They developed a list of ten fundamental oppositions: 1, limited and unlimited; 2, odd and even; 3, one and many; 4, right and left; 5, masculine and feminine; 6, rest and motion; 7, straight and crooked; 8, light and darkness; 9, good and evil.... The union of opposites in which consists the existence of things is harmony; hence the expression that the whole heaven or the whole universe is harmony. Pointing out that it is only by a combination of odd and even numbers that a harmonious cycle is created, I continue to cite from Mr. Oliver's work: “The decade, as the basis of the numerical system, appeared to them to comprehend all other numbers in itself, and to it are applied, therefore, the epithets quoted above of number in general. Similar language is held of the number ‘four’ because it is the first square number and is also the potential decade (1+2+3+4=10). Pythagoras is celebrated as the discoverer of the holy ‘Tetraktos’ the fountain and root of ever-living nature, or the Cosmos consisting of Fire, Air, Earth, Water, the four roots of all existing things.
“Number,” says Philolaus, “is great and perfect and omnipotent, and the principle and guide of divine and human life. Number then is the principle of order, the principle on which cosmos or ordered world exists.” Without number and the limitation which number brings, there would only be chaos and the illimitable, a thought abhorrent to the Greek mind.
“The four Ionic tribes were abolished by Kleisthenes (510 B.C.) who created, in their place, ten new tribes founded on a new principle, independent of the gentes and phratries. Each new tribe comprised a certain number of demes or cantons with the enrolled proprietors and residents in each of them. Each tribe had a chapel, sacred rites and festivals and a common fund for such meetings, in honor of its eponymous hero, administered by members of its own choice; and the statues of all the ten eponymous heroes, fraternal patrons of the democracy, were planted in the most conspicuous part of the agora of Athens.... The demes taken altogether, included the entire surface of Attica. Simultaneously Kleisthenes divided the year into ten portions called Prytanies,—the fifty senators of each tribe taking by turns the duty of constant attendance during one prytany and receiving during that time, the title of The Prytanes. The order of precedence among the tribes in these duties was annually determined by lot.... Moreover, a further subdivision of the prytany into five periods of seven days each and of the fifty tribe-senators into five bodies of ten each, was recognized; each body of ten presided in the senate for one period of seven days, drawing lots every day among their number for a new chairman called Epistates, to whom, during his day of office were confided the keys of the acropolis and the treasury, together with the city seal.” The remaining senators, not belonging to the prytanizing tribe, might of course attend if they chose, but the attendance of nine among them, one from each of the remaining nine tribes, was imperatively necessary to constitute a valid meeting and to insure a constant representation of the collective people. During those later times—the ekklesia or formal assembly of the citizens, was convened four times regularly during each prytany ... (op. cit., vol. iv, p. 138). Special attention is drawn here to the intimate association of the system of government and the calendar, analogous to the ancient Mexican system.
“The number of inhabitants an ideal state should contain and their numerical organization were evidently subjects of supreme interest to Greek statesmen and philosophers. The great work by Aristoteles (384-322 B.C.) on Politics, ‘according to Grote,’ was based on a collection made by himself, of 158 different constitutions of states, which collection has, unfortunately, been lost.” “The purpose of comfortable subsistence for which commonwealths are instituted, requiring a minute subdivision of labor,” Aristotle says, that “in this particular view, the more populous the community its end will be the more completely attained.... All things considered he declares in favour of what would be now deemed a very small commonwealth, consisting of 15,000 or 20,000 citizens....”
“In his ‘Book of Laws’ Plato intended to delineate a more practicable scheme of government than that of his first.... His two republics nearly agree in form, though they differ in magnitude; the first containing one thousand and the second five thousand and forty men bearing arms.... In his second republic he equalizes estates but leaves population unlimited.... A regulation directly the reverse of this is introduced by one of the most ancient writers on the subject of politics, Pheidon of Corinth, who limits population, but does not equalize possessions.... The republic, planned by the architect Hippodamus, consisted of ten thousand men, divided into the three classes of artificers, husbandmen and soldiers. The territory he likewise divides into three portions: the sacred, destined for the various exigencies of public worship; the common, to be cultivated for the common benefit of the soldiers; and the private, to be separately appropriated by the husbandmen. His laws were also divided into three kinds....” (Aristotle's Ethics and Politics, John Gillies, LL.D., London 1804).
The knowledge that a republic was actually planned on the scheme of three-fold division naturally suggests the possibility that the Sicilian coat of arms, the triskeles, may be a survival of a period when a similar republic existed in Sicily and the year was divided into three seasons only. (For interesting details concerning the employment and spread of a year of three seasons in ancient times, see Hewitt, op. cit. Preface xvi, vol. i.)
In Grote's history we learn that after the establishment of the first Athenian democracy by Kleisthenes and the victory they gained over the Bœotians and Chalkidians, the Athenians planted a body of four thousand of their citizens as kleruchs (lot-holders) or settlers upon the lands of the wealthy conquered Chalkidians. This is a system which we shall find hereafter extensively followed out by the Athenians in the days of their power; partly with a view of providing for their poorer citizens, partly to serve as garrison among a population either hostile or of doubtful fidelity. These Attic kleruchs did not lose their birthright as Athenian citizens: they were not colonists in the Grecian sense and they are known by a totally different name—but they corresponded very nearly to the colonies formally planted out on the conquered lands by Rome. The increase of the poorer population was always more or less painfully felt in every Grecian city ... the numerous kleruchies sent out by Athens, of which this to Eubœa was the first, arose in a great measure out of the multiplication of the poorer population, which her extended power was employed in providing for ... (op. cit. vol. 4, p. 171). The number “four thousand” specially designated is of particular interest because the letter of the Greek alphabet expressing it was the delta, in the form of a triangle or pyramid, which also signified “the fourth” or “a quarter.” The ideas suggested by these facts are: that the foundation of such a colony would have been commemorated by the building of a pyramid by the conquered race, the division of labor amongst them preparing the way for the institution of a social organization on the familiar plan (cf. p. 273). It is only when we reflect what an admirable means of establishing communal life and activity the mere act of building under direction and guidance must have been, that we appreciate the fine wisdom of the ancient kings, civilizers and culture-heroes, who were, first of all, master builders, architects and masons and who began the work of rearing an empire by directing the erection of a monument which, by its form, expressed the all-pervading plan of organization.
“Taylor says that the reason Plato adopted this division is because the number 12, the image of all-perfect progression, is the product of 3 by 4, both of which numbers, according to the Pythagoreans, are images of perfection. On the other hand, Ast conceives that Plato had in mind the division of the country in twelve parts found in Egypt and elsewhere, and which seems, as may be inferred from other portions of his work, to have been connected with the division of the year into twelve months, each under the superintendence of one of the twelve greater gods.” To this note I add the remark that, in B. vi, C. 8, Plato distinctly refers to the twelve tribes as “the thrice four tribes, recommending that they should appoint thrice four interpreters,” one for each tribe. It should also be recalled that Cecrops is said to have employed the division into twelve and is supposed to have brought it from Egypt. In the present summary the employment of the same division in other countries can be verified.
It may be of interest to note here that, like the Egyptians, the Greeks divided their month into 3 decades. The year consequently contained 3×12=36 decades+5 days.
An interesting interpretation of this somewhat obscure sentence is obtained by collating it with the conception of “the revolving eye of the Norse world mill-stone which was directly above Oergelmer and through which the waters flowed to and fro from the great fountain of the Universe mountains” (p. 472). The analogy is strengthened by the fact that the mountainous region in which Kyrênê was situated has always been noted for its fertility, the water, from the mountains enclosing its plains, settling in pools and lakes, affording a constant supply, during the summer months, to the Arabs who frequent it. The feature of Kyrênê, most renowned in antiquity, was its inexhaustible Fountain of Apollo, and travellers describe how, to this day, the Bedouin Arabs flock to it when their supply of water and herbage fails in the interior. Grote states that the same circumstance must have operated in ancient times to hold the nomadic Libyans in a sort of dependence upon Kyrênê (Grote, op. cit. vol. iv, p. 37).