Re: MWI & universal prior

From: Juergen Schmidhuber <juergen.domain.name.hidden>
Date: Thu, 11 Nov 1999 10:32:27 +0100

Fritz Griffith:

>Hi, I'm new to this mailing list. I have a question regarding Everett's
>MWI. How and why is there a more likely probability of certain states
>than others? Everette proved that the same probability laws exist in
>every world. I have read that some states are more likely to be our
>world because there are more worlds corresponding to that state than
>Lother states. Normally, I would assume that the probability laws describe
>how many worlds there are corresponding to a given state, but as far as I
>understand it, any two different worlds existing in exactly the same state
>is strictly forbidden. Considering that every possible state does exist
>in some world, it seems safe for me to conclude that there is only one
>world corresponding to every state, and the chance of finding ourselves
>in any possible universe is just as likely as any other. The result
>would be total chaos. It is obvious that this is not the situation.

>The only possible explanation I can think of is that the probability
>laws don't describe how many worlds of a given state exist, but rather
>directly describe the actual likelihood of a given world being ours.
>But this description doesn't make sense either, because for every split
>in which we are favored to follow a certain world, there exists another
>world of equally real people who assumed they would they would follow
>the same path, who instead ended up in the so-called unlikely world.
>Because the people in both worlds are equally real, there is no way to
>say that we are more likely to follow either path; rather, between this
>single-split example, the chance would be 50/50 as to which world we
>would end up in. Considering all possible worlds, we are back to the
>drawing board - the chance of us actually being in a world that isn't
>chaotic is pretty much nonexistant. So, how does the MWI explain the
>stability of our world?

MWI does not. Neither does the anthropic principle. To make predictions
using Bayes rule you need something else: a prior on the many worlds.
There is a natural one. I am quoting from the 1997 paper:

 An automatic by-product of the Great Programmer's set-up is the
 well-known ``many worlds hypothesis'', (C) Everett III. According
 to it, whenever our universe's quantum mechanics allows for alternative
 next paths, all are taken and the world splits into separate universes.
 From the Great Programmer's view, however, there are no real splits ---
 there are just a bunch of different algorithms which yield identical
 results for some time, until they start computing different outputs
 corresponding to different noise in different universes.

And from the next chapter on the universal Solomonoff-Levin prior:

 Now back to our question: are we run by a relatively compact algorithm?
 So far our universe could have been run by one - its history could
 have been much noisier and thus much less compressible. Hence universal
 prior and coding theorems suggest that the algorithm is indeed short. If
 it is, then there will be less than maximal randomness in our future,
 and more than vanishing predictability. We may hope that our universe
 will remain regular, as opposed to drifting off into irregularity.

To elaborate, according to the universal distribution, whenever there
is a ``split'' the continuation corresponding to the shorter algorithm
will be more likely. Roughly speaking, you probably are in one of the
simplest universes compatible with past data.

Juergen
Received on Thu Nov 11 1999 - 01:35:37 PST