Newsgroups: comp.ai,comp.ai.philosophy,comp.ai.alife
From: stevem@comtch.iea.com (Steve McGrew)
Subject: Re: rand() - implementation ideas [Q]
Organization: New Light Industries, Ltd.
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In article <jqbE080Gu.HrM@netcom.com>, jqb@netcom.com (Jim Balter) wrote:
>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).
[snip]
>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.

        You misunderstood.  I am not looking for an argument; I am hoping for 
an explanation so I'll understand something I do not understand yet-- and 
there are many such things!

        Suppose you send me a long sequence of numbers you tell me has been 
generated at random.  Suppose I find in it a string of 100 contiguous 1's.  I 
should be able to re-send that sequence in somewhat compressed form, as long 
as you know my compression algorithm in advance.  It won't happen very often-- 
but sometimes it will.  And on those rare occasions you can get a little bit 
of compression.  

        If there is a theorem that takes into account the need to communicate 
the algorithm in advance, or to send it along with each message, it is 
immediately plausible to me that there will be *on the average* no way to 
compress a lot of random sequences.  

        I am curious to know how the theorem is stated, and its proof.  Can 
you refer me to it?  I'll try the FAQ you mentioned.  I gave up on trisecting 
the angle (with a compass and straightedge, not with mechanical linkages which 
make it easy) and perpetual motion machines (that generate power) 36 years 
ago.  I gave up on universal compression the first time I thought about it.  I 
did not give up on trying to understand things I don't understand yet, nor 
decide to believe whatever I'm told by the loudest, most forceful voice!

        This all came from the thought that you would not really have a random 
sequence of numbers if you took out all the compressible numbers.  I'll stand 
by that intuition, until someone gives me a clear proof it's not so.  : )

Steve

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