Is the universe computable?

jbone at jbone at
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
From: "Stephen Paul King" <stephenk1 at>
Date: Mon Nov 3, 2003  23:01:58 US/Central
To: <everything-list at>
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:
    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,

----- Original Message -----
From: David Barrett-Lennard
To: everything-list at
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 


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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