The Theology of Arithmetic

...the ratio in the Triad Three compared to those before it; for two is greater than the one that precedes it—I mean the One the Monad—and this is according to the most fundamental ratio original: pythmenikotatēn; refers to the "root" or lowest-term ratio of the Greater; but four is less than the sum of three, two, and one 4 < 3+2+1 (6) according to the most fundamental ratio of the Lesser; and three is equal to two and one according to the inseparable Equality. Thus, in the Triad itself, as in a side a one-dimensional line, the "Greater" is fitted, while in its power original: dynamei; here meaning the square, or the two-dimensional plane, the "Lesser" is fitted.

Deficiency and Excess are also called Matter, which they also call the "Indefinite Dyad" a fundamental Platonic and Pythagorean concept representing the principle of multiplicity, flux, and the "unlimited" which must be shaped by the Monad synonymously with this number, because it is deprived of Form, Species, and any kind of Definition,

13 at least as far as its own nature is concerned; yet it is of such a nature as to be defined and bounded by Reason original: logos and Art.

[It is said] that the Dyad appears formless original: aschēmatistos, since while the infinite variety of polygons proceeds in actual practice from the Triangle and the Triad, and everything exists potentially all at once within the Monad, no rectilinear figure a shape made of straight lines is ever composed of only two lines or two angles. Therefore, in its own nature alone, the Dyad is Indefinite and Formless.

It also appears to be Infinite, since it is "the other" the principle of difference, and this, beginning from the one, falls away into infinity. It can also be called the "provider of the infinite," because the first manifestation of length the one-dimensional line is in the Dyad, as if originating from the point of the Monad; and this length is both divided and increased unto infinity. Furthermore, the nature of Inequality, which is destined to proceed unto infinity, begins from the Dyad, being paired in opposition to the Monad; its first division is into the Greater and the Lesser.

The Dyad is not considered a number, nor is it even, because it does not exist in actuality In Pythagorean theory, 1 and 2 are the principles of number, rather than numbers themselves. Certainly, every even number can be divided into both equal and unequal parts; but the Dyad alone cannot be divided into unequal parts. Even when divided into equal parts, it is unclear which "kind" those parts will belong to since 2 divides into 1+1, and the Monad was seen as both odd and even or as the father of all kinds, as it is a kind of source-principle.

They say that the Dyad is also called Erato the Muse of lyric poetry and desire; for by drawing to itself the approach of the Monad as if it were Form, through Love original: erota; a pun on the name Erato, it generates the remaining results, beginning from the Triad and the Tetrad. It was named...