346
DOCS.
355,
356
JUNE
1917
from
the
improbability
that
all
of
the
light rays
emitted
from
the
sun
intersect
one
another
again
at
the
antipodal
point.-In
this
elliptic
space, however,
there
are
no
negative
parallaxes.[11]
For
the
parallax is
n = a
cot
r/R
(better,
tan
n
=
sina/R
.cotr/R).
Also in
system
B
it would have to be assumed
that
r
1/2nrR.
In
this
system,
the
parallax
has
a
minimum
n0
= a/R.
The
establishment of
a
[lower]
limit
for
R
from
the
nonexistence of
negative
parallaxes is
thus
also eliminated.
With
cordial
regards, yours,
W. de Sitter.
356. To
Willem
de
Sitter
[Berlin,]
22
June
1917
Dear de
Sitter,
Your detailed
letter
pleased
me
very
much because
I
see
how
deeply you
have
been
thinking
about the
problem
of
mutual
interest
to
us.
I
have
just
a
few
comments to add.[1]
1)
My opinion
is
not
that the
sphere
must
approximate
the
world
well.
The
system
could
actually
be
quite irregularly curved,
also
on a
large scale,
that
is,
it
could
relate
to
the
spherical
world
like
a
potato’s
surface
to
a
sphere’s
surface.
Large
parts
of it could
then
really
be void
(without
matter).
The
sphere
only
serves
to
show,
through
an
idealization,
that
a
spatially
closed
(finite)
system
is
possible.[2]
If,
therefore,
coordinated
Milky Way systems really
do
exist
(a
view
which,
as
far
as
I
know,
not all astronomers
share),
there
does
not
have
to
be
matter
in
the
space
between
them, by any
means.
It
is not
necessary
to
assume
that
matter
in
any
form
other than that
of the
stars
exists.
However,
it
is
necessary
to
assume
that the
world
is
considerably bigger
than the
Milky
Way’s
104
light-y[ears].
2)
I
do
not
quite
know
what
you
mean
by finitude
and
boundedness;
I
think
of
it
as
follows.
Between two
points,
A
and
B,
there
are
space-like
geodetic
paths;
the
length of
the shortest
of these
paths is
lAB.
Now,
if
a
number
G
exists such
that
for
any
choice of A
and
B
lAB
G,
I call
the
world
(spatially)
finite.
It
is
probably always possible
to
regard
such
a
continuum
as
closed
in
my
sense.
The
naturally
measured volume
is
then
finite
(strictly speaking,
one can
only
talk about the
world
being
closed if it
is “static”).
3)
When
I
say
that
your
world has
a
preferred center,[3]
I
mean
that the
points
are
not
of
equal
value, apart
from in
their
coordinate
system
arrangement.