396 DOC.
42 SPECIAL AND GENERAL RELATIVITY
Relativity
and
the
Problem
of
Space
157
analytical geometry.
The
idea
of
space,
however, is suggested
by
certain
primitive experiences. Suppose
that
a
box has
been
constructed.
Objects
can
be
arranged
in
a
certain
way
inside
the
box,
so
that
it becomes
full.
The
possibility
of
such
ar-
rangements
is
a
property
of
the material
object
"box,"
some-
thing
that
is
given
with
the
box,
the
"space
enclosed"
by
the
box.
This
is
something
which
is
different for different
boxes,
something
that
is
thought
quite
naturally at
being indepen-
dent of
whether
or
not, at
any
moment,
there
are any objects
at
all
in the
box.
When
there
are
no objects
in
the
box,
its
space appears to
be
"empty."
So
far,
our
concept
of
space
has
been
associated with
the
box.
It
turns
out, however,
that
the
storage possibilities
that
make
up
this
box-space
are
independent
of
the thickness
of
the
walls
of the
box.
Cannot this thickness be reduced
to zero,
without the
"space"
being
lost
as a
result?
The
naturalness
of
such
a
limiting process is
obvious,
and
now
there
remains
for
our
thought
the
space
without the
box,
a
self-evident
thing,
yet
it
appears to
be
so
unreal
if
we forget
the
origin
of
this
concept.
One
can
understand
that it
was repugnant
to
Des-
cartes to
consider
space as
independent
of material
objects,
a
thing
that
might
exist without
matter.1 (At
the
same
time,
this
does
not
prevent
him from
treating space
as a
fundamental
concept
in
his
analytical
geometry.)
The
drawing
of
attention
to
the
vacuum
in
a
mercury
barometer
has
certainly
disarmed
1
Kant's
attempt
to remove
the
embarrassment
by
denial of
the
objectivity
of
space can,
however, hardly
be taken
seriously.
The
possibilities
of
packing
inherent in the inside
space
of
a
box
are
objective
in the
same sense as
the box
itself,
and
as
the
objects
which
can
be
packed
inside
it.