DOCS.

321,

322

APRIL

1917 313

It

is

obvious

that

“my”

world

is

finite

like

yours;[8]

I have forced

it

into

a

Carte-

sian Euclidean coordinate

system merely

to show

that the

finiteness in

natural

measure

is

equivalent

to

the

requirement

of

the

guv’s becoming

zero

at

Euclidean

infinity.

As

concerns

the

singularity,

I

have

nothing

here,

no

books, etc.,

thus

I

cannot

do

the

calculations.

But

I

think that it

is just apparent

and

that

it stems from

my

description

of

my

actually

hyperbolic

world

as

spherical.[9]

Thus

the

hyperboloids’

infinity

is

dragged

into the finite

realm,

where

it

naturally

must

appear as a

singularity.

If

the

guv's

on

the

hyperboloid are

finite at

infinity,

the

g'uv's

must

necessarily

become infinite

there,

when

this

infinite

part of

the

hyperboloid

is

mapped

onto

a

finite

region

of

a

flat

space.[10]

I cannot

agree

with

the

second

part

of

your

letter.

I

must

emphatically

contest

your

assumption

that the

world

is

mechanically quasi-stationary.[11]

We

only

have

a

snapshot

of

the

worl,

and

we

cannot and must not conclude from

the

fact

that

we

do not

see

any large changes

on

this

photograph

that

everything

will

always

remain

as

at

that instant

when

the

picture

was

taken.

I

believe

that

it

is

probably

certain

that

even

the

Milky Way

is

not

a

stable

system.

Is

the

entire universe

then

likely

to

be stable? The

distribution

of

matter

in

the

universe

is

extremely inhomogeneous

[I

mean

of

the

stars, not

your

“world

matter”],

and it cannot be

substituted,

even

in

rough

approximation, by

a

distribution

of constant

density.

The

assumption you

tacitly

make

that the

mean

stellar

density

is

the

same

throughout

the

universe[12]

[naturally,

for vast

spaces

of,

e.g.,

(100,000 light-years)3]

has

no

justification whatsoever,

and

all

our

observations

speak against

it. I do not have

the data

here to do

anything

other

than

express my

conviction;

I do not intend to

try

to

prove

it

today.

With

cordial

greetings, yours truly,

W. de Sitter.

322. To Hendrik A. Lorentz

Berlin, 3 April 1917

Dear

Colleague,

Your

warm

words[1]

were

most

comforting

to

me.

In

you,

nature

was

seized

by

the

rare

impulse

of

combining

a

keen mind with

warm

sentiment. If

only

this

were more

often

the

case;

the

public

at

large

would be

considerably

better

off! My

condition

is

probably

not connected

appreciably

to

work;

it

is probably

attributable

to

a

constitutional

flaw.[2]

I

have

not

been

working

much

at

all,

and

that under

ideal

external

circumstances.