An introduction to mathematics, by A. N. Whitehead.

248 INTRODUCTION TO MATHEMATICS
What then are the requisites which such
a rule ought to have? In the first place it
should lead to the assignment of nearly equal
durations to events which common sense
judges to possess equal durations. A rule
which made days of violently different
lengths, and which made the speeds of apparently similar operations vary utterly out
of proportion to the apparent minuteness of
their differences, would never do. Hence the
first requisite is general agreement with common sense. But this is not sufficient absolutely to determine the rule, for common
sense is a rough observer and very easily
satisfied. The next requisite is that minute
adjustments of the rule should be so made as
to allow of the simplest possible statements
of the laws of nature. For example, astronomers tell us that the earth's rotation is slowing down, so that each day gains in length by
some inconceivably minute fraction of a
second. Their only reason for their assertion
(as stated more fully in the discussion of
periodicity) is that without it they would
have to abandon the Newtonian laws of
motion. In order to keep the laws of motion
simple, they alter the measure of time. This
is a perfectly legitimate procedure so long as
it is thoroughly understood.
What has been said above about the abstract nature of the mathematical properties