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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 I tell 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. Well, take the ducat of the rich man and the ducat of the poor man to a money-changer and they are rated exactly equal, but to the mind of the thinker one is of greater importance than the other; one represents a month of comfort, the other an ephemeral caprice. Two and two, therefore, only make four through a false conception.

"Again: fraction does not exist in Nature, where what you call a fragment is a finished whole. Does it not often happen (have you not many proofs of it?) that the hundredth part of a substance is stronger than what you term the whole of it? If fraction does not exist in the Natural Order, still less shall we find it in the Moral Order, where ideas and sentiments may be as varied as the species of the Vegetable kingdom and yet be always whole. The theory of fractions is therefore another signal instance of the servility of your mind.

"Thus Number, with its infinite minuteness and its infinite expansion, is a power whose weakest side is known to you, but whose real import escapes your perception. You have built yourself a hut in the Infinite of numbers, you have adorned it with hieroglyphics scientifically arranged and painted, and you cry out, 'All is here!'

"Let us pass from pure, unmingled Number to corporate Number. Your geometry establishes that a straight line is the shortest way from one point to another, but your astronomy proves that God has proceeded by curves. Here, then, we find two truths equally proved by the same science,--one by the testimony of your senses reinforced by the telescope, the other by the testimony of your mind; and yet the one contradicts the other. Man, liable to err, affirms one, and the Maker of the worlds, whom, so far, you have not detected in error, contradicts it. Who shall decide between rectalinear and curvilinear geometry? between the theory of the straight line and that of the curve? If, in His vast work, the mysterious Artificer, who knows how to reach His ends miraculously fast, never employs a straight line except to cut off an angle and so obtain a curve, neither does man himself always rely upon it. The bullet which he aims direct proceeds by a curve, and when you wish to strike a certain point in space, you impel your bombshell along its cruel parabola. None of your men of science have drawn from this fact the simple deduction that the Curve is the law of the material worlds and the Straight line that of the Spiritual worlds; one is the theory of finite creations, the other the theory of the infinite. Man, who alone in the world has a knowledge of the Infinite, can alone know the straight line; he alone has the sense of verticality placed in a special organ. A fondness for the creations of the curve would seem to be in certain men an indication of the impurity of their nature still conjoined to the material substances which engender us; and the love of great souls for the straight line seems to show in them an intuition of heaven. Between these two lines there is a gulf fixed like that between the finite and the infinite, between matter and spirit, between man and the idea, between motion and the object moved, between the creature and God. Ask Love the Divine to grant you his wings and you can cross that gulf. Beyond it begins the revelation of the Word.

"No part of those things which you call material is without its own meaning; lines are the boundaries of solid parts and imply a force of action which you suppress in your formulas,--thus rendering those formulas false in relation to substances taken as a whole. Hence the constant destruction of the monuments of human labor, which you supply, unknown to yourselves, with acting properties. Nature has substances; your science combines only their appearances. At every step Nature gives the lie to all your laws. Can you find a single one that is not disproved by a fact? Your Static laws are at the mercy of a thousand accidents; a fluid can overthrow a solid mountain and prove that the heaviest substances may be lifted by one that is imponderable.

"Your laws on Acoustics and Optics are defied by the sounds which you hear within yourselves in sleep, and by the light of an electric sun whose rays often overcome you. You know no more how light makes itself seen within you, than you know the simple and natural process which changes it on the throats of tropic birds to rubies, sapphires, emeralds, and opals, or keeps it gray and brown on the breasts of the same birds under the cloudy skies of Europe, or whitens it here in the bosom of our polar Nature. You know not how to decide whether color is a faculty with which all substances are endowed, or an effect produced by an effluence of light. You admit the saltness of the sea without being able to prove that the water is salt at its greatest depth. You recognize the existence of various substances which span what you think to be the void,--substances which are not tangible under any of the forms assumed by Matter, although they put themselves in harmony with Matter in spite of every obstacle.

"All this being so, you believe in the results of Chemistry, although that science still knows no way of gauging the changes produced by the flux and reflux of substances which come and go across your crystals and your instruments on the impalpable filaments of heat or light conducted and projected by the affinities of metal or vitrified flint. You obtain none but dead substances, from which you have driven the unknown force that holds in check the decomposition of all things here below, and of which cohesion, attraction, vibration, and polarity are but phenomena. Life is the thought of substances; bodies are only the means of fixing life and holding it to its way. If bodies were beings living of themselves they would be Cause itself, and could not die.

"When a man discovers the results of the general movement, which is shared by all creations according to their faculty of absorption, you proclaim him mighty in science, as though genius consisted in explaining a thing that is! Genius ought to cast its eyes beyond effects. Your men of science would laugh if you said to them: 'There exist such positive relations between two human beings, one of whom may be here, and the other in Java, that they can at the same instant feel the same sensation, and be conscious of so doing; they can question each other and reply without mistake'; and yet there are mineral substances which exhibit sympathies as far
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