On Tue, 6 Jul 1999, Alastair Malcolm wrote:
> From: Jacques M Mallah <mailto:jqm1584.domain.name.hidden>
> > On Sat, 3 Jul 1999, Alastair Malcolm wrote:
> > > If our world can be equated to a mathematical structure which is
> > > related by the physical laws that are apparent to us, then it can also
> be
> > > a far more complex mathematical structure which explicitly specifies the
> > > universe as it has evolved during our lifetimes (for example a phase
> > > space specification of all the particle positions/momenta for a universe
> > > coming into existence say in 1850, and happening to obey
> > > classical/quantum-mechanical laws as required to convince us that the
> > > universe does follow simple laws).
> >
> > Yes, but that structure would not implement any computations.
> > Many of us are computationalists.
> >
> > > Now there would seem to be far more different mathematical structures
> > > where this type of scenario occurs (but with sufficient deviation from
> > > 'normality' such that we would notice - the odd white rabbit scuttling
> > > across a ceiling, for instance, to reuse an earlier example), than there
> > > is of the relatively simple mathematical structure(s) that science
> > > implies underlies our phenomenal world. So statistically we should be in
> > > one of these 'contrived' universes.
> >
> > In the case of typical 'junk' data, yes, but there would be no
> > computations.
>
> As a counter to the challenge to Tegmark's hypothesis, I am afraid I can't
> see the relevance of this or the other statement above (a contrived
> computation (or appearance of computation, if you prefer) can readily be
> produced from a sufficiently complex mathematical structure, and it only has
> to convince us that it looks like a computation),
OK, I'd better fill in some background.
(First, I am not defending Tegmark's hypothesis, but the
everything hypothesis. It was independently discovered by many of the
people on the list (I don't know who was first and that can't be proven
anyway, but surely not Tegmark), and we each have our own interpretation
of it. Also, I disagree with many of the others on major issues.)
Under what circumstances is a computation implemented? First of
all, the proper causal relationships must exist between the states. So a
structure in which all variables are explicitly specified does not lead to
any computations. Similarly a string of bits implements no computations.
That much is a matter of definition and is not controversial. A
computationalist believes that computations suffice for consciousness and
that the causal relationships are required. Not everyone believes this
but those who don't are not computationalists.
As far as a 'contrived computation', it sounds like you are
talking about a second issue, the implementation problem. My web page
discusses this under interpretation of QM. Maybe it's not what you mean
but it's interesting so you might as well look. Suffice it to say that I
believe there is a way of rejecting contrived computations while keeping
real ones.
> Any cgu idea must fall into one of two exhaustive categories:
>
> 1. There is a required process of execution of programs which leads to the
> existence of universes.
>
> For this category, then clearly any program must be executed from a universe
> other than the one (or more) that is produced by it. Where does this
> 'higher' universe come from? Schmidhuber implies a chain of universes, but
> if there is an original universe somewhere, why can't it be this (our) one,
> and forget the chain? Similarly, an infinite hierarchy of TM's solves
> nothing, it just sweeps the problem under the carpet of infinity. [Note to
> BM: this is where the turtles come in.]
No. The idea is just that all mathematical stuctures exist. Yes,
stuctures that explicitly specify everything fall into that category. But
so do possible laws of physics, such as the laws that are needed to run a
Turing machine. A running TM is a mathematical structure, but is
qualitatively different from a stucture that explicitly specifies the
state of each memory unit as a function of time. So all TMs would exist
and they would run all possible programs.
It is of course also possible to have a not-quite-everything
hypothesis in which only such stuctures exist, which would be easier to
deal with. This would not simplify physics as much as the everything
hypothesis, but if it worked, would just be a new theory of physics and
simpler than our existing ones.
- - - - - - -
Jacques Mallah (jqm1584.domain.name.hidden)
Graduate Student / Many Worlder / Devil's Advocate
"I know what no one else knows" - 'Runaway Train', Soul Asylum
My URL:
http://pages.nyu.edu/~jqm1584/
Received on Wed Jul 07 1999 - 16:28:25 PDT