DOC. 42

SPECIAL AND GENERAL RELATIVITY 397

158

Relativity

the

last of the Cartesians. But it

is

not to

be denied

that,

even

at

this

primitive stage, something unsatisfactory clings to

the

concept

of

space,

or

to

space

thought

of

as an

independent

real

thing.

The

ways

in which bodies

can

be

packed

into

space

(e.g.

the

box)

are

the

subject

of three-dimensional Euclidean

geome-

try,

whose axiomatic

structure

readily

deceives

us

into

forget-

ting

that it

refers

to

realisable situations.

If

now

the

concept

of

space

is

formed

in

the

manner

out-

lined

above,

and

following

on

from

experience

about

the

"fill-

ing"

of the

box,

then

this

space

is

primarily

a

bounded

space.

This

limitation does

not appear to

be

essential, however, for

apparently

a

larger

box

can always

be introduced

to

enclose

the smaller

one.

In this

way space appears

as something un-

bounded.

I

shall

not

consider here how

the

concepts

of

the three-

dimensional and the Euclidean

nature

of

space

can

be traced

back

to relatively primitive experiences.

Rather, I

shall

con-

sider first

of

all from

other

points

of view the role

of

the

concept

of

space

in the

development

of

physical

thought.

When

a

smaller box

s

is

situated,

relatively

at

rest,

inside the

hollow

space

of

a

larger

box

S,

then the

hollow

space

of

s

is

a

part

of the hollow

space

of

S,

and

the

same

"space,"

which

contains both

of

them,

belongs

to

each

of

the

boxes. When

s

is

in motion with

respect

to

S,

however,

the

concept

is

less

simple.

One

is

then

inclined

to

think that

s

encloses

always

the

same space,

but

a

variable

part

of the

space

S.

It then

becomes

necessary

to

apportion

to

each box

its

particular