When Abaris the Scythian came from the Hyperboreans, he was already of an advanced age, and unskilled and uninitiated in the Greek learning. Pythagoras did not compel him to wade through introductory theorems, the period of silence, and long lectures, not to mention other trials, but considered him to be fit as an immediate listener to his doctrines, and instructed him in the shortest way, in his treatise On Nature, and one On the Gods.

This Hyperborean Abaris was elderly, and most wise in sacred concerns, being a priest of the Apollo there worshipped. At that time he was returning from Greece to his country, in order to consecrate the gold which he had collected to the God in his temple among the Hyperboreans. As therefore he was passing through Italy, he saw Pythagoras, and identified him as the God of whom he was the priest.

Believing that Pythagoras resembled no man, but was none other than the God himself, Apollo, both from the venerable indications he saw around him, and from those the priest already knew, he paid him homage by giving him a sacred dart. This dart he had taken with him when he had left his temple, as an implement that would stand him in good stead in the difficulties that might befall him in so long a journey for in passing through inaccessible places, such as rivers, lakes, marshes, mountains and the like, it carried him, and by it he was said to have performed lustrations and expelled winds and pestilences from the cities that requested him to liberate them from such evils. For instance, it was said that Lacedaemon, after having been by him purified, was no longer infected with pestilence, which formerly had been endemic, through the noxious nature of the ground, in the suffocating heat produced by the overhanging mountain Taygetus, just as happens with Cnossus in Crete. Many other similar circumstances were reported of Abaris.

Pythagoras, however, accepted the dart, without expressing any amazement at the novelty of the thing, nor asking why the dart was presented to him, as if he really was a God. Then he took Abaris aside, and showed him his golden thigh, as an indication that he was not wholly mistaken [in his estimate of his real nature.] Then Pythagoras described to him several details of his distant Hyperborean temple, as proof of deserving being considered divine. Pythagoras also added that he came [into the regions of mortality] to remedy and improve the condition of the human race, having assumed human form lest men, disturbed by the novelty of his transcendency should avoid the discipline he advised. He advised Abaris to stay with him, to aid him in correcting [the manners and morals] of those they might meet, and to share the common resources of himself and his associates, whose reason led them to practice the precept that the possessions of friends are common.

So Abaris stayed with him, and was compendiously taught physiology and theology; and instead of divining by the entrails of beasts, he revealed to him the art of prognosticating by numbers, conceiving this to be a method purer, more divine and more kindred to the celestial numbers of the Gods. Also he taught Abaris other studies for which he was fit.

Returning, however, to the purpose of the present treatise, Pythagoras endeavored to correct and amend different persons according to their individual abilities. Unfortunately most of these particulars have neither been publicly transmitted nor is it easy to describe that which has been transmitted to us concerning him.

20. Psychological Requirements

WE MUST NOW set forth a few of the most celebrated points of the Pythagoric discipline, and landmarks of their distinctive studies.

When Pythagoras tested a novice, he considered the latter's ability to hold his counsel, echemuthein being his technical term for this referring to whether they could reserve and preserve what they had heard and learned. Next, he examined their modesty, for he was much more anxious that they should be silent, than that they should speak. Further, he tested every other quality -- for instance, whether they were astonished by the energies of any immoderate desire or passion. His examination of how they were affected by desire or anger, their contentiousness or ambition, their inclination to friendship or discord, was by no means superficial. If then after an accurate survey these novices were approved as of worthy manners, he then directed his attention to their facility in learning, and their memory. He examined their ability to follow what was said, with rapidity and perspicuity; and then, whether they were impelled to the disciplines taught them by temperance and love. For he laid stress on natural gentleness, and this he called culture. Ferocity he considered hostile to such a kind of education. For savage manners are attended by impudence, shamelessness, intemperance, sloth, stupidity, licentiousness, disgrace, and the like, while the opposite attends mildness and gentleness.

These things then he considered in making trial of those that came to him, and in these the Learners were exercised. Those that were adapted to receive the goods of the wisdom he possessed he admitted to discipleship; endeavoring to elevate them to scientific knowledge; but if he perceived that any novice was unadapted to them, he expelled him as a stranger and a barbarian.

21. The Daily Program

THE STUDIES which he delivered to his associates, were as follows; for those who committed themselves to the guidance of his doctrine acted thus.

They took solitary morning walks to places which happened to be appropriately quiet, to temples or groves, or other suitable places. They thought it inadvisable to converse with anyone until they had gained inner serenity, focusing their reasoning powers. They considered it turbulent to mingle in a crowd as soon as they rose from bed, and that is the reason why these Pythagoreans always selected the most sacred spots to walk.

After their morning walk they associated with each other, especially in temples, or, if this was not possible, in similar places. This time was employed in the discussion of disciplines and doctrines, and in the correction of manners.

After an association so holy, they turned their attention to the health of the body. Most of them were rubbed down, and raced; fewer wrestled, in gardens or groves; others exercised in leaping with leaden weights on their hands, or in oratorical gesticulations, with a view to the strengthening of the body, studiously selecting for this purpose alternating exercises.

They lunched on bread and honey, or on the honey-comb, avoiding wine. Afterwards, they held receptions to guests and strangers, conformably to the mandates of the laws, which receptions were restricted to this time of day.

In the afternoon, they once more betook themselves to walking, yet not alone, as in the morning walk, but in parties of two or three, rehearsing the disciplines they had learned, and, exercising themselves in attractive studies.

After the walk, they patronized the bath; and after ablutions they gathered in the common dining-room, which accommodated no more than a group of ten. Then were performed libations and sacrifices, with fumigations and incense. Then followed supper, which closed before the setting of the sun. They ate herbs, raw and boiled, maize, wine, and every food that is eaten with bread. Of any animals lawful to immolate, they ate the flesh, but they rarely partook of fish, which was not useful to them, for certain causes. Animals not naturally noxious were neither to be injured, nor slain. This supper was followed by libations, succeeded by readings. The youngest read what the eldest advised, and as they suggested.

When they were about to depart, the cupbearer poured out a libation for them, after which the eldest would announce precepts, like the following: that a mild and fruitful plant should neither be injured nor corrupted, nor should any harmless animal. It was further enjoined that we should speak piously, forming suitable conceptions of divine, tutelary and heroic beings, and similarly of parents and benefactor and that we should aid, and not obstruct the enforcement of laws. Whereafter, all separated, to go home.

They wore a white garment, that was pure. They also lay on white and pure beds, the coverlets of which, were made of linen, not wool. They did not hunt, nor undertake any similar exercise. Such were the precepts delivered daily to the disciples of Pythagoras, in respect to eating and living.

22. On Pythagorean Friendship

TRADITION tells of another kind of teaching by Pythagorean maxims pertaining to human opinions and practices, some examples of which may here be mentioned. It is advised to remove strife from true friendship. If possible, this should apply to all friendship; but at all events to that towards parents, elders, and benefactors. Existing friendships with such as these would not be preserved [but destroyed] by rivalry, contention, anger and subsequent graver passions. The scars and ulcers which their advice sometimes cause should be minimized as much as possible, which will be effected if especially the younger of the two should learn how to yield, and subdue his angry emotions. On the other hand, the so-called paedartases, or corrections and admonitions of the elder towards the younger, should be made with much suavity of manners, and great caution; also with much solicitude and tact, which makes the reproof all the more graceful and useful.

Faith should never be separated from friendship, whether seriously or in jest. Existing friendship cannot survive the insinuation of deceit between professors of friendship.

Nor should friendship be affected by misfortune or other human vicissitude, and the only rejection of friendship which is commendable is that which follows definite and incurable vice.

Such is an example of the Pythagorean exhortatory maxims, which extended to all the virtues, and to the whole of life.

23. The Use of Symbols in Instruction

PYTHAGORAS considered most necessary the use of symbols in instruction. Most of the Greeks had adopted it, as the most ancient; and it had been both preferentially and in principle employed by the Egyptians, who had developed it in the most varied manner. In harmony with this it will be found that Pythagoras attended to it sedulously, if from the Pythagoric symbols we unfold their significance and arcane intentions, developing their content of rectitude and truth, liberating them from their enigmatic form. When, according to straightforward and uniform tradition, they are accommodated to the sublime intelligence of these philosophers, they deify beyond human conception.

Those who came from this school, not only the most ancient Pythagoreans, but also those who during his old age were still young, such as Philolaus, and Eurytus, Charondas and Zaleucus, Brysson and the elder Archytas, Aristaeus, Lysis and Empedocles, Zalmoixis and Epimenides, Milo and Leucippus, Alcmaeon and Hippasus, and Thymaridas were all of that age, a multitude of savants, incomparably excellent all these adopted this mode of teaching, both in their conversations, commentaries and annotations. Their writings also, and all the books which they published, most of which have been preserved, to our times, were not composed in popular or vulgar diction, or in a manner usual to all other writers, so as to be immediately understood, but in a way not to be easily apprehended by their readers. For they adopted Pythagoras' law of reserve, in an arcane manner concealing divine mysteries from the uninitiated, obscuring their writings and mutual conversations.

The result is that they who present these symbols without unfolding their meaning by a suitable exposition, run the danger of exposing them to the charge of being ridiculous and inane, trifling and garrulous. When, however, the meanings are expounded according to these symbols, and made clear and obvious even to the crowds, then they will be found analogous to prophetic sayings such as the oracles of the Pythian Apollo. Their admirable meaning will inspire those who unite intellect and scholarliness.

It might be well to mention a few of them, in order to explain this mode of discipline. Do not negligently enter into a temple, nor adore carelessly, even if only at the doors. Sacrifice and adore unshod. Shunning public roads, walk in unfrequented paths. Do not without light speak about Pythagoric affairs.

Such is a sketch of the symbolic mode of teaching adopted by Pythagoras.

24. Dietary Suggestions

SINCE FOOD, used properly and regularly, greatly contributes to the best discipline, it may be interesting to consider Pythagoras' precepts on the subject. Forbidden was generally all food causing flatulence or indigestion, while he recommended the contrary kinds of food, that preserve and are astringent. Wherefore he recommended the nutritious qualities of millet. Rejected was all food foreign to the Gods, as withdrawing us from communion with them. On the other hand, he forbade to his disciples all food that was sacred, as too honorable to subserve common utility. He exhorted his disciples to abstain from such things as are an impediment to prophecy or to the purity and chastity of the soul, or to the habit of temperance, and virtue. Lastly, he rejected all things that are an impediment to sanctity and disturb or obscure the other purities of the soul, and the phantasms which occur in sleep. Such were the general regulations about food.

Specially, however, the most contemplative of the philosophers, who had arrived at the summit of philosophic attainments, were forbidden superfluous, food such as wine, or unjustifiable food such as was animated; and not to sacrifice animals to the Gods, nor by any means to injure animals, but to observe most solicitous justice towards them. He himself lived after this manner, abstaining from animal food, and adoring altars undefiled with blood. He was likewise careful to prevent others from destroying animals of a nature kindred to ours, and rather corrected and instructed savage animals, than injuring them as punishment. Further, he ordered abstaining from animal food even to politicians; for as they desired to act justly to the highest degree, they must certainly not injure any kindred animals. How indeed could they persuade others to act justly, if they themselves were detected in an insatiable avidity in devouring animals allied to us. These are conjoined to us by a fraternal alliance through the communion of life, and the same elements, and the co-mingling of these. Eating of the flesh of certain animals was however permitted to those whose lives were not entirely purified, philosophic and sacred; but even for these was appointed a definite time of abstinence. Besides, these were not to eat the heart, nor the brain, which entirely forbidden to all Pythagoreans. For these organs are predominant, and are as it were ladders and seats of wisdom and life.

Food other than animal was by him also considered sacred, due to the nature of divine reason. Thus his disciples were to abstain from mallows, because this plant is the first messenger and signal of the sympathy of celestial with terrestrial Gods. Moreover, the fish melanurus was interdicted because it was sacred to the terrestrial gods. Likewise, the erythinus. Beans also were interdicted, due to many causes, physical, psychic and sacred.

Many other similar precepts were enjoined in the attempt to lead men to virtue through their food.

25. Music and Poetry

PYTHAGORAS was likewise of the opinion that music, if properly used, greatly contributed to health. For he was wont to use it in no careless way, but as a purification. Indeed, he restricted this word to signify music used as medicine.

About the vernal season he used a melody in this manner. In the middle was placed a person who played on the lyre, and seated around him in a circle were those able to sing. Then the lyrist in the center struck up and the singers raised certain paeans, through which they were evidently so overjoyed that their manners became elegant and orderly. This music instead of medicines was also used at certain other times.

Certain melodies were devised as remedies against the passions of the soul, as also against despondency and lamentation, which were invented by Pythagoras specifically for this. Further, he employed other melodies against anger and rage, and all other aberrations of the soul. Another kind of modulation was invented against desires. He likewise used dancing, which was accompanied by the lyre, instead of the pipe, which he conceived to have an influence towards insolence, being theatrical, and by no means liberal. For the purpose of correcting the soul, he also used select verses of Homer and Hesiod.

It is related among the deeds of Pythagoras that once, through a spondaic song, he extinguished the rage of a Tauromenian lad who after feasting by night, intended to burn the vestibule of the house of his mistress, on seeing her issuing from the house of a rival. [To this rash attempt the lad had been inflamed, by a Phrygian song, which however Pythagoras at once suppressed.] As Pythagoras was astronomizing he happened to meet this Phrygian piper at an unseasonable time of night, and persuaded him to change his Phrygian song for a spondaic one. Through this the fury of the lad was immediately repressed, and he returned home in an orderly manner, although but a little while before he had stupidly insulted Pythagoras on meeting him, and would bear no admonition, and could not be restrained.

Here is another instance. Anchitus, the host of Empedocles, had as judge, condemned to death the father of a youth, who rushed on Anchitus with drawn sword, intending to slay him. Empedocles changed the youth's intention by singing, to his lyre, that verse of Homer (Odyssey, 4):

Nepenthe, without gall, o'er every ill
Oblivion spreads, --

thus saving his host Anchitus from death, and the youth from committing murder. It is said that from that time on the youth became one of the most faithful disciples of Pythagoras.

The Pythagoreans distinguished three states of mind, called exartysis, or readiness; synarmoge, or fitness, and epaphe, or contact, which converted souls to contrary passions, and these could be produced by certain appropriate songs.

When they retired, they purified their reasoning powers from the noises and perturbations to which they had been exposed during the day, by certain odes and hymns which produced tranquil sleep, and few, but good dreams. But when they arose from slumbers, they again liberated themselves from the dazedness and torpor of sleep by songs of another kind. Sometimes the passions of the soul and certain diseases were, as they said, genuinely lured by enchantments, by musical sounds alone, without words. This is indeed probably the origin of the general use of this word epode or enchantment.

Thus through music Pythagoras produced the most beneficial correction of manners and lives.

26. Theoretical Music [7]

WHILE DESCRIBING PYTHAGORAS' WISDOM in instructing his disciples, we must not fail to note that he discovered the harmonic science and ratios. But to explain this we must go a little backwards in time. Once as he was intently considering music, and reasoning with himself whether it would be possible to devise some instrumental assistance to the sense of hearing, so as to systematize it, as sight is made precise by the compass, rule, and telescope, or touch is made reckonable by balance and measures -- so thinking of these things Pythagoras happened to pass by a brazier's shop where he heard the hammers beating out a piece of iron on anvil, producing sounds that harmonized, except one. But he recognized in these sounds, the concord of the octave, the fifth, and the fourth. He saw that the sound between the fourth and the fifth, taken by itself, was a dissonance, and yet completed the greater sound among them.

Delighted, therefore, to find that the thing he was anxious to discover had by divine assistance succeeded, he went into the smithy, and by various experiments discovered that the difference of sound arose from the magnitude of the hammers, but not from the force of the strokes, nor from the shape of the hammers, nor from the change of position of the beaten iron. Having then accurately examined the weights and the swing of the hammers, he returned home, and fixed one stake diagonally to the walls, lest some difference should arise from there being several of them, or from some difference in the material of the stakes.

From this stake he then suspended four gut-strings, of similar materials, size, thickness and twist. A weight was suspended from the bottom of each. When the strings were equal in length, he struck two of them simultaneously, he reproduced the former intervals, forming different pairs. He discovered that the string stretched by the greatest weight, when compared with that stretched by the smallest weight, had the interval of an octave. The weight of the first was twelve pounds, and that of the latter six. Being therefore in a double ratio, it formed the octave, which was made plain by the weights themselves. Then he found that the string from which the greatest weight was suspended compared with that from which was suspended the weight next to the smallest, and which weight was eight pounds, produced the interval known as the fifth. Hence he discovered that this interval is in a ratio of one and a half to one, or three to two, in which ratio the weights also were to each other. Then he found that the string stretched by the greatest weight produced, when compared with that which was next to it, in weight, namely, nine pounds, the interval called the fourth, analogous to the weights. This ratio, therefore, he discovered to be in the ratio of one and a third to one, or four to three; while that of the string from which a weight of nine pounds was suspended to the string which had the smallest weight, was again in a ratio of three to two, which is 9 to 6. In like manner, the string next to that from which the smallest weight was suspended, was to that which had the smallest weight, in the ratio of 4 to 3 (being 8 to 6), but to the string which had the greatest weight, in a ratio of 3 to 2, being 12 to 8. Hence that which is between the fifth and the fourth, and by which the fifth exceeds the fourth, is proved to be as nine is to eight. But either way it may be proved that the octave is a system consisting of the fifth in conjunction with the fourth, just as the double ratio consists of three to two, and four to three; as for instance 12, 8 and 6; or, conversely of the fourth and the fifth, as in the double ratio of four to three and three to two, as for instance, 12, 9 and 6.

Thus therefore, and in this order, having conformed both his hand and hearing to the suspended weights, and having established according to them the ratio of the proportions, by an easy artifice he transferred the common suspension of the strings from the diagonal stake to the head of the instrument which he called chordotonon, or string-stretcher. Then by the aid of pegs he produced a tension of the strings analogous to that effected by the weights.

Employing this method, therefore, as a basis, and as it were an infallible rule, he afterward extended the experiment to other instruments, namely, the striking of pans, to pipes and to monochords, triangles, and the like in all of which he found the same ratio of numbers to obtain. Then he named the sound which participates in the number 6, tonic; that which participates in the number 8, and is four to three, subdominant; that which participates in the number 9, and is one tone higher than the subdominant, he called dominant, and 9 to 8; but that which participates of the number 12, octave.

Then he filled up the middle spaces with analogous sounds in diatonic order, and formed an octochord from symmetric numbers; from the double, the three to two, the four to three, and from the difference of these, the 8 to 9. Thus he discovered the harmonic progression, which tends by a certain physical necessity from the lowest to the most acute sound, diatonically.

Later, from the diatonic he progressed to the chromatic and enharmonic orders, as we shall later show when we treat of music. This diatonic scale however, seems to have the following progression, a semi-tone, a tone, and a tone; and this is the fourth, being a system consisting of two tones, and of what is called a semi-tone. Afterwards, adding another tone, we produce the fifth, which is a system consisting of three tones and a semi-tone. Next to this is the system of a semi-tone, a tone, and a tone, forming another fourth, that is, another four to three ratio. Thus in the more ancient octave indeed, all the sounds from the lowest pitch which are with respect to each other fourths, produce everywhere with each other fourths; the semi-tone, by transition, receives the first, middle and third place, according to that tetrachord. Now in the Pythagoric octave, however, which by conjunction is a system of the tetrachord and pentachord, but if disjoined is a system of two tetrachords separated from each other, the progression is from the gravest to the most acute sound. Hence all sounds that by their distance from each other are fifths, with each other produce the interval of the fifth. The semi-tone successively proceeds into four places, the first, second, third, and fourth. This is the way in which music was said to have been discovered by Pythagoras. Having reduced it to a system, he delivered it to his disciples as being subservient to everything that is most beautiful.

27. Mutual Political Assistance

MANY DEEDS OF THE PYTHAGOREANS in the political sphere are deservedly praised. At one time the Crotonians were in the habit of making funerals and internments too sumptuous. Thereupon one of them said to the people that once he had heard Pythagoras converse about divine natures, during which he had observed that the Olympian divinities attended to the dispositions of the sacrificers, and not to the multitude of the offerings. The terrestrial Gods, on the contrary, as being interested in less important matters, rejoiced in lamentations and banquets, libations, delicacies, and luxurioius expense; and as proof thereof, the divinity of Hades is called Pluto (plutos = wealth), from his wish to receive. Those that honor him slenderly [he does not much care for], and permits to stay quite a little while in the upper world; but he hastens to draw down those disposed to spend profusely on funeral solemnities, that he may obtain the honors offered in commemoration of the dead. The result was that the Crotonians who heard this advice were persuaded that if they conducted themselves moderately in misfortunes, they would be promoting their own salvation, but would die prematurely if immoderate in such expenses.

A certain difference arose about an affair in which there was no witness. Pythagoras was made arbitrator, and he led both litigants to a certain monument, announcing that the man buried was exceedingly equitable. The one prayed that he might receive much reward for his good life, while the other declared that the defunct was no better-off for his opponent's prayers. Pythagoras condemned the latter, confirming that he who praised the dead man for his worth had earned credibility.

At another time, in a case of great moment, he decided that one of the two who had agreed to settle the affair by arbitration, should pay four talents, but that the other should receive two. Afterwards, he condemned the defendant to pay three talents, and thus he appeared to have given a talent to each of them. [9]

Two persons had fraudulently deposited a garment with a woman who belonged to a court of justice, and told her that she was not to give it to either of them unless both were present. Later, with intent to defraud, one claimed and got the common deposit, saying he had the consent of the other party. The other one turned informer and related the compact made at the beginning to the magistrates. A certain Pythagorean, however, as arbitrator, decided that the woman was guiltless, construing the claimed assent as constructive presence.

Two other persons, who had seemed to be great friends, had gotten to suspect each other through calumnies of a flatterer, who told one that other had taken undue liberties with his wife. A Pythagorean, however, happened to enter the smithy where the injured party was finding fault with the blacksmith for not having sufficiently sharpened a sword he had brought him for that purpose. The Pythagorean suspecting the use to which the sword was to be put said, "The sword is sharper than all things except calumny." This caused the prospective avenger to consider that he should not rashly sin against a friend who was within an invitation.

A stranger in the temple of Asklepius accidentally dropped his belt, on which were gold ornaments. When he tried to pick it up, he was informed that the temple-regulations forbade picking up anything on the floor. He was indignant, and a Pythagorean advised him to remove the golden ornaments which were not touching the floor, leaving the belt which was.

During a public spectacle, some cranes flew over the theatre. One sailor said to his companion, "Do you see the witnesses?" A Pythagorean nearby summoned the sailors into a court presided over by a thousand magistrates, where, being examined, they confessed to having thrown certain boys into the sea, who on drowning had called on the cranes, flying above them, to witness the deed. This story is mistakenly located elsewhere, but it really happened at Croton.

Certain recent disciples of Pythagoras were at variance with each other, and the junior came to the senior, declaring there was no reason to refer the matter to an arbitrator, inasmuch as all they needed to do was to dismiss their anger. The elder agreed, but regretted he had not been the first to make that proposition.

We might relate here the story of Damon and Phintias, of Plato and Archytas, and of Clinias and Prorus. [10] At present, however, we shall limit ourselves to that of Eubulus the Messenian, who, when sailing homeward, was taken captive by the Tyrrhenians, where he was recognized by a Pythagorean named Nausithus, who redeemed him from the pirates, and sent him home in safety.

When the Carthaginians were about to send five thousand soldiers into a desert island, the Carthaginian Miltiades saw among them the Argive Possiden, [both of whom were Pythagoreans]. Approaching him, and without revealing his intentions, he advised him to return home with all possible haste. He placed him in a ship then sailing near the shore, supplied him with the travel necessities, and thus saved him from the impending danger.

He who would try to relate all the fine deeds that beautified the mutual relations of the Pythagoreans would find the task exceeding space and patience. I shall therefore pass on to show that some of the Pythagoreans were competent administrators, adapted to rule. Many were custodians of the laws, and ruled over certain Italian cities, unfolding to them, and advising them to adopt the most salutary measures, while themselves refusing all pay. Though greatly calumniated, their probity and the desire of the citizens prevailed to make them administrators. At this time the best governed states seem to have been in Italy and Sicily. One of the best legislators, Charondas the Catanean, was a Pythagorean, and so were the celebrated Locrian legislators Zaleucus and Timares. Pythagoreans also established those Rheginic polities, called the Gymnasiarchic, named after Theocles. Excelling in studies and manners which were then adopted by their fellow-citizens, were Phytius, Theocles, Elecaon and Aristocrates. Indeed, it is said that Pythagoras was the originator of all political erudition, when he said that nothing existent is pure, inasmuch as earth participates of fire, fire of air, and air of water, and water of spirit. Likewise the beautiful participates in the deformed, the just of the unjust, and so on; so that from this principle human impulse may (by proper direction) be turned in either direction. He also said that there were two motions, one of the body which is irrational, and one of the soul, which is the result of deliberate choice. He also said polities might be likened to three lines whose extremities join, forming a right angle the lines being 4, 3, 2, so that one of them is as 4 to 3, another as 3 to 2, and the other 3 is the arithmetical medium between 2 and 4. Now when, by reasoning, we study the mutual relations of these lines, and the places under them, we shall find that they represent the best image of a polity. Plato plagiarized, for in his Republic he clearly says, "That the result of the 4 to 3 ratio, conjoined with the 5 ratio, produces two harmonies." [This means that] he cultivated the moderation of the passions, and the middle path between extremes, rendering happy the life of his disciples by relating them to ideals of the good.

We are also told that he persuaded the Crotonians to give up associations with courtesans and prostitutes. Crotonian wives came to the wife of the Pythagorean Brontinus, who was a wise and splendid woman, the author of the maxim that "It is proper for women to sacrifice on the same day they have risen from the embraces of their husbands" -- which some ascribe to Pythagoras' wife Theano -- and entreated her to persuade Pythagoras to discourse to them on their continence as due to their husbands. This she did, and Pythagoras accordingly made an address to the Crotonians, which successfully ended the then prevalent incontinence.

When ambassadors came from Sybaris to Croton to demand the return of the exiles, Pythagoras, seeing one of the ambassadors who with his own hand had slain one of Pythagoras' friends, made no answer whatever. But when this man insisted on an explanation and addressed Pythagoras, the latter said it was unlawful to converse with murderers. This induced many to believe he was Apollo.

All these stories, together with what we mentioned above about the destruction of tyrants, and the democratization of the cities of Italy and Sicily, and many other circumstances, are eloquent of the benefits conferred on mankind by Pythagoras, in political respects.
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Re: The Pythagorean Sourcebook and Library

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28. Divinity of Pythagoras

HENCEFORWARD we shall confine ourselves to the works flowing from Pythagoras' virtues. As usual, we shall begin from the divinities, endeavoring to exhibit his piety, and marvelous deeds. Of his piety, let this be a specimen: that he knew what his soul was, whence it came into the body, and also its former lives, of this giving the most evident indications. Again, once passing over the river Nessus along with many associates, he addressed the river, which, in a distinct and clear voice, in the hearing of all his associates, answered, "Hail, Pythagoras!"

Further, all his biographers insist that during the same day he was present in Metapontum in Italy, and at Tauromenium in Sicily, discoursing with his disciples in both places, although these cities are separated, both by land and sea by many stadia, the travelling over which consumes many days.

It is also a matter of common report that he showed his golden thigh to the Hyperborean Abaris, who said that he resembled the Apollo worshipped among the Hyperboreans, of whom Abaris was the priest; and that he had done this so that Abaris might be certified thereof, and that he was not deceived therein.

Many other more admirable and divine particulars are likewise unanimously and uniformly related of the man, such as infallible predictions of earthquakes, rapid expulsions of pestilences, and hurricanes, instantaneous cessations of hail, and tranquilizations of the waves of rivers and seas, in order that his disciples might the more easily pass over them. The power of effecting miracles of this kind was achieved by Empedocles of Agrigentum, Epimenides the Cretan, and Abaris the Hyperborean, and they performed in many places. Their deeds were so manifest that Empedocles was surnamed a wind-stiller, Epimenides an expiator, and Abaris an air-walker, because, carried on the dart given him by the Hyperborean Apollo, he passed over rivers, and seas and inaccessible places like one carried on air. Many think that Pythagoras did the same thing, when in the same day he discoursed with his disciples at Metapontum and Tauromenium. It is also said that he predicted there would be an earthquake from the water of a well which he had tasted; and that a ship sailing with a prosperous wind, would be submerged in the sea. These are sufficient proofs of his piety.

Pitching my thoughts on a higher key, I wish to exhibit the principle of the worship of the Gods, established by Pythagoras and his disciples: that the mark aimed at by all plans, with respect to undertaking or not undertaking something, is consent with the divinity. The principle of their piety, and indeed their whole life is arranged with a view to follow God. Their philosophy explicitly asserts that men act ridiculously in searching for good from any source other than God; and that in this respect the conduct of most men resembles that of a man who, in a country governed by a king should reverence one of the city magistrates, neglecting him who is the ruler of all of them. Since God exists as the lord of all things, it is evident and acknowledged that good must be requested of him. All men impart good to those they love, and admire, and the contrary to those they dislike. Evidently we should do those things in which God delights. Not easy, however, is it for a man to know which these are, unless he obtains this knowledge from one who has heard God, or has heard God himself, or procures it through divine art. Hence also the Pythagoreans were studious of divination, which is an interpretation of the benevolence of the Gods. That such an employment is worthwhile will be admitted by one who believes in the Gods; but he who thinks that either of these is folly will also believe that both are foolish. Many of the precepts of the Pythagoreans were derived from the Mysteries, which were not the fruits of arrogance, in their estimation, but were derived from divinity.

Indeed, Pythagoreans give full belief to mythological stories such as are related of Aristeas the Proconesian, and Abaris the Hyperborean, and such like. To them every such thing seems credible, and worthy of being tried out. They also frequently recollect apparently fabulous particulars, not disbelieving anything which may be referred to the divinity. For instance, it is said that the Pythagorean Eurytus, a disciple of Philolaus, related that a shepherd feeding his flock near Philolaus' tomb heard someone singing. His interlocutor, instead of disbelieving the story, asked what kind of harmony it was. Again, a certain person told Pythagoras that he once seemed to be conversing with his deceased father, in his dreams, and asked Pythagoras what this might signify. The answer was "Nothing," even though the conversation with his father was genuine. "As therefore," said he, "nothing is signified by my conversing with you, neither is anything signified by your conversing with your father."

In all these matters they considered that the stupidity lay with the sceptics, rather than with themselves; for they did not conceive that some things, and not others, are possible with the Gods, as fancy the Sophists; they thought that with the Gods all things are possible. This very assertion is the beginning of some verses attributed to Linus:

All things may be the objects of our hopes,
Since nothing hopeless anywhere is found;
All things with ease Divinity effects
And naught can frustrate his almighty power.

They thought that their opinions deserved to be believed, because he who first promulgated them was not some chance person, but a divinity. This indeed was one of their pet puzzlers: "What was Pythagoras?" For they say he was the Hyperborean Apollo, of which this was an indication: that rising up, while at the Olympian games, he showed his golden thigh; and also that he received the Hyperborean Abaris as his guest, and was presented by him with the dart on which he rode through the air. But it is said that this Abaris came from the Hyperborean regions to collect gold for his temple, and that he predicted a pestilence. He also dwelt in temples, and was never seen to eat or drink. It is likewise said that rites [of his] are performed by the Lacedaemonians, and that on this account Lacedaemon is never infested with pestilence. Pythagoras therefore caused this Abaris to acknowledge [that he was more than man], receiving from him at the same time the golden dart, without which it was not possible for him to find his way. In Metapontum also, certain persons praying that they might obtain what a ship contained that was sailing into port, Pythagoras said to them, "You will then have a dead body." In Sybaris, too, he caught a deadly serpent and drove it away. In Tyrrhenia also he caught a small serpent, whose bite was fatal. In Croton it is said that a white eagle allowed Pythagoras to stroke it. When a certain person wished to hear him converse, Pythagoras said it was impossible until some sign appeared. Later a white bear was seen in Cauconia, whose death he declared to a person who came to announce to him its death. He likewise reminded Myllias the Crotonian that he had formerly lived as Midas the son of Gordius, and Myllias journeyed to Asia to perform at the sepulchre of Midas such rites as Pythagoras had commanded him. The person who purchased Pythagoras' residence dug up what had been buried in it, but did not dare to tell anyone what he saw [on this occasion]. Although he did not suffer [any divine vengeance] for this offence, he was seized and executed for the sacrilege of taking a golden beard that had fallen from a statue. The fact that these stories and other such are related by the Pythagoreans lend authority to their opinions. As their veracity is generally acknowledged, and as they could not possibly have happened to a mere man, they consequently think it is clear that the stories about Pythagoras should be received as referring not to a mere man, but to a super-man. This also what is meant by their maxim, that man, bird, and another thing are bipeds, thereby referring to Pythagoras. Such, therefore, on account of his piety, was Pythagoras; and such he was truly thought to be.

Oaths were religiously observed by the Pythagoreans, who were mindful of that precept of theirs,

As duly by law, thy homage pay first to the immortal Gods;
Then to thy oath, and last to the heroes illustrious.

For instance, a certain Pythagorean was in court, and asked to take an oath. Rather than to disobey this principle, although the oath would have been a religiously permitted one, he preferred to pay to the defendant a fine of three talents.

Pythagoras taught that no occurrence happened by chance or luck, but rather conformably to divine Providence, and especially so to good and pious men. This is well illustrated by a story from Androcydes' treatise On Pythagoric Symbols about the Tarentine Pythagorean Thymaridas. For when he was sailing away from his country, his friends were all present to embrace him and bid him farewell. He had already embarked when someone cried to him, "O Thymaridas, I pray that the Gods may shape all your circumstances according to your wishes!" But he retorted, "Predict me better things; namely, that what may happen to me may be conformable to the will of the Gods !" For he thought it more scientific and prudent to not resist or grumble against divine providence.

If asked about the source whence these men derived so much piety, we must acknowledge that the Pythagorean number-theology was clearly foreshadowed, to some extent, in the Orphic writings. Nor is it to be doubted that when Pythagoras composed his treatise Concerning the Gods, he received assistance from Orpheus, on which account also he called it The Sacred Discourse, because it contains the flower of the most mystical place in Orpheus. [It is uncertain] whether this work was in reality written by Pythagoras, as by most authors it is said to have been, or as some of the Pythagorean school assert, was composed by Telauges, being taken by him from the commentaries which were left by Pythagoras himself to his daughter, Damo, the sister of Telauges, and which it is said after her death were given to Bitale the daughter of Damo and to Telauges the son of Pythagoras, and also to the husband of Bitale, when he was of a mature age. For when Pythagoras died, Telauges was left very young with his mother Theano. In this Sacred Discourse also, or treatise Concerning the Gods (for it has both these inscriptions), who it was that delivered to Pythagoras what is there said concerning the Gods is rendered manifest. For we read:

Pythagoras, the son of Mnesarchus was instructed in what pertains to the Gods when he celebrated rites in the Thracian Libethra, being therein initiated by Aglaophemus; and that Orpheus, the son of Calliope, having learned wisdom from his mother in the mountain Pangaeus, said that the eternal essence of Number is the most providential principle of the universe, of heaven and earth, and of the intermediate nature; and further still, that it is the root of the permanency of divine natures, of Gods, and daimons.

From this it is evident that he learned from the Orphic writers that the essence of the Gods is defined by Number. Through the same numbers also, he produced a wonderful prognostication and worship of the Gods, both of which are particularly allied to numbers.

As conviction is best produced by an objective fact, the above principle may be proved as follows. When Abaris performed sacred rites according to his customs, he procured a foreknowledge of events, which is studiously cultivated by all the Barbarians, by sacrificing animals, especially birds; for they think that the entrails of such animals are particularly adapted to this purpose. Pythagoras, however, not wishing to suppress his ardent pursuit of the truth, but to guide it into a safer way, without blood and slaughter, and also because he thought that a cock was sacred to the sun, "furnished him with a consummate knowledge of all truth, through arithmetical science." From piety, also, he derived faith concerning the Gods. For Pythagoras always insisted that nothing marvelous concerning Gods or divine teachings should be disbelieved, inasmuch as the Gods are competent to effect anything. But the divine teachings in which we must believe are those delivered by Pythagoras. The Pythagoreans therefore assumed and believed what they taught [on the a priori ground that] they were not the offspring of false opinion. Hence Eurytus the Crotonian, the disciple of Philolaus, said that a shepherd feeding his sheep near Philolaus' tomb had heard someone singing. But the person to whom this was related did not at all question this, merely asking what kind of harmony it was. Pythagoras himself also, being asked by a certain person the significance of the conversation with his defunct father in sleep, answered that it meant nothing. "For neither is anything portended by your speaking with me," said he.

Pythagoras wore clean white garments, and used clean white sheets, avoiding the woolen ones. This custom he enjoined on his disciples.

In speaking of superior natures, he used honorable appellations, and words of good omen, on every occasion mentioning and reverencing the Gods; so, while at supper, he performed libations to the divinities, and taught his disciples, daily to celebrate the superior beings with hymns. He attended likewise to rumors and omens, prophecies and lots, and in short to all unexpected circumstances. Moreover, he sacrificed to the Gods with millet, cakes, honey-combs, and fumigations. But he did not sacrifice animals, nor did any of the contemplative philosophers. His other disciples, however, the Hearers and the Politicians, were by him ordered to sacrifice animals such as a cock, or a lamb, or some other young animal, but not frequently; but they were prohibited from sacrificing oxen.

Another indication of the honor he paid the Gods was his teaching that his disciples must never use the names of the divinities uselessly in swearing. For instance, Syllus, one of the Crotonian Pythagoreans, paid a fine rather than swear, though he could have done so without violating the truth. Just as the Pythagoreans abstained from using the names of the Gods, so also, through reverence, they were unwilling to name Pythagoras, indicating him whom they meant as the inventor of the Tetraktys. Such is the form of an oath ascribed to them:

I swear by the discoverer of the Tetraktys,
Which is the spring of all our wisdom,
The perennial root of Nature's fount.

In short, Pythagoras imitated the Orphic mode of writing, and [pious] disposition, and the way they honored the Gods, representing them in images and in brass not resembling our [human form], but the divine receptacle [of the Sphere], because they comprehend and provide for all things, being of nature and form similar to the universe.

But his divine philosophy and worship was compound, having learned much from the Orphic followers, but much also from the Egyptian priests, the Chaldeans and Magi, the mysteries of Eleusis, Imbrus, Samothracia, and Delos and even the Celtic and Iberian. It is also said that Pythagoras' Sacred Discourse is current among the Latins, not being read to or by all, but only by those who are disposed to learn, the best things, avoiding all that is base.

He ordered that libations should be made thrice, observing that Apollo delivered oracles from the tripod, the triad being the first number. Sacrifices to Venus were to be made on the sixth day, because this number is the first to partake of every number and when divided in every possible way, receives the power of the numbers subtracted, and those that remain. Sacrifices to Hercules, however, should be made on the eighth day, of the month, counting from the beginning, commemorating his birth in the seventh month.

He ordained that those who entered into a temple should be clothed in a clean garment, in which no one had slept; because sleep, just as black and brown, indicates sluggishness, while cleanliness is a sign, of equality and justice in reasoning.

If blood should be found unintentionally spilled in a temple, there should be made a lustration, either in a golden vessel, or with seawater; gold being the most beautiful of all things and the measure of exchange of everything else, while the latter is derived from the principle of moistness, the food of the first and more common matter. Also, children should not be born in a temple, where the divine part of the soul should not be bound to the body. On a festal day neither should the hair be cut, nor the nails pared, as it is unworthy to disturb the worship of the Gods, to attend to our own advantage. Nor should lice be killed in a temple, as divine power should not participate in anything superfluous or degrading.

The Gods should be honored with cedar, laurel, cypress, oak and myrtle; nor should the body be purified with these; nor should any of them be cut with the teeth.

He also ordered that what is boiled should not be roasted, signifying hereby that mildness has no need of anger.

The bodies of the dead he did not suffer to be burned, herein following the Magi, being unwilling that anything [so[ divine [as fire[ should be mingled with mortal nature. He thought it holy for the dead to be carried out in white garmentsm thereby obscurely prefiguring the simple and first nature, according to Number, and the principle of all things.

Above all, he ordained that an oath should be taken religiously; since that which is behind [i.e., the futurity of punishment] is long.

He said that it is much more holy to be injured than to kill a man; for judgment is pronounced in Hades, where the soul and its essence, and the first nature of things is correctly appraised.

He ordered that coffins should not be made of cypress, either because the scepter of Zeus was made of this wood, or for some other mystic reason.

Libations were to be performed before the altar of Zeus the Savior, of Hercules, and the Dioscuri, thus celebrating Zeus as the presiding cause and leader of the meal, Hercules as the power of Nature, and the Dioscuri, as the symphony of all things. Libations should not be offered with closed eyes, as nothing beautiful should be undertaken with bashfulness and shame.

When it thundered, he said one ought to touch the earth, in remembrance of the generation of things.

Temples should be entered from places on the right hand, and exited from the left hand; for the right hand is the principle of what is called the odd number, and is divine; while the left hand is a symbol of the even number, and of dissolution.

Such are many of the injunctions he is said to have adopted in the pursuance of piety. Other particulars which have been omitted may be inferred from what has been given. Hence the subject may be closed.

29. Sciences and Maxims

THE PYTHAGOREANS' COMMENTARIES best express his wisdom; being accurate, concise, savoring of the ancient elegance of style, and deducing the conclusions exquisitely. They contain the most condensed conceptions, and are diversified in form and matter. They are both accurate and eloquent, full of clear and indubitable arguments, accompanied by scientific demonstration, in syllogistic form; as indeed will be discovered by any careful reader.

In his writings, Pythagoras, from a supernal source, delivers the science of intelligible natures and the Gods. Afterwards, he teaches the whole of physics, completely unfolding ethics and logic. Then come various disciplines and other excellent sciences. There is nothing pertaining to human knowledge which is not discussed in these encyclopedic writings. If therefore it is acknowledged that of the [Pythagorean] writings which are now in circulation, some were written by Pythagoras himself, while others consist of what he was heard to say, and on this account are anonymous, though of Pythagoric origin -- if all this be so, it is evident that he was abundantly skilled in all wisdom.

It is said that while he was in Egypt he very much applied himself to geometry. For Egyptian life bristles with geometrical problems since, from remote periods, when the Gods were fabulously said to have reigned in Egypt, on account of the rising and falling of the Nile, the skillful have been compelled to measure all the Egyptian land which they cultivated, wherefrom indeed the science's name, geometry (i.e., "earth measure"), was derived. Besides, the Egyptians studied the theories of the celestial orbs, in which Pythagoras also was skilled. All theorems about lines also seem to have been derived from that country.

All that relates to numbers and computation is said to have been discovered in Phoenicia. The theorems about the heavenly bodies have by some been referred to the Egyptians and Chaldeans in common. Whatever Pythagoras received, however, he developed further, he arranged them for learners, and personally demonstrated them with perspicuity and elegance. He was the first to give a name to philosophy, describing it as a desire for and love of wisdom, which later he defined as the science of objectified truth. Beings he defined as immaterial and eternal natures, alone possessing a power that is efficacious, as are incorporeal essences. The rest of things are beings only figuratively, and considered such only through the participation of real beings; such are corporeal and material forms, which arise and decay without ever truly existing. Now wisdom is the science of things which are truly existing beings, but not of the mere figurative entities. Corporeal natures are neither the objects of science, nor admit of a stable knowledge, since they are indefinite, and by science incomprehensible, and when compared with universals resemble non-beings, and are in a genuine sense indeterminate. Indeed it is impossible to conceive that there should be a science of things not naturally the objects of science; nor could a science of non-existent things prove attractive to anyone. Far more desirable will be things which are genuine beings, existing in invariable permanency, and always answering to their description. For the perception of objects existing only figuratively, never truly being what they seem to be, follows the apprehension of real beings, just as the knowledge of particulars is posterior to the science of universals. For, as said Archytas, he who properly knows universals will also have a clear perception, of the nature of particulars. That is why beings are not alone, only-begotten, nor simple, but various and multiform. For those genuine beings are intelligible and incorporeal natures, while others are corporeal, falling under the perception of sense, communicating with that which is really existent only by participation. Concerning all these, Pythagoras formed the most appropriate sciences, leaving nothing uninvestigated. Besides, he developed the master-sciences of method, common to all of them, such as logic, definitions, and analysis, as may be gathered from the Pythagorean commentaries.

To his intimates he was wont to utter symbolically oracular sentences, wherein the smallest number of words were pregnant with the most multifarious significance, not unlike certain oracles of the Pythian Apollo, or like Nature herself in tiny seeds, the former exhibiting conceptions, and the latter effects innumerable in multitude, and difficult to understand. Such was Pythagoras' own maxim, "The beginning is the half of the whole." In this and similar utterances the most divine Pythagoras concealed the sparks of truth, as in a treasury, for those capable of being kindled thereby. In this brevity of diction he deposited an extension of theory most ample, and difficult to grasp, as in the maxim, "All things accord in number," which he frequently repeated to his disciples. Another one was, "Friendship is equality; equality is friendship." He even used single words, such as kosmos or, "adorned world," or, by Zeus, philosophia, or further, "Tetraktys!"
All these and many other similar inventions were by Pythagoras devised for the benefit and amendment of his associates; and by those that understood them they were considered to be so worthy of veneration, and so divinely inspired, that those who dwelt in the common auditorium adopted this oath:

I swear by the discoverer of the Tetraktys,
Which is the spring of all our wisdom,
The perennial root of Nature's fount.

This was the form of his so admirable wisdom.

Of the sciences honored by the Pythagoreans not the least were music, medicine and divination.

Of medicine, the most emphasized part was dietetics; and they were most scrupulous in its exercise. First, they sought to understand the physical symptoms of symmetry, labor, eating and repose. They were nearly the first to make a business of the preparation of food, and to describe its methods. More frequently than their predecessors the Pythagoreans used poultices, disapproving more of medicated ointments, which they chiefly limited to the cure of ulcerations. Most of all they disapproved of cuts and cauterizations. Some diseases they cured by incantations. Music, if used in a proper manner, was by Pythagoras supposed to contribute greatly to health. The Pythagoreans likewise employed select sentences of Homer and Hesiod for the amendment of souls.

The Pythagoreans were habitually silent and prompt to hear, and he won praise who listened [most effectively]. But that which they had learned and heard was supposed to be retained and preserved in memory. Indeed, this ability of learning and remembering determined the amount of disciplines and lectures, inasmuch as learning is the power by which knowledge is obtained, and remembering that by which it is preserved. Hence memory was greatly honored, abundantly exercised, and given much attention. In learning also it was understood that they were not to dismiss what they were taught, till its first rudiments had been entirely mastered. This was their method of recalling what they daily heard. No Pythagorean rose from his bed till he had first recollected the transactions of the day before; and he accomplished this by endeavoring to remember what he first said, or heard, or ordered done by his domestics before rising; or what was the second or third thing he had said, heard or commanded. The same method was employed for the remainder of the day. He would try to remember the identity of the first person he had met on leaving home, and who was the second; and with, whom he had discoursed first, second or third. So also he did with everything else, endeavoring to resume in his memory all the events of the whole day, and in the very same order in which each of them had occurred. If however, after rising there was enough leisure to do so, the Pythagorean reminisced about the day before yesterday. Thus they made it a point to exercise their memories systematically; considering that the ability of remembering was most important for experience, science and wisdom.

This Pythagorean school filled Italy with philosophers; and this place which before was unknown, was later, on account of Pythagoras called Greater Greece, which became famous for its philosophers, poets and legislators. Indeed the rhetorical arts, demonstrative reasonings and legislation was entirely transferred from Greece. As to physics, we might mention the principal natural philosophers, Empedocles and Parmenides of Elea. As to ethical maxims, there is Epicharmus, whose conceptions are used by almost all philosophers.

Thus much concerning the wisdom of Pythagoras, how in a certain respect he very much impelled all his hearers to its pursuit, so far as they were adapted to its participation, and how perfectly he delivered it.

30. Justice and Politics

HOW HE CULTIVATED and delivered justice to humanity we shall best understand if we trace it to its first principle, and ultimate cause. Also we must investigate the ultimate cause of injustice, which will show us how he avoided it, and what methods he adopted to make justice fructify in his soul.

The principle of justice is mutuality and equality, through which, in a way most nearly approximating union of body and soul, all men become cooperative, and distinguish the mine from the thine, as is also testified by Plato, who learned this from Pythagoras. Pythagoras effected this in the best possible manner by erasing from common life everything private, while increasing everything held in common, so far as ultimate possessions, which after all are the causes of tumult and sedition. For among his disciples everything was common, and the same to all, no one possessing anything private. He himself, indeed, who most approved of this communion, made use of common possessions in the most just manner; but disciples who changed their minds were given back their original contribution, with an addition, and left. Thus Pythagoras established justice in the best possible manner, beginning at its very first principle.

In the next place, justice is introduced by association with other people, while injustice is produced by unsociability and neglect of other people. Wishing therefore to spread this sociability as far as possible among men, he ordered his disciples to extend it to the most kindred animal races, considering these as their intimates and friends, and would forbid injuring, slaying, or eating any of them. He who recognizes the community of element and life between men and animals will in much greater degree establish fellowship with those who share a kindred and rational soul. This also shows that Pythagoras promoted justice beginning from its very root principle. Since lack of money often compels men sometimes to act contrary to justice, he tried to avoid this by practicing such economy that his necessary expenses might be liberal, and yet retain a just sufficiency. For as cities are only magnified households, so the arrangement of domestic concerns is the principle of all good order in cities. For instance, it was said that he himself was the heir to the property of Alcaeus, who died after completing an embassy to the Lacedaemonians; but that in spite of this Pythagoras was admired for his economy no less than for his philosophy. Also when he married, he so educated the daughter that was born to him, and who afterwards married the Crotonian Meno, that while unmarried she was a choir-leader, while as wife she held the first place among those who worshipped at altars. It is also said that the Metapontines preserved Pythagoras' memory by turning his house into a temple of Demeter, and the street on which he lived a place sacred to the Muses.

Because injustice also frequently results from insolence, luxury, and lawlessness, he daily exhorted his disciples to support the laws, and shun lawlessness. He considered luxury the first evil that usually glides into houses and cities; the second insolence, the third destruction. Luxury therefore should by all possible means be excluded and expelled, and men from birth should be accustomed to living temperately, and in a manly fashion. He also added the necessity of purification from bad language, whether it be piteous, or provocative, reviling, insolent or scurrilous.

Besides these household justices, he added another and most beautiful kind, the legislative, which both orders what to do and what not to do. Legislative justice is more beautiful than the judicial kind, resembling medicine which heals the diseased, but differs in that it is preventive, planning the health of the soul from afar.

That is why the best of all legislators graduated from the school of Pythagoras: first, Charondas the Catanean, and next Zaleucus and Timaratus, who legislated for the Locrians. Besides these were Theaetetus and Helicaon, Aristocrates and Phytius, who legislated for the Rhegini. All these aroused from the citizens honors comparable to those offered to divinities. For Pythagoras did not act like Heraclitus, who agreed to write laws for the Ephesians, but also petulantly added that in those laws he would order the citizens to hang themselves. What laws Pythagoras endeavored to establish were benevolent and scientific.

Nor need we specially admire those [above-mentioned professional] legislators. For Pythagoras had a slave by the name of Zalmoxis, hailing from Thrace. After hearing Pythagoras' discourses, and obtaining his freedom, he returned to the Getae, and there, as has already been mentioned at the beginning of this work, exhorted the citizens to fortitude, persuading them that the soul is immortal. So much is this true that even at present all the Galatians and Trallians, and many others of the Barbarians, persuade their children that the soul cannot be destroyed, but survives death, so that the latter is not to be feared, and that [ordinary] danger is to be met with a firm and manly mind. For instructing the Getae in these things, and for having written laws for them, Zalmoxis was by them considered as the greatest of the Gods. [11]

Further, Pythagoras conceived that the dominion of the divinities was most efficacious for establishing justice; and from this principle he deduced a whole polity, particular laws and a principle of justice. Thus his basic theology was that we should realize God's existence, and that his disposition towards the human race is such that he inspects and does not neglect it. This theology was very useful: for we require an inspection that we would not be disposed to resist, such as the inspective government of the divinity, for if divine nature is of this nature, it deserves the empire of the universe. For the Pythagoreans rightly taught that [the natural] man is an animal naturally insolent, and changeable in impulse, desire and passions. He therefore requires an extraordinary inspectionary government of this kind, which may produce some chastening and ordering. They therefore thought that any who recognizes the changeableness of their nature should never be forgetful of piety towards and worship of Divinity, ever keeping Him before the eye of the mind, as watching and inspecting the conduct of mankind. Everyone should pay heed, beneath the divine nature, and that of the genii, to his parents and the laws, and obey them unfeignedly and faithfully. In general, they thought it necessary to believe that there is no evil greater than anarchy, since the human race is not naturally adapted to salvation without some guidance.

The Pythagoreans also considered it advisable to adhere to the customs and laws of their ancestors, even though somewhat inferior to other regulations. For it is unprofitable and not salutary to evade existing laws, or to be studious of innovation. Pythagoras, therefore, to evince that his life was conformable to his doctrines gave many other specimens of piety to the Gods.

It may be quite suitable to mention one of these, as example of the rest. I will relate what Pythagoras said and did relative to the embassy from Sybaris to Croton, relative to the return of the exiles. By order of the ambassadors, some of his associates had been slain, a part of them, indeed, by one of the ambassadors himself, while another one of them was the son of one of those who had excited the sedition, and had died of disease. When the Crotonians therefore were deliberating how they should act in this affair, Pythagoras told his disciples he was displeased that the Crotonians should be so much at odds over the matter, and that in his opinion the ambassadors should not even be permitted to lead victims to the altar, let alone drag thence the suppliant exiles. When the Sybarites came to him with their complaints, and the man who had slain some of his disciples with his own hands was defending his conduct, Pythagoras declared he would make no answer [to a murderer]. Another [ambassador] accused him of asserting that he was Apollo, because when, in the past, some person had asked him about a certain subject, why the thing was so, and he had retorted, "Would he think it sensible, when Apollo was delivering oracles to him, to ask Apollo why he did so?" Another one of the ambassadors derided his school, wherein he taught the return of souls to this world saying that, as Pythagoras was about to descend into Hades, the ambassador would give Pythagoras an epistle to his father, and begged him to bring back an answer when he returned. Pythagoras responded that he was not about to descend into the abode of the impious, where he clearly knew that murderers were punished. As the rest of the ambassadors reviled him, Pythagoras, followed by many people, went to the sea-shore, and sprinkled himself with water. After reviling the rest of the ambassadors, one of the Crotonian counsellors observed that he understood they had defamed Pythagoras, whom not even a brute would dare to blaspheme, though all animals should again utter the same voice as men, as prehistoric fables relate.

Pythagoras discovered another method of restraining men from injustice, namely the fear of judgment. He knew that this method could be taught, but also that fear was often able to suppress justice. He asserted therefore that it is much better to be injured, than to kill a man, for judgment is dispensed in Hades, where the soul and its essence and the first nature of beings, are accurately appraised.

Desiring to exhibit among human unequal, indefinite and unsymmetrical affairs the equality, definiteness and symmetry of justice, and to show how it ought to be exercised, he likened justice to a diagram [of a right-angled triangle], the only one among geometrical forms, which, though, having an infinite diversity of adjustments of indeed unequal parts [the length of the sides], yet has equal powers [for the square on the hypotenuse is equal to the squares on the other two sides].

Since all associations [imply relations with some other person] and therefore entail justice, the Pythagoreans declared that there were two kinds of associations: the seasonable, and the unseasonable, according to age, merit, familiarity, philanthropy, and so forth. For instance, the association of a younger person with an elderly one is unseasonable, while that of two young persons is seasonable. No kind of anger, threatening or boldness is becoming in a younger towards an elderly man, all which unseasonable conduct should be cautiously avoided. So also with respect to merit for, towards a man who has arrived at the true dignity of consummate virtue, neither an unrestrained form of speech, nor any other of the above manners of conduct is seasonable.

Not unlike this was what he taught about the relations towards parents and benefactors. He said that the use of the opportune time was various. For of those who are angry or enraged, some are so seasonably, and some unseasonably. The same distinction obtains with desires, impulses and passions, actions, dispositions, associations and meetings. He further observed that to a certain extent, opportuneness is to be taught, and also that the unexpected might be analyzed artificially, while none of the above qualifications obtain when applied universally, and simply. Nevertheless its results are very similar to those of opportuneness, namely elegance, propriety, congruence, and the like.

Reminding us that unity is the principal of the universe, being its principle element, so also is it in science, experiment, and growth. However two-foldness is most honorable in houses, cities, camps, and suchlike organizations. For in sciences we learn and judge not by any single hasty glance, but by a thorough examination of every detail. There is therefore grave danger of entire misapprehension of things, when the principle has been mistaken; for while the true principle remains unknown, no consequent conclusions can be final. The same situation obtains in things of another kind. Neither a city nor a house can be well organized unless each has an effective ruler who governs voluntary servants. For voluntariness is as necessary for the ruler to govern as in the ruled to obey. So also must there be a concurrence of will between teacher and learner, for no satisfactory progress can be made while there obtains resistance on either side. Thus he demonstrated the beauty of being persuaded by rulers, and being obedient to preceptors.

This was the greatest objective illustration of this argument. Pherecydes the Syrian had been his teacher, but now was afflicted with the morbus pedicularis. Pythagoras therefore went from Italy to Delos, to nurse him, tending him until he died, and piously performing whatever funeral rites were due to his former teacher. That is how diligent was he in the discharge of his duties towards those from whom he had received instruction.

Pythagoras insisted strenuously with his disciples on the fulfillment of mutual agreements. Lysis had once completed his worship in the temple of Hera, and was leaving as he met in the vestibule with Euryphamus the Syracusan, one of his fellow disciples, who was then entering into the temple. Euryphamus asked Lysis to wait for him, till he had finished his worship also. So Lysis sat down on a stone seat there, and waited. Euryphamus went in, finished his worship, but, having become absorbed in some profound considerations, forgot his appointment, and passed out of the temple by another gate. Lysis however continued to wait, without leaving his seat, the remainder of that day, and the following night, and also the greater part of the next day. He might have stayed there still longer, perhaps unless, the following day, in the auditorium, Euryphamus had heard that. Lysis' associates were missing him. Recollecting his appointment, he hastened to Lysis, relieved him of the engagement, telling him the cause of his forgetfulness as follows: "Some God produced this oblivion in me, as a trial of your firmness in keeping your engagements."

Pythagoras also ordained abstinence from animal food, for many reasons, besides the chief one that it is conducive to peaceableness. Those who are trained to abominate the slaughter of animals as iniquitous and unnatural will think it much more unlawful to kill a man, or engage in war. For war promotes slaughter, and legalizes it, increasing it, and strengthening it.

Pythagoras' maxim "Touch not the balance above the beam" is in itself an exhortation to justice, demanding the cultivation of everything that is just, as will be shown when we study the Pythagorean symbols. In all these particulars, therefore, Pythagoras paid great attention to the practice of justice; and to its preachment to men, both in deeds and words.
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Re: The Pythagorean Sourcebook and Library

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31. Temperance and Self-Control

TEMPERANCE is our next topic, cultivated as it was by Pythagoras, and taught to his associates. The common precepts about it have already been detailed, in which we learned that everything irregular should be cut off with fire and sword. A similar precept is the abstaining from animal food, and also from anything likely to produce intemperance, and lull the vigilance and genuine energies of the reasoning powers. A further step in this direction is the precept to introduce, at a banquet, sumptuous fare, which is to be shortly sent away, and given to the servants, having been exhibited merely to chasten the desires. Another one was that none but courtesans should wear gold, and not the free women. Further the practice of taciturnity, and even entire silence, for the purpose of governing the tongue. Next, the intensive and continuous puzzling out of the most difficult speculations, for the sake of which wine, food and sleep would be minimized. Then would come genuine discrediting of notoriety, wealth, and the like; a sincere reverence towards those to whom reverence is due; joined with an unassumed democratic geniality towards one's equals in age, and towards the juniors guidance and counsel, free from envy, and everything similar which is to be deduced from temperance.

The temperance of the Pythagoreans, and how Pythagoras taught this virtue, may be learned from what Hippobotus and Neanthes narrate of Myllias and Timycha, who were Pythagoreans. It seems that Dionysius the tyrant could not obtain the friendship of anyone of the Pythagoreans, though he did everything possible to accomplish that purpose; for they had noted, and condemned his monarchical leanings. He therefore sent a troop of thirty soldiers, under the command of Eurymenes the Syracusan, who was the brother of Dion, through [whose] treachery he hoped to take advantage of the Pythagoreans' usual annual migration to catch some of them; for they were in the habit of changing their abode at different seasons of the year, and they selected places suitable to such a migration.

Therefore in Phalae, a rugged part of Tarentum, through which the Pythagoreans were scheduled to pass, Eurymenes insidiously concealed his troop; and when the unsuspecting Pythagoreans reached there about noon, the soldiers rushed upon them with shouts, after the manner of robbers. Disturbed and terrified at an attack so unexpected, at the superior number of their enemies -- the Pythagoreans amounting to no more than ten, and being unarmed against regularly equipped soldiery -- the Pythagoreans saw that they would inevitably be taken captive, so they decided that their only safety lay in flight, which they did not consider inadmissible to virtue. For they knew that according to right reason, courage is the art of avoiding as well as enduring. So they would have escaped, and their pursuit would have been given up by Eurymenes' soldiers, who were heavily armed, had their flight not led them up against a field sown with beans, which were already flowering. Unwilling to violate their principle not to touch beans, they stood still, and driven to desperation turned, and attacked their pursuers with stones and sticks, and whatever they found at hand, till they had wounded many, and slain some. But [numbers told and] all the Pythagoreans were slain by the spearmen, as none of them would suffer himself to be taken captive, preferring death, according to the Pythagorean teachings.

As Eurymenes and his soldiers had been sent for the express purpose of taking some of the Pythagoreans alive to Dionysius, they were much crest-fallen; and having thrown the corpses in a common sepulchre, and piled earth thereupon, they turned homewards. But as they were returning they met two of the Pythagoreans who had lagged behind. Myllias the Crotonian, and his Lacedaemonian wife Timycha, who had not been able to keep up with the others, being in the sixth month of pregnancy. These therefore the soldiers gladly made captive, and led to the tyrant with every precaution, so as to insure their arrival alive. On learning what had happened, the tyrant was very much disheartened, and said to the two Pythagoreans, "You shall obtain from me honors of unusual dignity if you shall be willing to reign in partnership with me." All his offers, however, were by Myllias and Timycha rejected. Then said he, "I will release you with a safe-guard if you will tell me one thing only." On Myllias asking what he wished to learn, Dionysius replied: "Tell me only why your companions chose to die rather than to tread on beans?" But Myllias at once answered, "My companions did indeed prefer death to treading on beans; but I had rather do that than tell you the reason." Astonished at this answer, Dionysius ordered him forcibly removed, and Timycha tortured, for he thought that a pregnant woman, deprived of her husband, would weaken before the torments, and easily tell him all he wanted to know. The heroic woman, however, with her teeth bit her tongue until it was separated and spat it out at the tyrant, thus demonstrating that the offending member should be entirely cut off, even if her female nature, vanquished by the torments, should be compelled to disclose something that should be reserved in silence. Such difficulties did they make to the admission of outside friendships, even though they happened to be royal.

Similar to these also were the precepts concerning silence, which tended to the practice of temperance; for of all continence, the subjugation of the tongue is the most difficult. The same virtue is illustrated by Pythagoras' persuading the Crotonians to relinquish all sacrilegious and questionable commerce with courtesans. Moreover Pythagoras restored to temperance a youth who had become wild with amatory passion, through music. Exhortations against lascivious insolence promote the same virtue.

Such things were delivered to the Pythagoreans by Pythagoras himself, who was their cause. They took such care of their bodies that they remained in the same condition, not being at one time lean, and at another stout, which changes they considered anomalous. With respect to their mind also, they managed to remain uniformly mildly joyful, and not at one time hilarious, and at another sad, which could be achieved only by expelling perturbations, despondency or rage.

It was a precept of theirs that no human casualties ought to be unexpected by the intelligent, expecting everything which it is not in their power to prevent. If however at any time anyone of them fell into a rage, or into despondency, he would withdraw from his associates' company, and seeking solitude, endeavor to digest and heal the passion.

Of the Pythagoreans it is also reported that none of them punished a servant or admonished a free man during anger but waited until he had recovered his wonted serenity. They use a special word, paidartan, to signify such [self-controlled] rebukes, effecting this calming by silence and quiet. So Spintharus relates of Archytas the Tarentine that on returning after a certain time from the war against the Messenians waged by the Tarentines, to inspect some land belonging to him, and finding that the bailiff and the other servants had not properly cultivated it, greatly neglecting it, he became enraged, and was so furious that he told his servants that it was well for them that he was angry, for otherwise, they would not have escaped the punishment due to so great an offence. A similar anecdote is related of Clinias, according to Spintharus, for he also was wont to defer all admonitions and punishments until his mind was restored to tranquility.

Of the Pythagoreans it is further related that they restrained themselves from all lamentation, weeping and the like; and that neither gain, desire, anger or ambition, or anything of the like, ever became the cause of dissension among them, all Pythagoreans being disposed towards each other as parents towards their offspring.

Another beautiful trait of theirs was that they gave credit to Pythagoras for everything, naming it after him, not claiming the glory of their own inventions, except very rarely. Few there are who acknowledged their own works.

Admirable too is the careful secrecy with which, they preserved the mystery of their writings. For during so many centuries, prior to the times of Philolaus, none of the Pythagorean commentaries appeared publicly. Philolaus first published those three celebrated books which, at the request of Plato, Dion of Syracuse is said to have bought for a hundred minae. For Philolaus had been overtaken by sudden severe poverty, and he capitalized the writings of which he was partaker through his alliance with the Pythagoreans.

As to the value of opinion, such were their views: a stupid man should defer to the opinion of everyone, especially to that of the crowds. Only a very few are qualified to apprehend and opine rightly; for evidently this is limited to the intelligent, who are very few. To the crowds, such a qualification of course does not extend. But to despise the opinion of everyone is also stupid, for such a person will remain unlearned and incorrigible. The unscientific should study that of which he is ignorant, or lacks scientific knowledge. A learner should also defer to the opinion of the scientific, and who is able to teach. Generally, youths who wish to be saved should attend to the opinion of their elders, or of those who have lived well.

During the course of human life there are certain ages by them called endedasmenae, which cannot be connected by the power of any chance person. Unless a man from his very birth is trained in a beautiful and upright manner, these ages antagonize each other. A well-educated child, formed to temperance and fortitude, should be given a great part of his education during the stage of adolescence. Similarly, when the adolescent is trained to temperance and fortitude, he should focus his education on the next age of manhood. Nothing could be more absurd than the way in which the general public treats this subject. They fancy that boys should be orderly and temperate, abstaining from everything troublesome or indecorous, but as soon as they have arrived at the age of adolescence, they may do anything they please. In this age, therefore, there is a combination of both kinds of errors, puerile and virile. To speak plainly, they avoid anything that demands diligence and good order, while following anything that has the appearance of sport, intemperance and petulance, being familiar only with boyish affairs. Their desires should be developed from the boyish stage into the next one. In the meanwhile ambition and the rest of the more serious and turbulent inclinations and desires of the virile age prematurely invade adolescence; wherefore this adolescence demands the greatest care.

In general, no man ought to be allowed to do whatever he pleases, for there is always need, of a certain inspection, or legal and cultured government, to which each of the citizens is responsible. For animals, when left to themselves, and neglected, rapidly degenerate into vice and depravity.

The Pythagoreans [who did not approve of men being intemperate], would often compel answers from, and puzzle [such intemperate people] by asking them why boys are generally trained to take food in an orderly and moderate manner, being compelled to learn that order and decency are beautiful, and that their contraries, disorder and intemperance are base, while drunkards and gormandizers are held in great disgrace. For if no one of these is useful to us when we have arrived at the age of virility, it was in vain that we were accustomed, when boys, to an order of this kind. The same argument holds good in respect to other good habits to which children are trained. Such a reversal of training is not seen in the case of the education of other lower animals. From the very first a whelp and a colt are trained, and learn those tricks which they are to exercise when arrived at maturity.

The Pythagoreans are generally reported to have exhorted not only their intimates, but also to whomsoever they happened to meet, to avoid pleasure as a danger demanding the utmost caution. More than anything else does this passion deceive us, and mislead us into error. They contended that it was wiser never to do anything whose end was pleasure, whose results are usually shameful and harmful. They asserted we should adopt the beautiful, and fair, and do our duty. Only secondarily should we consider the useful and advantageous. In these matters there is no need for special consideration.

Of desire, the Pythagoreans said that desire itself is a certain tendency, impulse and appetite of the soul, wishing to be filled with something, or to enjoy the presence of something or to be disposed according to some sense-enjoyment. There are also contrary desires, of evacuation and repulsion, and to terminate some sensation. This passion is manifold, and is almost the most Protean of human experiences. However, many human desires are artificially acquired, and self-prepared. That is why this passion demands the utmost care and watchfulness, and physical exercise that is more than casual. That when the body is empty it should desire food is no more than natural; and then it is just as natural that when it is full it should desire appropriate evacuation. But to desire superfluous food, or luxurious garments or coverlets, or residences, is artificial. The Pythagoreans applied this argument also to furniture, dishes, servants and cattle raised for butchering. Besides, human passions are never permanent, but are ever changing, even to infinity. That is why education of the youth should begin at the earliest moment possible, that their aspirations may be directed towards ends that are proper, avoiding those that are vain and unnecessary, so as to be undisturbed by, and remain pure from such undesireable passions; and may despise those who are objects of contempt, because they are subjected to [myriad] fleeting desires. Yet it must be observed that senseless, harmful superfluous and insolent desires subsist in the souls of such individuals who are the most powerful; for there is nothing so absurd that the soul of such boys, men and women would not lead them to perform.

Indeed, the variety of food eaten is beyond description. The kinds of fruits and roots which the human race eats is nothing less than infinite. The kinds of flesh eaten are innumerable; there is no terrestrial, aerial, or aquatic animal which has not been partaken of. Besides, in the preparation of these, the contrivances used are endless and they are seasoned with manifold mixtures of juices. Hence, according to the motions of the human soul, it is no more than natural that the human race should be so various as to include those actually insane; for each kind of food that is introduced into the human body becomes the cause of a certain peculiar disposition.

[Quantity] is as important as quality, for sometimes a slight change in quantity produces a great change in quality, as with wine. First it makes men more cheerful, later it undermines morals and sanity. This difference is generally ignored in things in which the result is not so pronounced, although everything eaten is the cause of a certain peculiar disposition. Hence it requires great wisdom to know and perceive what quality and quantity of food to eat. This science, first unfolded by Apollo and Paeon, was later developed by Asklepius and his followers.

About propagation, the Pythagoreans taught as follows. First, they prevented untimely birth. Not even among plants or animals is prematurity good. To produce good fruit there is need of maturation for a certain time to give strong and perfect bodies to fruits and seeds. Boys and girls should therefore be trained to work and exercise, with endurance, and they should eat foods adapted to a life of labor and temperance, with endurance. There are many things in human life which it is better to learn at a late period in life, and the use of sex is one of them. It is therefore advisable that a boy should be educated so as not to begin sex-connection before the twentieth year, and even then rarely. This will take place if he holds high ideals of a good habit for the body. Bodily hygiene and intemperance are not likely to subsist in the same individual. The Pythagoreans, praised the earlier Greek laws forbidding intercourse with a woman who is a mother, daughter or sister in a temple or other public place. It is advisable that there be many impediments to the practice of this energy. The Pythagoreans forbade entirely intercourse that was unnatural, or resulting from wanton insolence, allowing only the natural, and temperate forms, which occur in the course of chaste and recognized procreation of children.

Parents should make circumstantial provision for their offspring. The first precaution is a healthful and temperate life, not unseasonably filling oneself with food, nor using foods which create bad body-habits, above all avoiding intoxication. The Pythagoreans thought that an evil, discordant, trouble-making character produced depraved sperma. They insisted that none but an indolent or inconsiderate person would attempt to produce an animal, and introduce it to existence, without most diligently providing for it a pleasing and even elegant ingress into this world. Lovers of dogs pay the utmost possible attention to the breeding of their puppies, knowing that goodness of the offspring depends on goodness of parents, at the right season, and in proper surroundings. Lovers of birds pay no less attention to the matter; procreators of generous animals therefore should by all possible means manage that their efforts be fruitful. It is therefore absurd for men to pay no attention to their own offspring, begetting casually and carelessly, and after birth, feeding and educating them negligently. This is the most powerful and manifest cause of the vice and depravity of the greater part of mankind, for the multitude undertake procreation on impulse, like beasts.

Such were the Pythagoreans' teachings about temperance, which they defended by work and practiced in deed. They had originally received them from Pythagoras himself, as if they had been oracles delivered by the Pythian Apollo.

32. Courage or Fortitude

FORTITUDE, the subject of this chapter, has already been illustrated, by the heroism of Timycha, and those Pythagoreans who preferred death, to transgression of Pythagoras' prohibition to touch beans, and other instances. Pythagoras himself showed it in the generous deeds he performed when travelling everywhere alone, undergoing heart-breaking labors and serious dangers, and in choosing to leave his country and to live among strangers. Likewise when he dissolved tyrannies, ordered confused commonwealths, and emancipated cities, he ended illegalities, and impeded the activities of insolent and tyrannical men. As a leader, he showed himself benignant to the just and mild, but expelled rough and licentious men from his society, refusing even to answer them, resisting them with all his might, although he assisted the former.

Of these courageous deeds, as well as of many upright actions, many instances could be adduced; but the greatest of these is the prevailing freedom of speech he employed towards the tyrant Phalaris, the most cruel of those who detained him in captivity. A Hyperborean sage named Abaris visited him, to converse with him on many topics, especially sacred ones, respecting statues and worship, the divine Providence, natures terrestrial and celestial, and the like. Pythagoras, under divine inspiration, answered him boldly, sincerely and persuasively, so that he converted all listeners. This roused Phalaris' anger against Abaris, for praising Pythagoras and increased the tyrant's resentment against Pythagoras. Phalaris swore proudly as was his wont, and uttered blasphemies against the Gods themselves. Abaris however was grateful to Pythagoras, and learned from him that all things are suspended from, and governed by the heavens, which he proved from many considerations, but especially from the potency of sacred rites. For teaching him these things, so far was Abaris from thinking Pythagoras an enchanter, that his reverence for him increased till he considered him a God. Phalaris tried to counteract this by discrediting divination, and publicly denying there was any efficacy of the sacraments performed in sacred rites. Abaris, however, guided the controversy towards such things as are granted by all men, seeking to persuade him of the existence of a divine providence, from circumstances that lie above human influence, such as immense wars, incurable diseases, the decay of fruits, incursions of pestilence, or the like, which are hard to endure, and are deplorable, arising from the beneficent [purifying] energy of the powers celestial and divine.

Shamelessly and boldly Phalaris opposed all this. Then Pythagoras, suspecting that Phalaris intended to put him to death, but knowing he was not destined to die through Phalaris, retorted with great freedom of speech. Looking at Abaris, he said that from the heavens to aerial and terrestrial beings there was a certain descending communication. Then from instances generally known he showed that all things follow the heavens. Then he demonstrated the existence of an indisputable power of freedom of will in the soul, proceeding further to amply discuss the perfect energy of reason and intellect. With his [usual] freedom of will he even [dared to] discuss tyranny, and all the prerogatives of fortune, concerning injustice and human avarice, solidly teaching that all these are of no value. Further, he gave Phalaris a divine admonition concerning the most excellent life, earnestly comparing it with the most depraved. He likewise clearly unfolded the manner of subsistence of the soul, its powers and passions; and, what was the most beautiful of all, demonstrated to him that the Gods are not the authors of evils, and that diseases and bodily calamities are the results of intemperance, at the same time finding fault with the poets and mythologists for the unadvisedness of many of their fables.

Then he directly confuted Phalaris, and admonished him, experimentally demonstrating to him the power and magnitude of heaven, and by many arguments demonstrated to him that reason dictates that punishments should be legal. He demonstrated to him the difference between men and other animals, scientifically demonstrating the difference between internal and external speech. Then he expounded the nature of the intellect, and the knowledge that is derived therefrom; with its ethical corollaries. He discoursed about the most beneficial of useful things adding the mildest possible admonitions of what ought not to be done. Most important of all, he unfolded to him the distinction between the productions of fate and intellect, and the difference between the results of destiny and fate. Then he reasoned about the divinities, and the immortality of the soul.

All this, really, belongs to some other chapter, the present one's topic being the development of courage or fortitude. But if, when situated in the midst of the most dreadful circumstances, Pythagoras philosophized with firmness of decision, if on all sides he resisted fortune, and repelled it, enduring its attacks strenuously, if he employed the greatest boldness of speech towards him who threatened his life, it must be evident that he entirely despised those things generally considered dreadful, rating them as unworthy of attention. If also he despised execution, when this appeared imminent, and was not moved by its imminence, it is evident that he was perfectly free from the fear of death.

But he did something still more generous, effecting the dissolution of the tyranny, restraining the tyrant when he was about to bring the most deplorable calamities on mankind, and liberating Sicily from the most cruel and imperious power. That it was Pythagoras who accomplished this, is evident from the oracles of Apollo, which had predicted that the dominion of Phalaris would come to an end when his subjects would become better men, and cooperate; which also happened through the presence of Pythagoras, by his imparting to them instruction and good principles. The best proof of this may be found in the time when it happened. For on the very day that Phalaris condemned Pythagoras and Abaris to death, he himself was by stratagem slain.

Another argument for the truth of this are the adventures of Epimenides. He was a disciple of Pythagoras; and when certain persons planned to destroy him, he invoked the Furies and the avenging divinities, and thereby caused those who had attempted his life to destroy each other. In the same way Pythagoras, who assisted mankind, imitating both the manner and fortitude of Hercules for the benefit of men punished and occasioned the death of him who had behaved insolently and in a disorderly manner towards others and this through the very oracles of Apollo, in the class of which divinity both he and Epimenides had naturally since birth belonged. This admirable and strenuous deed was the effect of his fortitude.

We shall present another example of preservation of lawful opinion; for following it out, he did what to him seemed just and dictated by right reason, without permitting himself to be diverted from his intention by pleasure, labor, passion or danger. His disciples also preferred death to transgression of any precept of his. They preserved their manners unchanged under the most varying fortunes. Being involved in myriad calamities could not cause them to deviate from his rules. They never ceased exhorting each other to support the laws, to oppose lawlessness, and from birth to train themselves to a life of temperance and fortitude, so as to restrain and oppose luxury. They also used certain original melodies which Pythagoras had invented as remedies against the passions of the soul; against lamentation and despondency, as affording the greatest relief in these maladies. Other melodies they employed against anger and rage, through which they could increase or diminish those passions, till they reduced them to moderation, and compatibility with fortitude. The thought which afforded them the greatest support in generous endurance was the conviction that no human casualty should be unexpected by men of intellect, but that they must resign themselves to all vicissitudes beyond human control.

Moreover, whenever overwhelmed by grief or anger, they immediately forsook the company of their associates, and in solitude endeavored to digest and heal the oppressing passion. They took it for granted that studies and disciplines implied labor, and that they must expect severe tests of different kinds, and be restrained and punished even by fire and sword, so as to exorcise innate intemperance and greediness, for which purpose no labor or endurance should be spared. Further to accomplish this, they unselfishly abstained from animal food, and also some other kinds. This also was the cause of their slowing of speech and complete silence, as means to the entire subjugation of the tongue, which demanded a year-long exercise of fortitude. In addition, their strenuous and. assiduous investigation and resolution of the most difficult theorems, their abstinence from wine, food and sleep, and their contempt of wealth and glory, were means by which they trained themselves to fortitude.

But this is not all. They restrained themselves from lamentations and tears. They abstained from entreaty, supplication, and adulation, as being effeminate and abject. To the same practice of fortitude must be referred their peculiarity of absolute reserve concerning the arcana of the first principles of their discipline, preserving them from being divulged to strangers, committing them unwritten to memory, and transmitting them orally to their successors as if they were the mysteries of the Gods. That is why nothing worth mentioning of their philosophy was ever made public and though it had been taught and learned for a long while, it was not known beyond their walls. Those outside, whom I might call the profane, sometimes happened to be present; and under such circumstances the Pythagoreans would communicate only obscurely, through symbols, a vestige of which is retained by celebrated precepts still in circulation, such as, "Fire should not be poked with a sword," and other like ones which, taken literally, resemble old wives' tales, but which, when properly unfolded, are to the recipients admirable and venerable.

That precept which, of all others, was of the greatest efficacy in the achievement of fortitude, is that one which helps defend and liberate from the life-long bonds that retain the intellect in captivity, and without which no one can perceive or learn anything rational or genuine, whatever be the sense in activity. Thus they said,

'Tis mind that sees all things, and hears them all;
All else is deaf and blind.

The next most efficacious precept is that which exhorts one excessively to be studious of purifying the intellect, and by various methods adapting it through mathematical disciplines to receive something divinely beneficial, so as neither to fear a separation from the body, nor, when directed towards incorporeal natures, through their most refulgent splendor to be compelled to turn away the eyes, nor to be converted to those passions which fasten and even nail the soul to the body, and makes her rebellious to all those passions which are the progeny of procreation, degrading her to a lower level. The training of ascent through all these is the study of the most perfect fortitude. Such are important instances of the fortitude of Pythagoras and his followers.

33. Universal Friendship

FRIENDSHIP of all things towards all was most clearly unfolded by Pythagoras. Indeed, the friendship of Gods towards men he explained through piety and scientific cultivation; but that of teachings towards each other, and generally of the soul to the body, of the rational towards the unfolded, through philosophy and its teachings. That of men towards each other, and of citizens, he justified through proper legislation; that of strangers, through the common possession of a body; that between man and wife, children, brothers or kindred, through the unperverted ties of nature. In short, he taught the friendship of all for all; and still further, of certain animals, through justice, and common physical experiences. But the pacification and conciliation of the body, which is mortal by itself, and of its latent immortal powers, he enforced through health, and a temperate diet suitable thereto, in imitation of the ever-healthy condition of the mundane elements.

In all these, Pythagoras is recognized as the inventor and summarizer of them in a single name, that friendship. So admirable was his friendship to his associates, that even now when people are extremely benevolent mutually people call them Pythagoreans. We should therefore narrate Pythagoras's discipline related thereto, and the precepts he taught his disciples.

The Pythagoreans therefore exhorted the effacing of all rivalry and contention from true friendship; and if not from all friendship, at least from parental friendship, and generally from all gratitude towards seniors and benefactors. To strive or contend with such, out of anger or some other passion, is not the way to preserve existing friendship. Scars and ulcers in friendship should be the least possible; and this will be the case if those that are friends know how to subdue their anger. If indeed both of them know this, or rather, the younger of the two, and who ranks in some one of the above mentioned orders, [their friendship will be the more easily preserved]. They also taught that corrections and admonitions, which they called paidartases should take place from the elder to the younger, and with much suavity and caution; and likewise, that much careful and considerate attention should be manifested in admonitions. For thus they will be persuasive and helpful. They also said that confidence should never be separated from friendship, whether in earnest, or in jest. Existing friendship cannot survive, when once falsehood insinuates itself into the habits of professed friends. According to them, friendship should not be abandoned on account of misfortune, or any other human vicissitude; the only permissible rejection of friend or friendship is the result of great and incorrigible vice. Hatred should not be entertained voluntarily against those who are not perfectly bad, but when once formed, it should be strenuously and firmly maintained, unless its object should change his morals, so as to become a better man. Hostility should not consist in words, but in deeds and such war is commendable and legitimate when conducted in a manly manner.

No one should ever permit himself to become the cause of contention, and we should so far as possible avoid its source. In a friendship which is intended to be pure, the greater part of the things pertaining to it should be definite and legitimate. These should be properly distinguished and not be casual; and moreover our conversation should never grow casual or negligent, but remain orderly, modest and benevolent. So also with the remaining passions and dispositions.

We should not decline foreign friendships carelessly, but accept and guard them with the greatest care.

That the Pythagoreans preserved friendship towards each other for many ages may be inferred from what Aristoxenus in his treatise On the Pythagoric Life says he heard from Dionysius the tyrant of Sicily, when having been deposed he taught language at Corinth. Here are the words of Aristoxenus:

"So far as they could these men avoided lamentations and tears, and the like; also adulation, entreaty, supplication and other emotions. Dionysius therefore, having fallen from his tyranny and come to Corinth, told us the detailed story about the Pythagoreans, Phintias and Damon, who were sponsors for each other's death.

"This is how it was: certain intimates of his had often mentioned the Pythagoreans, defaming and reviling them, calling them arrogant and asserting that their gravity, their pretended fidelity, and stoicism, would disappear on falling into some calamity. Others contradicted this; and as contention arose on the subject, it was decided to settle the matter by an experiment. One man accused Phintias, before Dionysius, of having conspired with others against his life. Others corroborated the charges, which looked probable though Phintias was astonished at the accusation .When Dionysius had unequivocally said that he had verified the charges, and that Phintias must die, the latter replied that if Dionysius thought that this was necessary, he requested the delay of the remainder of the day, to settle the affairs of himself and Damon, as these two men lived together; and had all things in common; but as Phintias was the elder, he mostly undertook the management of the household affairs. He therefore requested that Dionysius allow him to depart for this purpose, and that he would appoint Damon as his surety.

Dionysius claimed surprise at such a request, and asked him if any man existed who would stand surety for the death of another. Phintias asserted that there was, and Damon was sent for; and on hearing what had happened, agreed to become the sponsor, and that he would remain there until Phintias' return. Dionysius declared astonishment at these circumstances, and they who had proposed the experiment derided Damon as the one who would be caught, sneering at him as the 'vicarious stag.' When, however, sunset approached, Phintias came to die, at which all present were astonished and subdued. Dionysius, having embraced and kissed the men, requested that they would receive him as a third into their friendship. They however would by no means consent to anything of the kind, though he entreated them to comply with his request." These words are related by Aristoxenus, who received them from Dionysius himself.

It is also said that the Pythagoreans endeavored to perform the offices of friendship to those of their sect, though they were unknown, and had never seen each other. on receiving a sure indication of participation in the same doctrines; so that judging from such friendly offices it may be believed, as is generally reported, that worthy men, even though they should dwell in the remotest parts of the earth, are mutually friends, and this before they become known to, and salute each other.

The story runs that a certain Pythagorean, travelling through a long and solitary road on foot, came to an inn; and there from over-exertion, or other causes fell into a long and severe disease, so as at length to want the necessities of life. The innkeeper however, whether from pity or benevolence, supplied him with everything requisite, sparing neither personal service, nor expense. Feeling the end near, the Pythagorean wrote a certain symbol on a tablet, and desired the innkeeper, in event of his death, to hang the tablet near the road, and observe whether any traveller read the symbol. "For that person," said he, "will repay you what you have spent on me, and will also thank you for your kindness." On the Pythagorean's death the innkeeper buried him and attended to the funeral details without any expectation of being repaid, nor of receiving any remuneration from anybody who might read from the tablet. However, struck with the Pythagorean's request, he was induced to expose the writing in the public road. A long time thereafter a Pythagorean passed that way, and on understanding the symbol, found out who had placed the tablet there, and having also investigated every particular, paid the innkeeper a sum very much greater than he had disbursed.

It is also related that Clinias the Tarentine, when he learned that the Cyrenaean Prorus, who was a zealous Pythagorean, was in danger of losing all his property, sailed to Cyrene, and after having collected a sum of money, restored the affairs of Prorus to a better condition, though thereby he diminished his own estate and risked the peril of the sea-voyage.

Similarly, Thestor Posidoniates, having from mere report heard that the Pythagorean Thymaridas Parius had fallen from great wealth into abject poverty, is said to have sailed to Paros, and after having collected a large sum of money, reinstated Thymaridas in affluence. These are beautiful instances of friendship.

But much more admirable than the above examples were the Pythagoreans' teachings respecting the communion of divine goods, the agreement of intellect, and their doctrines about the divine soul. They were ever exhorting each other not to tear apart the divine soul within them. The significance of their friendship both in words and in deeds was an effort to achieve a certain divine union, or communion of intellect with the divine soul. Anything better than this, either in what is uttered in words, or performed by deeds, is not possible to find. For I am of opinion that in this all the goods of friendship are united. In this, as a climax we have collected all the blessings of Pythagorean friendship; there is nothing left to say.

34. Miscellaneous Topics

HAVING THUS, according to plan discussed Pythagoras and Pythagoreanism, we may be interested in scattered points which do not fall under any of the former topics.

[First, as to language]. It is said that each Greek novice was ordered to use his native language, as they did not approve of the use of a foreign language. Foreigners also joined the Pythagoreans: Messenians, Lucani, Picentini, and Romans. Metrodorus, the son of Thyrsus, the father of Epicharmus, who specialized in medicine, in explaining his father's writings to his brother, says that Epicharmus, and prior to him Pythagoras, conceived that the best and most musica dialect was the Doric. The Ionic and Aeolic relate to chromatic harmony, which however is still more evident in the Attic. The Doric, consisting of pronounced letters, is enharmonic.

Myths also bear witness to the antiquity of this dialect. Nereus was said to have married Doris, the daughter of Ocean, by whom he had fifty daughters, one of whom was the mother of Achilles. Metrodorus also says that some insist that Helen was the offspring of Deucalion, who was the son of Prometheus and Pyrrha, the daughter of Epimetheus; and from him descended Dorus and Aeolus. Further he observes that from the Babylonian sacred rites he had learned that Helen was the offspring of Jupiter, and that the sons of Helen were Dorus, Xuthus, and Aeolus; with which Herodotus also agrees. Accuracy in particulars so ancient is difficult for moderns, to enable them to decide which of the accounts is most trustworthy. But either of them claim that the Doric dialect is the most ancient, that the Aeolic, whose name derives from Aeolus, is the next in age, and that the third is the Ionic, derived from Ion, the son of Xuthus. Fourth is the Attic, named from Creusa, the daughter of Erechtheus, and it is three generations younger than the others, for it existed about the time of the Thracians and the rape of Orithyia, as is evident from the testimony of most histories. The Doric dialect was also used by the most ancient of the poets, Orpheus.

Of medicine, the most emphasized part was dietetics, and they were most scrupulous in its exercise. First they sought to understand the physical symptoms of symmetry, labor, eating and repose. They were nearly the first to make a business of the preparation of food, and to describe its methods. More frequently than their predecessors the Pythagoreans used poultices, disapproving more of medicated ointments, which they chiefly limited to the cure of ulcerations. Most of all they disapproved of cuts and cauterizations. Some diseases they cured by incantations. Music, if used in a proper manner, was by Pythagoras supposed to contribute greatly to health. The Pythagoreans likewise employed select sentences of Homer and Hesiod for the amendment of souls.

The Pythagoreans objected to those who offered disciplines for sale, who open their souls like the gates of an inn to every man that approaches them; and who, if they do not thus get buyers, diffuse themselves through the cities, and in short, hire gymnasia, and require a reward from young men for those things that are without price. Pythagoras indeed hid the meaning of much that was said by him, in order that those who were genuinely instructed might clearly be partakers of it; but that others, as Homer says of Tantalus, might be pained in the midst of what they heard, in consequence of receiving no delight therefrom.

The Pythagoreans thought that those who teach for the sake of reward, show themselves worse than sculptors, or artists who perform their work sitting. For these, when someone orders them to make a statue of Hermes, search for wood suited to receive the proper form; while those pretend that they can readily produce the works of virtue from every nature.

The Pythagoreans likewise said that it is more necessary to pay attention to philosophy, than to parents or to agriculture; for no doubt it is owing to the latter that we live, but philosophers and preceptors are the causes of our living well, and becoming wise, on discovering the right mode of discipline and instruction.

Nor did they think fit either to speak or to write in such a way that their conceptions might be obvious to the first comer; for the very first thing Pythagoras is said to have taught is that, being purified from all intemperance, his disciples should preserve the doctrines they had heard in silence. It is accordingly reported that he who first divulged the theory of commensurable and incommensurable quantities to those unworthy to receive it was by the Pythagoreans so hated that they not only expelled him from their common association, and from living with him, but also for him constructed a [symbolic] tomb, as for one who had migrated from the human into another life. It is also reported that the Divine Power was so indignant with him who divulged the teachings of Pythagoras, that he perished at sea, as an impious person who divulged the method of inscribing in a sphere the dodecahedron, one of the so-called solid figures, the composition of the icostagonus. But according to others, this is what happened to him who revealed the doctrine of irrational and incommensurable quantities.

All Pythagoric discipline was symbolic, resembling riddles and puzzles, and consisting of maxims, in the style of the ancients. Likewise the truly divine Pythian oracles seem to be somewhat difficult of understanding and explanation; to those who carelessly receive the answers given. These are the indications about Pythagoras and the Pythagoreans collected from tradition.

35. The Attack on Pythagoreanism

THERE WERE, however, certain persons who were hostile to the Pythagoreans, and who rose against them. That stratagems were employed to destroy them, during Pythagoras' absence, is universally acknowledged; but the historians differ in their account of the journey which he then undertook. Some say that he went to Pherecydes the Syrian, and others, to Metapontum. Many causes of the stratagems are assigned. One of them, which is said to have originated from the men called Cylonians, is as follows: Cylon of Croton was one of the most prominent citizens, in birth, renown and wealth; but in manners he was severe, turbulent, violent, tyrannical. His greatest desire was to become partaker of the Pythagoric life, and he made application to Pythagoras who was now advanced in age, but was rejected for the above reasons. Consequently, he and his friends became violent enemies of the brotherhood. Cylon's ambition was so vehement and immoderate that with his associates, he persecuted the very last of the Pythagoreans. That is why Pythagoras moved to Metapontum, where he ended his existence.

Those who were called Cylonians continued to plot against the Pythagoreans, and to exhibit the most virulent malevolence. Nevertheless for a time this enmity was subdued by the Pythagoreans' probity, and also by the vote of the citizens, who entrusted the whole of the city affairs to their management.

At length, however, the Cylonians became so hostile to "the men," as they were called, that they set fire to Milo's residence, where were assembled all the Pythagoreans, holding a council of war. All were burnt, except two, Archippus and Lysis, who escaped through their bodily vigor. As no public notice was taken of this calamity, the Pythagoreans ceased to pay any further attention to public affairs, which was due to two causes: the cities's negligence, and through the loss of those men most qualified to govern.

Both of the saved Pythagoreans were Tarentines, and Archippus returned home. Lysis resenting the public neglect went into Greece, residing in the Achaian Peloponnesus. Stimulated by an ardent desire, he migrated to Thebes, where he had as disciple Epaminondas, who spoke of his teacher as his father. There Lysis died.

Except Archytas of Tarentum, the rest of the Pythagoreans departed from Italy, and dwelt together in Rhegium. The most celebrated were Phanto, Echecrates, Polymnastus, and Diocles, who were Phlyasians, and Xenophilus Chalcidensis of Thrace. But in course of time, as the administration of public affairs went from bad to worse, these Pythagoreans nevertheless preserved their pristine manners and disciplines; yet soon the sect began to fail, till they nobly perished. This is the account by Aristoxenus.

Nicomachus agrees with Aristoxenus, except that he dates the plot against the Pythagoreans during Pythagoras' journey to Delos, to nurse his preceptor Pherecydes the Syrian, who was then afflicted with morbus pedicularis, and after his death performed the funeral rites. Then those who had been rejected by the Pythagoreans, and to whom monuments had been raised, as if they were dead, attacked them, and committed them all to the flames. Afterwards they were overwhelmed by the Italians with stones, and thrown out of the house unburied. Then science died in the breasts of its possessors, having by them been preserved as something mystic and incommunicable. Only such things as were difficult to be understood, and which were not expounded, were preserved in the memory of those who were outside the sect -- except a few things, which certain Pythagoreans, who at that time happened to be in foreign lands, preserved as sparks of science very obscure, and of difficult investigation. These men being solitary, and dejected at this calamity, were scattered in different places, retaining no longer public influence. They lived alone in solitary places, wherever they found any, each preferred association with himself to that with any other person.

Fearing however lest the name of philosophy should be entirely exterminated from among mankind, and that they should, on this account incur the indignation of the Gods, by suffering so great a gift of theirs to perish, they made a collection of certain commentaries and symbols, gathered the writings of the more ancient Pythagoreans, and of such things as they remembered. These relics each left at his death to his son, or daughter, or wife, with a strict injunction not to divulge them outside the family. This was carried out for some time and the relics were transmitted in succession to their posterity.

Since Apollonius dissents in a certain place regarding these particulars, and adds many things that we have not mentioned, we must record his account of the plot against the Pythagoreans. He says that from childhood Pythagoras aroused envy. So long as he conversed with all that came to him, he was pleasing to all; but when he restricted his intercourse to his disciples the general peoples' good opinion of him was altered. They did indeed permit him to pay more attention to strangers than to themselves, but they were indignant at his preferring some of their fellow-citizens before others, and they suspected that his disciples assembled with intentions hostile to themselves. In the next place, as the young men that were indignant with him were of high rank, and surpassed others in wealth -- and when they arrived at the proper age, not only held the first honors in their own families, but also managed the affairs of the city in common -- they, being more than three hundred in number, formed a large body, so that there remained but a small part of the city which was not conversant with their habits and pursuits.

Moreover, so long as the Crotonians confined themselves to their own country, and Pythagoras dwelt among them, the original form of government continued; but the people had changed, and they were no longer satisfied with it; and were therefore seeking a pretext for a change. When they captured Sybaris, and the land was not divided by lot, according to the desire of the multitude, this veiled hatred against the Pythagoreans burst forth, and the populace forsook them.

The leaders of this dissension were those that were nearest to the Pythagoreans, both by kindred and intercourse. These leaders, as well as the common folk were offended by the Pythagoreans' actions, which were unusual, and the people interpreted that peculiarity as a reflection on them.

[None of the Pythagoreans called Pythagoras by his name. While alive, they referred to him as divine; after his death as that man, just as Homer makes Eumaeus refer to Ulysses thus:

Though absent he may be, O guest, I fear
To name him; so great is my love and care.

Such were some of his precepts: They were to get up before sunrise, and never to wear a ring on which the image of God was engraved, lest that image be defiled by being worn at funerals, or other impure places. They were to adore the rising sun. Pythagoras ordered them never to do anything without previous deliberation and discussion, in the morning forming a plan of what was to be done later, and at night to review the day's actions, which served the double purpose of strengthening the memory, and considering their conduct. If anyone of their associates appointed to meet them at some particular place and time they should stay there till he came, regardless of the length of time, for Pythagoreans should not speak carelessly, but remember what was said and regard order and method. At death they were not to blaspheme, but to die uttering propitious words, such as are used by those who sail out of the port into the Adriatic Sea.] [12]

The Pythagoreans' kindred were indignant that they associated with none, their parents excepted; that they shared in common their possessions to the exclusion of their kindred, whom they treated as strangers. These personal motives turned the general opposition into active hostility. Hippasus, Diodorus and Theages united in insisting that the assembly and the magistracy should be opened to every citizen, and that the rulers should be responsible to elected representatives of the people. This was opposed by the Pythagoreans Alcimachus, Dimachus, and Meton and Democedes, who disagreed with changes in the inherited constitution. They were however defeated, and were formally accused in a popular as assembly by two orators, the aristocrat Cylon, and the plebeian Ninon. These two planned their speeches together, the first and longer one being made by Cylon, while Ninon concluded by pretending that he had penetrated the Pythagorean mysteries, and that he had gathered and written out such particulars as were calculated to incriminate the Pythagoreans, and to a scribe he gave to read a book which was entitled the Sacred Discourse.

Friends, it was said in the book, are to be venerated in the same manner as Gods; but others are to be treated as brutes. This very sentiment is ascribed to Pythagoras himself, but in verse such as,

Like the blessed Gods, his friends he e'er revered
But reckoned others as of no account.

Pythagoras considered that Homer deserved to be praised for calling a king the shepherd of the people which implied approval of aristocracy, in which the rulers are few, while the implication is that the rest of men are like cattle, because they are used in voting, inasmuch as the Pythagoreans selected office holders by appointment. To rule should be an object of desire, for it is better to be a bull for one day only, than for all one's life to be an ox. While other states' constitutions might be laudable, yet it would be advisable to use only that which is known to oneself.

In short, Ninon showed that their philosophy was a conspiracy against democracy. He advised the people not even to listen to the defendants, considering that they would never have been admitted into the assembly if the Pythagoreans' council had had to depend for admission on the session of a thousand men, and said that they should not allow speech to those who, had used their utmost power to prevent the speech of others. The people must remember that when they raised their right hands to vote, or even counted their votes, that their right hand was constructively rejected by the Pythagoreans, who were aristocrats. It was also disgraceful that the Crotonian masses who had conquered thirty myriads of men at the river Tracis should be outweighed by a thousandth part of the same number through sedition in the city itself.

Through these calumnies Ninon so exasperated his hearers that a few days later a great multitude assembled intending to attack the Pythagoreans as they were sacrificing to the Muses in a house near the temple of Apollo. Foreseeing this, the Pythagoreans fled to an inn, while Democedes with the youths retired to Plataea. The partisans of the new constitution decreed an accusation against Democedes of inciting the youths to capture power, putting a price of thirty talents on his head, dead or alive. A battle ensued, and the victor. Theages was given thirty talents promised by the city. The city's evils were spread to the whole region, and the exiles were arrested in Tarentum, Metapontum, and Caulonia.

The envoys from these cities that came to Croton to get the charges were, according to the Crotonian record, bribed, with the result that the exiles were condemned as guilty, and driven out further. The Crotonians then expelled from the city all who were dissatisfied with the existing regime; banishing along with them all their families, on the two-fold pretext that impiety was unbearable, and that the children should not be separated from their parents. They then repudiated the debts, and redistributed the lands.

Many years after, when Dinarchus and his associates had been slain in another battle, and when Litagus, the chief leader of the sedition, was dead, pity and repentance induced the citizens to recall from exile what remained of the Pythagoreans. They therefore sent for messengers from Achaia who were to come to an agreement with the exiles, and file their oaths at Delphi. The Pythagoreans who returned from exile were about sixty in number, not to mention the aged among whom were some physicians and dieticians who worked along original lines. When these Pythagoreans returned, they were welcomed by the crowds, who silenced dissenters by announcing that the Ninon regime was ended. Then the Thurians invaded the country, and the Pythagoreans were sent to procure assistance but they perished in battle, mutually defending each other. So thoroughly had the city become Pythagoreanized that beside the public praise, they performed a public sacrifice in the temple of the Muses which had originally been built at the instigation of Pythagoras.

That is all concerning the attack made on the Pythagoreans.

36. The Pythagorean Succession

PYTHAGORAS' acknowledged successor was Aristaeus, the son of the Crotonian Damophon, who was Pythagoras' contemporary, and lived seven ages before Plato. Being exceedingly skillful in Pythagoric dogmas, he carried on the school, educated Pythagoras' children, and married his wife Theano. Pythagoras was said to have taught his school 39 years, and to have lived a century. Aristaeus growing old, relinquished the school to Pythagoras' son Mnesarchus. He was followed by Bulagoras, in whose time Croton was plundered. After the war, Gartydas the Crotonian who had been absent on a journey, returned, and took up the school; but he so grieved about his country's calamity that he died prematurely. But the Pythagoreans who became very old were accustomed to liberate themselves from the body, as from a prison.

Later, being saved through certain strangers, Aresas Lucanus undertook the school; and to him came Diodorus Aspendius, who was received into the school because of the small number of genuine Pythagoreans.

Clinias and Philolaus were at Heraclea, Theorides and Eurytus at Metapontum, and at Tarentum, Archytas, Epicharmus was also said to have been one of the foreign Hearers, but he was not one of the school. However, having arrived at Syracuse, he refrained from public philosophizing, in consideration of the tyranny of Hiero. But he wrote the Pythagorean views in metre, and published the occult Pythagorean dogmas in comedies.
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