Predictions & duplications

> From: Marchal <[EMAIL PROTECTED]> Thu Oct  4 11:58:13 2001
> [...]
> You have still not explain to me how you predict your reasonably next
> experience in the simple WM duplication. [...]
> So, how is it that you talk like if you do have an algorithm
> capable of telling you in advance what will be your personal
> experience in a self-duplication experience. [...]
> Where am I wrong? 
> Bruno

I will try again: how can we predict what's going to happen?

We need a prior probability distribution on possible histories.
Then, once we have observed a past history, we can use Bayes' rule to
compute the probability of various futures, given the observations. Then
we predict the most probable future.

The algorithmic TOE paper discusses several formally describable priors
computable in the limit. But for the moment let me focus on my favorite,
the Speed Prior.

Assume the Great Programmer has a resource problem, just like any other
programmer. According to the Speed Prior, the harder it is to compute
something, the less likely it gets. More precisely, the cumulative prior
probability of all data whose computation costs at least O(n) time is
at most inversely proportional to n.

To evaluate the plausibility of this, consider your own computer: most
processes just take a few microseconds, some take a few seconds, few
take hours, very few take days, etc...

We do not know the Great Programmer's computer and algorithm for computing
universe histories and other things. Still, we know that he cannot do
it more efficiently than the asymptotically fastest algorithm.

The Speed Prior reflects properties of precisely this optimal algorithm.
It turns out that the best way of predicting future y, given past x,
is to minimize the (computable) Kt-complexity of (x,y).  As observation
size grows, the predictions converge to the optimal predictions.

To address Bruno Marchal's questions: Many of my duplications in parallel
universes with identical past x will experience different futures y.
None of my copies knows a priori which one it is. But each does know:
Those futures y with high Kt(x,y) will be highly unlikely; those with
low Kt(x,y) won't.

Under the Speed Prior it is therefore extremely unlikely that I will
suddenly observe truly random, inexplicable, surprising events, simply
because true randomness is very hard to compute, and thus has very high
Kt complexity.

Juergen Schmidhuber

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