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From: jqb@netcom.com (Jim Balter)
Subject: Re: rand() - implementation ideas [Q]
Message-ID: <jqbE080Gu.HrM@netcom.com>
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References: <54lr8o$ndm@nntp.seflin.lib.fl.us> <P1ZDtGA4sIeyEwCM@wandana.demon.co.uk> <jqbE05zJw.BAK@netcom.com> <3279fbac.0@news.iea.net>
Date: Sat, 2 Nov 1996 02:05:18 GMT
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In article <3279fbac.0@news.iea.net>,
Steve McGrew <stevem@comtch.iea.com> wrote:
>In article <jqbE05zJw.BAK@netcom.com>, jqb@netcom.com (Jim Balter) wrote:
>>There is a fallacy here.  I suggest you check out the comp.compression FAQ.
>>The number of sequences that can be expressed in n bits is 2**n.  Any
>>algorithm that compresses some to a smaller number of bits will necessarily
>>expand others to a greater number of bits.
>
>        The reasoning must be based on the idea that the algorithm has to be 
>transmitted along with each sequence.

The reasoning above is simple and straightforward and doesn't mention anything
about encoding the algorithm as part of the sequence; it certainly isn't
"based upon" such a thing, and I can't imagine what leads you to think so
(other than perhaps a desire to disbelieve the conclusion).

>Otherwise, it seems that you could just 
>agree ahead of time that any repeating sequence of the form 1,1,1,--- can be 
>represented as 1,n -- and that you will only bother to compress it that way if 
>n is longer than, say, ten.  In any long series of sequences, or any long 

How many bits is n encoded in?  Say 4.  Then does 11011 mean 11011, or
11111111111?

Look, it's a theorem; I already gave the short informal explanation.  Since
you haven't shown any error in the explanation, what makes you think it is
wrong?

Many people have tried to come up with "universal compression" schemes; they
are just as bogus as angle trisection with compass and straightedge, perpetual
motion machines, and proofs that pi is exactly 3.1416.  Go read the
comp.compreion FAQ instead of depending upon faulty intuition.  Please.

>sequence, there will probably be some such subsequences and they will end up 
>being compressed (slightly).  However, if the decompression algorithm has to 
>be transmitted with each sequence there would be a lot of useless baggage 
>carried along that would outweigh the slight amount of compression.  If the 
>decompression algorithm is only transmitted along with those sequences that 
>need to use it, it would need to be bigger (I think); again outweighing the 
>slight compression.
-- 
<J Q B>

