"You believe, for instance, in Number,--a base on which you have built the edifice of sciences which you call 'exact.' Without Number, what would become of mathematics? Well, what mysterious being endowed with the faculty of living forever could utter, and what language would be compact to word the Number which contains the infinite numbers whose existence is revealed to you by thought? Ask it of the loftiest human genius; he might ponder it for a thousand years and what would be his answer? You know neither where Number begins, nor where it pauses, nor where it ends.Here you call it Time, there you call it Space.Nothing exists except by Number.Without it, all would be one and the same substance; for Number alone differentiates and qualifies substance.
Number is to your Spirit what it is to Matter, an incomprehensible agent.Will you make a Deity of it? Is it a being? Is it a breath emanating from God to organize the material universe where nothing obtains form except by the Divinity which is an effect of Number? The least as well as the greatest of creations are distinguishable from each other by quantities, qualities, dimensions, forces,--all attributes created by Number.The infinitude of Numbers is a fact proved to your soul, but of which no material proof can be given.The mathematician himself tells you that the infinite of numbers exists, but cannot be proved.
"God, dear pastor, is a Number endowed with motion,--felt, but not seen, the Believer will tell you.Like the Unit, He begins Number, with which He has nothing in common.The existence of Number depends on the Unit, which without being a number engenders Number.God, dear pastor is a glorious Unit who has nothing in common with His creations but who, nevertheless, engenders them.Will you not therefore agree with me that you are just as ignorant of where Number begins and ends as you are of where created Eternity begins and ends?
"Why, then, if you believe in Number, do you deny God? Is not Creation interposed between the Infinite of unorganized substances and the Infinite of the divine spheres, just as the Unit stands between the Cipher of the fractions you have lately named Decimals, and the Infinite of Numbers which you call Wholes? Man alone on earth comprehends Number, that first step of the peristyle which leads to God, and yet his reason stumbles on it! What! you can neither measure nor grasp the first abstraction which God delivers to you, and yet you try to subject His ends to your own tape-line! Suppose that I plunge you into the abyss of Motion, the force that organizes Number.If Itell you that the Universe is naught else than Number and Motion, you would see at once that we speak two different languages.I understand them both; you understand neither.
"Suppose I add that Motion and Number are engendered by the Word, namely the supreme Reason of Seers and Prophets who in the olden time heard the Breath of God beneath which Saul fell to the earth.That Word, you scoff at it, you men, although you well know that all visible works, societies, monuments, deeds, passions, proceed from the breath of your own feeble word, and that without that word you would resemble the African gorilla, the nearest approach to man, the Negro.
You believe firmly in Number and in Motion, a force and a result both inexplicable, incomprehensible, to the existence of which I may apply the logical dilemma which, as we have seen, prevents you from believing in God.Powerful reasoner that you are, you do not need that I should prove to you that the Infinite must everywhere be like unto Itself, and that, necessarily, it is One.God alone is Infinite, for surely there cannot be two Infinities, two Ones.If, to make use of human terms, anything demonstrated to you here below seems to you infinite, be sure that within it you will find some one aspect of God.
But to continue.
"You have appropriated to yourself a place in the Infinite of Number;you have fitted it to your own proportions by creating (if indeed you did create) arithmetic, the basis on which all things rest, even your societies.Just as Number--the only thing in which your self-styled atheists believe--organized physical creations, so arithmetic, in the employ of Number, organized the moral world.This numeration must be absolute, like all else that is true in itself; but it is purely relative, it does not exist absolutely, and no proof can be given of its reality.In the first place, though Numeration is able to take account of organized substances, it is powerless in relation to unorganized forces, the ones being finite and the others infinite.The man who can conceive the Infinite by his intelligence cannot deal with it in its entirety; if he could, he would be God.Your Numeration, applying to things finite and not to the Infinite, is therefore true in relation to the details which you are able to perceive, and false in relation to the Whole, which you are unable to perceive.Though Nature is like unto herself in the organizing force or in her principles which are infinite, she is not so in her finite effects.
Thus you will never find in Nature two objects identically alike.In the Natural Order two and two never make four; to do so, four exactly similar units must be had, and you know how impossible it is to find two leaves alike on the same tree, or two trees alike of the same species.This axiom of your numeration, false in visible nature, is equally false in the invisible universe of your abstractions, where the same variance takes place in your ideas, which are the things of the visible world extended by means of their relations; so that the variations here are even more marked than elsewhere.In fact, all being relative to the temperament, strength, habits, and customs of individuals, who never resemble each other, the smallest objects take the color of personal feelings.For instance, man has been able to create units and to give an equal weight and value to bits of gold.