# Re: Fw: Numbers

This is the way I put the argument in my upcoming book. You can also
read the Universal Dovetailer Argument in Bruno Marchal's SANE04
paper.

\item That a description logically capable of observing itself is
enough to bootstrap itself into existence. Let me speak to this by
means of an example: The C programming language is a popular
language for computer applications.  To convert a program written in
C into machine instructions that can execute on the computer, one
uses another program called a compiler. Many C compilers are
available, but a popular compiler is the GNU C compiler, or gcc. Gcc
is itself a C language program, you can download the program source
code from http://www.gnu.org, and compile it yourself, if you
already have a working C compiler. Once you have compiled gcc, you
can then use gcc to compile itself. Thus gcc has bootstrapped itself
onto your computer, and all references to any preexisting compiler
forgotten.

What I'm tryng to say here is that the description is a complete
specification of a conscious being, when interpreted (observed) by
the conscious being. There may have been an initial interpreter
(conscious or not) to bootstrap the original conscious being. It
matters not which interpreter it is --- any suitable one will do. If
{\em computationalism} \S\ref{computationalism} is correct, any
universal Turing machine will suffice. In fact since the 3rd person
world has to be a timeless {\em ideal} structure, it is not
necessary to actually run the initial interpreter. The logical
possibility of a conscious observer being able to instantiate itself
is sufficient in a timeless Plenitude of all possibilities. Thus we
close the ontology of the bitstring Plenitude, and find an answer
to Stephen Hawking's question What breathes fire into the
equations''\cite[p. 174]{Hawking88}. Paraphrasing the words of
Pierre-Simon Laplace to Napoleon Bonaparte, we have no need of a
hypothesis of a concrete reality\cite{Marchal98}.

I appreciate that some can never do this ontological closure, that for
them there must always be a machine somewhere doing the running. This
is reminiscient of those people for whom there must be a prime mover
to start the universe off.

I know that Bruno says he's eliminated the "extravagent hypothesis",
but really I think he's shown that it is unnecessary, and can be pared
away by Occam's razor, not that it is contradictory.

Cheers

On Sat, Mar 18, 2006 at 10:37:51PM -0800, Norman Samish wrote:
>
> 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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