That’s all very interesting, but I don’t think it makes the right point about how likely a universe in which beings could develop and comment, would be orderly in the future. I don’t really care how many copies there are of “me” anyway, and that’s not even definable since the variations are graduated. It just isn’t what matters. What matters is the overall picture of “someone/s” and “how many universes” of different kinds can they end up in, even temporarily. Also, you still seem stuck on “programs” and don’t realize that the descriptions themselves are the larger field of platonic realms. The programs come up with descriptions, but why not just think of the descriptions directly … Programs are a biased and limiting concept, since you will imagine rules specifying outcomes, but really any description (configuration of distributions, characteristics, events, etc.) is a part of the platonic omniverse. That omniverse is too large for us to have any hope sans “controlling authority” of randomly ending up in a universe with a predictable continuation, no matter what “happened” in that world up to the time of asking the questions (and regardless of how you conceptualize time.)

BTW, considering the delicate timing of synapse firings and how they come together to influence another neuron to fire, not in a specific classically predictable way (or explain that it is), the brain is not like a computer. Each neuron is on an edge of maybe firing and maybe not, depending on a rough and sloppy sensitivity to the frequency of other signals arriving at about the same time. The butterfly effect and indeterminacy of electrons etc. ruins any attempt to make either individual neurons or the brain into computing machines, and aside from whether specific speculations like QM in microtubules pan out.

I think that Schhmidhuber explains it in this article.

You could also reason heuristicaly like this. Clearly not all worlds can be equally likely, because there are an infinite number of possible worlds. You cannot define a correctly normalized probability distribution that is constant over an infinite set.

Suppose that the probability of a world, which in our setting is just a program or algorithm, depends only on program length. Then the probability that you will find yourself in a particular world will be the proportional to the probability of that world multiplied by the number of copies of you that exist in tat world.

For any given program P, you can consider the program P(n) which just runs P n times. Then the probability that you’ll find yourself in
P(n) is n times the intrinsic probability of
p(n). But this means that the probability of P(n) has to fall of faster than 1/n. otherwise you can’t properly normalize the probability.

Now, the program p(n) will have to have
Log(n)/Log(2) extra instructions compared to P just to program the number n into it. The n-dependence of the program size will thus be

Log(n)/Log(2)

And you see that 2^(-program length) is proportional to 1/n.

I’m adding you to my blog roll.

I can’t imagine that the orderly universes would be more numerous than the disorderly ones (consider which is more numerous: orderly possible arrangements of pixels, or disorderly ones….) but in any case, please explain “…as long as the measure falls of faster than 2^(-program length) you’ll exponentially supress “messy worlds”…” Well, maybe “as long as”, but why should it be so, and could you take a minute to justify the conditional, since I am not really hip on that sort of framing of the issue.

(A friend of mine read TWF just before bed and woke up from a nightmare screaming, “I don’t even know what the f—k a cobordism is!” Seriously.)

That just cracked me up… I feel much better. Give them my apologies, though, and tell them to read Wikipedia before bed instead.

Sean, knowing you, there is a high probability that you have already read it, but if you have not you are bound to enjoy it: Miguel de Unamuno wrote the book, literally, on this subject above (El Sentido Tragico de la Vida). Hopefully the English translation does justice to the original.

(Trivia: If you have seen the Oscar winning “Belle Epoque”, the priest hangs himself and is found holding a book in his hand. This is it. I guess that tells you something)

Big hug from Chicago,

I don’t buy your argument about the brain not being equivalent in principle to a program that can be run on a computer. Brain processes can be described well by classical laws of physics…

About time, I don’t think that time really exists in the sense of a pointer making the “now” real and the past and the future not real. I think that the past, this moment and the future are all equally real. The description of what is happening today can be extracted, in principle from the description of the events in the early universe.

If our universe had magically disappeared one second after the Big Bang we would still have experienced being alive 13.7 billion years after the Big Bang. This is because our mental experience can, in principle, be defined in terms of quantum fields and reformulated in terms of fields at any time in the history of the universe, using a unitary transformation.

Strong AI implies that it doesn’t matter how you generate a particular person. You could just as well replace a brain by an ants nest, if the ants perform the same tasks as the neurons, neurotransmitters etc. Therefore “today” also exists in a hidden way in “yesterday” and thus also in the early universe. To me all this suggests that the notion of a physical universe is bogus.

You’d have to wonder about anyone who wouldn’t take that kind of blue pill.