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

DYNAMICS 51
world, also not essentially dependent upon
any particular sensations or upon any particular individual. Is such a world merely
but one huge fairy tale? But fairy tales are
fantastic and arbitrary: if in truth there
be such a world, it ought to submit itself
to an exact description, which determines
accurately its various parts and their mutual
relations. Now, to a large degree, this
scientific world does submit itself to this
test and allow its events to be explored
and predicted by the apparatus of abstract
mathematical ideas. It certainly seems that
here we have an inductive verification of
our initial assumption. It must be admitted
that no inductive proof is conclusive; but
if the whole idea of a world which has existence independently of our particular perceptions of it be erroneous, it requires careful
explanation why the attempt to characterize
it, in terms of that mathematical remnant
of our ideas which would apply to it, should
issue in such a remarkable success.
It would take us too far afield to enter into
a detailed explanation of the other laws of
motion. The remainder of this chapter must
be devoted to the explanation of remarkable
ideas which are fundamental, both to mathematical physics and to pure mathematics:
these are the ideas of vector quantities and
the parallelogram law for vector addition.