Is the universe computable?
jbone at place.org
jbone at place.org
Mon Nov 3 21:59:28 PST 2003
Interesting exchange from [everything] on computational cosmology.
David --- an [everything] newbie --- poses a line of thinking that
Turpin's come close to floating here before, namely the "magical
universes" argument and the risk that CC implies that "normal"
universes are likely to be in the minority. Stephen steps in to point
at some work by Vaughan Pratt that tackles (obliquely) related issues.
BTW - I've recommended [everything] before to folks interested in this
topic. I'd like to add a caveat: after several *months* of virtually
no activity, [everything] has heated up again, to the order-10 posts /
day level. Interesting stuff, but most of this seems to be a rehash of
older topics for a new crop of newbies, w/ the old hands pitching in to
nudge in the right direction. On the upside: less metaphysical
mumbo-jumbo. (It got pretty weird back in the spring, briefly.) (And
that's saying something, given the subject matter. ;-)
--
Begin forwarded message:
Resent-From: everything-list at eskimo.com
From: "Stephen Paul King" <stephenk1 at charter.net>
Date: Mon Nov 3, 2003 23:01:58 US/Central
To: <everything-list at eskimo.com>
Subject: Re: Is the universe computable?
Dear David,
This is a very good post! I would like to point you to a proposal
that Vaughan Pratt discusses in several of his papers found here:
http://chu.stanford.edu/guide.html
http://chu.stanford.edu/guide.html#ratmech
The basic idea goes like this:
A causes B if and only if the information of B implies the information
of A.
or A => B iff A* <- B*
This goes into a commutation diagram that can be chained:
... A ----> B -----> C ...
| | |
... A* <== B*< == C* ...
The idea is that physical events chain together only if their
representations imply each other and the "arrows" of "causation" and
"logical implication" go in opposite directions. In this way we can
make sense of how the past is "so well behaved" while the future is
wide open to possibilities that include pathologies. BTW, this idea is
very much in line with Wheeler's "Surprise 20 Questions".
Kindest regards,
Stephen
----- Original Message -----
From: David Barrett-Lennard
To: everything-list at eskimo.com
Sent: Monday, November 03, 2003 10:45 PM
Subject: Is the universe computable?
In the words of Tegmark, let’s assume that the physical world is
completely mathematical; and everything that exists mathematically
exists physically.
I have been thinking along these lines since my days at university -
where it occurred to me that any alternative is mystical. However, the
problem remains to explain induction - ie the predictability of the
universe. Why is it that the laws of physics can be depended on when
looking into the future, if we are merely a “mathematical construction”
- like a simulation running on a computer. It seems to me that in the
ensemble of all possible computer simulations (with no limits on the
complexity of the “laws”) the ones that remain well behaved after any
given time step in the simulation have measure zero.
Given the “source code” for the simulation of our universe, it would
seem to be possible to add some extra instructions that test for a
certain condition to be met in order to tamper with the simulation. It
would seem likely that there will exist simulations that match our own
up to a certain point in time, but then diverge. Eg it is possible for
a simulation to have a rule that an object will suddenly manifest
itself at a particular time and place. The simulated conscious beings
in such a universe would be surprised to find that induction fails at
the moment the simulation diverges.
In other words, at each time step in a simulation the state vector can
take different paths according to slightly different software programs
with special cases that only trigger at that moment in time. It seems
that a universe will continually split into vast numbers of child
universes, in a manner reminiscent of the MWI. However there is a
crucial difference – most of these spin off universes will have bizarre
things happen. It is difficult to see how a computable system can be
tamper proof. How can a past which has been well behaved prevent
strange things from happening in the future?
In the thread “a possible paradox”, there was talk about a vanishingly
small number of “magical” universes where strange things
happen. However, it seems to me that the bigger risk is that a “normal”
universe like ours will be the atypical in the ensemble!
A possible argument is to invoke the anthropic principle – and suggest
that our universe is predictable in order for SAS’s to evolve and
perceive that predictability. However, that predictability only needs
to be a trick – played on the inhabitants for long enough to develop
intelligence. There is no reason why the trick needs to continue to be
played.
I suggest that the requirement of a tamper-proof physics is an
extremely powerful principle. For example, we deduce that SAS’s only
exist in mathematical systems that aren’t computable. In particular
our Universe is not computable.
- which is what Penrose has been saying.
I have assumed that non-computability coincides with being tamper-proof
but this is far from clear. For example, it is conceivable that the
Universe is a Turing machine running an infinite computation (cf
Tipler’s Omega point), and “awareness” only emerges in the totality of
this infinite computation. Perhaps our awareness is a manifestation of
advanced waves sent backwards in time from the Omega Point!
I think it’s important to distinguish between an underlying
mathematical system, and the formal system that tries to describe
it. I think this is a crucial distinction. For example, the real
number system can be defined uniquely by a finite set of
axioms. Uniqueness is (formally) provable - in the sense that it can
be shown that an isomorphism exists between all systems that satisfy
the axioms. However the real numbers are uncountably infinite - and
therefore are very poorly understood using formal mathematics - which
is limited to only a countably infinite set of statements about
them. So formal mathematics should be regarded as an imperfect and
coarse tool which only gives us limited understanding of a complicated
beast! This is after all what Godel’s incompleteness theorem tells us.
It is not surprising that a computer will never exhibit awareness -
because it is merely using the techniques of formal mathematics, and
not tapping into the “good stuff”.
- David
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