212 DOC. 52 GEOMETRY AND EXPERIENCE
236
CONTRIBUTIONS TO
SCIENCE
assertions
as
to
the
reality
which
can
be
experienced,
but
can
do
so
only
in combination with
physical
laws,
it should
be
pos-
sible
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 Eucli-
dean
geometry.
If
we
reject
the relation between the
practi-
cally-rigid
body
and
geometry,
we
shall indeed
not easily
free
ourselves from the convention that
Euclidean
geometry
is to
be
retained
as
the
simplest.
[14]
Why
is
the
equivalence
of the
practically-rigid
body
and the
body
of
geometry-which
suggests
itself
so
readily-rejected
by
Poincaré and other
investigators? Simply
because
under
closer
inspection
the real solid bodies in
nature
are
not rigid,
because their
geometrical
behavior,
that
is,
their
possibilities
of relative
disposition,
depend upon temperature,
external
forces,
etc.
Thus the
original,
immediate
relation
between
geometry
and
physical
reality
appears
destroyed,
and
we
feel
impelled
toward the
following more general
view,
which char-
acterizes Poincaré’s
standpoint.
Geometry
(G)
predicates
noth-
ing
about the behavior of real
things,
but
only geometry to-
gether
with the
totality
(P)
of
physical
laws
can
do
so.
Using
symbols,
we
may
say
that
only
the
sum
of
(G)
+
(P)
is subject
to
experimental
verification.
Thus
(G)
may
be chosen
arbitrarily,
[p.
127]
and also
parts
of
(P);
all these
laws
are
conventions. All
that
is
necessary to
avoid
contradictions
is to
choose the
remainder of
(P) so
that
(G)
and
the whole of
(P) are
together
in accord with
experience. Envisaged
in
this
way,
axiomatic
geometry
and the
part
of
natural law which has been
given a
conventional
status
appear
as epistemologically
equivalent.
Sub
specie
aeterni
Poincaré,
in
my
opinion,
is
right.
The idea
of the
measuring-rod
and
the
idea of the clock
coordinated with
it in the
theory
of
relativity
do
not
find
their
exact
correspond-
ence
in the real world. It
is also
clear
that
the solid
body
and
the
clock do
not
in
the
conceptual
edifice of
physics play
the
part
of
irreducible
elements,
but
that
of
composite
structures,
which
must not
play
any independent part
in theoretical
[15]