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 ****** 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 ****** 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.