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Updated: May 6, 2025
By the Pythagoreans and by the ancient Egyptians sex was attributed to numbers, odd numbers being conceived of as masculine or generating, and even numbers as feminine or parturitive, on account of their infinite divisibility. Harmonious combinations were those involving the marriage of a masculine and a feminine an odd and an even number.
And since in any bulk of matter our thoughts can never arrive at the utmost divisibility, therefore there is an apparent infinity to us also in that, which has the infinity also of number; but with this difference, that, in the former considerations of the infinity of space and duration, we only use addition of numbers; whereas this is like the division of an unit into its fractions, wherein the mind also can proceed in infinitum, as well as in the former additions; it being indeed but the addition still of new numbers: though in the addition of the one, we can have no more the POSITIVE idea of a space infinitely great, than, in the division of the other, we can have the positive idea of a body infinitely little; our idea of infinity being, as I may say, a growing or fugitive idea, still in a boundless progression, that can stop nowhere.
Regarded as One, She is the Fourth, making possible the activity of the Three, the Field of Their operations by virtue of Her infinite divisibility, at once the "Handmaid of the Lord," and also His Mother, yielding of Her substance to form His Body, the universe, when overshadowed by His power.
Of course it is unthinkable that indivisible particles of matter can occupy space and have dimensions. But science goes upon this hypothesis, and the hypothesis proves itself. After we have reached the point of the utmost divisibility of matter in the atom, we are called upon to go still further and divide the indivisible.
What remains of smallness is as far from his thoughts as when he first began; and therefore he never comes at all to have a clear and positive idea of that smallness which is consequent to infinite divisibility. What is positive, what negative, in our Idea of Infinite.
He made it his business to champion the doctrine of his master by showing that those who refused to accept it were obliged to give their assent to views which were at least as repugnant to common sense, and in this way he incidentally did much for mathematics and philosophy by raising the difficulties of infinite divisibility and continuity in an acute form.
Could the mind, as in number, come to so small a part of extension or duration as excluded divisibility, THAT would be, as it were, the indivisible unit or idea; by repetition of which, it would make its more enlarged ideas of extension and duration.
A reasonable enough conclusion on the surface, considering that you might have millions of atoms of iron in one corner of your eye and not know it. But why should the atom be incapable of further division? If it is any size at all it can be thought of as split. Where does the divisibility of matter end, if anywhere? What is there SOLID about iron?
Thus one appearance may represent many things, and to this process there seems no end. Hence in the limit, when we approach indefinitely near to the thing there will be an indefinite number of units of matter corresponding to what, at a finite distance, is only one appearance. This is how infinite divisibility arises. The whole causal efficacy of a thing resides in its matter.
Yahi-Bahi, on appeal, decided that diamonds, though less pleasing to Buddha than rubies, possessed the secondary Hindu virtues of divisibility, movability, and disposability. On the evening in question the residence of Mrs. Rasselyer-Brown might have been observed at midnight wrapped in utter darkness. No lights were shown.
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