When do centuries end?—at the termination of years marked 99 (as commo — 1 (number)

"The observable efforts of Greek philosophy were generally directed toward the resolution of multiplicity into unity. Empedocles is reported to have said, "the universe is alternately in motion and at rest—in motion when love is making one out of many, or strife is making many out of one, and at rest in the intermediate periods of time." Even here, where two states are posited, the unifying impulse is obviously felt to be the more desirable. Hence it is very natural that the Pythagoreans should have considered the monad as the first principle from which the other numbers flow. Itself not a number, it is an essence rather than a being and is sometimes, like the duad, designated as a potential number, since the point, though not a plane figure, can originate plane figures. As first originator, the monad is good and God. It is both odd and even, male and female... It is the basis and creator of number... In short, it is always taken to represent all that is good and desirable and essential, indivisible and uncreated."

"A theory of the world was gradually developed on the fundamental conception of the unity of all things. Beneath the changes which seem to occur... there must be... some unchanging and unchangeable essence. A hidden thread of unity must run through all phenomena. To find that unchangeable essence, to discover that secret binding unity, became the quest of alchemy, the art which rested on the conception of the one and the all."

"Nicomachus gives three definitions of number. ...The third stream of quantity composed of units Philoponus explains as another attempt to distinguish the particular kind of quantum treated in Arithmetic. The Unit was conceived either mystically as an Idea whose "essence" passes in some way into concrete individuals and even into the Ideas to organize them, or spatially and temporally as the boundary of individuals. The former conception gave rise to fantastic speculations on the cosmic meaning of number, examples of which Nicomachus has... given us; the latter gave rise to the s..."

"But let us return to unity itself, asserting that it always remains the same, though all things flow from it as their inexhaustible fountain. In numbers, indeed, while unity abides in the simplicitly of its essence, number producing another is generated according to this abiding one. But the one which is above beings, much more abides in ineffable station. But while it abides, another does not produce beings, according to the nature of one: for it is sufficient of itself to the generation of beings. But as in numbers the form of the first monad is preserved in all numbers, in the first and second degree while each of the following numbers do not equally participate of unity; so in the order of things, every nature subordinate to the first, contains something of the first, as it were his vestige or form in its essence. And in numbers, indeed, the participation of unity produces their quantity. But here the vestige of one gives essence to all the series of divine numbers, so that being itself, is as were the footstep of ineffable unity."

"Those numbers... independent of the particular things which happen to undergo counting—of what are these... ? To pose this question means to raise the problem of "scientific" arithmetic or logistic. ...we are no longer interested in the requirements of daily life ...now our concern is rather with understanding the very possibility of this activity, with understanding... that knowing is involved and that there must... be a corresponding being which possesses that permanence of condition which first makes it capable of being "known." But the souls turning away from the things of daily life, the changing of the direction... the "conversion" and "turning about"... leads to a further question... What is required is an object which has a purely noetic character and which exhibits at the same time... the countable... This requirement is exactly fulfilled by the "pure" units, which are "nonsensual," accessible only to the understanding, indistinguishable from one another, and resistant to all participation. The "scientific" arithmetician and logistician deals with numbers of pure monads. And... Plato stresses emphatically that there is "no mean difference" between these and the ordinary numbers. ...Only a careful consideration of the fact... forces us into the further supposition that there must indeed be a special "nonsensual" material to which these numbers refer. The immense propaedeutic importance... within Platonic doctrine is immediately clear, for is not a continual effort made in this doctrine to exhibit as the true object of knowing that which is not accessible to the senses? Here we have indeed a "learning matter"... "capable of hauling [us] toward being". It forces the soul to study, by thought alone, the truth as it shows itself by itself. ...ability to count and to calculate presupposes the existence of "nonsensual" units. Thus an unlimited field of "pure" units presents itself to the view of the "scientific" arithemetician and logistician."

"Since each number is with respect to its own kind one and without parts but with respect to its own material, as it were, divisible into parts, though not with respect to all of the material either; but rather what is ultimate [in it, i.e., the unit] is without parts even in the material, and in this ultimate thing [counting or calculation and, above all, partitioning] comes to a stop."