Re: Logically possible universes and Occam's razor
Russell Standish wrote: I raised this very issue in Why Occams Razor, and came to the conclusion that the only satisfactory interpreter is the observer itself. And so the question resumes into 'what is the observer itself'. I propose the answer 'the self-referentially sound Lobian machine' (LM). (exemple: PEANO ARITHMETIC, ZF, VNBG, first-order extension of programming language, Second order Arithmetic, etc.) The Universal Dovetailer argument (UDA) shows that observation is selection (by LM) on near possibilities. Modelising near possibilities by consistent extensions (UD accessible) in the language of the Lobian machine, makes it possible to asks the Lobian machine what it can observe. The nuances, introduced by the incompleteness phenomenon, between p provable(p) provable(p) and p provable (p) and consistent(p) provable (p) and consistent(p) and p can then help to extract the fungibility equivalence structure (Deutsch sense ?, Fredkin or Toffoli?) of the possible sheaf of computational histories. The structure I got from that looks like a quantum logic. (to be short) It is at least enough rich for translating little quantum gates in arithmetic (where the LM can observe). Coincidence? If I get enough gates the schroedinger equation will be shown necessary for all consistent machine looking near enough. Bruno PS Sorry for this merging of the two mailing list. But if universe can differentiate and merge, how could many worlder comp mailing lists not interfere too. O gosh that was a metacomment, and that too, and ..., I will be moderated out! (from the for-list) nh!!! Here I am using Gordon famous cry when dreaming meeting Bill Gates, iirc, hoping that works :o
Re: Logically possible universes and Occam's razor
Bruno, before we get phased out: you quoted Russell: I raised this very issue in Why Occams Razor, and came to the conclusion that the only satisfactory interpreter is the observer itself then you write very smart thoughts (like: Modelising near possibilities by consistent extensions (UD accessible) etc. all, including Occam, reducing the concept of 'all' into the segment we can stuff into our mind. Our limited capabilities are not limiting nature (or call it whatever), we just don't comprehend/observe the rest of it. Not even the 'logically possible' part of it. Our way of talking is not too humble, I can say modestly. John Mikes [EMAIL PROTECTED] http://pages.prodigy.net/jamikes; - Original Message - From: Marchal [EMAIL PROTECTED] To: [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Wednesday, January 31, 2001 1:02 PM Subject: Re: Logically possible universes and Occam's razor S N I P
Re: FIN insanity
Charles Goodwin wrote: -Original Message- From: Jacques Mallah [mailto:[EMAIL PROTECTED]] On the other hand I can't see how FIN is supposed to work, either. I *think* the argument runs something like this... Even if you have just had, say, an atom bomb dropped on you, there's still SOME outcomes of the schrodinger wave equation which just happen to lead to you suriviving the explosion. Although these are VERY unlikely - less likely than, say, my computer turning into a bowl of petunias - they do exist, and (given the MWI) they occur somewhere in the multiverse. For some reason I can't work out, all the copies who are killed by the bomb don't count. Only the very very very (etc) small proportion who miraculously survive do, and these are the only ones you personally experience. Is that a reasonable description of FIN? Ignoring statistical arguments, what is wrong with it? There are different versions of QTI (let's not call it FIN). The most reasonable one (my version, of course) takes into account the possibility that you find yourself alive somewhere else in the universe, without any memory of the atomic bomb that exploded. I totally ignore the possibility that one could survive an atomic bomb exploding above one's head. My version doesn't imply that your a priory expected lifetime should be infinite. Death involves the destruction of your brain. But there are many brains in the universe which are almost identical to yours. Jacques says that you can't become one of them. I say: 1) If you are hurt in a car accident and the surgeon performes brain surgery and you recover fully, then you are the same person. 2) You would also be the same person if the surgeon made a new brain identically to yours. 3) From 2) it follows that if your brain was first copied and then destroyed, you would become the copy. 4) From 3) you can thus conclude that you will always experience yourself being alive, because copies of you always exist. 5) It doesn't follow that you will experience surviving terrible accidents. Saibal
RE: FIN too
From: Charles Goodwin [EMAIL PROTECTED] you can't apply any sort of statistical argument to your own experience unless you assume that you're a typical observer. But if you do that you're just assuming the result you want. Not so. You don't assume you're typical exactly, just that you are more likely to be typical. You have no choice but to believe that, or else you reject basic Bayesian logic. My objections to the QTI are more along the lines of how the mechanism is supposed to work - why can't you experience your own death, or just stop having experiences altogether, in 99.9(etc)% of the universes that contain you? It's nice that you reject FIN! Of course, those who support it can give (and have given) no reason, since it's a nonsensical belief. From: Jacques Mallah [mailto:[EMAIL PROTECTED]] The problem is that the probability isn't 0% that you'd find yourself at your current age (according to the QTI - assume I put that after every sentence!). Because you HAVE to pass through your current age to reach QTI-type ages, the probability of finding yourself at your current age at some point is 100%. At some point, yes. At a typical point? 0%. Using your argument (assuming QTI...) then your chances of finding yourself at ANY age would be 0%. This imples to me that the SSA can't be used in this case, rather than that QTI *must* be wrong. Nope! It's just that with FIN, your expected age diverges. If you want to say that's impossible, fine with me. FIN is logically impossible for a sane person to believe! But there's one exception: your brain can only hold a limited amount of information. So it's possible to be too old to remember how old you are. *Only if you are that old, do you have a right to not reject FIN on these grounds.* Are you that old? (Of course, you must still reject it on other grounds!) After all whether QTI is correct or not, you can imagine that it is and see what the results would be; and one result is that you will find yourself (at some point) having any age from 0 to infinity, which is consistent with your current observations. Consistent with them, but not nearly as likely in the FIN case. Remember Bayes' theorem: the posterior favored hypothesis is the one that would be more likely to predict your observations. That's OK so far. And it turns out correctly for most cases (i.e. 99.(etc)% of observers WILL turn out to have ages of infinity (if QTI etc)). But an infinitesimal fraction won't - including everyone you observe around you (the multiverse is very very very (keep typing very til doomsday) big! (assuming MWI)). Right. Do you think you are in an infinitesimal fraction, or in a typical fraction? In the same way, the SSA helps you guess things. It's just a procedure to follow which usually helps the people that use it to make correct guesses. It doesn't seem to help in this case though. I don't need to guess my age, it's a given. Maybe the following example will help. Suppose there are two possibilities: 1. 90% of people see A, 10% see B 2. 10% of people see A, 90% see B You see A. But you want to know whether #1 or #2 is true. A priori, you feel that they are equally likely to be true. Should you throw up your hands simply because both #1 and #2 are both consistent with your observation? No. So use Bayes' theorem as follows: p(1|A) = [p(A|1) p_0(1)] / [p(A|1) p_0(1) + p(A|2) p_0(2)] = [ (.9) (.5) ] / [ (.9) (.5) + (.1) (.5) ] = .9 So you now think #1 is 90% likely to be true, if you use this procedure. So you will guess #1. OK, lets try and check to see if this procedure is good. If #1 is true then 90% of people who use the procedure guess #1 (right). If #2 is true then 10% of people who use the procedure guess #1 (wrong). Well I'd say that's pretty good, and also the best you can do. I gotta go. - - - - - - - Jacques Mallah ([EMAIL PROTECTED]) Physicist / Many Worlder / Devil's Advocate I know what no one else knows - 'Runaway Train', Soul Asylum My URL: http://hammer.prohosting.com/~mathmind/ _ Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp
