A few years ago I posted a speculation about Harry Potter universes,
from the Schmidhuber perspective.  Schmidhuber argues that the reason
we don't see such a universe is that its program would be more complex,
hence its algorithmic-complexity measure would be less.  Such a universe
would basically have natural laws identical to what we see, but in
addition it would have exceptions to the laws.  You wave a wand and say
"Lumino!" and light appears.  (Here I am taking the Harry Potter name
rather literally, but the same thing applies to the more general concept
of universes with magical exceptions to the rules.)

You could also argue, as Wei does, on anthropic grounds that in such a
universe the ease of exploiting magic would reduce selection pressure
towards intelligence.  Indeed in the Harry Potter stories there are
magical animals but it is never explained why their amazing powers did
not allow them to dominate the world and kill off mundane creatures long
before human civilization arose.

I suggested that the Schmidhuber argument has a loophole.  It's true that
the measure of a simple universe is much greater than a universe with
the same laws plus one or more exceptions.  But if you consider the set
of all universes built on those laws plus exceptions, considering all
possible variants on exceptions, the collective measure of all these
universes is roughly the same as the simple universe.  So Schmidhuber
gives us no good reason to reject the possibility that our universe may
have exceptions to the natural laws.

If we do live in an exceptional universe, we are more likely to live in
one which is only "slightly" exceptional, i.e. one whose laws are among
the simplest possible modifications from the base laws.  Unfortunately,
without a better picture of the true laws of physics and an understanding
of the language that expresses them most simply, we can't say much about
what form exceptions might take.  We know that they would be likely
to be simple, in the same language that makes our base laws simple,
but since we don't know that language it is hard to draw conclusions.

Here is where the anthropic argument advanced by Wei Dai sheds some
light; one thing we could say is that these simple exceptions should not
be exploitable by life and make things so easy as to remove selection
pressure.  So this would constrain the kinds of exceptions that could

Ironically, waving a wand and speaking in Latin would indeed be the
kind of exception that would not likely be exploited by unintelligent
life forms.  So purely on anthropic principles we could not fully rule out
Harry Potter magic.  But the complexity of embedding Latin phrases in the
natural laws would argue strongly against us living in such a universe.

Hal Finney

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