"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