Re: normalization
In a message dated 01/18/2000 1:09:02 PM Pacific Standard Time, [EMAIL PROTECTED] writes: > On Tue, 18 Jan 2000 [EMAIL PROTECTED] wrote: > > [EMAIL PROTECTED] writes: > > > The RSSA is not another way of viewing the world; it is a > > > category error. > > > > I use the RSSA as the basis for calculating what I call the relative > > probability, in this group the first person probability, or, equivalently, > > > the probability conditional on the life of the observer. The ASSA is by > > extension, the assumption for calculating the 3rd person probability. > > > > Let us perform a thought experiment. > > Imagine that you are the scientist in the Schroedinger cat experiment. > > Scratch that. Right now let's stick to the example with Bruno and > the 3 cities, because it's better for the current point. > Suppose Bruno, in 1999, wants to know if he is more likely to be > in Washington or in Moscow during 2001. > First of all, that is not a well defined question, because > "Bruno" must be defined. Suppose we define it to mean the set of all > Bruno-like observations, where by "Bruno-like" we can assume we know what > qualifies. > But then the question becomes meaningless, because it is 100% > certain that he will be in *both* cities. A 3rd person would have to > agree with that, he is in *both* cities. > So let's ask a meaningful question. Among the set of Bruno-like > observations in 2001, what is the effective probability of such an > observation being in Moscow? > This is just a conditional effective probability so we use the > same rule we always use: > p(Moscow|Bruno in 2001) = > M(Moscow, Bru. 2001) / [M(Moscow, Bru. 2001) + M(Washington, Bru. 2001)] > where M is the measure. > So in this case the conditional effective probability of him > seeing Moscow at that time is 10%, and in *1999* he knows he should brush > up on his English because his future 'selves' will be affected by that. > Fine, you have computed the third person probability. Unfortunately, your example does not have the option of having an independent observer, and therefore does not illustrate the concept I am trying to communicate. Please follow and answer my thought experiment the way I posed it, that is with an observer who is not threatened with death and a subject who is. It is the only way to bring out the concept of relative probability or 1st and 3rd person probability. George Levy
Re: normalization
On Tue, 18 Jan 2000 [EMAIL PROTECTED] wrote: > [EMAIL PROTECTED] writes: > > The RSSA is not another way of viewing the world; it is a > > category error. > > I use the RSSA as the basis for calculating what I call the relative > probability, in this group the first person probability, or, equivalently, > the probability conditional on the life of the observer. The ASSA is by > extension, the assumption for calculating the 3rd person probability. > > Let us perform a thought experiment. > Imagine that you are the scientist in the Schroedinger cat experiment. Scratch that. Right now let's stick to the example with Bruno and the 3 cities, because it's better for the current point. Suppose Bruno, in 1999, wants to know if he is more likely to be in Washington or in Moscow during 2001. First of all, that is not a well defined question, because "Bruno" must be defined. Suppose we define it to mean the set of all Bruno-like observations, where by "Bruno-like" we can assume we know what qualifies. But then the question becomes meaningless, because it is 100% certain that he will be in *both* cities. A 3rd person would have to agree with that, he is in *both* cities. So let's ask a meaningful question. Among the set of Bruno-like observations in 2001, what is the effective probability of such an observation being in Moscow? This is just a conditional effective probability so we use the same rule we always use: p(Moscow|Bruno in 2001) = M(Moscow, Bru. 2001) / [M(Moscow, Bru. 2001) + M(Washington, Bru. 2001)] where M is the measure. So in this case the conditional effective probability of him seeing Moscow at that time is 10%, and in *1999* he knows he should brush up on his English because his future 'selves' will be affected by that. - - - - - - - Jacques Mallah ([EMAIL PROTECTED]) Physicist / Many Worlder / Devil's Advocate "I know what no one else knows" - 'Runaway Train', Soul Asylum My URL: http://pages.nyu.edu/~jqm1584/
Re: normalization
In a message dated 01/17/2000 4:58:50 PM Pacific Standard Time, [EMAIL PROTECTED] writes: > The RSSA is not another way of viewing the world; it is a > category error. I use the RSSA as the basis for calculating what I call the relative probability, in this group the first person probability, or, equivalently, the probability conditional on the life of the observer. The ASSA is by extension, the assumption for calculating the 3rd person probability. Let us perform a thought experiment. Imagine that you are the scientist in the Schroedinger cat experiment. Please calculate the probability that the cat stays alive. Let's call this the 3rd person probability. Assume that the vial of cyanide has an 50% (objective) probability of breaking during the experiment. Now imagine that you are the cat. (A very intelligent cat with a knowledge of probabilities) Please calculate the probability of staying alive. Call this the first person probability. Now imagine testing your calculations with experiment. First, pretend you are the scientist and perform a large number of cat experiments. Does your third person calculation statistically agrees with the experimental data? (i.e. you should see about 50% of the cats meet their demise) Now, pretend you are the cat, and perform a large number of experiments. Does the first person calculation statistically agrees with the experimental data that you have accumulated? (you should see your survival 100% of the time) The relative probability concept (1st and 3rd persons) can be used in other ways. Here is another example: You take a flight from New York to Los Angeles. Assume the following: The objective (3rd person) probability of a crash is 0.001 The objective (3rd person) probability of a hijacking to Cuba is 0.001. What are the first and third person probabilities of reaching Havana and Los Angeles? Answer: The third person probabilities are: Probability of a crash = 0.001 Probability of going to Havana = 0.001 Probability of going to LA = (1- 0.001) x (1-0.001) = 0.998001% The first person probabilites are Probability of a crash = 0.000 Probability of going to Havana = 0.001 Probability of going to LA = (1 - 0.000 ) x (1 - 0.001) = 0.999 This is just to illustrate the point that depending on the frame of reference of the observer, the experimental results will be different. George Levy
Re: Normalization
Hal and Marchal: I guess the fundamental reason why I insist that the world is quantized is because of the equivalence I make between 1) the universe of thoughts, 2) The universe of Turing simulation and 3) the physical universe. In my opinion, this equivalence originates from the "rationality-X" constraints imposed by the Anthropic principle on the transitions from observer moment to observer moment. This rationality-X constraint gives rise to consciousness-X, and to physicality-X. These constraints restrict the physical world and the mental world in exactly the same way. In other words, we can only move from one observer moment to another if there is no white rabbit that pops up and make us crazy. Rationality of the mental world is matched by the comprehensibility of the physical world. The equivalence derive from the fact that the physical world and the mental world are generated by exactly the same phenomenon. This approach explains why the world is comprehensible, one of the mysteries pondered by Einstein. Adding Church's thesis to the mix we can also include Turing machine simulation in the equivalence. Hence physics, machine psychology and human psychology are exactly equivalent. Roughly they correspond to "real" reality, Turing emulable virtual reality and dreaming. I believe that in this respect I am very close to what Marchal is saying. I believe comp is valid. but as I have explained before, to explain free will we have to look beyond comp... where comp breaks down. George Levy
Re: normalization
[EMAIL PROTECTED] wrote: \/ > In my opinion, the RSSA is the conditional probability of you observing > something happening given that you are alive to observe it. Thus is it a > first person probability measure. In that case, if by "is" you mean "gives results equal to", it would just be a matter of definition, no? So it could not give results in conflict with the ASSA. > In my (unpublished) book I have developed the concept of "relative > probability", which may be called in this group "first-person > probability. By extension, the ASSA (I think) is the third person > probability. I don't know what you mean by those terms. As far I'm concerned, the ASSA gives the (effective) probabilities of observer-moments, and that's all there is to it since all other questions can be phrased in terms of that. > Thus the computation of probability requires > 1) specifying if the probability is for the first or third person (ie. RSSA > or ASSA) > 2) the definition of measure at two points. I, of course, would say that #2 determines everything and that #1 does not make any sense since the RSSA doesn't. > The example provided by Jacques about teleporting Bruno, was excellent. Thanks. > The following post is an attempt on my part to go through Jacques' reasonning. > Thus if Bruno is teleported from: > 1) state A: one copy in Brussel to > 2) state B 9 copies in Moscow and one copy in Washington, > > then for the transition AB, the 1st person probability that Bruno finds > himself in Moscow is 9 times higher than in Washington. In this particular > case, the first person probability of observing such an event is also equal > to the 3rd person probability. Thus, in this case, the results from ASSA and > RSSA coincide. Looking at this result, it is clear that Bruno while still in > Brussel should buy himself a Russian dictionnary to prepare himself for the > trip. > > -- > > Consider now, as Jacques suggested, a state C created such that 8 out of the > 9 copies in Moscow are killed by the Chechnians and 8 copies are created from > the single copy in Washington by a Hollywood Jurassic Park project. > > Let us now calculate the first and third person probabilities for the > transition AC. > > The ASSA says that the 3rd person probability of finding Bruno in Washington > is 9 times higher than finding him in Moscow, since the measure is 9 times > larger. No - the ASSA says that the (effective) probability of Bruno-like observer-moments that see Washington is 9 times higher than that of those that see Moscow, after the second event. For a "3rd person", self-sampling would not be at issue. Note also, as I said, no one of the copies is more connected to the original than the other copies; so either they are all Bruno, or only the original observer-moment was Bruno, depending on the definition. > Thus, according to ASSA, Bruno should have bought himself an English > dictionnary while he was in Brussel. Yes - that is true, independent of any quibbles about what "you" (in this case "Bruno") means. > Now let us compute the probability of transition AC from the first person > point of view (RSSA). This probability is the product of the first person > probabilities for transition AB and BC. > First person probability of transition AB from Brussel to Moscow trip = 9/10 > First person probability of transition BC for destruction of 8 out of 9 of > Bruno's copies = 1 !!! (Bruno is not aware of the carnage of his own copies > in Moscow) (Note here that I do not include the Washington experience yet > -See note on renormalization **) > Hence combined first person probability for being in Moscow for transition AC > = 9/10. > > Now for the Washington trip: > First person probability of transition AB from Brussel to Washington = 1/10 > First person probability of transition BC for Jurassic Park cloning of Bruno > = 1. (Here I do not include the Moscow experience - See note on > renormalization **) > Combined first person probability for being in Washington for transition AC = > 1/10 > > Thus according to RSSA, looking back on his purchase choice, Bruno should > have bought a Russian dictionnary while he was in Brussel. > > This case illustrates how the decision making process differs if the world is > viewed from a first person or third person perspective. Impossible. Either he should get one dictionary, or the other (or both but let's ignore that possibility and make his decision easier by shortening the time between events AB and BC to one second instead of a year.) The ASSA tells him to do one thing; the RSSA something different; so they are proved to be in direct conflict. Only one can be correct. The RSSA is not another way of viewing the world; it is a category error. There is no damn such thing as a "1st person probability". There is only the effective pr
