“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.