suffice to show how realistic are the mathematical concepts which we
have here tried to build up.

*

When we set out earlier in this book (Chapter VIII) to discover the
source of Galileo's intuition, by which he had been enabled to find the
theorem of the parallelogram of forces, we were led to certain
experiences through which all men go in early childhood by erecting
their body and learning to walk. We were thereby led to realize that
man's general capacity for thinking mathematically is the outcome of
early experiences of this kind. It is evident that geometrical concepts
arising in man's mind in this way must be those of Euclidean geometry.
For they are acquired by the will's struggle with gravity. The dynamic
law discovered in this way by Galileo was therefore bound to apply to
the behaviour of mechanical forces - that is, of forces acting from
points outward.

In a similar way we can now seek to find the source of our capacity to
form polar-Euclidean concepts. As we were formerly led to experiences
of man's early life on earth, so we are now led to his embryonic and
even pre-embryonic existence.

Before man's supersensible part enters into a physical body there is no
means of conveying to it experiences other than those of levity, and
this condition prevails right through embryonic development. For while
the body floats in the mother's foetal fluid it is virtually exempt
from the influence of the earth's field of gravity.

History has given us a source of information from these early periods