Mathematical_Recreations-Kraitchik-2e

138 Mathematical Recreations
a to an amount b, I have gained an advantage which can be
measured by
fbdx = log. b - log. a = log. ~.
Ja x
a
No account was ever settled in such a manner. But thanks
to the approbation of eminent persons, the theory of moral
expectation brought no less fame to Daniel Bernoulli than
did his admirable works on physics.
The eloquent Buffon increased the importance attached to
Bernoulli's idea. The miser, Buffon said, is like the mathematician.
Both value money by its numerical quantity.
The reasonable man disregards both its mass and numerical
measure. He sees only the advantages that he can derive
from it. His reasoning is better than the mathematician's.
The nickel that the poor man puts aside for his living expenses
or the nickel that completes the banker's million
have the same value for the miser and for the mathematician.
The miser will grab it with equal pleasure, the mathematician
will count it with the same unit. But the reasonable man
will count the nickel of the poor man as a dollar, and the
dollar of the banker as a nickel.
Quetelet adds: "Thus a thousand dollars possesses the
same importance for a man who has only two thousand, as
500 thousand has for the owner of a million."
Bertrand comments as follows: "If one seek to escape the
reproach of avarice by this lofty disdain of all fortune beyond
one's needs, he merits a still heavier charge. A man who
possesses one million and gains a second will change his manner
of life very little, if at all. Is this the only fruit of riches
for one who is not miserly? If Buffon's reasonable man is not
a cynical egotist he can find some use other than hoarding
for those millions we suppose him to possess. We could double
his fortune, multiply it by ten, and double it again, without
diminishing the constant increase in the good that he can