IFQ Complexity Workshop ｜ Don Page

I'm kind of going to give a talk that's a little bit different maybe more for entertainment, but hopefully some of the things may relate to the topic of the conference Here's picture from the province of Albura from the top of Mount Temple looking at Marine Lake and the Valley of the Ten Peaks and so on Okay, so I'm a simple-minded person that loves Occam's razor And I believe that God also loves simplicity so he created a universe That is a very elegant way of producing wonderful sentient experiences, and I have especially wonderful experiences being in this conference however, a simple whole contain complex parts So for example a simple set of all natural numbers or positive integers contains integers giving binary encodings of the content of the Bible of the Library of Congress of all books ever written of The archive of everything on the internet of all the data and all the computers of the world etc So each one you can in some sense some encoding to have some integer So it's just you know one element out of this simple set So the complexity of course arises from the choice of each of these particular integers out of the simple whole So okay, maybe perhaps the universe is similar with a simple whole but complex parts Of course there's the question of what selects the division of the simple whole into the complex parts So now I'm going to take an Everettian view that the wave function never collapses I'm maybe not a full Everettian and thinking that there's some preferred basis But at least at least Everett in the sense that I don't believe in collapse of the wave function So in the Heisenberg picture, there's one single fixed quantum state of the universe and it might be by universe I'll include if it's a multiverse and then you have as many different parts with different effective coupling constants and so on But maybe I differ a little bit from traditional Everettians and think instead of thinking of quote many worlds There are instead many different actual existing observations and for me fundamentally Observations or sentient experiences or sometimes I call conscious perceptions all that you're aware of at once But I'm assuming that each one of these sentient experiences each one of these observations have different Measures different positive measures is mu K Which will be some function of the of the particular observation O sub K is an observation or a sentient experience So in some sense these measures Tell how much the various observations occur But the measures are not determined just by the content of the observations I can't tell for my present conscious observation what the measure is. That's something that should be given by a theory We can try to look for a theory predicting this but and we may have many alternative theories we have to choose from Okay for simplicity, I'm going to assume there's a countable discrete set of observations Perhaps it's perhaps an infinite number, but I won't do a continuum Just first for simplicity here and that the total measure is normalized unity for each possible complete theory So T sub I is a complete theory that gives the normalized measures for all possible observations So ultimately I think a theory should give measures normalized managers for observations Then for a basic analysis because we'd like that we'd like to choose What's you know, what's a reasonable theory that can express our observations? I shall interpret the normalized measures of each of the observation Okay that each theory gives as the probability of that observation given the theory so probably of the observation given the theory Which were the observation is statisticians call this the likelihood of the theory the likelihood is not the probability of the theory But the probability of the observation given the theory so Now this is something that may relate to Likely, I don't know but it's the map from the quantum state to the measures for observations could be nonlinear And I think if people talk about it depending on entanglement and so on maybe it would be But here I'm going to assume it to me. I might it seems simpler to assume. It's a linear relationship and I and I've called this sensible quantum mechanics. I've also called it another paper for our puppet thing mindless sensationalism Because it proposes that what's fundamental is not minds, but conscious perceptions these individual observations that we have And they might crudely be thought of sensations though. I include more of what's what's consciously aware of like memories But anyway because it involves sensations and not lines I'll call it mindless sensationalism sometime just to give a sensational title for it. Okay, so I'm sorry. Yeah So I'm assuming that there's this measure for this observation it's it's a functional of the of the quantum state the expectation by of this operator or Just put the brackets for the for the expectation by the operator without explicitly writing the state so it's an expectation value of this or I could write this operator as Well an operator that depends on what the observation is So here the Sigma's the quantum state of the universe Positive linear functional of quantum operators, and this is what just to give it a word. I'll call it an awareness operator It's it's the operator that gives the measure for our awareness Corresponding to the observation or sentient experience the conscious perception. Oh some K. So the quantum state Okay, I'm using it a more general sense than Libby did last night I'm allowing it to be a pure state a mixed state Given my density matrix or C star algebra state anyway something allows you to get to get that I guess together from last night that Lenny was saying that okay state should be pure state So maybe being Canadian instead of calling this a state. It's a province, but so mixed province or C star algebra province wedding and the awareness operators along with the linear relationship above it and A complete description of also the content what the what the actual subject they should all be given by a complete theory now of course We're nowhere near having this theory, but I'm just this is sort of the framework, and we did have a complete theory I think it should predict the measures of all observations And in some sense it would say all these observations occur with the different measures There's nothing really probabilistic about the idea about the theory But to test it we can take the normalized measure of our observation as if it were a probability and use that as the likelihood in a basic analysis Okay, and possibly the universe is simple and postulate the quantum state sigma and the complete set of pairs of the the operator I'm sorry this observation That's that's the actual sensing experience what you're aware of including the qualia and all the details of each What you're aware of any time and then the corresponding quantum operator of sentient experiences and corresponding awareness operators is simple Though most of the individual experiences and Presumably these corresponding operators may be very complex Just as a set of positive integers is simple even though most individual integers are very complex Now presumably the complete set of logically possible sentient experiences is infinite I don't know, but I mean sure I don't see any logical limit to it And even if I restricted to a countable set of discrete sentient experiences that can be labeled by a positive integer I'm doing this for simplicity. I don't really know how to do basic analysis of the continuum I mean you have to be in it, and I don't think that raises eyes so for simplicity of analysis I'm just assuming there's a countably infinite number of Observations it might not really be simpler from God's point of view so my assumption of a countable set of discrete sentient experience It's just a working hypothesis. I mean You know it depends what you call the graph complexity It depends what your computer is up to some you know some finite amount And I don't know what what computer God runs when he's if he's trying to say Which is the simplest thing to do that will fit his purposes? Okay, if there's a countably infinite set of distinct sentient experiences labeled by the positive integers Then the average complexity of the individual members of any set in of them would be expected to be a bar at least Login such one can't distinguish in elements without at least this bits of information you have these bits of information to distinguish the thing And I'm taking the complexity of a member of the set to be in the order of the number of bits Of information needed to select them in and I shall ignore order one factors like long two It'll be just kind of sloppy to write this Now the subjective experience suggests to me that my sentient experiences have rather large, but maybe not extraordinarily large complex Complexity I can see you, but I can't I don't think in one experience. I have detailed Awareness of all the details of I mean I can sort of see a lot of people here And I can see you know certain things that can be aware of at once you know a beard and a striped red shirt Yellow shirt striped and so on and so on but I'm not aware of all the details at once so The amount seems as if it might be finite Though of course I can't rule out the possibility for example a very fine graining say of the pleasure I'm having in this talk. I mean maybe maybe there's not just discreet latinals, but maybe it's very fine I don't know, but but at least it's hard for me to Be sure that it's so I'm saying that at least at least if I want to put a lower value Information he's saying it's it's maybe not utterly huge so okay if most of the information and most of my sentient experiences visual which I tend to think it is and if I assume that this information is not much greater than the Minimum information for a change in my visual field that I would remember Then if I look at these digits, I can't it doesn't seem to be I'm really aware of very many of them I think I'm sort of aware of Some of the patterns, but probably not a huge number So I don't know how many bits you know maybe I'm aware of a hundred bits or a thousand But I don't think I'm aware of a bit. You know of a million bits So in support of my subjective intuition that my sentient experiences are not too large Complexity one might argue that a Bayesian analysis favors theories in which the mean observed complexity is finite and not unnecessarily large and Okay the argument for that let's first just say how I'm proposing the test theories. This is of course very much in principle Because we don't have any complete theories, but if we had a theory T survive that for each possible observation That each gives the probability for that observation given a theory in an observation It should get a probability for that or which is really a normalized measure, but I'm going to interpret it as if it were probabilities Now we have to To do a Bayesian analysis we have their prior probabilities for the theory as far as I can tell that's subjective But presumably most of us make them higher for simpler theories, so we would tend to say simpler theories have higher prior probability Yeah, so So by Occam's razor we favor that then if we use an observation paid To test the theory that this is that the likelihood of the theory by Bayes there We can calculate the posterior probability of the theory. It's basically the likelihood on the prior, and then you have to normalize it by By summing this product over all possible theories, so that's what you that would be to get that I mean of course You know this is way down the line before we could perhaps do that because we don't even know how to do this We don't even know how to do this for one Single reasonable theory and then of course to normalize you have to be able to do it for all read all theories for which you assign the positive prior So we would like to get this posterior probably as high as possible by choosing a simple theory high prior probability It gives a good statistical fit to one's observations high likelihood, so we have two things. We're trying. We're trying to do a trade-off for Now there's a likelihood cost if you have too many probable observations So suppose a theory predicts that there's in observations Which I'm taking this acting experiences that each or at least as probable as the one used to test the theory e.g. Your observation goes here using your observation right now to test the theory and your observation of course include Memory of everything you've learned about physics or whatever you can remember right now about what you learned about physics Well in order for the sum of probabilities to be unity the probability observation used to test the theory can't be greater than this because there's In other other observations that have higher edge, so it can't be greater than that So taking the likelihood of the theory to be the probability that the theory assigns to that observation That implies that the likelihood of a theory can't be more than 1 over n if it predicts at least n Observations as least as probable as the one being used to test the theory So This is my main argument against theories that give a domination of the total probability of observations by a vast number of Boltzmann brain Observations, so if they're if these Boltzmann brain really could have very different kinds of observations if you have a huge number of them, and they're and they're at least as probable as as Say ours, then that means for the total probability to add up to unity then it's diluted by all these Boltzmann brains so Boltzmann brains might dilute us, but here they my main argument is they dilute the probabilities And they make the likelihood of such theories much smaller than better theories that exclude Boltzmann brain domination So basically I'm saying that Bayes holds Boltzmann brain brains at bay And I'm sort of our Sean Carroll has a paper out recently that he suggested well You should react because it makes things cognitively unstable or something, but I don't think you need to go to that I think a Bayesian analysis by itself is sufficient to rule out theories that have huge Boltzmann brain Domination because it's just it's basically predicting Well, we're I'm assuming at least that it's predicting a whole lot of disordered observations Whereas we tend to have more ordered observations, and if you have this huge number of disordered observations Then they're going to dilute the probability and reduce the likelihood, so that's that's basically my argument against theories that have Boltzmann brains This simultaneously rules out our most plausible current theories of cosmology, right? So this is a very Why most theories of cosmology you know expand out into the infinite future with you know that would eventually produce these fluctuations Yeah But I mean there's ways I think rock you know rock you on ways and regularize it I have maybe rather ad hoc and not very beautiful ways, but I have Ways that that you can regularize it to avoid having this this domination, and I'm saying Okay, we don't know what we don't know one that has a really high prior but but but It changes the likelihood so enormous that even if even if we have sort of Even a not very elegant way of getting rid of Boltzmann brains Even though that may make the theory more complicated and reduce the reduce the prior Because it has such an enormous effect on the likelihood. I think it's better than Somewhat simpler theory that has all these both Well, maybe I mean perhaps not by yeah because it because there's this connection between the between the quantum state and the observations That these awareness operators. I don't know what they are But it could be that there's properties in those that basically Maybe gives low measure to things that are long ways away from the Big Bang or long ways away from the Bounce at the universe start with a bounce Anyway, I mean okay, maybe it's a bit ad hoc But if you somehow if you somehow say that that these operators if in some sense that they're very far away from the Big Bang Maybe that they go down. It doesn't have to go down. I mean you can have us Well, you can have volume averaging where you you don't count up all the observers Observers on a hypersurface and then divide by the volume of the hypersurface So you get the density of observers or you can do a thick and gd6, which is a sort of equivalent. Yes You don't even know whether they dominate or not where you specify both your theory and the method that you use to regulate And then the absence or dominance of all some brains is a constraint of the nomination of the theory in the measure Now whether there's more one or the other is Well, we don't I guess I would say that we don't have nice elegant theories or yet But in my case this theory is including not only cosmology, but also the measure. It's the theory of everything I mean, it's not the soap not the so-called to e which is a very weak form That was just theory of dynamics You know so-called particle physics to e is very very far away from the theory of everything's and it doesn't include the quantum state and it doesn't include these The rules for getting the measures of conscious Experiences out. Okay. So suppose we have these current probabilities for theories and here I mean a full theory including not only the dynamics But the quantum state and the connection to consciousness and then okay these conditional probabilities either the likelihoods and then the posterior ones are that normalized The prior ones are subjective usually higher for simpler theories, but even if everybody agreed What's the order you still have to how to do the weighting? So the highest prior probability might for a theory I might think that the highest prior problem would be a for theory that nothing concrete or contingent exists just a blank So but that would give no observations. I mean if because observations I consider is logically contingent It's that don't have to exist. So that's what has zero likelihood. So that's why I throw that out another theory that some people say is that everything exists and if I Provide a bit more if I say that all observations exist equally But there's an infinite number of observations again because if there is a 20 exists equally But there's an infinite number of the door the probability for each one is one over infinity So again, you get you get zero likelihood for that theory Now the other extreme which I don't think is correct either is a maximum likelihood theory and that would give if if we use One if say you use your a present observation to test the theory if that were the only observation that really existed If some theory predicted that it would it would predict that a junior probability because it would say that there's a probably zero for all other ones But it seems to me that this seems to require a very complex theory If if you imagine that only your present experience existed and no other ones despite the fact that your experience You know include seeing around that there's other people that look like they're pretty much You know I look around and see all the rest of you and It would seem to be required a very complex theory for imagining that you're all zombies and not conscious So I think that would complicate the theory so much it seems to be a much simpler theory to assume that all of you are conscious at least if you're awake and well, and also if you're dreaming if you're asleep and dreaming I think you're conscious too, but but Anyway, so I think this would have a very low and so My mind is that in this would be a case where the prior would be so low that I pull it up So there's a trade-off between the prior probabilities and the likelihoods that is between intrinsic plausibility That's the prior and fit to observations. That's the likelihood so Now my amazing argument against Boltzmann brain domination that they would dilute the probabilities of our observation too much Might also to be taken as an argument against multiverse theories by producing vast numbers of additional subuniverses They presumably give rise to many more observations with comparable probability stars if these if the landscape is populated and there's other parts out there that have Conscious beings then you have to to normalize the total measure you have to include theirs So they give many more observations of comparable and that would dilute the probability of any of our Observations and make the resulting likelihood of any multiverse theory much less than a single universe theory that also predicts the existence of this Yeah, I would apply it would apply that if universe were yeah I mean you would say the likelihood would be bigger if we had a small universe and there weren't weren't any other Conscious beings anywhere else that only occurs on earth So I agree that so yeah so I am saying that the light because I want to I want to talk to some of the Normalized Avengers to add up the one it would the likelihood is less if there is more out there. Yes Measure Well just wait to see I'm not using this to reject multiverses yet But I'm just saying as far as the likelihood goes it does make the likelihood a lot less Well So Well, I agree that that seemed out of the region would increase the would increase the likelihood and so Despite what I'm saying here. You're going to find I'm not opposed to multiverses But I'm saying that Yeah, okay So it certainly finding that finding evidence that it fits string theory and and if you find the string theory predicts the multiverse that's of course increases the likelihood I just Right Or another way to put it you're you're assuming that both theories contain a universe that looks just like ours And the question is whether there's other universes be the argument compensating factor of the numerator where if there's a multiverse You're more there's more different kinds of universes and therefore our universe is more likely to appear the way you're doing it Which is of course deeply controversial, but I'll just take that for granted Yeah, so I'm definitely taking the view that you should get likelihoods in the theory You don't say that the theory because suppose the theory predicts that at least somewhere in the multiverse I exist I'm not taking the view that that means the probability unity because I want that I want these probabilities to be probabilities Out of all possible observations, so it's sort of like as if you as if someone randomly chose an observation out of the full set What's the probability you would get mine? And that seems to be the trouble is if you do it the other way you say that well okay, suppose we have a theory that's that produces a universe or multiverse so big that almost certainly You exist in that if you then say the probability is that unity and you use that in your Bayesian analysis? You've got to essentially have unit likelihood for any theory that has this character You're not going to be able to test it then reduces purely down to the to the prior probabilities and and science no longer becomes observational Point is doing it your way doing it the way you want to do it, right? Yes, it's still true that a multiverse is more likely to predict our observations There's more our universe is more likely to appear in a multiverse Sorry, then if there's suppose you have a multiverse of a hundred different universes Okay, okay, I'll compare to a single universe right okay, and suppose each of the hundred universes has one being Okay, so if if you are comparing the way you're doing it if you're comparing it to a single universe that looks like us Then you would say the single universe is a hundred times better But if you don't know that the single universe would contain us if it could look like any of the hundred universes Then now it's equally good Yeah, of course. I'm also. I'm also assuming this theory is an absolute complete theory it means absolutely nothing to chance So this this complete theory specifies exactly what occurs all over the whole thing So therefore it's not leaving it to chance as to whether so the theory I agree to get any the theory has to predict That we exist somewhere in it for it to have any likelihood that that just converts the same factor to a lower prior Probability that you could find if that just reduces it back to one point that it might be much harder to find a single universe Theory that explains our observation right right? That's what I think That's what I think that's going to be is that's going to be my resolution to the thing But I I do think that we should take this into account I don't think it's fair to just throw out a multiverse theory and says well We have a multiverse theory and so it's so fast that it produces us somewhere in it. That's sufficient I think you have to get the light you have to do the Bayesian analysis And you have to get the product of the likelihoods of the prior is obvious And I am saying that there is a cost for the likelihood that I think it's a cost that should be paid And right now I'm tentatively willing to pay it yes For anything that can actually bury and is not a fundamental thing I can ask the question What is the probability distribution for the observations of that buried thing? Conditioned and observed is still a non trivial distribution but we might be in the tail I mean there are tons of theories like this like I was a drunk, I just want to move out because we don't stand in the universe I mean I think you're just saying that there are more opportunities for something to go wrong Yeah, that could be. Okay, I'm sympathetic to the people that say that some people object that when you produce a multiverse theory In some sense they say it explains everything, it explains nothing And if you take a naive view about that I'm saying that that's not really the situation It really should predict for a viable one it really should predict the distribution Such that when you do take this distribution you take the likelihood of r is multiplied by the priority Get something that's that's high and so if it's a theory that produces lots of moles and brains That's not a good theory because the likelihood is very low Okay, I'm not going to rely on the counter arguments most of the alternate universes They're not effective constants of physics fine-tuned so presumably they're not as efficient Even though I believe that most of them do I suspect there's still even a huge number of other biophilic ones So for example if you take a common estimate I understand that the estimates have gone up I don't know what's the latest thing for is 10 to the 500 Is there some canonical number that the 10 to the 500 is now going up to or somebody Yeah, yeah, so this must be some restriction to even things that might be conceivably five Yeah, yeah Okay, so even if you said that there was something like that and then that could have potentially Well potentially something so I'm trying to I'm trying to be generous to the people that say it's finite Maybe there's a finite number that have some property who knows There might be So there must some restriction there because there appear to be mathematically consistent configurations with infinitely many topologies Even say so if you if you need the cosmological constant to be roughly as small as it is then perhaps something Since it's a roughly 10 to the minus 20 part 22 or evenly distributed only maybe that fraction would happen There might be other restrictions from effective coupling constants Let's suppose yeah, I'm just putting in numbers. I mean as you say this is you're not supposed to take any number literally But suppose the fraction were as low as that if there really were something like that or more There's a huge number that would have that could be biophilic. They can have life in it. So This is sort of a side. You can't interesting from these anthropic Arguments you can you can get crude estimates for things that carter and carl reese found Our relations with stars I don't have to go into them that the math and plankton is the mass of process roughly the electron chart of the elementary charts at 18th, and that's this and then I found from using some papers of rg flow that you could Get a relation like that by assuming the the the the the the patient mass is logarithmically near the plank mass If you put these three equations together you get equations And if you take if you if you take the approximate equations That's exact you're going to get an estimate for the charge of the electron Or the are the absolute value that's within within two percent of the actual value And then you can also calculate other things the mass of proton because it's raised to large power It's off by a factor of roughly two But the logarithms are only off by about a percent or so And you can get the density of water and and the masses of stars all from this number just mostly simple powers i'm not going to give all all the The arguments and for the size of the universe and that and the density of the of the dark matter and the number of stars Uh, well, this is one estimate on wikipedia of how many there are so it's off by a factor of 13 Gravitational wave strength from things across the universe, which is interesting more or less the reciprocal of that At the height of a giraffe. Okay, that's more involved. But anyway, you can That's the highest the largest running animal that doesn't overheat. So anyway, okay All right, so Okay, let's go back to this if there's that 300 fire Then that that means there's so many that might reduce the probability of our observation by a factor of something like that So now we reduce the likelihood of a multiverse theory this this particular factor by a factor of a google google google But i'm personally hopeful that a good multiverse theory With no need to specify unique definite values for effective constants of physics to produce this landscape will be sufficiently simpler That it would be plausible to assign the power probabilities much more than 10 to the 300 times greater That's a pretty big number. Yeah, I agree. It's a pretty big I guess i'm a pretty pretty big number. I just but i'm just i'm saying that if you really wanted to specify You know a huge number of course We don't know we don't know what the constants is the fine structure constant and the mass ratios We don't know what they are to a huge number of digits But if you knew what they were and you had roughly 300 digits for these for these things or more then then Saying that it's this particular value would reduce the probability Well, I mean it's subjective, but I think it's quite plausible It would reduce the probability by basically 10 to the minus the number of digits that you say are expressed in that so Anyway, I think that this factor 10 to the 300 can't be accounted for by by By basically the priors and of course it includes a fifth to you know If you find that there's fifth of string theory and so on I don't think it works for bolts and brains because if bolts and brains exist I mean one estimate for the action of something like a human brain size if you you produce the human brain and the antimatter Then this is roughly the density of Planck units And throughout the future universe if you say that it's not cut off by something I mean, I agree that there are ways to cut it off Up to the time of that or maybe even the exponential of the square root of that That's a double exponential It would reduce the likelihood of theories with bolts and brains far far more than the single exponential number of sub-universes In the super string landscape. Well assuming this really is finite So i'm saying as far as the as far as the priors you shouldn't worry about a google cube But you should worry about a googolplex So I think we want to worry about giving up bolts and brains. Uh, let's see how much I started late, but how much time do I have? Six or seven minutes. Okay So, let's see. So Now another question is if these if our observations are given by expectation values of operators How local how non-local are there? Now presumably it doesn't matter where brain is the operator whose expectation value gives the measure presumably involves some integral over space-time And and also ideally over the Lorentz group, although this brings into parts the fact that it's non-compact. So there's normalization issues I don't know how to deal with that But what I mean is how local a seed operator has to be so suppose I said It's it's like a projection operator to some state of my brain But then I take that seed operator and I integrate it over all possible locations for the thing And possibly over the Lorentz group To get an awareness operator But the question is how big is it sufficient for the seed operator to be just the size of a brain or maybe Maybe there's just a relevant part of the brain that's really responsible for consciousness um now sometimes people say a sensitive experience takes a time of a tenth of a second And if you wanted to have a tube this way if you wanted to express it on one spatial hypersurface You'd have to have this tube that lasted a tenth of a second Within some causal patch and that would be you know, a tenth of a light second across for 30 000 kilometers That would be about bigger reason Region, but it's not obvious to me why it couldn't be Produced instantaneously. So i'm taking the view that if the configuration is right It doesn't need to stay right for a tenth of a second. It just needs to be right for for a very short time Maybe a blank time if you doubt that instance really exists um So then I I don't see any reason why it should take any significant time for the result of What's in there to give rise to the sensitive experience? And so on Now An argument for non-locality is by having globally non-local seed operators You can define them to give zero expectation value in the vacuum to avoid multiple brain problem and empty space time Because it seems like if you have localized operators any positive localized operator tends to have a positive expectation value even in the Lorentz vacuum and I think That was one thing I pointed out about both brains not only in thermal decider, but also just in the vacuum so It seems difficult to do with localized But if you had a global operator like the square of the total charge Then that would be zero in the vacuum And so if our experience is really dependent upon something that's global like that Then you could perhaps avoid moles or grades with that thing, but I find it very hard to fathom It's very hard for me to imagine myself as infinite So I mean it sounds too megalomaniac So I tend to think that I localize at least the seed operator before you integrate with space time So there's ways the way that I mean that that that rockfield talked about and I have some other ways Now another question is entanglement and here. I'm a little have some skepticisms about how the importance of entanglement How much entanglement do we need? Well, if these seed operators are are fairly localized then they would be insensitive to quantum correlations over larger regions They could of course certainly be Sensitive to what to the state in the small region and that state could include or that that province could include entanglement But but but over larger regions, it doesn't seem like that. They're important Unless the operations are much more non-local And of course, it's a logical probability that the probabilities are not given by expectation values of operators with non-linear functionals And I'm with benchy last night Even if it was an expectation by a race to a power slightly different from unity that would be consistent with observations Uh, though it wouldn't be so simple. So i'm not saying I believe it but it's it's possible So how much complexity do we need for? observation well, it it seems to be relative some particular initial state is not clear to me what picks out this state or Anyway, this is just some issues. I don't yet understand about complexity But my version doesn't give a preferred basis of quantum states Though these awareness operators do give a preferred set of operators Perhaps there's some way to define the complexity of this set of operators relative to each other relative to quantum state But this is beyond my understanding So as you see I can't I don't have enough to really get into a lot of these very fun interesting ideas that i've heard about complexity but Uh, you know, I did so it does raise questions. Okay. So let me conclude the entire universe may be simple but with complex parts Observations may be individually complex to form a simple set The probability might be given by the expectation that I have positive awareness operators Also individually complex with forming a simple whole These might be integrals over space-time of seed operators localized to brain size regions And maybe this integral involves some weight factors that depend how far away you are from the big bang or something or Or rather there might be some way to get bolts from brains. You may need weight factors to exclude bolts from brains Are you? To an enormously dilute reduce the likelihoods of theories and i'm saying the analogous problem for a multiverse which should be considered It seems much less severe So and it's also not clear to me how important long-range quantum correlations entangle on par for observations Or complexity for that matter. I don't understand yet How complex okay, so that's a bunch of ideas that okay They may they're a little bit outside the main topic of the of the talk, but I hope they're It stimulates some talk and maybe maybe some of you that understand complexity theory better can relate them to complexity. So, thanks