# Re: Fw: Numbers

```
--- 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
> > ~~~~~~~~~~~~~~~~`
> >
> >
>
> --
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>
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> Mathematics                                  0425
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>

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