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--- Russell Standish <[EMAIL PROTECTED]> wrote: > > But the tape can also hold an encoding of the Turing > machine to > perform the interpretation. This is the essence of > the "compiler > theorem". One can simply iterate this process such > that there is no > "concrete" machine interpreting the tape. I think > this is another way > of putting the UDA. > > Cheers Russell, I think you left ou one itzy-bitzy word from your sentence: "But the tape can also hold an encoding of the ----[WORKING]---- Turing machine to perform the interpretation." A Turing machine does nothing (by itself). Don't take the power for granted. Something has to OPERATE it to do anything. And not 'any kind' of power. Don't expect from a cadaver of a wise man to solve Fermat's puzzle. John > > > On Fri, Mar 17, 2006 at 01:31:22PM -0800, Norman > Samish wrote: > > > > [EMAIL PROTECTED] wrote: > > > > > "Hal Finney" wrote: > > > The first is that numbers are really far more > complex than they seem. > > > When we think of numbers, we tend to think of > simple ones, like 2, or 7. > > > But they are not really typical of numbers. > Even restricting ourselves to > > > the integers, the information content of the > "average" number is enormous; > > > by some reasoning, infinite. Most numbers are a > lot bigger than 2 or 7! > > > They are big enough to hold all of the > information in our whole universe; > > > indeed, all of the information in virtually > every possible variant of our > > > universe. A single number can (in some sense) > hold this much information. > > > > How ? Surely this claim needs justification! > > ~~~~~~~~~~~~~~~~~~~~~ > > The single number can be of infinite length, with > infinite digits, and can therefore contain unlimited > information. One could compare the single number to > a tape to a Universal Turing Machine. Granted, the > UTM needs a head and a program to read the tape, so > the tape by itself is not sufficient to hold > information. > > > > Norman > > ~~~~~~~~~~~~~~~~` > > > > > > -- > *PS: A number of people ask me about the attachment > to my email, which > is of type "application/pgp-signature". Don't worry, > it is not a > virus. It is an electronic signature, that may be > used to verify this > email came from me if you have PGP or GPG installed. > Otherwise, you > may safely ignore this attachment. > > ---------------------------------------------------------------------------- > 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 -~----------~----~----~----~------~----~------~--~---