Re: (Quantum) suicide not necessary?
I checked out your website, but it still seems to me there is a big gap between saying all universes with physics that are consistent with the WAP are experienced and saying that all thoughts (observer moments) exists. In the later case there is no explanation for the seeming existence of coherent sequences of thoughts such as 'me', except to say that if all thoughts exist then this sequence must exist too. The trouble with this is that an explanation that can explain anything explains nothing. Brent Meeker Before I was blind but now I see. I was the one who came up with the expression, 'Quantum Theory of Immortality', and I now see that it's false - and all this stuff in this thread is based on the same mistake. See www.higgo.com/qti , a site dedicated to the idea. There is no 'you'. 'You' don't 'travel'. There are just different observer moments, some including 'I am Micky and I'm, sick'. Even thinking in your passe Newtonian terms, how can a universe in which 'you have a disease' be the same as one in which 'you do not have the disease', just because you don't know it? I see why Jacques gets so irritated by this type of thinking, but it's nice to see him back on the list now then.
Re: (Quantum) suicide not necessary?
Bruno wrote: Saibal Mitra wrote: Instead of the previously discussed suicide experiments to test various versions of many-worlds theories, one might consider a different approach. By deleting certain sectors of one's memory one should be able to travel to different branches of the multiverse. Suppose you are diagnosed with a rare disease. You don't have complaints yet, but you will die within a year. If you could delete the information that you have this particular disease (and also the information that information has been deleted), branches in which you don't have the disease merge with the branches in which you do have the disease. So with very high probability you have travelled to a different branch. Be careful because in the process you take the risk of losing a friend. More aptly (3 1 switch) a friend risks losing you. Do you agree that at *some* level we do that all the time? Does death works as personal local and relative memory eraser ? Your suggestion is risky, if not egoist, but, is there another way when the rare disease is fatal? Indeed. Death will erase my memory anyway, so why not do it in a controlled way to maximize the probability of some desired outcome. Thought experiment with speculative memory capture raised quickly the interesting question: how many (first) person exists, really. I don't know the answer. One ? Why not an infinite number? In another post Saibal wrote: I think the source of the problem is equation 1 of Jürgens paper. This equation supposedly gives the probability that I am in a particular universe, but it ignores that multiple copies of me might exist in one universe. Let's consider a simple example. The prior probability of universe i (i0) is denoted as P(i), and i copies of me exist in universe i. In this case, Jürgen computes the propability that if you pick a universe at random, sampled with the prior P, you pick universe i. This probability is, of course, P(i). Therefore Jürgen never has to identify how many times I exist in a particular universe, and can ignore what consciousness actually is. Surerly an open univere where an infinite number of copies of me exist is infinitely more likely than a closed universe where I don't have any copies, assuming that the priors are of the same order? Would you agree that a quantum multiverse could play the role of a particular open universe where an infinite number of copies of me exists? I agree that this could be the case. If you agree, would that mean we have anthropic reasons to believe in a quantum-like multiverse? That's an interesting point! Saibal
Re: QTI
The point is, 'you' have no 'age'. An observer moment exists, it does not have any temporal attributes _per se_ - although it may contain externally-meaningless concepts such as 'it is 12:45pm'. The statement, 'one OM outlives another' is a category mistake. - Original Message - From: Saibal Mitra To: James Higgo ; Michael Rosefield ; [EMAIL PROTECTED] Sent: Saturday, March 03, 2001 4:34 PM Subject: QTI I also don't think that 'Quantum Theory of Immortality' is correct in its conventional form. I do believe, however, that a different versionis implied by James' Theory of Observer Moments. Since there exists a set S of observer moments, one element of which represents my state now, I will ''always'' find myself in some subset of S. This doesn't mean that I could outlive everyone. The observer moment: I am 10^100 years old is simply inconsistent with I am Saibal. I posted earlier about an article by Caticha that explains how fundamental laws of physics (including notions such as time and space) can be derived from nothing more than an arbitrary probability distribution defined over some arbitrary set. See http://xxx.lanl.gov/abs/math-ph/0008018 Saibal - Original Message - From: James Higgo To: Michael Rosefield ; Saibal Mitra ; [EMAIL PROTECTED] Sent: Saturday, March 03, 2001 1:53 PM Subject: Re: (Quantum) suicide not necessary? Before I was blind but now I see. I was the one who came up with the expression, 'Quantum Theory of Immortality', and I now see that it's false - and all this stuff in this thread is based on the same mistake. See www.higgo.com/qti , a site dedicated to the idea. There is no 'you'. 'You' don't 'travel'. There are just different observer moments, some including 'I am Micky and I'm, sick'. Even thinking in your passe Newtonian terms,how can a universe in which 'you have a disease' be the same as one in which 'you do not have the disease', just because you don't know it? I see why Jacques gets so irritated by this type of thinking, but it's nice to see him back on the list now then. - Original Message - From: Michael Rosefield To: Saibal Mitra ; [EMAIL PROTECTED] Sent: Tuesday, February 27, 2001 3:30 PM Subject: Re: (Quantum) suicide not necessary? *Phew!*; this afternoon I finally got round to reading the 190-odd messages I have received from this list From: Saibal Mitra Instead of the previously discussed suicide experiments to test variousversions of many-worlds theories, one might consider a different approach. By deleting certain sectors of one's memory one should be able to travelto different branches of the multiverse. Suppose you are diagnosed with a rare disease. You don't have complaints yet, but you will diewithin a year. If you could delete the information that you have thisparticular disease (and also the information that information hasbeen deleted), branches in which you don't have the diseasemerge with the branches in which you do have the disease. So withvery high probability you have travelled to a different branch. I don't know whether to be relieved or annoyed that I'm not the only person to think of this ;D. http://pub45.ezboard.com/fwastelandofwondersfrm1.showMessage?topicID=353.topicindex=5 I'm guessing this is quite a common idea? Rats, I thought I was so great I_did_ thinkof the following today, though: If you take this sort of thing one step further, an afterlife is inevitable; there will always be systems - however improbable - where the mind lives on. For instance, you could just be the victim of an hallucination, your mind could be downloaded, you could be miraculously cured, and other _much_ more bizzare ones. Since you won't be around to notice the worlds where you did die, they don't count, and you are effectively immortal. Or at least you will perceive yourself to live on, which is the same thing. When I thought of it, it seemed startlingly original and clever. Looking at the posts I have from this list, I'm beginning to suspect it's neither Anyhow, while this sort of wild thinking iswonderfully pure andcathartic, itnever seems to lead anywhere with testable or useful implications. So far, anyway What's the opinion here on which are more fundamental - minds or universes? I'd say they're both definable and hence exist de facto, and that each implies the
Re: on formally describable universes and measures
Jürgen wrote: - Original Message - From: [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Thursday, February 22, 2001 5:32 PM Subject: Re: on formally describable universes and measures Saibal Mitra wrote: I think the source of the problem is equation 1 of Juergen's paper. This equation supposedly gives the probability that I am in a particular universe, but it ignores that multiple copies of me might exist in one universe. Let's consider a simple example. The prior probability of universe i (i0) is denoted as P(i), and i copies of me exist in universe i. In this case, Juergen computes the propability that if you pick a universe at random, sampled with the prior P, you pick universe i. This probability is, of course, P(i). Therefore Juergen never has to identify how many times I exist in a particular universe, and can ignore what consciousness actually is. Surely an open universe where an infinite number of copies of me exist is infinitely more likely than a closed universe where I don't have any copies, assuming that the priors are of the same order? To respond, let me repeat the context of eq. 1 [In which universe am I?] Let h(y) represent a property of any possibly infinite bitstring y, say, h(y)=1 if y represents the history of a universe inhabited by yourself and h(y)=0 otherwise. According to the weak anthropic principle, the conditional probability of finding yourself in a universe compatible with your existence equals 1. But there may be many y's satisfying h(y)=1. What is the probability that y=x, where x is a particular universe satisfying h(x)=1? According to Bayes, P(x=y | h(y)=1) = (P(h(y)=1 | x=y) P(x = y)) / (sum_{z:h(z)=1} P(z)) propto P(x), where P(A | B) denotes the probability of A, given knowledge of B, and the denominator is just a normalizing constant. So the probability of finding yourself in universe x is essentially determined by P(x), the prior probability of x. Universes without a single copy of yourself are ruled out by the weak anthropic principle. But the others indeed suggest the question: what can we say about the distribution on the copies within a given universe U (maybe including those living in virtual realities running on various computers in U)? I believe this is the issue you raise - please correct me if I am wrong! (Did you really mean to write i copies in universe i?) I did mean to write i copies in universe i, maybe it would have been better to write n(i) copies in universe i. Anyway, according to equation 1 the probability of universe x given that n(x) 0 is proportional to P(x), which is also intuitively logical. My point is that from the perspective of the observer, of which there are n(x) copies in universe x, things look different. Intuitively, it seems that the measure of the observer should be n(x)* P(x). E.g. suppose there exist x1 and x2 such that P(x1) = P(x2) and n(x1) n(x2) 0. It seems to me that the observer is more likely to find himself in universe x1 compared to universe x2. Intuitively, some copies might be more likely than others. But what exactly does that mean? If the copies were identical in the sense no outsider could distinguish them, then the concept of multiple copies wouldn't make sense - there simply would not be any multiple copies. So there must be detectable differences between copies, such as those embodied by their different environments. So my answer would be: as soon as you have a method for identifying and separating various observer copies within a universe U, each distinguishable copy_i is different in the sense that it lives in a different universe U_i, just like you and me can be viewed as living in different universes because your inputs from the environment are not identical to mine. In general, the pair (U_i, copy_i) conveys more information than U by itself (information is needed to separate them). The appropriate domain of universes x (to use the paper's notation) would be the set of all possible pairs of the form (separate universe, separate observer). Equation 1 above is perfectly applicable to this domain. Okay, but since I don't know which of the copies I am, the probability that I am one of the copies inside universe i is given as: Sum_{i = 1}^{n(U)} P(U_i) Is this proportional to P(U) or is it proportional to n(U) P(U) ? Saibal
Re: (Quantum) suicide not necessary?
From: James Higgo Before I was blind but now I see. I was the one who came up with the expression, 'Quantum Theory of Immortality', and I now see that it's false - and all this stuff in this thread is based on the same mistake. See www.higgo.com/qti , a site dedicated to the idea. Hey, I'm still counting it as original! I _did_ come up with it independently And I still can't see anything wrong with it. Thanks for the web-site, though. There is no 'you'. 'You' don't 'travel'. There are just different observer moments, some including 'I am Micky and I'm, sick'. So? This is trivial. We still percieve ourselves as continuous beings, and the qualia is what I'm talking about here. The point is that one will _always_ have observer moments to go to. The illusion of self is maintained. I'm pretty sure at least one of us is misunderstanding the other. Even thinking in your passe Newtonian terms,how can a universe in which 'you have a disease' be the same as one in which 'you do not have the disease', just because you don't know it? Oh Please don't do that. You don't know how I think, and I really don't see why you jumped to this conclusion. The wayI see it now, the observer moment is all we have. I think I may have picked up the followingmetaphor here, but I'll use it nonetheless: did Jack and Jill go up the hill in August? Does it matter? The rhyme leaves it undefined, so it's a meaningless question; they did and they didn't. We belong to all universes that generate this observer moment, and only a sort of statistical Ockham's Razor says which ones we'll perceive ourselves to be in next. What's the problem here? I see why Jacques gets so irritated by this type of thinking, but it's nice to see him back on the list now then. What type of thinking? Please, I don't want to get into a catfight here. I'm on this list, presumably, for the same reasonyou are: to try and see the whole picture.
Re: on formally describable universes and measures
Guys, this is really good stuff. This is answering my question of a couple of weeks ago. I will quote it in a paper with your permission. James - Original Message - From: Marchal [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Friday, March 02, 2001 1:32 PM Subject: Re: on formally describable universes and measures Jacques Mallah wrote: Sorry, that doesn't help. What do you mean by a real actual one? What other kind is there, a fake one? Either it exists, or not. OK. In that sense we agree that the DU exist. I am glad to see that you are a classical platonist. An intuitionist would'nt accept the idea that something exist ... or not. Of course, in your macintosh example, the UD was itself implemented by some other mathematical structure - your local decor. Does that matter? A big part of my reasoning is that it *doesn't matter* indeed. For most people this is a difficulty. Actually, I would say that any mathematical structure that has real existance (in the strong sense) should be called physical.I do not know of any better definition for physical existance. What is that strong sense of existence? And why do you want to classify as physical any mathematical structures. If you do that (a little like Tegmark) you are obliged to explain how we feel a difference between physicalness and mathematicalness (why is there math courses and physics courses) etc. Tegmark, like Everett, *do* distinguish the first and third person, which helps to make sense of that idea. The physical would be some mathematical structures sufficiently rich for having inside point of views (through SAS point of views for exemple). The physical point of view (pov) would correspond to these internal pov. Nowhere did I say that _only_ a physical system could implement a computation. But you did bring to my attention the fact that I should make the definition of implementation more clear on this point. In other places, I do point out that one computation can implement another. (In turn, the second one might implement another, etc.; the first one will therefore implement all of those.) So, your objection is irrelevant. You do believe a UD implements other computations. Sure. Yes. UD implements all computations, and even all implementations of all computations. Actuality is a first person concept. I have no clue as to what you mean. In Newtonian Physics one could imagine some third person time (objective time), but since relativity I guess most believe that time is either a parameter or do refer to some relative measurement done by an observer. Actuality, modern, here, now, there, elsewhere, are words with meaning dependent of the locutor. Indexicals, as the philosophers call them. Most are true or false only from a first person point of view. 3rd person view is everything you can communicate in a scientific manner without taking into account the subjective view of a person. If the person has some set of beliefs, they can be described as part of the true description of the situation. (Which you is what I thought you call the 3rd person view.) Concerning *believes* the case is arguable. For *knowledge* I don't think you will ever succeed in describing them in some provable (objectively, 3-person) way. This can be proved with very reasonable definition. See ref by Benacerraf, or Kaplan and Montague in my thesis. (It is linked with that reconstruction of Lucas which makes difficult for Schmidhuberians to locate an observer in *a* computational history, but I think that point is obvious once you get the computational indeterminacy from the duplication thought experience). Science is (ideally) a pure 3-person discourse and will ever be. But with definition of 1-person you can make science (i.e. 3-person discourses) *about* the possible 1-person discourses. I give two definitions of 1-person discourses. The first one appears in the self duplication thought experiment, and is just personal memory (what is written in *your* personal diary). The second one, which I use in the formal part of my work is the one given by Thaetetus to Socrate. Mathematically it gives intuitionnistic logic (topos, constructive math, etc.). The use of topos(*) by quantum cosmologist (cf Lee Smolin) is the logical move made by those who want the other universal stories away. It is cosmo-solipsism. Someone who would have only first person insight is a solipsist. Someone who would have only third person insight is a zombie. If I duplicate myself succesfully in Washington and Moscow, both Bruno1 and Bruno2 can communicates the success of the experience from a third person point of view, but none can explain you that he feels to be the Washingtonian (resp Moscovian) one. The difference between the first person and the third person is basically the same as the difference between having an headache and having a friend having an headhache. From
Re: (Quantum) suicide not necessary?
Oh, as to 'this is trivial - we still perceive ourselves as continuous beings' - I guess as far as you're concerned,the Earth does not move. - Original Message - From: Michael Rosefield To: James Higgo ; Saibal Mitra ; [EMAIL PROTECTED] Sent: Saturday, March 03, 2001 3:34 PM Subject: Re: (Quantum) suicide not necessary? From: James Higgo Before I was blind but now I see. I was the one who came up with the expression, 'Quantum Theory of Immortality', and I now see that it's false - and all this stuff in this thread is based on the same mistake. See www.higgo.com/qti , a site dedicated to the idea. Hey, I'm still counting it as original! I _did_ come up with it independently And I still can't see anything wrong with it. Thanks for the web-site, though. There is no 'you'. 'You' don't 'travel'. There are just different observer moments, some including 'I am Micky and I'm, sick'. So? This is trivial. We still percieve ourselves as continuous beings, and the qualia is what I'm talking about here. The point is that one will _always_ have observer moments to go to. The illusion of self is maintained. I'm pretty sure at least one of us is misunderstanding the other. Even thinking in your passe Newtonian terms,how can a universe in which 'you have a disease' be the same as one in which 'you do not have the disease', just because you don't know it? Oh Please don't do that. You don't know how I think, and I really don't see why you jumped to this conclusion. The wayI see it now, the observer moment is all we have. I think I may have picked up the followingmetaphor here, but I'll use it nonetheless: did Jack and Jill go up the hill in August? Does it matter? The rhyme leaves it undefined, so it's a meaningless question; they did and they didn't. We belong to all universes that generate this observer moment, and only a sort of statistical Ockham's Razor says which ones we'll perceive ourselves to be in next. What's the problem here? I see why Jacques gets so irritated by this type of thinking, but it's nice to see him back on the list now then. What type of thinking? Please, I don't want to get into a catfight here. I'm on this list, presumably, for the same reasonyou are: to try and see the whole picture.
Re: (Quantum) suicide not necessary?
You miss the point. You do not go anywhere. You are this observer moment. No observer moment 'becomes' another OM, or it would be a different OM to begin with. I guess this is extremely hard for people to understand, because it denies that people exist. - Original Message - From: Michael Rosefield To: James Higgo ; Saibal Mitra ; [EMAIL PROTECTED] Sent: Saturday, March 03, 2001 3:34 PM Subject: Re: (Quantum) suicide not necessary? From: James Higgo Before I was blind but now I see. I was the one who came up with the expression, 'Quantum Theory of Immortality', and I now see that it's false - and all this stuff in this thread is based on the same mistake. See www.higgo.com/qti , a site dedicated to the idea. Hey, I'm still counting it as original! I _did_ come up with it independently And I still can't see anything wrong with it. Thanks for the web-site, though. There is no 'you'. 'You' don't 'travel'. There are just different observer moments, some including 'I am Micky and I'm, sick'. So? This is trivial. We still percieve ourselves as continuous beings, and the qualia is what I'm talking about here. The point is that one will _always_ have observer moments to go to. The illusion of self is maintained. I'm pretty sure at least one of us is misunderstanding the other. Even thinking in your passe Newtonian terms,how can a universe in which 'you have a disease' be the same as one in which 'you do not have the disease', just because you don't know it? Oh Please don't do that. You don't know how I think, and I really don't see why you jumped to this conclusion. The wayI see it now, the observer moment is all we have. I think I may have picked up the followingmetaphor here, but I'll use it nonetheless: did Jack and Jill go up the hill in August? Does it matter? The rhyme leaves it undefined, so it's a meaningless question; they did and they didn't. We belong to all universes that generate this observer moment, and only a sort of statistical Ockham's Razor says which ones we'll perceive ourselves to be in next. What's the problem here? I see why Jacques gets so irritated by this type of thinking, but it's nice to see him back on the list now then. What type of thinking? Please, I don't want to get into a catfight here. I'm on this list, presumably, for the same reasonyou are: to try and see the whole picture.
Re: (Quantum) suicide not necessary?
Before I was blind but now I see. I was the one who came up with the expression, 'Quantum Theory of Immortality', and I now see that it's false - and all this stuff in this thread is based on the same mistake. See www.higgo.com/qti , a site dedicated to the idea. There is no 'you'. 'You' don't 'travel'. There are just different observer moments, some including 'I am Micky and I'm, sick'. Even thinking in your passe Newtonian terms,how can a universe in which 'you have a disease' be the same as one in which 'you do not have the disease', just because you don't know it? I see why Jacques gets so irritated by this type of thinking, but it's nice to see him back on the list now then. - Original Message - From: Michael Rosefield To: Saibal Mitra ; [EMAIL PROTECTED] Sent: Tuesday, February 27, 2001 3:30 PM Subject: Re: (Quantum) suicide not necessary? *Phew!*; this afternoon I finally got round to reading the 190-odd messages I have received from this list From: Saibal Mitra Instead of the previously discussed suicide experiments to test variousversions of many-worlds theories, one might consider a different approach. By deleting certain sectors of one's memory one should be able to travelto different branches of the multiverse. Suppose you are diagnosed with a rare disease. You don't have complaints yet, but you will diewithin a year. If you could delete the information that you have thisparticular disease (and also the information that information hasbeen deleted), branches in which you don't have the diseasemerge with the branches in which you do have the disease. So withvery high probability you have travelled to a different branch. I don't know whether to be relieved or annoyed that I'm not the only person to think of this ;D. http://pub45.ezboard.com/fwastelandofwondersfrm1.showMessage?topicID=353.topicindex=5 I'm guessing this is quite a common idea? Rats, I thought I was so great I_did_ thinkof the following today, though: If you take this sort of thing one step further, an afterlife is inevitable; there will always be systems - however improbable - where the mind lives on. For instance, you could just be the victim of an hallucination, your mind could be downloaded, you could be miraculously cured, and other _much_ more bizzare ones. Since you won't be around to notice the worlds where you did die, they don't count, and you are effectively immortal. Or at least you will perceive yourself to live on, which is the same thing. When I thought of it, it seemed startlingly original and clever. Looking at the posts I have from this list, I'm beginning to suspect it's neither Anyhow, while this sort of wild thinking iswonderfully pure andcathartic, itnever seems to lead anywhere with testable or useful implications. So far, anyway What's the opinion here on which are more fundamental - minds or universes? I'd say they're both definable and hence exist de facto, and that each implies the other. Well,I'm new here. Is there anything I should know about this list? Apart from the fact that everyone's so terribly educated Feel free to go a bit OT ;). Michael Rosefield, Sheffield, England "I'm a Solipsist, and I must say I'm surprised there aren't more of us." -- letter to Bertrand Russell
QTI
I also don't think that 'Quantum Theory of Immortality' is correct in its conventional form. I do believe, however, that a different versionis implied by James' Theory of Observer Moments. Since there exists a set S of observer moments, one element of which represents my state now, I will ''always'' find myself in some subset of S. This doesn't mean that I could outlive everyone. The observer moment: I am 10^100 years old is simply inconsistent with I am Saibal. I posted earlier about an article by Caticha that explains how fundamental laws of physics (including notions such as time and space) can be derived from nothing more than an arbitrary probability distribution defined over some arbitrary set. See http://xxx.lanl.gov/abs/math-ph/0008018 Saibal - Original Message - From: James Higgo To: Michael Rosefield ; Saibal Mitra ; [EMAIL PROTECTED] Sent: Saturday, March 03, 2001 1:53 PM Subject: Re: (Quantum) suicide not necessary? Before I was blind but now I see. I was the one who came up with the expression, 'Quantum Theory of Immortality', and I now see that it's false - and all this stuff in this thread is based on the same mistake. See www.higgo.com/qti , a site dedicated to the idea. There is no 'you'. 'You' don't 'travel'. There are just different observer moments, some including 'I am Micky and I'm, sick'. Even thinking in your passe Newtonian terms,how can a universe in which 'you have a disease' be the same as one in which 'you do not have the disease', just because you don't know it? I see why Jacques gets so irritated by this type of thinking, but it's nice to see him back on the list now then. - Original Message - From: Michael Rosefield To: Saibal Mitra ; [EMAIL PROTECTED] Sent: Tuesday, February 27, 2001 3:30 PM Subject: Re: (Quantum) suicide not necessary? *Phew!*; this afternoon I finally got round to reading the 190-odd messages I have received from this list From: Saibal Mitra Instead of the previously discussed suicide experiments to test variousversions of many-worlds theories, one might consider a different approach. By deleting certain sectors of one's memory one should be able to travelto different branches of the multiverse. Suppose you are diagnosed with a rare disease. You don't have complaints yet, but you will diewithin a year. If you could delete the information that you have thisparticular disease (and also the information that information hasbeen deleted), branches in which you don't have the diseasemerge with the branches in which you do have the disease. So withvery high probability you have travelled to a different branch. I don't know whether to be relieved or annoyed that I'm not the only person to think of this ;D. http://pub45.ezboard.com/fwastelandofwondersfrm1.showMessage?topicID=353.topicindex=5 I'm guessing this is quite a common idea? Rats, I thought I was so great I_did_ thinkof the following today, though: If you take this sort of thing one step further, an afterlife is inevitable; there will always be systems - however improbable - where the mind lives on. For instance, you could just be the victim of an hallucination, your mind could be downloaded, you could be miraculously cured, and other _much_ more bizzare ones. Since you won't be around to notice the worlds where you did die, they don't count, and you are effectively immortal. Or at least you will perceive yourself to live on, which is the same thing. When I thought of it, it seemed startlingly original and clever. Looking at the posts I have from this list, I'm beginning to suspect it's neither Anyhow, while this sort of wild thinking iswonderfully pure andcathartic, itnever seems to lead anywhere with testable or useful implications. So far, anyway What's the opinion here on which are more fundamental - minds or universes? I'd say they're both definable and hence exist de facto, and that each implies the other. Well,I'm new here. Is there anything I should know about this list? Apart from the fact that everyone's so terribly educated Feel free to go a bit OT ;). Michael Rosefield, Sheffield, England "I'm a Solipsist, and I must say I'm surprised there aren't more of us." -- letter to Bertrand Russell