336 DOC. 42 SPECIAL AND GENERAL RELATIVITY
TWENTY-FOUR
Euclidean
and
Non-Euclidean
Continuum
The
surface
of
a
marble table
is
spread
out
in
front of
me.
I
can
get
from
any
one
point
on
this table
to
any
other
point by passing continuously
from
one point
to
a
"neighbouring" one,
and
repeating
this
process
a
(large)
number
of
times,
or,
in other
words, by going
from
point to
point
without
executing
"jumps."
I
am sure
the reader
will
appreciate
with sufficient clearness what
I
mean
here
by
"neighbouring"
and
by
"jumps"
(if
he
is
not too
pedantic).
We
express
this
property
of the surface
by describing
the
latter
as a
continuum.
Let
us now
imagine
that
a
large
number of little rods of
equal length
have
been
made,
their
lengths being
small
com-
pared
with the dimensions of the marble
slab.
When
I
say
they
are
of
equal length,
I
mean
that
one can
be laid
on
any
other
without the ends
overlapping.
We
next
lay
four of these little
[50]
rods
on
the marble slab
so
that
they
constitute
a quadrilateral
figure (a square),
the
diagonals
of which
are
equally
long.
To
ensure
the
equality
of
the
diagonals,
we
make
use
of
a
little
testing-rod.
To
this
square
we
add similar
ones,
each of
which
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