have just set forth, because without it I should have been unable
to formulate the theory of relativity. Without it the following
reflection would have been impossible:--In a system of reference
rotating relatively to an inert system, the laws of disposition of
rigid bodies do not correspond to the rules of Euclidean geometry
on account of the Lorentz contraction; thus if we admit non-inert
systems we must abandon Euclidean geometry. The decisive step in
the transition to general co-variant equations would certainly not
have been taken if the above interpretation had not served as a
stepping-stone. If we deny the relation between the body of axiomatic
Euclidean geometry and the practically-rigid body of reality,
we readily arrive at the following view, which was entertained by
that acute and profound thinker, H. Poincare:--Euclidean geometry
is distinguished above all other imaginable axiomatic geometries
by its simplicity. Now since axiomatic geometry by itself contains
no assertions as to the reality which can be experienced, but can
do so only in combination with physical laws, it should be possible
and reasonable--whatever may be the nature of reality--to retain
Euclidean geometry. For if contradictions between theory and
experience manifest themselves, we should rather decide to change
physical laws than to change axiomatic Euclidean geometry. If we
deny the relation between the practically-rigid body and geometry,
we shall indeed not easily free ourselves from the convention
that Euclidean geometry is to be retained as the simplest. Why
is the equivalence of the practically-rigid body and the body of
geometry--which suggests itself so readily--denied by Poincare and
other investigators? Simply because under closer inspection the
real solid bodies in nature are not rigid, because their geometrical
behaviour, that is, their possibilities of relative disposition,
depend upon temperature, external forces, etc. Thus the original,