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
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.
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?).
> -----Original Message-----
> From: Bruno Marchal <[EMAIL PROTECTED]>
> To: email@example.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
> It is not entirely obvious. There is a proof of this in the Hardy and
> Wright Introduction to Number Theory.
> 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: firstname.lastname@example.org
> > 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
> > >
A/Prof Russell Standish Phone 8308 3119 (mobile)
Mathematics 0425 253119 (")
UNSW SYDNEY 2052 [EMAIL PROTECTED]
International prefix +612, Interstate prefix 02
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