I remembered Wei Dai posting on this topic in the early days of this list, and indeed some of his postings influenced my "Why Occam's Razor" paper. However, I do not recall his suggestions as being as detailed as what you describe here. Do you have a reference to where this might be written up? I'm also intrigued by the possibility of demonstrating that transhumanist observer moments would have substantially less measure than human observer moments. Such a result would be a transhumanist counter to the Doomsday argument of course.
Cheers On Fri, Jun 03, 2005 at 11:10:15AM -0700, "Hal Finney" wrote: ... > > Years ago Wei Dai on this list suggested a better approach. He proposed > a formula for determining how much of a universe's measure contributes to > an OM that it instantiates. It is very specific and also illustrates > some problems in the rather loose discussion so far. For example, > what does it really mean to instantiate an OM? How would we know if a > universe is really instantiating a particular OM? Aren't there fuzzy > cases where a universe is only "sort of" instantiating one? What about > the longstanding problem that you can look at the atomic vibrations in > a crystal, select a subset of them to pay attention to, and have that > pattern match the pattern of any given OM? Does this mean that every > crystal instantiates every OM? (Hans Moravec sometimes seems to say yes!) > > To apply Wei's method, first we need to get serious about what is an OM. > We need a formal model and description of a particular OM. Consider, for > example, someone's brain when he is having a particular experience. He is > eating chocolate ice cream while listening to Beethoven's 5th symphony, > on his 30th birthday. Imagine that we could scan his brain with advanced > technology and record his neural activity. Imagine further that with the > aid of an advanced brain model we are able to prune out the unnecessary > information and distill this to the essence of the experience. We come > up with a pattern that represents that observer moment. Any system which > instantiates that pattern genuinely creates an experience of that observer > moment. This pattern is something that can be specified, recorded and > written down in some form. It probably involves a huge volume of data. > > So, now that we have a handle on what a particular OM is, we can more > reasonably ask whether a universe instantiates it. It comes down to > whether it produces and contains that particular pattern. But this may > not be such an easy question. It could be that the "raw" output format of > a universe program does not lend itself to seeing larger scale patterns. > For example, in our own universe, the raw output would probably be at > the level of the Planck scale, far, far smaller than an atomic nucleus. > At that level, even a single brain neuron would be the size of a galaxy. > And the time for enough neural firings to occur to make up a noticeable > conscious experience would be like the entire age of the universe. > It will take considerable interpretation of the raw output of our > universe's program to detect the faint traces of an observer moment. > > And as noted above, an over-aggressive attempt to hunt out observer > moments will find false positives, random patterns which, if we are > selective enough, happen to match what we are looking for. > > Wei proposed to solve both of these problems by introducing an > interpretation program. It would be take as its input, the output of the > universe-creation program. It would then output the observer moment in > whatever formal specification format we had decided on (the exact format > will not be significant). > > So how would this program work, in the case of our universe? It would > have encoded in it the location in space and time of the brain which > was experiencing the OM. It would know the size of the brain and the > spatial distribution of its neurons. And it would know the faint traces > and changes at the Planck scale that would correspond to neural firings > or pauses. Based on this information, which is encoded into the program, > it would run and output the results. And that output would then match > the formal encoding of the OM. > > Now, Wei applies the same kind of reasoning that we do for the measure > of the Schmidhuber ensemble itself. He proposes that the size of the > interpretation program should determine how much of the universe's measure > contributes to the OM. If the interpretation program is relatively small, > that is evidence that the universe is making a strong contribution to > the OM. But if the interpretation program is huge, then we would say > that little of the universe's measure should go into the OM. > > In the most extreme case, the interpretation program could just encode the > OM within itself, ignore the universe state and output that data pattern. > In effect that is what would have to be done in order to find an OM > within a crystal as described above. You'd have to have the whole OM > state in the program since the crystal doesn't actually have any real > relationship to the OM. But that would be an enormous interpretation > program, which would deliver only a trivial measure. > > For a universe like our own, the hope and expectation is that the > interpretation program will be relatively small. Such a program takes > the entire universe as input and outputs a particular OM. I did some > back of the envelope calculations and you will probably be amazed that > I estimate that such a program could be less than 1000 bits in size. > (This is assuming the universe is roughly as big as what is visible, and > neglecting the MWI.) Compared to the information in an OM, which I can't > even guess but will surely be at least gigabytes, this is insignificant. > Therefore we do have strong grounds to say that the universe which > appears real is in fact making a major contribution to our OMs. > > To be specific, Wei's idea was to count the measure of a universe's > contribution to an OM as 1/2^(n+m), where n is the size of the program > that creates the universe, and m is the size of the interpretation > program that reads the output of the first program, and outputs the OM > specification from that. In effect, you can think of the two programs > together as a single program which outputs the formal spec of the OM, > and ask what are the shortest ways to do that. In this way you can > actually calculate the measure of an OM directly without even looking at > the intermediate step of calculating a universe. But I prefer thinking of > the two step method as it gives us a handle on such concepts as whether > we are living in the Matrix or as a brain in a vat. > > Overall I think this is a very attractive formulation. It's quantitative, > and it gives the intuitively right answer for many cases. The counting > program contributes effectively no measure, because the only way we can > find an OM is by encoding the whole thing in the interpretation program. > And as another example, if there are multiple OMs instantiated by a > particular universe, that will allow the interpretation program to be > smaller because less information is needed to localize an OM. It also > implies that small universes will devote more of their measure to OMs > that they instantiate than large ones, which basically makes sense. > > There are a few unintuitive consequences, though, such as that large > instantiations of OMs will have more measure than small ones, and likewise > slow ones will have more measure than fast ones. This is because in each > case the interpretation program can be smaller if it is easier to find the > OM in the vastness of a universe, and the slower and bigger an OM is the > easier it is to find. I am inclined to tentatively accept these results. > It does imply that the extreme future vision of some transhumanists, > to upload themselves to super-fast, super-small computers, may greatly > reduce their measure, which would mean that it would be like taking a > large chance of dying. > > There is one big problem with the approach, though, which I have not yet > solved. I wrote above that a very short program could localize a given OM > within our universe. It only takes ~300 bits to locate a brain (i.e. a > brain-sized piece of space)! However this neglects the MWI. If we take > as our universe-model a world governed by the MWI, it is exponentially > larger than what we see as the visible universe. Every decoherence-time, > the universe splits. That's like picoseconds, or nanoseconds at best. > The number of splittings since the universe was created is vast, and > the size of the universe is like 2 (or more!) to that power. > > Providing the information to localize a particular OM within the vastness > of a universe governed by the MWI appears to be truly intractable. > Granted, we don't necessarily have to narrow it down to an exact branch, > but unless there are tremendous amounts of de facto convergent evolution > after splits, it seems to me that the percentage of quantum space-time > occupied by a given OM is far smaller than the 1/2^1000 I would estimate > in a non-MWI universe. It's more like 1/2^2^100. At that rate the > interpretation program to find an OM would be much *bigger* than the one > that just hard-codes the OM itself. In short, it would appear that an MWI > universe cannot contribute significant measure to an OM, under this model. > That's a serious problem. > > So there are a couple of possible solutions to this problem. One is to > reject the MWI on these grounds. That's not too attractive; this line of > argument is awfully speculative for such a conclusion. Also, creating a > program for a non-MWI universe requires a random number generator, which > is an ugly kludge and implies that quantum randomness is algorithmic > rather than true, a bizarre result. A more hopeful possibility is that > there will turn out to be structure in the MWI phase space that will > allow us to localize OM's much more easily than the brute force method > I assumed above. I have only the barest speculations about how that > might work, to which I need to give more thought. > > But even with this problem, I think the overall formulation is the > best I have seen in terms of grappling with the reality of a multiverse > and addressing the issue of where we as observers fit into the greater > structure. It provides a quantitative and approximable measure which > allows us to calculate, in principle, how much of our reality is as it > appears and how much is an illusion. It answers questions like whether > copies contribute to measure. And it provides some interesting and > surprising predictions about how various changes to the substrate > of intelligence (uploading to computers, etc.) may change measure. > In general I think Wei Dai's approach is the best foundation for > understanding the place of observers within the multiverse. > > Hal Finney -- *PS: A number of people ask me about the attachment to my email, which is of type "application/pgp-signature". Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics 0425 253119 (") UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 ----------------------------------------------------------------------------
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