D4 S1 Don Page - Possibilities for Probabilities

Okay, so welcome, everybody. I suggest we start the session. So it's my honor to introduce the first speaker. Yeah, thank you. It's, it's a great joy to be back here. It's my fifth trip, trip to Israel. I think I first went to conference 79 to 80 about well, some quantum cosmology stuff. Jim Hartle was giving a talk about and he first talked about the Hartle-Hawking no-boundary wave function. And then he decided he was going to talk about some others. He said, well, the Hartle-Hawking one is an ordained by God. So let's also consider another one. So I spoke up and said, well, if it's not ordained by God, does that mean it's not correct? And then Stephen Hawking spoke up and said, it's the only one not ordained by God. So anyway, I don't know. Okay, and then this anyway, just a scene from a top of Mount Temple, which is near not about five hour, five hour drive from Edmonton. So anyway, we got some nice scenery in Alberta. So welcome to come sometime to the Canadian Rock. Okay, today, I want to talk about well, first mention what I call the complete theory of the universe. But this is the same as what Eddie Chen was talking about a strongly deterministic theory. It would not only give a complete set of dynamical laws, what has been misleadingly called the theory of everything, it's not until you get other parts, but also the quantum state of the universe, which Hartle-Hawking have made one proposal for it. And Eddie Chen had some other proposals, and the so far unknown rules for extracting the probabilities of observations from the quantum state. I'm going to distinguish that from the probabilities of the branches, which Everett and Hartle and Saunders and others have have given for that I'm saying the probabilities of observations is not the same because you can have in one branch, you could have different numbers of one kind of observation from another. So the probabilities of observation can do can can differ. Now I'm going to propose a basic framework for these rules. Rules, you could say of psychophysics, well, for these rules that the measure for each observation is the expectation value in the quantum state of the universe of a corresponding positive quantum operator for each possible observation, which I shall call an awareness operator. Now, one needs to say what observations are, and I propose that they are fundamentally sentient experiences, each being the entirety of a conscious awareness, all at once consciously aware of at once. And I often use conscious perception as a synonym for sentient experience. So if I say sentient experience, I mean the same as conscious perception, all at once consciously aware of at once. And I shall point out, but I don't have time in this talk to explain that for a large universe with indistinguishable copies of observers, the quantum awareness operators cannot be projection operators, as one might have assumed from Born's rule. So Born's rule does not work in a large universe, or as one of my papers had it, the Born rule dies. Now, Bayer quantum theory describes the universe in terms of quantum states, operators, expectation values, wave functions, amplitudes, path integrals, etc. But it is not by itself connect these to observations. So Bayer quantum theory is not directly testable. To make comparison with observation, Max Born proposed, suggested that the wave function gives probabilities. Later, it was proposed that the probabilities are given by the absolute squares of amplitudes. And these can be taken to be the expectation values of projection operators. So in this talk, I shall take the mathematization of Born's rule to be the idea that the probabilities of observations are given by the expectation values of projection operators. So I'm going to reject that view. But that's what I'm, if I if I say Born's rule, I mean that expectation by that, that the that the probabilities are given by the expectation by projection operators, but I'm going to deny that that's the case. Okay, now let's consider a Bayesian analysis for probabilities of theories. So consider theories T sub i, that for each possible observation, O sub k, each theory T sub i gives a probability for that observation, P of, P of O sub, O sub k, and that bar means given, given T sub i, given T sub i what's the probability of the observation. Now to get to, but we want the posterior probability, which is the probability of the theory given the observation. And for that we use, need to use Bayes' theorem. If we said, assigns what seemed to be inevitably subjective prior probabilities, P sub T to the theory C sub i, presumably higher for simpler theories by Occam's razor. And if we use an observation O sub k to test the theory, then P, the probability of the observation given the theory is what's called the likelihood of the theory. But remember, that's not the probability of the theory. It's, it's called the likelihood, but it's the probability of the observation given the theory. And by Bayes' theorem, we can calculate the posterior probability of the theory, the probability of the theory given the observation as the product of the prior probability times the likelihood and then, and then normalize by dividing that, that same expression, but summed over all theories. So we would like to get this posterior probability as high as possible by choosing a simple theory for high prior probability, that gives a good statistical fit to one's observation, so high, high likelihood. Now, since a complete theory of the universe should completely specify all properties of the universe, one might think it has no room for probabilities between zero and one. So all likelihoods would be zero or one. Then the posterior probabilities of these theories, given the observation, okay, would just be proportional to the prior probabilities of the theories that give that observation as having one instead of zero. But for observations, even though I'm a theorist, I do think science is fundamentally, or maybe primarily, I don't know, observational physics, observational science, so I want observations to play a bigger role. So we'd like a way of getting a range of likelihoods between, between zero and one. So now, if the theories can give normalizable measures for the observations, then the normalized measures can be interpreted to be used as if there are likelihoods that can vary between zero and one. So even if this this complete theory determines everything, so it's deterministic, there's no room for uncertainty or probability within the whole theory. But if there are these measures, they could be used as if they were the likelihood. So in a classical theory, for example, the measures could be functionals of the phase space trajectory, such as the amount of time that a system spins in each different region of the phase space. In quantum theory, the measures could be certain functionals of the quantum states or maps from the quantum states to non-negative, non-negative numbers. Now, let me give another argument against likelihoods all zero or one. If a specific theory leads to the definite existence of more than one observation, O sub k, as indeed many worlds does, or even the single universe does, because there's lots of observations going on, one might be tempted to say that the likelihood, the probability of the observation given the theory is one, since it exists for all these observations. That would give unit likelihood for any theory predicting the definite existence of the particular actual observation used to test the theory. However, this procedure, this assumption would mean that you can construct a theory of maximum likelihood, which is one, I mean, the likelihoods can't be bigger than one, no matter what the observation turns out, just by having the theory predict that all possible observations definitely exist. But this seems to be too cheap, supposedly explaining everything, but actually explaining nothing. So I mean, some people say, well, the multiverse, since everything exists, it explains why we see it. No, we need more, we want, we want to get the probability of our observation, and then multiply by the prior and get the posterior probability, which it's not sufficient just to say that the theory predicts that our observation definitely exists. So therefore, I'm proposing the normalization principle or meta theory, that for each theory T sub i gives normalized, quote, probabilities are really measures, but quote probabilities for the different possible observations or predicts. So for each theory, the sum of these likelihoods over all O sub k is unity. So there's a trade off between prior probabilities and likelihoods. There's prior probabilities for the theories, that's the intrinsic plausibilities of them. Before, in this case, for the whole universe, before you have any observations, which is really impossible for us within the universe, then there's the conditional probabilities or measures for observation given the theory. So what are called likelihoods of the theory for fixed observation, and then the posterior probability, the probability of the theory given the observation proportional to the prior probability times that and then of course, normalize. So the prior probabilities are subjective, usually higher for simpler theories. So in my mind, the highest prior probability might be the theory T sub i, that nothing concrete or contingent exists. But then since our observations are certainly contingent, I mean, they don't logically need to exist, then the simplest theory would predict that there are no observations. So then the probability of the observation would just be zero. And of course, that then, by this up here, it leads to zero posterior probability. I think I can say there's zero probability that there's zero probability that nothing concrete exists. T sub 2 might be the theory that all possible observations exist equally. But then since surely there's an infinite number of possible observations, to normalize it, you'd have to take the one divided by the number and that gives zero and normalize. So that would be my argument against, if you extended modal realism of David Lewis and Novak or whoever else proposed that everything logically possible actually exists, if you augment that by saying that everything actually exists with equal measure, all possible observations, then this rules it out, because it says that the probability is diluted among an infinite number. So there's zero likelihood for any, for our observation. Now, the other extreme would be a maximal likelihood theory, giving the probability of the observation given the theory of one, for one's observation of k. But of course, since it's both, since I'm saying the sum over all observations has to be one, that means there's no measure for any other observation. So it's saying that only one observation exists. And this, if I put, if I imagine my own observation, and it's got a lot of order and complication, and there's a lot of details in it, it would, I would think it would require a very complex theory to predict that only my observation exists and not any, not any other ones, not any of yours, or not any of my mind that I think I had in the past, and so on. So, okay, so that would, that's, that would, I would assign that an extremely tiny prior probability giving a very low posterior. So this is a trade off between prior probabilities and likelihoods, that is between intrinsic plausibilities and fit to observation. Okay, so probabilities of observations, I'll take an Everettian view that the wave function never collapses. So in that sense of Everettian, at the end, I might ask you to see based on my talk, whether you consider me an Everettian or not. But anyway, for now, I'm Everettian as far as I believe there's no collapse of the wave function, the wave function never changes. So in the Heisen picture, there's only one single fixed quantum state for the universe. And the universe might be a multiverse might have different parts with different effective coupling constants, and so on. I assume that instead of, quote, many worlds are instead many different actually existing observations or sentient experiences, O sub k. But they have different positive measures, mu sub k, it depends on its function of the O sub k, which are in some sense, how much the various observations occur, but they're not determined by just the contents of an observation. The measure of a tooth, the sense of a toothache is not how painful it is or anything. It's not the content, but it's a measure. It's kind of a primitive concept. I don't have some other analogy. But I mean, if you wanted to think of an analogy, not that I'm doing it, but you might think that, okay, maybe God and his time is is is thinking in a sequence of all the possible observations that he the amount of time he spends on each one is is is proportional to this measure. I'm not taking that picture literally, but I'm saying the measure is kind of a primitive, primitive notion here. So what the measure of observations, I can't say it's it's like an electric field or a scalar field or mass or energy or anything else. It's just a measure. It's just a fundamental concept in here. Now for simplicity, well, to avoid having to bend things, I'll show soon there's a countable discrete set O sub k of observations. And the total measure is normalized to unity for each possible complete theory that gives the normalized measures for each for all possible observations. So then in a Bayesian analysis, I shall interpret the normalized measures, each theory as the quote probability of that observation given the theory, which for one's observation O sub k is the quote likelihood of the theory. I'll use those as likelihood. Okay, now we get to the my framework for what these what these measures are. The map from the quantum state to the measures of observations could be nonlinear. And I think in some sense, if you required some definite proposal for what the what the branches are, that would be nonlinear in the thing. So I think you'd end up with nonlinear measures. But I'm going to assume a linear relationship and what I call sensible quantum mechanics. I also in a paper for layman, I called it mindless sensationalism because it proposes what's fundamental is not minds. It's not a many mind series like lower and others, but conscious perceptions, which crudely might be, well, I stretched it to make the title might be called sensations. Oh, of course, a conscious perception includes more than just the sensations. It has includes memories and emotions and thoughts and, you know, a lot of other things besides sensation. But anyway, just to get that phrase. Okay, so the measure for the observation is the expectation that sigma is a quantum state that gives expectation values to operators. So it's there for each observation is a positive operator. And or I could just say the operator, I can condense this to say a sub k is the operator corresponding to that observation. And the brackets are expectation by it's the expectation by most of K, which is the same as this. So sigma is the quantum state of the universe, interpreted as a positive linear functional of quantum operators. And a sub k is a non negative awareness operator corresponding to the operator observation or sentient experience, or in other words, conscious perception of K. So the quantum state of this could be a pure state, it could be a mixed state given by density matrix, or it could be C star algebra state, it basically just needs to give expectation values of operators. And the awareness operators along with the linear relation above and a complete description of this, the theory would would also have to say what's the content of each of these observations, they're all would all be given by this complete theory. Of course, we don't have the theory, but I'm trying to give a framework for what I would believe could be a complete theory. Now I've shown elsewhere, I don't have time to describe it here, Born's rule does not work in a universe large enough that there may be identical copies of the observer at different locations. If you have one here with a part with spin up and another one with spin down, they should assign probabilities between zero and one for that, because they're not certain which one they are. But there's no projection operator that would give that at least if you could allow fixing the projection operator first and then and then having the state change. In other words, I think it's what's called non contextual, I guess, projection operator. Okay, so the failure of Born's rule means that in this theory tasted by the awareness operators whose expectation value in the quantum state sigma, the value of the universe give the probabilities or norm, quote probabilities or normalized measures for observations of sentient experience as this formula here, they cannot be projection operator. However, they could be weighted sums or integrals over spacetime of localized projection operators, p sub i, but depends on x that denotes the location in the spacetime. Say on the brain states there that would produce the observation. So if so part of it, one of it might be a projection operator on what's going on in my brain, and well, a suitable state of my brain that would lead to my present conscious awareness, for example. So now there is, okay, I would not expect it that the theory to say exactly where each one of these is. So I'd expect to be some integral or some it could be looking, you know, maybe if it's looking in here, if that contributes a significant part to the expectation by if it looks over here, it would be, you know, exponentially enormously suppressed. I mean, I suppose there's some quantum amplitude for brain to appear here, both from brain, and so on, but very negligible. And then so on and so on. But if you if I if I do the integral overall space, eventually somewhere, if it catches a brain somewhere, then it will get contribution there. But now there is a problem because our universe seems to be expanding exponentially or asymptotically exponentially and make might go on forever. That in local quantum field theory with definite globally hyperbolic spacetime, any positive localized operator such as a localized projection operator will have a strictly positive that is non zero, but and non negative positive expectation value and any non pathological quantum state including the vacuum. So such a positive localized operators integrated with uniform weight over a spacetime with infinite for volume, it will give an awareness operator with infinite expectation value, I won't be able to normalize. So integrating up over all these regions, even though after the stars have all died out, and us ordinary observers, or OOs as people call it have died out, there's still in some region of space, it's even no matter how empty, there's still possibility of a quantum fluctuation. So this operator will have a positive expectation value, maybe very small, maybe 10 to the minus some huge number, but non zero. And if you integrate that over infinite for volume, you'll get infinity. Now you can say, well, we'll cut it off at some finite cutoff time T sub c, and then you normalize it. Then for universe, it continues forever with a three volume bounded below by positive value. So in other words, the four volume is growing indefinitely, the intervals will be dominated by times of the same order of magnitude as the cutoff time. And so at these late times, the probability, if it's sufficiently late, that the probability for four volume ordinary observers is very low, then most of the measure will be contributed by thermal or vacuum fluctuations, which are so called Boltzmann brains. That is, Boltzmann brains will dominate the measure for observations, if you put if you just do a uniform integration over spacetime, and then cut it off at some place and then normalize it after that. Now, if Boltzmann brains dominate the measure for observations, one might ask, so what? Couldn't it be their observations are those of ordinary observance? Or couldn't be their observations really are Boltzmann brains, but they look like things look ordinary. However, my argument against that is that since Boltzmann brain observations are produced mainly by thermal or vacuum fluctuations, it would be expected only a very tiny fraction of their measure would be for observations so ordered as ours. It would be very rare for Boltzmann brain observation to have all the order that I have in mind of seeing faces that I recognize and correlate with memories of how I remember you looking yesterday, or in some cases, even decades ago. So anyway, so there's very tiny fraction of the ordered Boltzmann brain probability plus the even smaller fraction of ordered ordinary observer observations, assuming that they're dominated by the Boltzmann brain, in comparison with the dominant disorder Boltzmann brain would be only a very tiny fraction of the measure of all observations. That's the normalized probability of one of our ordered observations, which we would use as the likelihood of theory would be highly diluted by the other because remember, I'm requiring that the sum of these of these measures adds up to one. And so if there's if most of it is for the Boltzmann brains, then it only leaves a small, well, most of it for the disordered leaves only a very small part of the probability for the ordered one. So be much smaller than alternative theories in which Boltzmann brains do not dominate. So if you could come up with alternative theories do not have prior probabilities that are too small, they would dominate the posterior probability over the naive ones that have this Boltzmann brain domination. Now another observation that other observations that seem at least naively difficult to explain by Born's rule, include our observation that we are humans rather than ants, despite the much greater number of ants on Earth. Again, if that if each ant had as much measure of consciousness as as we do, then the probability would get diluted by all the the math, you know, if we had to sum up the unity, and so we would be, you know, it'd be improbable that we find ourselves to be human, very important. Now, not as bad as the Boltzmann brain. I mean, the ants don't outnumber as near as much as the volume of space time, compared to the early time. So it's not near as severe problem as that, but it still seems to be somewhat of a problem. Okay, as we shall see, modification of Born's rule can explain the probability of observation by copies of the observers. Well, okay, I won't get into that part here, I guess. But the fact that we apparently do not observe ourselves to be Boltzmann brains is the fact that we do not observe ourselves to be ants. However, it's not yet known when the correct modifications are. So there's many logical possibilities for the probability. I do think the universe really does have one particular rule. It has one thing and I'm conjecturing it has this this this form, but exactly what the awareness operators are, I don't know. So there's many logical, many possibilities that seem to be logically possible. And it would, you know, of course, we would like to learn which is the actually the correct one. So, yeah, the main open question in the sensible quantum mechanics framework in which the probabilities of observations are the expectation values of positive awareness operators, one corresponding to each observation is what these awareness operators are. So this SQM framework does not assume there's a space time. So it could be valid even in formulations of quantum gravity when space time is not fundamental. However, to kind of tie it a bit to what we presently know, rather than what we don't yet know, if we if the part of the quantum state that gives the dominant contribution to expectation values of the awareness operators can lead to an approximation of an effective space time or of a quantum superposition of space times. One idea is that the contribution to the expectation value of an awareness operator from each space time in the superposition was first the expectation by the existence of this space time that would be similar to the probability for the branch, if each space time has its own branch, multiplied by weighted sum or integral over the space time of localized projection operators for each region of the space time. So to avoid both the brain domination and the sum, it seems necessary to choose weight factors that get convergent integrals that are not dominated by the asymptotically empty regions, where almost all observations would be by bolts and brains. So for space time with preferred spatial hyper surfaces, such as proper time t from a Big Bang, or from a balanced minimal hyper surface, that each at each time have finite tree volume, though perhaps tending to infinity asymptotically with time. One simple procedure for avoiding divergent integrals over space time is to divide the contribution over each of these preferred spatial hyper surface by its tree volume. Then that gives the taking the contribution each time to be the volume average of the expectation by the localized operators there. So that would mean that that each time later would would would only give a finite and at late times a very tiny contribution to the awareness operators. But there's still a problem with the thing diverging if you integrate from t going to infinity. So here I propose something even more ad hoc, to replace the integral over dt which diverges by an integral over dt over 1 plus t squared. I call this Agnesi weighting, because that curve, well it's the Lorentz line shape or the Cauchy distribution, but in old times it was called, the curve is called the Witch of Agnesi. I'll tell you later the story about how I got the thing named Witch, but but anyway, Agnesi was a female mathematician, but there's no suggesting that she was a witch, but but the curve got called the Witch of Agnesi. Well, I can say it's due to a confusion between the Italian words for witch and for curve. So I guess witch is a twisted person. So I guess the words I guess were similar. I don't know Italian. Okay, now this last part is admittedly ad hoc. The other is a little bit ad hoc, but less so than this. So it should be a more elegant formation should be found. So then to explain why we observe ourselves to be humans, despite the much greater number of ants it seems plausible to postulate that human brains are much more efficient in producing sentient experiences than ants. So the total probability of human conscious perception is not far below that of ants to make human observations much less probable. If it's just half, if it's half and half, I don't care, doesn't make much difference if the probability is reduced by a factor of two, but if it's reduced by a factor of millions, then I start worrying about it. Therefore, one might postulate that the localized projection operators the human brain can figure should be much given weights, W sub k, then the localized projection operators, the ant brain configuration, perhaps part of this weighting factor should be the complexity of the corresponding human brains. So it's human brains seem to be much more complex than ant brains. But I'm skeptical of the process is simply getting high complexity or high information processing is itself sufficient for getting large weight multiplying the corresponding localized projection operator for the corresponding awareness operator. So just making a computer as complex as the human brain, I don't think that that implies it's conscious, or it has a significant measure of consciousness. I think everything has some exponentially tiny measure of consciousness, because there's always some some amplitude for the region in there to be a human brain configuration. Okay, so to suppose the expectation value of a given space time is E sub L, is S sub L is E sub L, that might be if you if you say that each different space time is one of the branches, then that might be the probability for the branch. And that in this space time, the expectation value of the localized projection operator is this, that the expectation value as a function of the space time position, goes further that this space time, the weight factor for the integration over four volume is capital W, the function, for example, it could be one divided by the volume of the space at that time, and one plus t squared to avoid the integration, and that the intrinsic weight factors for the observation is little w sub k, that's the one that makes humans better than ants, then the relativity of probability could be the relative that's before I normalize it, the weight factor for human ones, a sum over all the space times with their expectation values, and then over each space time, an integral over the four volume, but then with this weight, this position dependent, but diffeomorphism invariant, I mean, it's, it depends on the actual properties of the space time. So it's diffeomorphism invariant, but it's a non local, because it depends on, for example, the time since the Big Bang or the volume, this, this weight factor, and then the, and then the, the, the density of the expectation value. Okay, so then this formula shows because we don't know what the w, little w is, or the, well, the ELs, maybe you can calculate and the capital W is. So there's a lot of logical freedom in the modification of Born's rule for cosmology, even within the restrictions of sensible quantum mechanics, with the relative probabilities of observations or expectation values of the quantum operators, or the awareness operators corresponding to the observation. There'd be even more logical freedom if you abandon this and allowed the relative probabilities to be nonlinear in the expectation values, such as these expectation values raised to a power s, that is different from unity, or to be even more general nonlinear functionals of the quantum state. So therefore, in sensible quantum mechanics, what can be used instead of, quote, probabilities of observations are instead measures for many actually existing sentient experiences, each given by the expectation value of the quantum state of, in the quantum state of the universe of a corresponding positive awareness operator. The awareness operators cannot be projection operators as suggested by Born's rule. But in a spacetime picture, they might be given by a suitably weighted integral of localized projection operators within each spacetime, and then summed over spacetimes weighted with their quantum expectation values. There's considerable logical freedom in these weightings, so we are far from knowing what's actually the case for our universe or multiverse. So this talk was largely a summary of this paper. And I was grateful to discussions with Sean Carroll and his idea of the Huff where some of these ideas were developed. And I want to ask you whether he's right in saying this, he emphasized that by sensible quantum mechanics framework with the relative probability of observations being the expectation values of positive awareness operators is not ever ready in quantum mechanics, which he says assumes a particular branching of the quantum state and probabilities of observations depending on this branching. And that would be highly nonlinear functionals of the quantum state, you have to specify how the branching is going. So, okay, so that's my conclusion. I might ask, how many of you think, having heard these sort of radical ideas, or whatever, how many would say that I'm an Everettian? How many was, okay, one, two, three, four, four, four, yes. Or how many would say I'm not an Everettian? One, maybe one. Okay, okay, well, I hope people excuse me if sometimes I say I'm an Everettian, I'm certainly never an Everettian, this is no collapse. And the other thing, of course, I'd certainly appreciate it. I know these ideas are very speculative, and they're not going to be able to be fully developed, you know, probably within my lifetime. Anyway, but if anybody knows of some way to show that they're definitely wrong, I would definitely appreciate being shown if, you know, if something is, if something is wrong, well, and any suggestions on how to go further in this direction. Thank you. Thank you. Thank you very much. There is one thing which I like very much, what I believe we need formalism, the first year assumption, there is no collapse. And then we need additional rules, which is connected to our experience. Right? Which I think you believe is, you find it as a theory. As a what? Theory, you have some theory, your theory is this rule. The theory, the theories which you discuss, different theories, these are these rules connecting the universal functional experience. And then we need this awareness, right? But what I think all your troubles, there is a standard, I am a local person, I need only local awareness operation. And I think in one moment, you said, if you put it local, then everything is okay, there is no problem. There's no problem. Just put it local. There is no awareness operator, it's projection, of course, local projection, that I'm here, I have particular experience. And this will help me in only the special cases, when somehow I'm in the situation that I'm aware where I was before, now I have two rooms to be, then I will use my expectation here to make my prediction. And then if it's local, there will be no problem with the boardroom, no problem with everything. So just this, this idea that the beginning you said your awareness operator is global, the same for everyone. No, awareness operator should only for us, it's subjective. So you have to make it very, very local. And then and then of course, Ant will have his awareness operator, and he will, he will use it, it will be a born rule, which is your probably calculation will show that the born rule is the best. This is a bit beside the point, just make it subjective for every sentient being. Don't put it everywhere, don't make integral, don't put this Boltzmann brain all over, they're not important. Well, partly this is motivated by problems in cosmology, the measure problem in cosmology, how to get finite probabilities for observations from in a multiverse, if the universe is a multiverse, and you have different space times that have infinite volume, how do you how do you, I mean, there's problem of how you regularize that. And even if you said, well, we'll take some some fixed for volume. But then if you compare it to some other universe that has entirely different coupling constants, what do you do? Well, maybe you could do it in plank units and that. Anyway, it's they're very difficult problems. And I think I'm not necessarily saying I'm going to be able to solve these problems. But I think you need some framework like this that in the to calculate because you'd like to see what's the what's the probability of different cosmological theories to predict our observations, not just what's the probability that we get result A or result B from some local experiment, I agree that the born rule is a very good approximation for that sort of thing. Because these, you know, this, this integral of the weight factor is not going to change much on the on a human time, on a human time scale. But but if we're interested in cosmological problems, of what's the quantum state of the universe and, you know, and what's it, which may have maybe a multiverse not only having different Everett branches, but also different, different effective coupling constants, then, you know, we we need more to explain that. And I'm just trying to say this is a framework for trying to explain it. Of course, it's not a theory until we have the awareness operating. So exactly, just to mention, there is this conference about many words. And that's, and that is multiverse, cosmological multiverse, which, you know, I also have many words, this completely different story, different subject, and it seems that you put them together. And then I think it's to be clean to be separated clearly. What we discussed, we don't discuss cosmological and other things. You say Born Rule is dead. This is because you talk about multiverse, cosmological multiverse. People talk about many words in one without cosmology, as in it doesn't work, but your papers look like the Born Rule died. Well, it doesn't work. It died. Not it died. Yeah, it died with composite, but you don't need but you only need a single universe large enough, which had to be enormously large to get, you know, copies of observers, and then it doesn't work there. Then it's, again, we need probability in each one of them. This was a really rich and provocative talk. And there are a lot of things that I want to ask you about, about the role of sensation and the role of cosmological no hair theorems in the cosmological setup you're using. But I think that would that those are really long conversations. So I want to actually have a follow up on what you just were one of the things you were having said in response to love about them about the measure problem, right? You don't just want to normalize measure. You also want to be the case that that small perturbations don't change, don't change measure very much. So in some sense, you want something like a translation of a measure, right? You also want to be the case that like large measure corresponds to open sets in some reasonable topological sense and small measure corresponds to meager sets or something like that. So you also want to borrow measure. And you also want these two to play nicely together. So what you really want is a translation of a normal, that's not, I mean, forget it, forget normalizable. But I mean, on these big spaces you're talking about, there are there are very powerful theorems that tell us that you just can't have a non trivial translation So I'm, I'm, I'm very, I'm very skeptical of these kinds of arguments in cosmological settings that say, well, we don't know how to define a measure. Let's just assume there is one. I don't think we are, I don't think it's legitimate to say, let's assume there is one, given these very powerful mathematical theorems that tell us there aren't, at least of the kind we really want. So I think I think I really would like to hear more about how you how you think we can get around these Well, that was the thing. I'm assuming it's not translation invariant, particularly in time. No, I mean, I mean, translation invariant in the sense that when I want to make small perturbations to my space time model, so translation invariant in the space of models, not in the space time, so that if I make a small perturbation and get and get a model that is in some sense, very close to the original one, I'm not, I'm not changing the measure. Okay, I'm a little confused why I need that. If there's one correct, if there's one correct theory, why can't you use, in principle, the correct measure for that and not, you don't have to worry about. In fact, I would I would hope that the ultimate theory would not have any continuous parameters. String theory doesn't have any continuous parameters. I would hope that the ultimate theory doesn't have any continuous parameters. So there's a discrete set of these of these possible theories. So I don't think you have to worry about small perturbations of the of the theory. You don't even worry about that small changes in your awareness operators to give you things that are closer measures? You don't even want that? Well, I, no, no, I'm not, I'm not denying that. But I, it seems like that you're getting into a problem that, of course, it's not normalizable if you have uniform over some infinite space or something. And I'm saying, I'm saying that was the point of these, these admittedly present, not very elegant proposals. Well, the volume averaging is not too inelegant. The easy weighting, of course, is it's just the simplest function that gives a finite integral. So but those were things that specifically designed to get to get the measure of finite, even after integrating over infinite t. There's something that, if we go back to the very beginning of all this, that you put up that many people put up, I'm not pointing you out. People do it all the time and put a Bayes theorem. And you've got conditional probability of O on T. And there's this idea that, well, gee, the P of O on T, that's that I can kind of calculate. What I'm really interested is, in some sense, P of T on O. Right. But Bayes theorem is just a theorem about conditional probabilities. And the O's and the T's are just letters. Now, what happens, I think, is what also happens in the way you presented this, in the normal sense of the theory, like Newtonian mechanics is, say, with gravity is in the normal sense of the theory. It does not assign any probability to any obstacle. Because the theory just gives you the dynamics. Right. See, I'm talking about a more complete theory. It's inconsistent with the theory, no measurement, no conscious means. Yeah, that's precisely my point. That you not only need the dynamical laws, you also need the quantum state and the rules for extracting it. So the theory, in my sense, the complete theory is not just the dynamical law. So Newton's theory is not a complete theory. But then Bayes theorem, as you've written, it doesn't really apply. What, what Newtonian theory will give you is something like conditional probability, or, as I said, two balls to hit the ground together, conditional on the theory and on the initial condition, which is earlier in time, they will let go at the top of the tower. Now that requires, and this is why I said, I didn't think you were a many worlds person. That requires there being a temporal transition from the initial condition. This is the way we do experiments, right? Okay, I know this, this much about how the experiment is set up. I have the theory, I use that now to make a prediction about how the theory will come out. And that requires, of course, that you have something like a branch, even in standard Everett, you've got branches that connect the state at one time to states at earlier times. Without that branching, I don't even know how to make sense of a probability like that, right? There's the Bell many worlds, where you're kind of jumping around in those conditions. Okay, you know, so I think there's just a tremendous amount that goes into how we extract what we call predictions for observation, maybe statistical for various reasons, from a theory that are not represented well in Bayesian. And therefore, if you start with Bayesian and say, well, I'm going to start with that deterministic theory, I mean, you said it was a deterministic theory, they're all ones and zeros. Well, no. Even if you give me an initial, I mean, I don't know. So I think the connection between that very first ansatz and the way predictions are actually made and tested, there's a lot more detail in there that is not represented. Well, that admittedly, this is using Bayes theory for the for the whole theory, not just for some conditional probability of something, you know, within the universe. So admittedly, you know, this is usually but I don't see any particular reason why Bayes theorem couldn't be used for, for the, you know, for piece of tea being the entire complete theory that completely specifies everything and brand, you know, all the branches of everything and, and, you know, when in all the all the awarenesses. So I don't know if there's, if you have some strong reason for saying that Bayes theorem, I agree, this is not where it's usually used, usually it's used in, in partial, we make some, some observation in our branch or something. And we see something, and then we make some prediction, and then we test it, we get conditional probabilities. I agree that this is a much broader use of well, I don't know, it's broader, it's, it's, it's a much more global use of it, because I'm applying it to the, the, the complete theory out of us out of some countable set of complete theory. Okay. Yes. Oh, the, you know, the settings were this, and there were these currents and right, right. Usually, that description is consistent with many different descriptions at the fine grained physical level that the theory operates on, like the Newtonian mechanics of precise space. Okay, so what do I have to do, I go from the initial description, I then go by some probabilistic map, from that to a distribution over, say, phase space point, then I use the theory to evolve those phase space points, maybe deterministically, maybe stochastically. And then from that, I extract a probabilistic prediction about the outcome. Okay. And that's clearly what we have to be doing. And a lot of probabilities get in there that don't even have to be dynamical, right, going from the macro description of the initial state, to the micro description that I need to feed into the dynamics, then evolve it by the dynamics, then extract from that a macro description. It's just there's a lot of, you have to do all that stuff, to actually make predictions in the way that nobody has ever said, Oh, this theory just says, there's a probability of 8.5, that there'll be a sentient, you know, a sentient experience of such and such a time, right? Yeah, so I agree, if you want to do probably, I mean, once, say, once you focus on a particular theory, and then you want to test within it, you say, conditional upon my being aware that I set up the apparatus and such and such, what's the conditional probability that I got this result? So I could, I could, I could put that in there, what I'd have to do is then I'd have a particular theory, then I'd have the, I'd have the probability of, of my of the observations in which I have a memory of having set up the thing apparatus and such and such a thing. And then so that that's a whole bunch of things that have some probability. And then in the numerator, I take the smallest set of perceptions where I perceive not only that memory, but also a particular result of the experiment. So it's true, you I could do something, I, in principle, I could do something like that, once I have a theory for inside the theory, here, I was doing it in just the broader sense of trying to decide which of trying to get posterior probabilities for the theory. And indirectly related to that different way of asking Tim's question in some ways. And what's, how would you think about deriving just some sector of ordinary quantum mechanics on this? Sorry, how would you think about deriving some ordinary section of quantum mechanics? I mean, if this is a complete cosmological theory, we'd better better be able to get out of it as appropriate special case situations, mundane things like two-spit experiments and magnetic moments. And there is Tim says, the things we seem to want to get out would end up being conditional probabilities, rather than unconditional probabilities. I mean, I can, I can see the internal coherence of the scheme, and I'm just trying to work out how to relate it to the extent empirical data for quantum mechanics. Well, I think similarly, by I was trying to answer Tim that you could, if you did it in this scheme, then you'd have an, you'd have some observation, well, you do the experiment, and then because you want to be aware of the result, at the end, you'd assume that you're aware of the result, but also how you set it up. And then and then so so there's a whole, there's a set of different because I could be aware of other things, too, like whether I'm hungry or not. So there's going to be, there's going to be a measure of a whole bunch of things that, you know, they include the awareness of how to set up. So that's good. That's going to give me, you know, some measure in the bottom. And then on the top, I put the, the, where I also have aware of the results of the experiment. You're sort of flattening the conditionals down to absolute, absolute probabilities and memories. Yeah, yeah. So so so yeah, yeah. Thank you very much.