Re: lost in the many worlds
On Fri, Jan 30, 1998 at 10:12:22AM -0800, Hal Finney wrote: > So, the idea is that there is some probability that your brain could > form spontaneously in intergalactic space, and that probability per > brain-volume would be approximately 2^-L? No, that wouldn't work because the density of interstellar gas is too low. The idea is that if you look at an appropriately larger volume of space, there is some probability that the gas particles in it are lined up so that they have the same basic structure as WDB (i.e. the organic brain), even if they are much farther apart and are made of different atoms (these differences do not matter since they can be removed by simple transformations). This probability is approximately 2^-L. If you're worried about the encoding scheme L is defined in terms of, let's instead define L in terms of this probability. It seems any reasonable encoding scheme should encode WDB in not much more than L bits. I want to make two points: 1. The probability of finding WDB in a random brain-volume is much more than 2^-L. We should be able to derive this from quantum mechanics, but my argument is that otherwise I would have to believe I'm likely to be instantiated as interstellar gas. 2. The number of branches in the universal wavefunction is enormous (see Q11 of the many-worlds FAQ). It's much bigger than 2^L. The conclusion from this is that I and everyone else must be living in multiple branches simultaneously, and many of these branches do not share any recent history (i.e. they became decoherent early in the history of the universe). This implies that when someone observes a new piece of information, sometimes that causes a split, but other times it merely causes a differentiation. So many-worlds and many-minds interpretations are each correct in different situations.
Re: lost in the many worlds
Wei Dai, <[EMAIL PROTECTED]>, writes: > I now think that I was probably wrong about this, but I still don't > understand why. Suppose our administrator takes the universal wave > function (which assuming the Everett Postulate never collapses during > normal evolution), collapses it into a position eigenfunction according to > the familiar probabilistic rules, and then examines the resulting position > eigenfunction, treating it a sort of snapshot. Now if he just picks a > random volume of space to look at, chances are he would see some > unstructured interstellar gas. But with probability of about 2^-L, where L > is the length of a complete uncompressed description of my brain (WDB), > the volume of gas he sees would by coincidence turn out to have the same > positional structure as WDB. If I'm to believe that I'm much more likely > to be currently instantiated as a brain made of organic chemicals rather > than of interstellar gas, it must be that the probability of finding the > organic brain is much higher than 2^-L, which implies that it takes much > less than L bits of information to find a description of WDB in the > universal wave function. However I do not know how to derive this from the > principles of quantum mechanics. So, the idea is that there is some probability that your brain could form spontaneously in intergalactic space, and that probability per brain-volume would be approximately 2^-L? One thing I note is that you have introduced the idea of an "uncompressed" description of the brain, which is not clearly defined. Earlier you had just asked about the information needed to describe the brain, without reference to whether it was compressed or not. Probably there is no upper limit on ways of writing a description of the brain in uncompressed form, so L as described here is ambiguous. For this particular case, you need to look at the actual physical nature of the intergalactic medium in order to calculate the odds of it spontaneously forming some structure. This will no doubt be related to the complexity of the structure, but I'm not sure it would simply be exponential in the length of a description of the structure. Or at least you would have to set up your description language in a certain way. For example, intergalactic space is composed almost entirely of hydrogen atoms. The occasional carbon or oxygen is going to be very, very rare. So the form of the description language would have to take that into consideration. Then there is the extremely low density, which is going to have to increase by something like 30 orders of magnitude over the norm in order to form your brain. Does that just mean you have to look at 10^30 volumes the size of your brain? I don't think so. You'd have to look at a lot more than 10 brain-volumes to find one with a density ten times the norm. I think there may be an exponential factor just based on the density. (Sorry to be so vague; it's been a long time since I've studied thermodynamics.) So somehow the length L would have to become longer to reflect the higher density of your brain, which doesn't seem like a natural way for a description to behave. Hal
Re: lost in the many worlds
On Wed, Jan 28, 1998 at 03:27:41PM -0800, Hal Finney wrote: > I think you're right that the amount of data would be very large. > You'd have to count the information content of each wave function collapse > since the creation of the universe. I now think that I was probably wrong about this, but I still don't understand why. Suppose our administrator takes the universal wave function (which assuming the Everett Postulate never collapses during normal evolution), collapses it into a position eigenfunction according to the familiar probabilistic rules, and then examines the resulting position eigenfunction, treating it a sort of snapshot. Now if he just picks a random volume of space to look at, chances are he would see some unstructured interstellar gas. But with probability of about 2^-L, where L is the length of a complete uncompressed description of my brain (WDB), the volume of gas he sees would by coincidence turn out to have the same positional structure as WDB. If I'm to believe that I'm much more likely to be currently instantiated as a brain made of organic chemicals rather than of interstellar gas, it must be that the probability of finding the organic brain is much higher than 2^-L, which implies that it takes much less than L bits of information to find a description of WDB in the universal wave function. However I do not know how to derive this from the principles of quantum mechanics.
Re: lost in the many worlds
Wei Dai, <[EMAIL PROTECTED]>, writes: > Suppose our universe is actually a wave function evolving in a computer in > another universe acoording to the standard linear wave equations. If there > is a way to send a signal to the administrator of this computer, how many > bits of information would we need to send in order for him to be able to > find us in the wave function? > > My impression (please correct me if I'm wrong) is that this would be a > very large number, much larger than the number of bits needed to > completely describe a human brain. If this is true, then in what sense > does quantum mechanics offer an explaination for our perceptions of the > world (i.e. the inside view in Max Tegmark's terminology)? It seems like > a complete explaination would be longer than the data itself. By complete > explaination I mean boundary conditions of the wave function, the wave > equations, and the information needed to extract the inside view that > we're seeing from the wave function. I think you're right that the amount of data would be very large. You'd have to count the information content of each wave function collapse since the creation of the universe. With many-worlds, and also with an all-universes TM, you get a short program at the cost of creating multiple universes. Then if you want to select just one of those universes, you would have to specify a lot of information. These models do not offer an explanation for why we see the specific universe we do. What they do provide is a prediction that some observers like ourselves should exist, and that they should see the universe as we see it. So the model does, in that sense, predict what we see, and therefore could be said to explain what we see. I'm not sure what you are getting at in terms of comparing with the number of bits to specify a human brain. Are you thinking that it would be simpler to say that your brain was simply created in its current state than that all these events happened throughout history to produce it? Hal
lost in the many worlds
Suppose our universe is actually a wave function evolving in a computer in another universe acoording to the standard linear wave equations. If there is a way to send a signal to the administrator of this computer, how many bits of information would we need to send in order for him to be able to find us in the wave function? My impression (please correct me if I'm wrong) is that this would be a very large number, much larger than the number of bits needed to completely describe a human brain. If this is true, then in what sense does quantum mechanics offer an explaination for our perceptions of the world (i.e. the inside view in Max Tegmark's terminology)? It seems like a complete explaination would be longer than the data itself. By complete explaination I mean boundary conditions of the wave function, the wave equations, and the information needed to extract the inside view that we're seeing from the wave function.
