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 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 |

- Re: Is the universe computable? David Barrett-Lennard
- Re: Is the universe computable? Stephen Paul King
- Re: Is the universe computable? Frank
- RE: Is the universe computable? David Barrett-Lennard
- Re: Is the universe computable? Russell Standish
- RE: Is the universe computable? David Barrett-Lennard
- Re: Is the universe computable... Russell Standish

- RE: Is the universe computable? Hal Finney
- RE: Is the universe computable? David Barrett-Lennard

- Re: Is the universe computable? Federico Marulli