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From: desj@brahms.BERKELEY.EDU (David desJardins)
Newsgroups: net.space
Subject: Re: Clumping doesn't fix Olber's paradox
Message-ID: <12192@ucbvax.BERKELEY.EDU>
Date: Wed, 5-Mar-86 20:57:02 EST
Article-I.D.: ucbvax.12192
Posted: Wed Mar  5 20:57:02 1986
Date-Received: Sat, 8-Mar-86 18:34:52 EST
References: <8603041333.AA12454@s1-b.arpa> <12178@ucbvax.BERKELEY.EDU>
Sender: usenet@ucbvax.BERKELEY.EDU
Reply-To: desj@brahms.UUCP (David desJardins)
Organization: University of California, Berkeley
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Summary: I still think it does

JOSH@YKTVMH.BITNET ("Josh Knight") writes:
>>   Well, you may not think this, but you are wrong.  If the universe
>>is sufficiently "clumped" it is quite possible for most rays out from
>>the Earth to never intersect a star.
>
>What I meant by "not assuming that one is at the center of the universe"
>is that I assume the Universe is homogeneous and isotropic.  There is no
>preferred place and no preferred direction.  If any distribution
>satisfies this assumption, and extends infinitely in time and space,
>I believe there is no way to avoid the paradox.

   Well, "homogeneous" = "not clumped."  If the universe is clumped,
then it is not homogeneous.  This seems clear by definition.
   If the universe has an appropriate fractal dimension, it is possible
for it to be infinite in every direction and yet to have *no* point
from which all rays of sight terminate on a star.  You essentially need
only for stars to be in clumps ("galaxies"), galaxies in clumps ("clusters"),
clusters in clumps, etc., and adjust the "clumping parameters" correctly.
I think I can prove this with an arrangement where the fractions N1,N2,...
(Ni = fraction of sky covered by cluster level i) have the property that
the infinite product (1-n1)*(1-n2)*(1-n3)*... converges to a value > 0.

   Of course, the above seems hard to justify cosmologically.  But we
have accepted stranger things...

   -- David desJardins