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.

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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/ > > > > -- ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics 0425 253119 (") UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 ---------------------------------------------------------------------------- --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---