RE: Turing vs math
[I sent this privately by accident] James Higgo writes: What that postulates is that everything exists, and that means you exist and I exist in an infinity of all possible variations. I'm perfectly comfortable with this, as I am an MWI-er. In this view, the only reason you ever get a physical 'law' is that when the random relationships we see as laws break down (which is most of the time), we cease to be able to observe it, as the environment then ceases to be hospitable to life. The same reson an MWI-er will give for us never seeing a vacuum collapse: they occur, but we don't observe those eigenstates in which they do, as we aren't alive. Only if it's a major breakdown. Laws that have small exceptions and loopholes would still be consistent with our existence. The question is, given that all worlds exist, and that the WAP explains why we find ourselves in a congenial environment, WHY have I never seen a flying rabbit? Why should not the 'laws' break a little bit, to allow non-lethal event like that, then repair themselves? Well, I just asked you the same thing in another message! I don't think you can explain this without invoking multiple universes. The normal all-universe explanation is to consider two universes. One has physical laws as we know them: F=ma (one of Newton's laws), etc. The other has a law like F=ma except when Merlin waves his magic wand. This universe allows for flying rabbits and other magical objects, but is otherwise basically lawful and people can evolve in it. Now, obviously the program to compute the second universe is much more complicated than the program to compute the first one. It has all these special exceptions in it for when magic is allowed to work, and how. So it is a bigger program. We then invoke the principle that large-program universes are inherently less likely than small-program universes, and presto! we have it more likely that we live in a universe without flying rabbits, without magic, etc. That's the general argument we are striving to achieve. I do think that this argument has some problems, but it is appealing and if the holes can be filled it seems to offer an answer to the question. What do you think? Hal
RE: Turing vs math
Why can't the simplest possible program be taken as computing a universe which includes us? We tend to say it computes all universes as though it computes more than one. Then it is fair to object that the program is too simple, because it computes more than one universe. But this is a semantic objection based on the definition of a universe. How do we know how many universes a given program computes? Is there an objective, well defined measure? That seems necessary in order to rule out a trivial counting or dovetailing program as one which creates our observable universe and our minds as a subset of its output. Wei Dai proposed a solution to this, which was to say that it is not enough to compute a universe that matches what I see; it must compute a universe which includes my mind. And then, he proposes that the probability measure should not be calculated as just the size of the universe program, but rather as the size of the program that computes the universe PLUS the size of the program that localizes (finds, locates) my mind within that universe. This provides an objective measure of the degree of overkill/redundancy/extra-universes produced by the universe simulation. Something objective like this seems necessary to reject the notion that we live in a universe produced by a trivial program. Hal Finney [EMAIL PROTECTED] (Juergen Schmidhuber) writes: Ah! The point is: the information content of a particular universe U is the length of the shortest algorithm that computes U AND NOTHING ELSE. But the shortest algorithm for everything computes all the other universes too. Hence it does not convey the information about U by itself! Everything conveys much less info than most particular computable objects. More is less. But to calculate the probability of a particular universe you need to look at its particular algorithms, of course, not at the collective probability of all universes.
Re: Turing vs math
In a message dated 99-10-21 11:53:14 EDT, James Higgo writes: Yes but the everything universe has the shortest algorithm, containing just one bit of information. The sub-universes do not need algorithms, just the WAP. and Juergen Scmidhuber replies Ah! The point is: the information content of a particular universe U is the length of the shortest algorithm that computes U AND NOTHING ELSE. But the shortest algorithm for everything computes all the other universes too. Hence it does not convey the information about U by itself! Juergens seems to be talking as if the measure of information is absolute. It is not. Information is always conditional information (Shannon), where the condition is the observer's a-priori database of information. Thus a one bit universe could mean different things for different observers. As James inferred, the WAP is essential: the world we observe is conditionned by our own mental frame of reference. As it happens, because of the need for justifying our existence using an evolutionary history embedded in a physical world, and because of the need to share a common language and a common logic, the (physical and logical) frames that each different human observer occupies are very close to each other. Hence the illusion of objectivity - that is the illusion that the world is the same no matter who the observer is. To remove oneself from this illusion, we must distance ourselves far away from our physical, and logical frames. Einstein did it, for a short while, until he explained what he did to everybody (physicists). Then, everybody jumped in Einstein's frame, that is they accepted RT in their own a-priori database and the world regained its semblance of objectivity. George
Re: Turing vs math
Bruno wrote: I don't take the notion of observer for granted. Neither do I, of course. The observer O is something computable that evolves in some universe U. The problem is that to be in a universe has no clear meaning But it does. There is a computable predicate S such that S(U)=TRUE if O inhabits U. Fortunately, there is no need for us to further specify what it means to ``inhabit,'' to be ``conscious'' or ``self-aware,'' or whether there is some other observer who applies S to U and uses S(U) to identify O, etc. Now we have a formally defined, conditional probability distribution on all universes satisfying S. I thought this to be clear, but maybe I should have written it down explicitly. Juergen
