Re: Free Will Theorem
Ah John, if only I could understand what you're saying... On Fri, Apr 22, 2005 at 11:45:22AM -0400, John M wrote: - Original Message - From: Russell Standish [EMAIL PROTECTED] To: John M [EMAIL PROTECTED] Cc: Stathis Papaioannou [EMAIL PROTECTED]; [EMAIL PROTECTED]; everything-list@eskimo.com Sent: Tuesday, April 19, 2005 8:09 PM Subject: Re: Free Will Theorem Russell S. writes in his convoluted from attachment-digging out ways: Laplace's daemon is a hypothetical creature that knows the exact state of every particle in the universe. In a deterministic universe, the daemon could compute the future exactly. Of course the daemon cannot possibly exist, any more than omniscient beings. In a quantum world, or a Multiverse, such daemons are laughable fantasies. Nevertheless, they're often deployed in reductio ad absurdum type arguments to do with determinism. Again the stubborn anthropomorphic one-way thinking about the idea of a total determinism in one way only. Everything calculated 'in' there is only ONE outcome in the world - as the essence of the one-way universe's own determinism. This was the spirit that made the total greater than the sum of its components - the Aris-total of the epistemic level 2500 years ago. It is an age-old technique to invent a faulty hypothesis (thought experiment, etc.) and on this basis show the 'ad absurdity' of something. Determinism as I would like 'to speak about it' is the idea that whatever happens (the world as process?) originates in happenings - (beware: not a cause as in a limited model, but) in unlimited ensembles of happenings all over, not limited to the topical etc. boundaries we erect for our chosen observations. The happenings are including the 'ideational' part of the world, which is 'choice-accepting' - consequently not fully predictable. As in: endogenously impredicative complexities. Anticipatory is not necessarily predictable and (my) deterministic points to the other side: not where it goes TO, but comes FROM. Even there it is more than we can today encompass (compute?) in full. This may be a worldwide applicational principle of the spirit that made its minuscule example into QM as the 'uncertainty'. Or the cat, or a complimentarity. Alas, I cannot 'speak about it', because we are not up to such level. Not me, not you, not even the materialistic daemon. We all are rooted in the materialistic reductionist models what our neuronal brain can handle - in a world of unlimited interconnectedness. John Mikes -- *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) Mathematics0425 253119 () UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 pgp6ubIaIpqno.pgp Description: PGP signature
Re: follow-up on Holographic principle and MWI
On Thu, Apr 21, 2005 at 11:02:12PM -0400, danny mayes wrote: Well, as described in the FOR think of the multiverse as a block, made up of different stacks of pictures that comprise individual universes as they move through time. Now try to adjust that to what is really going on: space time is expanding out from the Big Bang. If you could remove yourself from the multiverse and watch it, time would be expanding at an increasing area, just as the spatial dimensions are. The reason information storage capacity would equal the surface area of a given object is that any object or area is actually existing in all these overlapping timelines, or virtually identically universes. Therefore, if you assume the time-area is expanding at a proportional rate to the spatial volume, you would need to divide a cube 10^300 Planck units on a side by 10^100 to take out the information that is moving into the This is very sloppy - if time-area were proportional to volume, then the divisor would be 10^300. Perhaps you meant proportional to length, but then I do not see why this should be. volume or area of time, since we lose this information as we are stuck on a solitary time line and losing the multiverse information to decoherence. This is simply another way of saying we lose the information to the other universes, I'm just explaining why it would be the amount it is through the mental imagery of time expanding to fill a space equivalent to the spatial dimensions. But decoherence increases information, not loses it. Taking a bird's eye view, and watching the cube moving through the multiverse, all the overlapping universes the cube comprises, the cube could store 10^300 bits of information- equal to it's volume. However, if you measure the information in any individual universe, you have to divide the cube over all the overlapping universes it comprises, or an area of time equal to the the area of one of it's sides (again assuming the expansion of time is proportional to the expansion of the spatial dimensions.) This leaves information storage capacity equal to the surface area of the object . I am basically taking the block view of the multiverse seriously, and dividing the information storage capacity by the area of all the stacks of pictures the cube exists on, because we can only measure the information on the one stack that is our universe. The area of the different stacks can be thought of as an area of time, and would equal one of the spatial areas that comprise the cube if time expansion is proportional to spatial expansion. This makes sense to me, but then again I am an attorney Danny Mayes The only thing that makes sense to me is that maximal decoherence occurs by arranging observers around the 4/3\pi solid angle of the volume in question. Thus the maximum decoherence rate is proportional to the surface area of the volume. Also, we know that linear spatial dimensions are increasing linearly in flat space-time, so combining the two implies that maximal decoherence will occur quadratically as a function of time. Does this give us the holographic principle? Hmm.. Also, what happens if space-time is not so flat - say spatial expansion starts to accelerate like its doing now? -- *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) Mathematics0425 253119 () UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 pgpHLuBXwEVmx.pgp Description: PGP signature
Re: Free Will Theorem
- Original Message - From: Russell Standish [EMAIL PROTECTED] To: John M [EMAIL PROTECTED] Cc: Stathis Papaioannou [EMAIL PROTECTED]; [EMAIL PROTECTED]; everything-list@eskimo.com Sent: Tuesday, April 19, 2005 8:09 PM Subject: Re: Free Will Theorem Russell S. writes in his convoluted from attachment-digging out ways: Laplace's daemon is a hypothetical creature that knows the exact state of every particle in the universe. In a deterministic universe, the daemon could compute the future exactly. Of course the daemon cannot possibly exist, any more than omniscient beings. In a quantum world, or a Multiverse, such daemons are laughable fantasies. Nevertheless, they're often deployed in reductio ad absurdum type arguments to do with determinism. Again the stubborn anthropomorphic one-way thinking about the idea of a total determinism in one way only. Everything calculated 'in' there is only ONE outcome in the world - as the essence of the one-way universe's own determinism. This was the spirit that made the total greater than the sum of its components - the Aris-total of the epistemic level 2500 years ago. It is an age-old technique to invent a faulty hypothesis (thought experiment, etc.) and on this basis show the 'ad absurdity' of something. Determinism as I would like 'to speak about it' is the idea that whatever happens (the world as process?) originates in happenings - (beware: not a cause as in a limited model, but) in unlimited ensembles of happenings all over, not limited to the topical etc. boundaries we erect for our chosen observations. The happenings are including the 'ideational' part of the world, which is 'choice-accepting' - consequently not fully predictable. As in: endogenously impredicative complexities. Anticipatory is not necessarily predictable and (my) deterministic points to the other side: not where it goes TO, but comes FROM. Even there it is more than we can today encompass (compute?) in full. This may be a worldwide applicational principle of the spirit that made its minuscule example into QM as the 'uncertainty'. Or the cat, or a complimentarity. Alas, I cannot 'speak about it', because we are not up to such level. Not me, not you, not even the materialistic daemon. We all are rooted in the materialistic reductionist models what our neuronal brain can handle - in a world of unlimited interconnectedness. John Mikes
Re: follow-up on Holographic principle and MWI
Russell Standish wrote: On Thu, Apr 21, 2005 at 11:02:12PM -0400, danny mayes wrote: Well, as described in the FOR think of the multiverse as a block, made up of different stacks of pictures that comprise individual universes as they move through time. Now try to adjust that to what is really going on: space time is expanding out from the Big Bang. If you could remove yourself from the multiverse and watch it, time would be expanding at an increasing area, just as the spatial dimensions are. The reason information storage capacity would equal the surface area of a given object is that any object or area is actually existing in all these overlapping timelines, or virtually identically universes. Therefore, if you assume the "time-area" is expanding at a proportional rate to the spatial volume, you would need to divide a cube 10^300 Planck units on a side by 10^100 to take out the information that is moving into the This is very sloppy - if "time-area" were proportional to volume, then the divisor would be 10^300. Perhaps you meant proportional to length, but then I do not see why this should be. You are correct. This is very sloppy. First, I made a typo in referring to the cube as 10^300 on a side when I intended to say 10^300 in volume. Also, the time area would be proportional to the other spatial dimensions (a side) of the cube, not the volume. My apologies. Again, the "time area" should equal a side if it is considered equivalent to a spatial dimension. volume or area of time, since we lose this information as we are stuck on a solitary time line and losing the multiverse information to decoherence. This is simply another way of saying we lose the information to the other universes, I'm just explaining why it would be the amount it is through the mental imagery of time expanding to fill a space equivalent to the spatial dimensions. But decoherence increases information, not loses it. It increases the information we have in this universe, by removing the interference of all the information from all the alternative outcomes. We gain the information of one possible outcome. From the multiverse view, there is no gain or loss of information, but from our perspective we gain one bit of information and the rest ends up in the alternative outcomes. Taking a bird's eye view, and watching the cube moving through the multiverse, all the overlapping universes the cube comprises, the cube could store 10^300 bits of information- equal to it's volume. However, if you measure the information in any individual universe, you have to divide the cube over all the overlapping universes it comprises, or an "area" of time equal to the the area of one of it's sides (again assuming the expansion of time is proportional to the expansion of the spatial dimensions.) This leaves information storage capacity equal to the surface area of the object . I am basically taking the block view of the multiverse seriously, and dividing the information storage capacity by the area of all the stacks of pictures the cube exists on, because we can only measure the information on the one stack that is our universe. The area of the different stacks can be thought of as an area of time, and would equal one of the spatial areas that comprise the cube if time expansion is proportional to spatial expansion. This makes sense to me, but then again I am an attorney Danny Mayes The only thing that makes sense to me is that maximal decoherence occurs by arranging observers around the 4/3\pi solid angle of the volume in question. Thus the maximum decoherence rate is proportional to the surface area of the volume. Also, we know that linear spatial dimensions are increasing linearly in flat space-time, so combining the two implies that maximal decoherence will occur quadratically as a function of time. Does this give us the holographic principle? Hmm.. Also, what happens if space-time is not so flat - say spatial expansion starts to accelerate like its doing now? With regards to your last, time area expansion would accelerate with with spatial acceleration. This means the number of stacks/outcomes become more numerous. With spatial collapse the time-area would decrease (stacks/outcomes decrease). (??)
RE: many worlds theory of immortality
Jesse, Stathis Papaioannou wrote: Now, look at p(n) again. This time, let's say it is not k, but a random real number greater than zero, smaller than 1, with k being the mean of the distribution. At first glance, it may appear that not much has changed, since the probabilities will on average be the same, over a long time period. However, this is not correct. In the above product, p(n) can go arbitrarily close to 1 for an arbitrarily long run of n, thus reducing the product value arbitrarily close to zero up to that point, which cannot subsequently be made up by a compensating fall of p(n) close to zero, since the factor 1-p(n)^(2^n) can never be greater than 1. (Sorry I haven't put this very elegantly.) p(n) *can* go arbitrarily close to 1 for an arbitrarily long period of time, but you're not taking into the account the fact that the larger the population already is, the more arbitrarily close to 1 p(n) would have to get to wipe out the population completely--and the more arbitrarily close a value to 1 you pick, the less probable it is that p(n) will be greater than or equal to this value in a given generation. So it's still true that the probability of the population being wiped out is continually decreasing as the population gets larger, which means it's still plausible there could be a nonzero probability the population would never be wiped out--you'd have to do the math to test this (and you might get different answers depending on what probability distribution you pick for p(n)). It also seems unrealistic to say that in a given generation, all 2^n members will have the *same* probability p(n) of being erased--if you're going to have random variations in p(n), wouldn't it make more sense for each individual to independently pick a value of p(n) from the probability distribution you're using? And if you do that, then the larger the population is, the smaller the average deviation from the expected mean value of p(n) given by that distribution. The conclusion is therefore that if p(n) is allowed to vary randomly, Real Death becomes a certainty over time, even with continuous exponential growth forever. I think you have any basis for being sure that Real Death becomes a certainty over time in the model you suggest (or the modified version I suggested above), not unless you've actually done the math, which would likely be pretty hairy. Jesse Jesse, It would be stubborn of me not to admit at this point that you have defended your position better than I have mine. I'm still not quite convinced that what I have called p(n) won't ultimately ruin the model you have proposed, and I'm still not quite convinced that, even if it works, this model will not constitute a smaller and smaller proportion of worlds where you remain alive, over time; but as you say, I would have to do the maths before making such claims. I may try out some of these ideas with Mathematica, but I expect that the maths is beyond me. Anyway, thank-you for a most interesting and edifying discussion! --Stathis Papaioannou _ SEEK: Now with over 80,000 dream jobs! Click here: http://ninemsn.seek.com.au?hotmail
Re: follow-up on Holographic principle and MWI
Russell Standish wrote: the divisor would be 10^300. Perhaps you meant proportional to length, but then I do not see why this should be. Don't know if I directly answered this in my first reply. If time-area equal an equivalent spatial area, we use length as the divisor to represent the fact that we have access to the information in one universe/one time line. We, of course do not have access to the information in the time area, which is all the possible outcomes.
