Re: FIN too
Convince me of this fact, and I would readily reject QTI. What you say would be disproof of the cul-de-sac assumption, which sadly I suspect to be true except in rather extreme circumstances like black holes. Nevertheless, if you can construct a situation using forbidden states where conscious continuation of provably impossible, I'd be most interested to hear about it. Cheers Fred Chen wrote: Hal, Charles, I think this is an unavoidable part of the QTI or FIN debate. It seems that with QTI, you could only be entering white rabbit (magical-type) universes, not continue in probable ones. But in general I have a more fundamental objection (to quantum immortality). In QM, not all quantum states are possible for a given situation. For example, an electron orbiting a proton can only occupy certain energy states, not arbitrary ones. The energy states in between are forbidden; an electron cannot be measured and found to be in one of these forbidden states. So I do not see why immortality is allowed by QM from our universe if physical mechanisms generally ban it. Survival seems to me (and I guess most people) a forbidden state in the situations where death is certain. Fred Dr. Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile) UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 () Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02
Re: FIN too
Fred Chen wrote: Hal, Charles, I think this is an unavoidable part of the QTI or FIN debate. It seems that with QTI, you could only be entering white rabbit (magical-type) universes, not continue in probable ones. But in general I have a more fundamental objection (to quantum immortality). In QM, not all quantum states are possible for a given situation. For example, an electron orbiting a proton can only occupy certain energy states, not arbitrary ones. The energy states in between are forbidden; an electron cannot be measured and found to be in one of these forbidden states. So I do not see why immortality is allowed by QM from our universe if physical mechanisms generally ban it. Survival seems to me (and I guess most people) a forbidden state in the situations where death is certain. But all the QTI problem (or the COMP I problem) is there. QM shows that even by taking account the forbidden states, from the point of view of the observer there are enough histories making hard to define a situation where death is certain. It is plausible that comp immortality makes that death entails a deviation from normality, but you always find yourself in the most near possible world such that you survive. Not really a happy thought *a priori*, but how to escape it? Now comp is rich enough for allowing the consistency of jump between type of normal world, amnesia bactracking, etc. The mortality question is harder with comp than with QM, and with QM the solution would be provided the SE applied to the agonising: just intractable. All the problem comes from the fact that although it is easy to imagine situation where 3-death is very probable, it is not easy at all to define a situation where 1-death is certain. Comp entails big ignorance here. Bruno
RE: FIN too
I'll have another go at explaining my position (maybe I'll spot a flaw in it if I keep examininig it long enough). Bayesian reasoning assumes (as far as I can see) that I should treat my present observer moment as typical. My objection to doing so is that this assumes the result you want to prove, because if my observer moment is typical and QTI is correct, then the likelihood of me experiencing a moment at which my age is less than infinity is infinitesimal. This either demonstrates that (1) my present observer moment is typical and QTI is wrong or (2) the present observer moment isn't typical and Bayesian reasoning is inappropriate ((2) doesn't imply that QTI is correct, of course, merely that it's compatible with observation). *Assuming* that QTI is correct, then the chances of you and me interacting at a typical observer moment (for either of us) is negligible. QTI guarantees that almost all interactions between observers will occur at highly non-typical observer moments, because (scary thought) for 99.999% of any given person's observer moments, the rest of the human race will be extinct. Hence Bayesian reasoning isn't appropriate because the fact that we're communicating with one another guarantees that at least one of us, and with overwhelming probability both of us, is experiencing highly atypical observer moments. The assumption of typicality can't be made without first checking that you're not dealing with a special case. To take an obvious example, if I was to apply Bayesian reasoning to myself I would be forced to assume that I am almost certainly a peasant of indeterminate sex living in the third world. Or more likely a beetle... Or even more likely a microbe (assuming microbes have observer moments). Which I believe isn't the case! (Even on those rare occassions when I argue with my better half, she very rarely calls me a microbe...) Charles PS - I could be a butterfly dreaming that I'm a man, I suppose... -Original Message- From: Jacques Mallah [mailto:[EMAIL PROTECTED]] Sent: Tuesday, 4 September 2001 2:32 p.m. To: [EMAIL PROTECTED] Subject: RE: FIN too From: Charles Goodwin [EMAIL PROTECTED] Um, OK, I don't want to get into an infinite argument here. I guess we both understand the other's viewpoint. (For the record: I don't see any reason to accept QTI as correct, but think that *if* it is, it would fit in with the available (subjective) observational evidence - that being the point on which we differ. Um, no, I still don't understand your view. I think the point that Bayesian reasoning would work with 100% reliability, even though the FIN is technically compatible with the evidence, is perfectly clear. Any reason for disagreeing, I have no understanding of. It may help you to think of different moments of your life as being different observers (observer-moments). That's really just a matter of definition. - - - - - - - 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
RE: FIN too
Oh, I forgot my main problem with QTI :-) Basically it's to do with the rate at which decoherence spreads (presumably at the speed of light?) and the finite time it takes someone to die. So if you were shot (say) the QTI would predict that there was some point in the process of your body ceasing to operate at which some unlikely quantum processes separated branches of the multiverse in which you died to ones in which you remained alive (forever, presumably). The problem is working out exactly where that happens (I suspect it gets worse if you include relativistic considerations). Another question is what happens in cases of very violent death, e.g. beheading. After someone's head is cut off, so they say, it remains conscious for a few seconds (I can't see why it wouldn't). According to QTI it experiences being decapitated but then survives indefinitely - somehow . . . well, I'd like to hear what QTI supporters think happens next (from the pov of the victim). Are they magically translated into a non-decapitated version of themselves, and if so, how? Surely it can't be in the same quantum state that they're in? If not, do they experience indefinitely continued survival as a severed head, or . . . what??? Just curious! Charles -Original Message- From: Charles Goodwin [mailto:[EMAIL PROTECTED]] Sent: Tuesday, 4 September 2001 1:42 p.m. To: [EMAIL PROTECTED] Subject: RE: FIN too Um, OK, I don't want to get into an infinite argument here. I guess we both understand the other's viewpoint. (For the record: I don't see any reason to accept QTI as correct, but think that *if* it is, it would fit in with the available (subjective) observational evidence - that being the point on which we differ. I also think that for QTI to be correct, a number of other things would have to hold - space-time would have to be quantised, objects in the same quantum state would have to be literally identical (no matter where they happened to be in the uni/multiverse) . . . and, either the multiverse has to exist, or our universe has to be infinite . . . and probably a few other points I can't think of right now!) Charles -Original Message- From: Jacques Mallah [mailto:[EMAIL PROTECTED]] Sent: Tuesday, 4 September 2001 1:12 p.m. To: [EMAIL PROTECTED] Subject: RE: FIN too From: Charles Goodwin [EMAIL PROTECTED] [Jacques Mallah wrote] 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? Yeah, that's one of my objections to QTI. Although perhaps add-on memory chips will become available one day :-) OK. (And even if the chips become available, you'd probably only be able to add a finite # before collapsing into a black hole.) Right. Do you think you are in an infinitesimal fraction, or in a typical fraction? Infinitesimal, if QTI is correct, otherwise fairly typical. Assuming QTI is correct and ignoring any other objections to it, it's *possible* for me to be in an infinitesimal fraction - in fact it's necessary. Right - which is why Bayesian reasoning falsifies FIN, but only with 100% reliability as opposed to complete reliability. but according to QTI I *must* pass through a phase when I see the unlikely bits, no matter how unlikely it is that a typical moment will fall into that phase. Even if I later spend 99.999% of my observer moments seeing the stars going out one by one, there still has to be that starting point! Right, again, that's why the reliability is just 100%. My (ahem) point is, though, that none of us ARE at a typical point (again, assuming QTI). In fact we're in a very atypical point, just as the era of stars might be a very atypical point in the history of the universe - but it's a point we (or the universe) HAVE TO PASS THROUGH to reach more typical points (e.g. very old, no stars left...). Hence it's consistent with QTI that we find ourselves passing through this point... Right, consistent with it but only 0% of the time, hence the Bayesian argument is to put 0 credence in the FIN rather than strictly no credence. I'm not arguing for QTI here, but I do think that you can't argue from finding yourself at a particular point on your world-line to that world-line having finite length, because you are guaranteed to find yourself at that particular point at some (ah) point. Right, which is why I'm (now) careful not to make *that* argument by arbritarily using one's current age to base a reference point on. (e.g. in my reply to Bruno.) Rather, I argue that from being at a point prior to some _natural reference point_ such as the can calculate my age crierion, one
RE: FIN too
From: Charles Goodwin [EMAIL PROTECTED] Um, OK, I don't want to get into an infinite argument here. I guess we both understand the other's viewpoint. (For the record: I don't see any reason to accept QTI as correct, but think that *if* it is, it would fit in with the available (subjective) observational evidence - that being the point on which we differ. Um, no, I still don't understand your view. I think the point that Bayesian reasoning would work with 100% reliability, even though the FIN is technically compatible with the evidence, is perfectly clear. Any reason for disagreeing, I have no understanding of. It may help you to think of different moments of your life as being different observers (observer-moments). That's really just a matter of definition. - - - - - - - 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
RE: FIN too
-Original Message- From: Russell Standish [mailto:[EMAIL PROTECTED]] This case bothers me too. The initial (or perhaps traditional) response is that consciousness is lost the instant blood pressure drops in the brain, a few hundred milliseconds after the neck is severed, thus the beheading is not experienced. However, there is some anecdotal evidence (eg the beheading of Lavoisier) that consciousness can survive up to 10-20 seconds after the neck is severed. Even if this is true, it still does not eliminate magical solutions, such as waking up Matrix-style in an alternative reality. Yesor in a tipler style afterlife inside some megacomputer trillions of years in the future (or equivalently, I suppose, somewhere else in the multiverse). Definitely starts to sound like an act of faith to believe that's what would happen, though Even if you lost consciousness a split second after having your head removed, QTI would still have to explain how you got from 'immediately after being beheaded' to anywhere else...! Charles
Re: FIN too
Charles Goodwin wrote: Another question is what happens in cases of very violent death, e.g. beheading. After someone's head is cut off, so they say, it remains conscious for a few seconds (I can't see why it wouldn't). According to QTI it experiences being decapitated but then survives indefinitely - somehow . . . well, I'd like to hear what QTI supporters think happens next (from the pov of the victim). Are they magically translated into a non-decapitated version of themselves, and if so, how? Surely it can't be in the same quantum state that they're in? If not, do they experience indefinitely continued survival as a severed head, or . . . what??? Just curious! Charles This case bothers me too. The initial (or perhaps traditional) response is that consciousness is lost the instant blood pressure drops in the brain, a few hundred milliseconds after the neck is severed, thus the beheading is not experienced. However, there is some anecdotal evidence (eg the beheading of Lavoisier) that consciousness can survive up to 10-20 seconds after the neck is severed. Even if this is true, it still does not eliminate magical solutions, such as waking up Matrix-style in an alternative reality. Cheers Dr. Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile) UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 () Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02
RE: FIN too
Charles Goodwin, [EMAIL PROTECTED], writes: Another question is what happens in cases of very violent death, e.g. beheading. After someone's head is cut off, so they say, it remains conscious for a few seconds (I can't see why it wouldn't). According to QTI it experiences being decapitated but then survives indefinitely - somehow . . . well, I'd like to hear what QTI supporters think happens next (from the pov of the victim). Are they magically translated into a non-decapitated version of themselves, and if so, how? Surely it can't be in the same quantum state that they're in? If not, do they experience indefinitely continued survival as a severed head, or . . . what??? Just curious! The answer is very simple. The future that is experienced is the least unlikely that allows for continuation of consciousness. (More precisely, the probability distribution over those futures where you are still alive determines the relative probability of experience given that you find yourself alive, a tautology.) So, your head has been cut off and clunk, you fall on the ground, getting a nasty knock on the head, not to mention the neck soreness and missing body. How could you survive? There are several alternatives. It is possible that entropy ceases to operate in your brain, and that you continue to think despite the loss of blood flow. This however would be an astronomically unlikely future. More likely, aliens or supernatural intelligences of some sort would intervene to keep you alive. Alternatively, it would turn out that you were playing a futuristic video game where you had temporarily blanked out your memory to make it more realistic. Then next thing you see is Game Over. These possibilities makes most sense if you consider the set of all physical systems where you have the same mental state, rather than just the systems which are part of your corner of the QM multiverse. There are universes where aliens are monitoring the earth, unknown to its inhabitants, and the mental states of residents of earth in such universes will be identical to the states of people in some other universes without aliens. When you find yourself with head chopped off, you don't know which class of universe you are in. I would argue that there is no fact of the matter about it (this is our old argument about whether your consciousness is tied to a specific instance of the many which instantiate it). Hence you will experience the most likely continuation which is consistent with your mental experiences in any branch of the QM universe which could produce that experience. I think we all agree with the objective facts of the situation here. For any observer moment there exist other observer moments which are subjectively in its future (equivalently, for which it is subjectively in the past). The question is whether to interpret this fact as meaning continued survival. Ultimately that is a matter of definitions. Hal Finney
RE: FIN too
From: Charles Goodwin [EMAIL PROTECTED] [Jacques Mallah wrote] 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? Yeah, that's one of my objections to QTI. Although perhaps add-on memory chips will become available one day :-) OK. (And even if the chips become available, you'd probably only be able to add a finite # before collapsing into a black hole.) Right. Do you think you are in an infinitesimal fraction, or in a typical fraction? Infinitesimal, if QTI is correct, otherwise fairly typical. Assuming QTI is correct and ignoring any other objections to it, it's *possible* for me to be in an infinitesimal fraction - in fact it's necessary. Right - which is why Bayesian reasoning falsifies FIN, but only with 100% reliability as opposed to complete reliability. but according to QTI I *must* pass through a phase when I see the unlikely bits, no matter how unlikely it is that a typical moment will fall into that phase. Even if I later spend 99.999% of my observer moments seeing the stars going out one by one, there still has to be that starting point! Right, again, that's why the reliability is just 100%. My (ahem) point is, though, that none of us ARE at a typical point (again, assuming QTI). In fact we're in a very atypical point, just as the era of stars might be a very atypical point in the history of the universe - but it's a point we (or the universe) HAVE TO PASS THROUGH to reach more typical points (e.g. very old, no stars left...). Hence it's consistent with QTI that we find ourselves passing through this point... Right, consistent with it but only 0% of the time, hence the Bayesian argument is to put 0 credence in the FIN rather than strictly no credence. I'm not arguing for QTI here, but I do think that you can't argue from finding yourself at a particular point on your world-line to that world-line having finite length, because you are guaranteed to find yourself at that particular point at some (ah) point. Right, which is why I'm (now) careful not to make *that* argument by arbritarily using one's current age to base a reference point on. (e.g. in my reply to Bruno.) Rather, I argue that from being at a point prior to some _natural reference point_ such as the can calculate my age crierion, one can conclude that one's world-line is finite. So I'm rejecting, not Bayesian logic per se, but the application of it to what (according to QTI) would be a very special (but still allowable) case. There are no grounds to reject it in this case, since it would be reliable almost all of the time. There's no difference between using a method because it works for most people vs. using a method because it works for me most of the time. At any given time, it works for most people, too. The basic problem is that we experience observer moments as a sequence. Hence we *must* experience the earlier moments before the later ones, and if we happen to come across QTI before we reach QTI-like observer moments then we might reject it for lack of (subjective) evidence. But that doesn't contradict QTI, which predicts that we have to pass through these earlier moments, and that we will observe everyone else doing so as well. I wish I could put that more clearly, or think of a decent analogy, but do you see what I mean? Our observations aren't actually *incompatible* with QTI, even if they do only cover an infinitsimal chunk of our total observer moments. Indeed so, I know only too well what you mean. This has come up more than once on the list. I hope you understand why I say it's irrelevant. _Just like_ in the A/B case, it would be wrong to not use Bayesian reasoning just because seeing A is, yes, compatible with both #1 and #2. Seeing A could even have been a way to confirm theory #2, if the rival theory #1 hadn't existed. The bottom line is that Bayesian reasoning usually works for most people. - - - - - - - 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
RE: FIN too
Jacques Mallah wrote: It's nice that you reject FIN! Of course, those who support it can give (and have given) no reason ... Surely this is an exageration. I recall that I am still waiting for you showing a flaw in the UDA (the Joel version). But here you betraye yourself: ... since it's a nonsensical belief. You admit not having read the reasons/explanations we propose because you know at the start it's a nonsensical belief!!! You are begging the question since the beginning. But I am still waiting *you* explain me how in the W M duplication, you can both still believe in comp and pretend the question of what I will feel is nonsense. Oh yes I remember, you don't see the difference between 1 and 3 person point of view ... Like some physicist you tranform the methodological evacuation of the subject in an ontological dogma. Indeed I see you say that words like me or you are mere definition. I believe the contrary, from the 1 person point of view, the word me is not even definissable. That is what makes grandma psychology not really intuitive in the multiplication settings, but that is why I replace it eventually by the self-reference logics where the consistency of comp immortality (and so at least the sensicalness) is beyond doubt. Of course I have infinite doubt about that immortality, but I have no doubt comp entails it logicaly/arithmeticaly. About your saying you are sane, at first i take it for an attempt being comical. Your last answer to Hal Finney is really uncomical. Scientist always doubt ... You talk like you have certainty on our subject matter, which as Hal said is certainly not easy (not easy at all). Also I (re)read you implementation paper where, as I said, you definitely and admittedly don't have solved the implementation problem, but then why do you injuriate us with seemingly certainties? I'm also less and less sure bayesian reasoning works in our mathematically infinite context ... Bruno
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
RE: FIN too
From: Charles Goodwin [EMAIL PROTECTED] Hi, I have just joined this list after seeing it mentioned on the Fabric of Reality list Hi. BTW, what's up on the FOR list? Ever see anything interesting there? I thought the book sucked except for chapter 2 (I think; the one explaining the MWI), but at least there are some MWIers on that list I would think. Would someone mind briefly explaining what FIN is (or at least what the letters stand for)? Is it some version of QTI (Quantum theory of immortality) ? Yes, any version of QTI is FIN. Why should a typical observer find himself to be older than the apparent lifetime of his species? I guess you mean assuming FIN, why ... so *very* few observeres are going to notice the TU versions of anyone else. So the only way to actually experience this phenomenon is to live to be that old yourself. Right ... I must ask, though, what makes you think that a typical observer ISN'T much older than the lifetime of his species would allow? I'm not so old, but if FIN were true, the effective chance of me being old would be 100%. So by Bayesian reasoning, it must be false. Given that you can't observe anyone but yourself in this state (or it's TU that you ever will) (and I'm assuming you haven't reached 120 yet), you can't really use a self-sampling argument on this, surely? On the contrary, you do use a SSA. After all, you will never (for any question) have more than the one data point for use in the SSA. But with a probability of 0% or 100%, that's plenty! It means - and I admit it does take a little thought here - _I want to follow a guessing procedure that, in general, maximizes the fraction of those people (who use that procedure) who get the right guess_. (Why would I want a more error-prone method?) So I use Bayesian reasoning with the best prior available, the uniform one on observer-moments, which maximizes the fraction of observer-moments who guess right. No soul-hopping in that reasoning, I assure you. I'm sorry, I still don't see how that applies to me. If I know which observer moments I'm in (e.g. I know how old I am) why should I reason as though I don't? Because you want to know things, don't you? It's no different from any Bayesian reasoning, in that regard. Suppose you know that you just flipped a coin 10 times in a row, and it landed on heads all ten times. Now you can apply Bayesian reasoning to guess whether it is a 2-headed coin, or a regular coin. How to do it? p(2-headed|got 10 heads) = [p(got 10 heads|2-headed) p_0(2-headed)] / N p(1-headed|got 10 heads) = [p(got 10 heads|1-headed) p_0(1-headed)] / N where N = p(got 10 heads) is the normalization factor so that these two conditional probabilities sum to 1 (they are the only possibilities). That's a standard use of Bayes' theorem. But - whoa there - what's the p(got 10 heads) and the like? You already _know_ you got 10 heads, so why not just set p(got 10 heads) to 1? Obviously, you consider the counterfactual case of (didn't get 10 heads) for a reason - that is, to help you guess something about the coin. 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. - - - - - - - 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
