# Re: Turing Machines Have no Real Time Clock (Was The Game of Life)

From: Russell Standish <R.Standish.domain.name.hidden>
Date: Mon, 17 Jan 100 12:22:05 +1100 (EST)

> I looked up codswallop in the dictionnary and I was very surprised to find
> that it is a recent British word coined around 1963. It means "nonsense."
> OK. This is your opinion.
> First sentence: The comp hypothesis depends on Turing Machines which are
> inherently discrete. A continuous universe would not by emulable by a Turing
> Machine. Read Bruno's latest post. He has a much better grasp of this issue
> then me.

Why do you think the only possibilities are that the universe is
either discrete or continuous? For example, the space Q^4 (4-D space
built from rational numbers) is neither.

a remarkably similar exchange in the NECSI lists over the last few
days!

OK - lets start from the beginning:

COMP is the hypothesis that I can survive the replacement of my brain
by some Turing emulation (this seems to be the most consistent
statement of this hypothesis).

Now assuming that I am some Turing emulation in the first place, then
COMP is obviously satisfied. If we further assume that the emulation
actually emulates my "observer-moments" in monotonic order (ie the
emulation computes each observer moments in time order) then my
perception of the universe will be discrete. This does not imply that
the universe is actually discrete however.

However, there is no need to compute observer moments in temporal
order. If one computes say every second timestep for a certain time
interval, then goes back and computes the odd timestep (backfilling),
the results of the computation are identical (the emulated observer
will not sense a difference). Now consider the following possibility:
do a discrete simulation for a certain number of timesteps, then
backfill the half timesteps, then the third timesteps, and so on. In
this case, the observer moments will be perceived to lie on the set of
rational numbers - most definitely not discrete.

This is with COMP. The same is true of Schmidhuber's
plenitude. However, with Schmidhuber, the universe cannot be a
continuum, as each state must be computable. However, the universe can
be indistinguishable from a continuum. The same applies to Tegmark,
who assumes all finitely describable consistent formal axiomatic
systems (fc-FAS appears to be the acepted abbreviation).

>
> Second sentence: To prove that if physical constants are to take any definite
> value, the universe must be quantized.
>
> Let us say that there exist a TOE based on one single physical constant X
> (for example Planck's constant). Without loss of generality, we can say that
> the value of X is 1, since there is no other constant to compare it to.
> Assuming that a Turing machine is used to apply this TOE to solve poblem and
> calculate any quantity in the world then any quantitiy derived from this TOE
> would have to belong to the set of integers -- including space time and
> energy.
> We can extend this reasonning to TOE's that include n arbitrary physical
> constants.
>
> George Levy
>
>

This argument is incorrect for precisely the same reasons as
above. The Turing machine can compute pi from within this TOE, and
unless you happen to live in Kansas, Pi is most definitely not an
integer.

It seems quite a few people are labouring under this misunderstanding
that Turing emulations (or equivalently fc-FASes) imply that the
emulation must be discrete. I shall return to this theme in some
subsequent posts. Of course there is nothing wrong intrinsically with
assuming the universe is discrete, however, it is an extra and special
assumption. It also appears to have some experimentally testable
consequences (such as Lorentz invariance can never be true in a
discrete universe).

My main objection to the discrete universe idea, is that I can't see
any obvious anthropic reason why the universe should be discrete, and
surrounding each discrete universe is a dense swarm on nondiscrete
universes that are Turing emulable - thus it seems unlikely we'd live
in a discrete universe by chance alone.

----------------------------------------------------------------------------
Dr. Russell Standish Director
High Performance Computing Support Unit,
University of NSW Phone 9385 6967
Sydney 2052 Fax 9385 6965
Australia R.Standish.domain.name.hidden
Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks
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Received on Sun Jan 16 2000 - 17:20:34 PST

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