Tom Caylor writes:
> To look at this from a different perspective, suppose there was a worm that  
> lived in an apple, and the worm was super-intelligent to the point of being 
> able  to grasp all of our mathematical concepts that Tegmark claims are  
> sufficient to describe all of reality.  Then the worm asks, "Why is it that  
> I'm in 
> this apple?"  Actually the apple is the whole of observed reality  for the 
> worm, so it is equivalent to our observed universe.  However the  observABLE 
> universe for the worm is the same as our observable universe.   Then the worm 
> comes 
> up with a multiverse theory along with a Wormopic  Principle, saying that the 
> whole observable universe is just complex enough to  sustain the inside of an 
> apple.  Surely this must be true, since the worm  can grasp all of 
> mathematics?

The worm would come up with a multiverse theory that says that everything
exists, including universes like ours with people, apple trees, apples and
worms, and also including other universes which consist of just a single
apple, possibly with a worm in it, and every other possibility besides.

Among these possible universes there are a certain fraction which contain
worms-in-apples consistent with the experiences, observations and memories
that the worm has experienced in his own apple.

He knows that he is one of those worms.

He applies some kind of measure, such as the Universal Distribution, over
all of these worms-in-apples and is able to come up with a probability
distribution for which one he is.  This results in first-person
indeterminacy and uncertainty.

It may well be that the simplest and most likely case is not a universe
containing a single apple, but a universe like ours.  The reason is that
apples and worms are actually very complex objects at the cellular level,
even more complex at the atomic level, and enormously complex at the
sub-atomic Planck scale.  The physics going on in the apple is every
bit as complex as the physics of our own universe.

Our universe has the advantage in that its initial condition was very
simple - some say it was completely smooth and uniform in the initial
instances of the Big Bang.  Then we went along in a very natural and
simple way and developed planets, where life evolved into apples and

The apple-only universe must create all this by fiat.  It must be
hard-wired into the initial conditions: everything about the apple,
about the worm, and about the physics.

It's very plausibly would take a more complex program to run a universe
consisting of just an apple and a worm, than our whole universe where
apples and worms evolve out of much simpler initial conditions.

Hence the worm might well conclude that he is likely to be in a giant
universe with billions of other apples and worms, as well as many other
forms of life.  Even though he has not yet observed any of these things,
not yet having come to the surface of the apple, he can deduce it.

But perhaps not.  Suppose that this super-intelligent worm deduces
that universes like ours are actually less likely than ones which
are all apple.  In that case, assuming that his reasoning is sound,
then he is probably right.  From the first-person perspective, when he
chews up to the surface, he will probably find that he is indeed in
an apple-only universe.  The multiverse has many kinds of universes
with worms in apples, and it may be that our own universe has only a
small fraction of all the worms in apples, that most worms do in fact
find themselves in other kinds of universes.  That would be a possible
conclusion of multiverse theory, and it might well be right.

In short, there is no reason to expect a super-intelligent worm in an
apple to come up with a different multiverse than the one we would, if
we were also super-intelligent.  We might be in different components of
the multiverse than the typical worm, but that is not evidence against
the theory or an example of a flaw in its explanatory power.

Hal Finney

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