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 se