I want to follow up on the discussion we had last December about "flying
rabbit" universes.  Let me first recap my understanding of the issues.

Suppose that all universes exist, and that they are associated with
computer programs that generate them.  The measure of a universe is
defined as 1/2^n, where n is the size of the smallest program that
generates a given universe.  Can we reconcile this theory with our
observations of the universe around us?  In particular, does it explain
why we seemingly live in a lawful universe?

Broadly speaking, the answer is yes.  As it happens, it appears that
the laws of physics are relatively simple.  Stephen Wolfram guesses
that the entire set of laws for our universe could be reduced to about
5 lines of Mathematica code.  So apparently a relatively simple program
would be sufficient to generate our universe, with all its complexity,
including ourselves.

Clearly even more complex programs would also be possible to generate
universes like ours.  With the additional complexity the laws of
nature could have more exceptions and allow for "miraculous" behavior.
Such universes are called "flying rabbit" universes, or sometimes
"white rabbit" (after Alice in Wonderland), "dragon", or "Harry Potter"
universes.  The idea is that these universes are basically lawful, but
there are rare exceptions which can be manipulated to produce results
which violate the natural laws which hold otherwise.  The question is,
why don't we live in such a universe?

The answer is that to change the program from one which just implements
the simple laws of physics to one which has the exceptions would greatly
increase its size.  To allow rabbits (but not other heavy, wingless
animals) to fly, for example, the laws of physics would have to encode the
definition of a rabbit.  And since these laws are presumably expressed at
the subatomic level, defining a rabbit from that perspective would take
an enormous amount of information.  Instead of 5 lines of Mathematica the
program would balloon to probably billions of lines or even more, most
of which was defining a rabbit.  Such a program would have infinitesimal
measure compared to our universe.  That's why we don't see rabbits fly.

Back in December I raised an objection.  A white rabbit universe is less
probable than a simpler one by a factor of roughly 2^R, where R is the
information content in defining the rabbit.  However, by the same token
there are 2^R possible information patterns that can be described in
those R bits.  So if we consider the collection of all universes which
allow for exceptions, not just for rabbit-shaped objects but for all
possible rabbit-sized objects, then the total measure of all of these
is approximately as large as for the simple universe.  So we can't
really reject white rabbit universes, if we extend the notion to refer
to any universe which allows for miracles based on some special pattern
of information.

The answer to this objection was basically that most patterns of
information are random.  So the vast majority of these universes, while
in principle allowing for miracles, would only have them be triggered
by a phenomenon which is so rare that it will never occur in practice.
You'd have to have a huge combination of particles take on some precise
configuration, and then maybe something bizarre would happen.  But the
chance of any such configuration arising would be so low, it would be
like waiting for random thermal motions to suck all of the air out of
your room.  You'd never see it in the lifetime of the universe.

Now, my new idea is to look at somewhat less extreme violations of laws.
Suppose we have a universe which has simple natural laws like ours, but
does allow for violations based on certain patterns or configurations
of matter.  As before, the larger the pattern necessary to trigger
exceptional behavior, the lower the measure of the universe; but
countering that, there are just as many possible patterns which could
be used to trigger the lawless behavior.  So collectively the set of
universes with some exceptions does not have much less measure than for
universes with simple laws and no exceptions.

It seems to me, then, that it is actually likely that we live in
such a universe.  Chances our that our universe has basically simple
natural laws, but has the chance for miracles to occur when the proper
arrangements are made.  And there's no inherent reason why the miracle
triggering configuration has to be huge as for a white rabbit.  It could
be as simple as a few subatomic particles coming together in a certain
way.  In fact, it's possible that such "miracles" happen at a relatively
high rate throughout the universe, events which violate natural laws.
I think our model even predicts that there is a reasonable likelihood
that such things happen.

The only real limitation I see on the probability of lawless events
is based on the anthropic principle.  The universe has to be lawful
enough for intelligent life to have arisen.  If it were too easy to
generate energy, say, or to repel gravity, then the universe might be
chaotic and unstable.  Or perhaps life would evolve to exploit these
possibilities and it would make things so easy that there would be no
incentive for intelligence to evolve.

This suggests that as we move forward with our investigations of physics,
exploring new realms of matter with new tools that could not have
been reasonably evolved naturally, we should expect, with a reasonably
high probability, to discover miracles.  We're not guaranteed to do so,
because after all even the collection of all miracle-containing universes
is still not quite as probable as the simple one that has no miracles.
But collectively I think they might be as much as 1/10 as probable,
and perhaps even 1/2 as probable.

So it seems to me that this is another prediction which we can make based
on the all-universe principle (AUP): that natural law may well have rare
exceptions, and that once we begin exploring realms and configurations
that are unlikely to have occured naturally, we may find one.  It's hard
to say what the outcome is likely to be, but most likely it is something
that can be described simply, in whatever programming language most
efficiently describes our universe's natural laws.  Maybe there's a sign
reversal somewhere, or a constraint is simply skipped or added.

We could get unlucky and blow up the planet with some kind of energy
release triggered by a particle accelerator.  Or maybe we'd get lucky
and find some way to exploit the miracle to our benefit.  But I think
the AUP gives us more reason than in conventional view of physics to
expect such miraculous behavior.

Hal Finney

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