# Re: Fw: Numbers

```Are you saying that a tape of infinite length, with infinite digits, is not
Turing emulable?```
```
I don't understand how the 'compiler theorem' makes a 'concrete' machine
unnecessary.  I agree that the tape can contain an encoding of the Turing
machine - as well as anything else that's describable.

Nevertheless, it seems to me there has to be a 'concrete' machine executing
the tape, irrespective of the contents of the tape.

Norman
~~~~~~~~~~~~~~~~~~~~~

----- Original Message -----
From: "Russell Standish" <[EMAIL PROTECTED]>
Sent: Friday, March 17, 2006 2:37 PM
Subject: Re: Fw: Numbers

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

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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