Re: Violations of physical law

From: Saibal Mitra <smitra.domain.name.hidden>
Date: Wed, 19 Jun 2002 00:51:56 +0200

Shouldn't the probability go to zero faster than 1/2^n ? If you consider the
sequence of programs p_{k} were p_{k} will run k idintical copies of a
certain observer. The probability that the observer finds himself in p_{i}
should be i times the measure of P_{i}. I conclude that the measure of p{i}
should go to zero faster than 1/i. The length of the program is some
constant plus Log(i)/Log(2), therefore, if the measure depends only on
program length, it should go to zero faster than 1/2^n.

Saibal

----- Original Message -----
From: Hal Finney <hal.domain.name.hidden>
To: <everything-list.domain.name.hidden>
Sent: Tuesday, June 11, 2002 9:30 PM
Subject: Violations of physical law


> I want to follow up on the discussion we had last December about "flying
> rabbit" universes. Let me first recap my understanding of the issues.
>
> Suppose that all universes exist, and that they are associated with
> computer programs that generate them. The measure of a universe is
> defined as 1/2^n, where n is the size of the smallest program that
> generates a given universe. Can we reconcile this theory with our
> observations of the universe around us? In particular, does it explain
> why we seemingly live in a lawful universe?
>
> Broadly speaking, the answer is yes. As it happens, it appears that
> the laws of physics are relatively simple. Stephen Wolfram guesses
> that the entire set of laws for our universe could be reduced to about
> 5 lines of Mathematica code. So apparently a relatively simple program
> would be sufficient to generate our universe, with all its complexity,
> including ourselves.
>
> Clearly even more complex programs would also be possible to generate
> universes like ours. With the additional complexity the laws of
> nature could have more exceptions and allow for "miraculous" behavior.
> Such universes are called "flying rabbit" universes, or sometimes
> "white rabbit" (after Alice in Wonderland), "dragon", or "Harry Potter"
> universes. The idea is that these universes are basically lawful, but
> there are rare exceptions which can be manipulated to produce results
> which violate the natural laws which hold otherwise. The question is,
> why don't we live in such a universe?
>
> The answer is that to change the program from one which just implements
> the simple laws of physics to one which has the exceptions would greatly
> increase its size. To allow rabbits (but not other heavy, wingless
> animals) to fly, for example, the laws of physics would have to encode the
> definition of a rabbit. And since these laws are presumably expressed at
> the subatomic level, defining a rabbit from that perspective would take
> an enormous amount of information. Instead of 5 lines of Mathematica the
> program would balloon to probably billions of lines or even more, most
> of which was defining a rabbit. Such a program would have infinitesimal
> measure compared to our universe. That's why we don't see rabbits fly.
>
> Back in December I raised an objection. A white rabbit universe is less
> probable than a simpler one by a factor of roughly 2^R, where R is the
> information content in defining the rabbit. However, by the same token
> there are 2^R possible information patterns that can be described in
> those R bits. So if we consider the collection of all universes which
> allow for exceptions, not just for rabbit-shaped objects but for all
> possible rabbit-sized objects, then the total measure of all of these
> is approximately as large as for the simple universe. So we can't
> really reject white rabbit universes, if we extend the notion to refer
> to any universe which allows for miracles based on some special pattern
> of information.
>
> The answer to this objection was basically that most patterns of
> information are random. So the vast majority of these universes, while
> in principle allowing for miracles, would only have them be triggered
> by a phenomenon which is so rare that it will never occur in practice.
> You'd have to have a huge combination of particles take on some precise
> configuration, and then maybe something bizarre would happen. But the
> chance of any such configuration arising would be so low, it would be
> like waiting for random thermal motions to suck all of the air out of
> your room. You'd never see it in the lifetime of the universe.
>
> Now, my new idea is to look at somewhat less extreme violations of laws.
> Suppose we have a universe which has simple natural laws like ours, but
> does allow for violations based on certain patterns or configurations
> of matter. As before, the larger the pattern necessary to trigger
> exceptional behavior, the lower the measure of the universe; but
> countering that, there are just as many possible patterns which could
> be used to trigger the lawless behavior. So collectively the set of
> universes with some exceptions does not have much less measure than for
> universes with simple laws and no exceptions.
>
> It seems to me, then, that it is actually likely that we live in
> such a universe. Chances our that our universe has basically simple
> natural laws, but has the chance for miracles to occur when the proper
> arrangements are made. And there's no inherent reason why the miracle
> triggering configuration has to be huge as for a white rabbit. It could
> be as simple as a few subatomic particles coming together in a certain
> way. In fact, it's possible that such "miracles" happen at a relatively
> high rate throughout the universe, events which violate natural laws.
> I think our model even predicts that there is a reasonable likelihood
> that such things happen.
>
> The only real limitation I see on the probability of lawless events
> is based on the anthropic principle. The universe has to be lawful
> enough for intelligent life to have arisen. If it were too easy to
> generate energy, say, or to repel gravity, then the universe might be
> chaotic and unstable. Or perhaps life would evolve to exploit these
> possibilities and it would make things so easy that there would be no
> incentive for intelligence to evolve.
>
> This suggests that as we move forward with our investigations of physics,
> exploring new realms of matter with new tools that could not have
> been reasonably evolved naturally, we should expect, with a reasonably
> high probability, to discover miracles. We're not guaranteed to do so,
> because after all even the collection of all miracle-containing universes
> is still not quite as probable as the simple one that has no miracles.
> But collectively I think they might be as much as 1/10 as probable,
> and perhaps even 1/2 as probable.
>
> So it seems to me that this is another prediction which we can make based
> on the all-universe principle (AUP): that natural law may well have rare
> exceptions, and that once we begin exploring realms and configurations
> that are unlikely to have occured naturally, we may find one. It's hard
> to say what the outcome is likely to be, but most likely it is something
> that can be described simply, in whatever programming language most
> efficiently describes our universe's natural laws. Maybe there's a sign
> reversal somewhere, or a constraint is simply skipped or added.
>
> We could get unlucky and blow up the planet with some kind of energy
> release triggered by a particle accelerator. Or maybe we'd get lucky
> and find some way to exploit the miracle to our benefit. But I think
> the AUP gives us more reason than in conventional view of physics to
> expect such miraculous behavior.
>
> Hal Finney
>
Received on Tue Jun 18 2002 - 15:59:36 PDT