Then followed the Eleatics, one of whom, Zeno, closes the second great line of independent inquiry opened by Anaximenes.

Heraclitus (b. 503 B. C.) conceived the doctrine of all things as a perpetual flux and reflux, and of Fire as the principle of all things. He affirmed Fire to be both the principle and the element—both the moving, mingling force and the mingled matter; and formulated the phrase: "Strife is the parent of all things."

Fire, which here stands as the semi-symbol of Life and Intelligence, because of its spontaneous activity, is but a modification of the Water of Thales and the Air of Anaximenes.

Anaxagoras proclaimed the All to be the Many and Intelligence [Nous] to be the moving force of the Universe which caused the mass of elements to become arranged in one harmonious, all-embracing system. "The Nous has moving power and knowledge . . . it initiates movement."

Drawing special attention to the fact that while vital importance was attached to "movement" by Anaxagoras, the central thought of Pythagorean philosophy is the idea of number. In his monograph on the subject1 the Rev. G. Oliver quotes Philolaus, who says:

"Number is great and perfect, omnipotent and the principle and guide of divine and human life. Number is then the principle of order, the principle on which the Cosmos or ordered world exists. . . . The decade, as the basis of the numerical system, appeared to (Pythagoreans) to comprehend all other numbers in itself. . . also the number four because it is the first square number and is also the potential decade: 1 +2+3+4= 10. Amongst the ten principia or fundamental oppositions formulated by the Pythagoreans are odd and even, right and left, male and female, light and darkness, etc.”

According to Oliver it was Pythagoras who was celebrated as the "discoverer of the holy Tetraktos, the fountain and root of ever-living nature, or the Cosmos consisting of Fire, Air, Earth and Water, the four roots of all existing things."

Lewes, on the other hand, attributed to Empedocles "the conception of earth as a fourth element" and the "principle that the primary elements were four, viz.: Earth, Air, Fire and Water. Out of these all things proceed; all things are but the various ming

The Pythagorean Triangle.

AM. ANTH, N. S., 7-10

lings of these four. Nothing is there but a mingling and then a

separation of the mingled . . Commenting on these theories Lewes here states (and I emphasize with italics the importance of his statement): "Now, that this is an advance on the preceding conceptions [of Heraclitus and Anaxagoras in particular] will scarcely be denied. It bears indubitable evidence of being a later conception and a modification of its predecessors." 1

1

To the four so-called Empedoclean elements later philosophers (Xenocrates and Philolaus) added a fifth, the All-embracing ether, the Greek name for which Philolaus gives as ἒλχας, όλας, etc.

To me it seems impossible that any one who has followed the evolution of Greek philosophical thought, as set forth by Lewes, can doubt the above-cited characterization of the doctrine of the four elements as the natural outgrowth of previous equally supposititious and artificial deductions.

At the same time I am aware that Prof. L. von Schroeder, of Dorpat, has attempted to prove that the five elements-earth, fire, water, air, and ether (Sanscrit ākaçā) — already figure in the Brahmas, were taught in the Samkya philosophy of the Kapila, and were therefore known in India at least as far back as the seventh century, B.C. It is Professor von Schroeder's opinion that Pythagorean philosophy derived the elemental divisions, as well as its science of geometry and number, from India, and in support of the latter assertion he mentions the fact that Samkya, the name of the ancient Indian school of philosophy, signifies "number" and that its followers were therefore designated as "philosophers or teachers of numbers." It is for Greek scholars to establish whether the Pythagoreans derived their tenets from India or whether the doctrines of Pythagoras and Empedocles were carried from India to Greece at the time of the Greek invasion under Alexander the Great in 327 B.C.

However this may ultimately be decided, the remarkable and undeniable fact exists that in the ancient Mexican calendar we have a numerical system of marvelous ingenuity which, according to tradition, was devised as a means of introducing order in the community, as "a guide for human life." It is formed by a combination 1 Op. cit., vol. 1, p. 95.

of odd and even numbers and is ruled by the number four, which is identified with the elements earth, air, fire, and water. What is more, as I have already pointed out, the symbols of the four elements (each in turn accompanied by the number four and in a square) are enclosed in the quadruplicate ollin, or sign for movement, which is carved in the center of the most remarkable monument of ancient Mexico.

Unprepared though one may be to face the possibility that the Mexican sculptor was embued with abstract philosophical ideas, his choice of the ollin sign, typifying movement, to encompass the symbols of the four elements, unquestionably demonstrates that he associated his ollin with a meaning analogous to that assigned by Philolaus to the öλas: "that which moves and carries the cosmos, which was composed of the four elements." Strange as it appears, it cannot be denied that the Mexican composite symbol calls to mind Plato's familiar dictum: "Thus there is a perpetual ebb and flow of the elements: the diversity of matter is the cause of constant motion." Much as we would naturally hesitate to invest the carved symbol with the whole significance of Plato's doctrine, one cannot but feel somewhat authorized to do so when one recalls the name Tloquenauaque: the "All-embracing One," which is recorded in Sahagun's Nahuatl text as that of the Supreme god of the foreign colonists. For this name is unquestionably identical in meaning with Plato's definition of God as "the One being comprising within Himself all other beings."1

Besides, the calendar system of ancient Mexico, which incorporates what Lewes designates as "the Empedoclean elements," is a masterpiece of the Science of Numbers, the equal of which does not seem to have been produced by any known disciple of Pythagoras, who, however, idealized Number as the principle of order and the guide of human life.

The more I study this marvelously ingenious cyclical system and realize the advanced knowledge of mathematics and astronomy that it reveals, the less I can understand how it could have been planned without the aid of a cursive method of writing or of registering numbers. From what I have been able to learn, in twenty years of study of the ancient Mexicans, I also find it incompre1 Lewes, op. cit., p. 263.

hensible how these unlettered people could have evolved independently such artificial correlated products of the human mind as the Tetraktos; its association with movement; a tetrarchical system of government; a science of numbers; a cyclical system based on a combination of odd and even numbers; a conception of the deity as "All-embracing," and the pyramid which, to me, seems to be a figuration of the Tetraktos, "the root of all things."

Were we dealing with any other part of the world but America, one would scarcely hesitate to claim that the presence, in Mexico, of the Tetraktos, of the cognate ideas which have been enumerated and of native testimony asserting their foreign origin, justifies the supposition of some form of contact with persons not only imbued with the theories of certain Greek philosophers, but bent on applying them practically.

But we have to do with a portion of the American continent which, though connected with the Old World by a great and comparatively smooth water-way, is generally considered too remote to have been visited by even those venturesome Mediterranean seafarers who, in precolumbian times, constantly braved the dangers of the Bay of Biscay and the northern seas.

I therefore merely present the foregoing data with my doubts and perplexities and the hope that they may receive the attention of those interested in the history of the origin of ancient Mexican civilization. It will be for them to meditate, as I have done, upon the striking contradiction between Brinton's dictum that, in America, "the simple theory of the four elements naturally presented itself to the primitive mind," and Lewes' conclusion that in Greece the identical theory, evolved after centuries of speculation, "bears indubitable evidence of being a later conception and modification of its predecessors." The idea that the Mexicans might, by mere chance, have formulated the theory without associating it with philosophical or cosmological speculations, is refuted by the positive facts that on the most important of native monuments the symbolized elements are enclosed in the sign for movement; that the deity was named "the All-embracing One," and that the four elements were incorporated in a cyclical system of marvelous ingenuity and perfection, which was used to regulate and control communal life under

the tetrarchical form of government. Will future text-books maintain that this whole group of cognate artificialities is a "universal trait of culture," an Elementargedanke, such as naturally presents itself to primitive man, and that its presence in ancient America merely proves that, in prehistoric times, this country produced its own school of philosophy, its mathematicians, its Pythagoras, and its Empedocles? To what natural causes will future autochthonists attribute the remarkable circumstance that the primitive aborigine of America hit upon the "Empedoclean elements" instead of the five equally spurious elements of ancient Chinese philosophy, viz., earth, water, fire, wood, and metal? Will the parallel development of the ancient Mexican and Greek tetraktos be cited as an instance of the psychic unity of mankind; or will it be recorded that the internal evidence furnished by the ancient Mexican civilization corroborates native tradition and reveals that its admirable artificial organization is attributable to a small band of learned foreign enthusiasts from over the sea who, at a remote and unknown period attempted, on American soil, what might well be described as a realization of the dream of Greek philosophy, namely, the establishment of "an ideal republic or polity" based on abstract philosophical, mathematical, and cosmological ideas?

In conclusion, the question: Does not Montezuma's evidence, in conjunction with the internal evidence supplied by the Mexican civilization itself, account for the incongruous elements it exhibits? Do they not explain the existence of positive proofs of highly advanced intellectual culture, such as the artificial, ingenious, calendric and governmental systems, along with barbarous and primitive superstitions and customs, an inconsistent combination which, years ago, was recognized and commented upon as follows by the eminent German anthropologist, Prof. Theodor Waitz?

"The Aztecs seem to have been the last offspring or heir of an extremely ancient and admirable civilization, which it had no share in creating or developing and only imperfectly assimilated. In its hands the ancient culture was rapidly deteriorating and becoming mixed with barbaric elements.'' 1

1 Anthropologie der Naturvölker, Leipzig, 1864, part IV, p. 129. CASA ALVARADO,

COYOACÁN, D.F., MEXICO.