"Thus, in the order of nature, two and two can never really make four, since the units would have to be exactly equal; and you know that it is impossible to find two leaves alike on one tree, or two specimens alike of the same species of tree. This axiom of arithmetic then, which is false as regards visible nature, is no less false in the invisible nature of your abstractions, where there is the same dissimilarity in your ideas which are derived from the objects of the visible world, only extended in their relations; in fact, differences are even more strongly marked there than elsewhere. Everything there being modified by the temperament, the strength, the manners, and the habits of individuals, who are never alike, the most trifling matters are representative of personal character.
"If man has ever succeeded in creating an unit, it was, no doubt, by assigning equal weight and value to certain pieces of gold. Well, add a rich man's ducat to a poor man's, and tell yourself that to the public treasury these are equal quantities; but in the eyes of a thoughtful man, one, morally speaking, is unquestionably greater than the other; one represents a month's happiness, the other the most transient caprice. Two and two only make four in the sense of a false and monstrous abstraction.
"A fraction, again, has no existence in nature, since what you call a part is a thing complete in itself; and does it not often happen—and have we not proof of the fact—that the hundredth part of some substance may be stronger than what you call the whole? And if a fraction has no existence in the natural world, far less does it exist in the moral world, where ideas and feelings may be as various as the species of the vegetable kingdom, but are always a whole. The theory of fractions, then, is another concession of the mind. Number, with its 'infinitely small' and its 'infinite total,' is a power of which a small part only is known to you, while its extent evades you. You have built a little cottage in the infinitude of number; you have adorned it with hieroglyphics very learnedly designed and painted; and you have said, 'Everything is here!'
"From abstract number we will pass on to number as applied to solids. Your geometry states it as an axiom that a straight line is the shortest way from one point to another; and astronomy shows you that God has given motion only in curves. Here, then, in the same science, are two facts equally well proved—one by the evidence of your senses, aided by the telescope; the other by the testimony of your mind; but one contradicts the other. Man, who is liable to error, asserts one, and the Maker of the worlds—whom you have never found in error—contradicts it. Who can decide between rectilinear and curvilinear geometry?—between the theory of straight lines and the theory of curved lines? If, in His work, the mysterious Maker, who attains His ends with miraculous directness, only makes use of the straight line to divide it at a right angle and obtain a curve, man himself cannot rely on it: the bullet a man wishes to send in a straight line follows a curve, and when you want to hit a point in space with certainty you propel the ball on its cruel parabola. Not one of your learned men has arrived at the simple induction that the curved line is that of the material world, and the straight line that of the spiritual world; that one is the theory of finite creation, and the other the theory of the infinite. Man alone—he alone here on earth having any consciousness of the infinite—can know the straight line; he alone, in a special organ, has the sense of the vertical. May not the predilection for curved lines in some men be an indication of the impurity of their nature, still too closely allied to the material substances which engender us? and may not the love for straight lines, seen in lofty minds, be in them a presentiment of heaven? Between these two lines lies a gulf as wide as between the Finite and the Infinite, between Matter and Spirit, between Man and the Idea, between Motion and the Thing moved, between the Creature and God. Borrow the wings of Divine Love and you may cross that gulf. Beyond it the revelation of the Word begins!
"The things you call material are nowhere devoid of thickness; lines are the edges of solids having a power of action which you ignore in your theorems, and that makes them false in relation to bodies regarded as a whole; hence the constant destruction of human works, to which you have unwittingly given active properties. Nature knows nothing but solid bodies; your science deals only with combinations of surfaces. And so nature constantly gives the lie to all your laws: can you name one to which no fact makes an exception? The laws of statics are contradicted by a thousand incidents in physics; a fluid overthrows the most stupendous mountains, and so proves that the heaviest substances may be upheaved by imponderable agents. Your laws of acoustics and optics are nullified by the sounds you hear in your brain during sleep, and by the light of an electric flash, of which the rays are often overpowering. You do not know how light is brought to your intelligence, any more than you know the simple and natural process by which it is changed to ruby, sapphire, opal, and emerald on the neck of an Indian bird, while it lies dim and gray on the same bird under the misty sky of Europe, nor why it beams perpetually white here in the heart of the polar regions. You cannot tell whether color is a faculty with which bodies are endowed, or an effect produced by the diffusion of light.
"You believe the whole sea to be salt without having ascertained that it is so in its deepest places.
"You recognize the existence of various substances which traverse what you call the Void: substances intangible under any known form assumed by matter, and which meet and combine with it in spite of every obstacle. That being the case, you believe in the results obtained by chemistry, though as yet it knows no method of estimating the changes produced by the currents to and fro of those substances as they pass through your crystals and your instruments on the inappreciable waves of heat or of light, conducted or repelled by the affinities of metals or vitrified flint. You obtain no substances but what are dead, out of which you have driven the unknown force which resists decomposition in all earthly things, the force of which attraction, undulation, cohesion, and polarity are manifestations.
"Life is the mind of body; bodies are but a mode of detaining it, of delaying it in its transit; if bodies were themselves living things, they would be a cause; they would not die. When a man establishes the results of the motion of which every form of creation has its share in proportion to its power of absorbing it, you call him a Learned Man, as though genius consisted in explaining what exists. Genius should lift its eyes above effects. All your learned men would laugh if you should say to them, 'There is a certain connecting relation between two beings, such as that if one of them were here and the other in Java, they might feel the same sensation at the same instant, and be aware of the fact, and question and answer each other without a mistake.' And yet there are some mineral substances which exhibit sympathies as far reaching as that of which I speak. You believe in the power of electricity when it is fixed on the lodestone, but you deny it as emanating from the soul. According to you, the moon, whose influence over the tides seems to you proven, has none over the winds, over vegetation, or over men; it can move the sea and eat into glass, but it cannot affect the sick; it has undoubted effects on one-half of the human race; none on the other half. These are your most precious convictions.
"We may go further: You believe in physics; but your physics are based, like the Catholic religion, on an act of faith. Do they not recognize an external force apart from bodies to which it imparts movement? You see its effects, but what is it? Where is it? What is its essence, its life? Has it any limits?——And you deny God!
"Thus most of your scientific axioms, though true in relation to man, are false in relation to the Whole. Science is one, and you have divided it. To know the true sense of the laws of phenomena, would it not be necessary to know the correlations existing between the phenomena and the laws of the whole? There is in all things an appearance, a presentment, which strikes your sense; behind this presentment there is a soul moving—the body, and the faculty. Where are the relations which hold things together studied or taught? Nowhere. Have you, then, no absolute finality? Your best ascertained theses rest on an analysis of the forms of matter, while the spirit is constantly neglected.