Yes, like you I thought the theorem was obvious, and started to fire
off an email with my "proof". However, I soon ran up against your
double counting problem, and couldn't see a simple way of dealing with
it, so decided against emailing. As Bruno said - the proof is somewhat
nonobvious. 

Don't feel too bad - its not at all clear who makes the better
mathematician - the one who publishes a foolish mistake, or the one
who holds back publishing a great mathematical discovery  simply
because there is some easily correctable flaw within it.

Cheers

On Mon, Apr 03, 2006 at 12:55:39PM -0400, [EMAIL PROTECTED] wrote:
> 
> Can this be shown with an extension of a "pre-fix/don't care bits" 
> argument?  I'm just making this up on the spot, so I'm sticking my neck 
> out.  It's not rigorous, but it could go something like this:
> 
> The binary (say) recording of "Gond With The Wind" can be viewed as one 
> huge but finite binary sequence of n bits:
> 
> GWTW = "01001010110 ... binary("Frankly, my dear,...") ... 01001101001".
> 
> Actually we can consider all numbers to be an infinitely long binary 
> sequence, finite ones having an infinite number of leading 0's.  So...
> 
> 1. Of all binary numbers, the probability that the 1st through nth bits 
> = GWTW is 1/(2^n).
> 2. So doesn't it follow that, likewise, the probability that the 2nd 
> through (n+1)th bits = GWTW is 1/(2^n)?
> 3. So the probability that either #1 or #2 is true is 2/(2^n) = 
> 1/(2^(n-1)).  (What about both being true?  See step #4.)
> 4. Now if it weren't for one complication, we would be able to say by 
> induction the probability that GWTW will be found in the first 2n bits 
> would be 1 (which obviously is false).  The complication is that as we 
> look at more bits in the pre-fix, there is a relatively small 
> probability that, depending on the nature of the patterns of 0's and 
> 1's in GWTW, we could find GWTW more than once in the extended prefix.  
> (e.g. To find GWTW more than once in the first n+1 bits, GWTW would 
> have to be either all 1's or all 0's.)  So we would have to refrain 
>  from counting those certain "multiple occurrence containing" numbers 
> more than once, slightly decreasing the probability.  However, we can 
> hand-wave and say that this probability is small and thus does not take 
> us far from a probability of 1 of finding GWTW in a number.
> 
> Especially considering all infinitely long numbers, intuitively I'd 
> guess it's a subset of measure zero that doesn't have a given finite 
> string inside it somewhere.  It might be analogous to saying,"What is 
> the measure of a subset of the reals that can be described as a 
> quotient a/b, given that b is fixed."  Well we know that is a subset of 
> the rationals which has measure zero in the reals.
> 
> More along the lines of this thread, I'm aware of the weirdnesses in 
> divergent series, and that it depends on the definition of 
> divergence/convergence and its context (for instance analytic 
> continuation).  This again gets to the controversial borders of what 
> mathematics is, and how it relates to reality, and what topology if any 
> we should choose for Everything (why the complex plane?).
> 
> Tom
> 
> -----Original Message-----
> From: Bruno Marchal <[EMAIL PROTECTED]>
> To: everything-list@googlegroups.com
> Sent: Sat, 1 Apr 2006 15:47:29 +0200
> Subject: Re: The Riemann Zeta Pythagorean TOE
> 
> 
> Let us just take the numbers, I mean the finite numbers 0, 1, 2, ...
> But let us take them all.
> Then it can be shown that numbers without an encoding of "Gone with the 
> 
> wind" are quite exceptional.  Almost all natural numbers, written in
> any base, has an encoding of "Gone with the wind", and of the complete
> work of Feynman too, and the complete archive of the everything-list.
> In the land of big numbers those numbers *who don't* are rare and
> exceptional.
> 
> It is not entirely obvious. There is a proof of this in the Hardy and
> Wright Introduction to Number Theory.
> http://www.amazon.com/gp/product/0198531710/103-1630254-7840640?
> v=glance&n=283155
> 
> Bruno
> 
> 
> 
> 
> Le 31-mars-06, à 23:34, [EMAIL PROTECTED] a écrit :
> 
> >
> > John,
> >
> > If I understand what you're asking:  A digital recording of "Gone With
> > The Wind", say on a CD, is recorded in bits, binary digits, 1's and
> > 0's.  You can also express pi in binary, it's simply the base-2
> > representation of pi, all 1's and 0's, just like the movie recording.
> > So you have an infinite sequence of 0's and 1's which is the
> > representation of pi in which to search for the finite sequence of the
> > movie recording.
> >
> > Tom
> >
> > -----Original Message-----
> > From: John M <[EMAIL PROTECTED]>
> > To: everything-list@googlegroups.com
> > Sent: Fri, 31 Mar 2006 12:59:20 -0800 (PST)
> > Subject: Re: The Riemann Zeta Pythagorean TOE
> >
> >
> > Tom,
> >
> > may I humblly ask for an example, HOW you would
> > imagine the 'sequence' in pi's infinite variety of
> > numbers the connotation for "Gone With The Wind - the
> > movie?"
> > Just 'per apices', show the kind of sequence included,
> > I don't want all the details.
> >
> > Thank you
> >
> > John M
> >
> > --- [EMAIL PROTECTED] wrote:
> >
> >> Interesting!  This reminds me of the old standby
> >> example of being able  to
> >> find any sequence of digits in the digits of pi, and
> >> therefore being  able to
> >> find whole digital "recordings" of "Gone With The
> >> Wind" or anything you  desire,
> >> including your-whole-life-as-you-desire-it-to-be, if
> >> you search  long enough.
> >> ;)  But that's the key, in my view.  It requires
> >> desiring, searching and
> >> finding.  That requires a person.   Similarly, it
> >> requires a person to combine
> >> addition and  multiplication.  This is because it
> >> requires a person to think of
> >> grouping  things.  This is because it takes a person
> >> to define meaning.
> >>
> >> Tom
> >>
> >> "An equation for me has no meaning unless it
> >> expresses a thought of  God."
> >> Ramanujan
> >> "Ask and it will be given to you, seek and you will
> >> find, knock and the  door
> >> will be opened to you." Jesus
> >>
> >>
> >>
> >>
> >>
> >
> >
> >
> >
> >
> > >
> >
> http://iridia.ulb.ac.be/~marchal/
> 
> 
> 
> 
-- 
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UNSW SYDNEY 2052                         [EMAIL PROTECTED]             
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