Universal semantics & the physical world / Algebraization of paraconsistent logical structure (& others)

0:00 I ordered four points. The logic. Yeah. What I'm saying here, that maybe does not exist, is that some professional logicians say that Parakasismic logic doesn't exist. That's all I'll say. If you say it's not clear that physics exists, you mean nobody sort of works on this? No, no, no. There are people who work on it, and as I said, there are conferences on the part of the people and everything. But some people criticize this and say that it is rubbish. So all these conferences... But then you see them, didn't you? Yes, exactly. Then you actually have to be right, because then you actually go wrong. So I won't comment on these metaphorical pitches by Stuart Kaufman. So that's where... It's interesting stuff. So different, these different metaphors of tetrahedron which are representing it to different degrees. So what really logical structure could this tetrahedron be? No, I probably should stop. I think we can fix it quite quickly. If you go to escape and then just put up the slides one by one using these. I'm going to get Bjorn in here. Do you want to go with Bjorn?

2:30 I think so. Oh dear, now I'm screwed up. I'm really sorry. Don't worry, it was very interesting anyway, isn't it? Sure, I'm not joking. I'm looking forward to this. I will sort of, what is left from the talk, I will tell everyone somehow individually. It's just impossible. Do you have a printout of it? Do you have a version of it? I've got it here. I've got the version of it on his computer. Is your version one any different, any better? No, no, no, it's the same. Let me try to control it with the keyboard, see if that's got any better channels. Okay, let's stop there. I'll just explain what I meant. You can make his comment. No, no, no. I won't guarantee it. Now, I've managed to do what you did a lot of times, but whether it keeps going, I don't know. Let's roll through to where you want to be and see if I can stop it. That one, anyway, that's remarkable. Pretty creative. I'll try clicking on it and see if I can get an opportunity to stop it that way. And I've stopped on that one. I don't want to do anything on it. And the clip doesn't do anything. Now, where do you want to stop? Somewhere? A bit further? Yeah, further than that. So, I'll just say a few words. The only real oscillation, or internal oscillation, which I know, is a paradox, like an Epimenides-Leyer paradox. All presence are lies, he said. It could be rewritten this way. This phrase is wrong. So in other way this could be rewritten when it is false it is true, when it is true it is false.

5:00 And so, this kind of oscillation. And this oscillation, this is the first order paradox, which cannot be a basis for triathlon. So we need a second order paradox, where if it is actual, it is possible. Yeah, this is it. This is it. This is where we've got a bit further. I think that's it, isn't it? Yeah, I think we've got a target here. So I think that now I can just... I'd best keep going, I think it might work a bit better for you. You just tell me where you want to go and I'll see if I can find you. Ok, let's try to go further. It doesn't go. You want to go to the next slide, don't you? Let's try, I just want to go... I'm going back to that one now. Do you want that one? Yeah. So, that's basically what I said. I know that the source of oscillation is a paradox, and paradox basically is self-preference and negation. So, if we consider... If we want to model negation and self-reference in this kind of oscillation, then paradox is good, but the first-level paradox won't work, and it could work further. The other thing... No, no, you take it to me, I'll join you. I just wanted to quote... Peres understood a given state of the universe as being the set of premises of an inference, and a subsequent state as being the conclusion of this inference, and his thought of the universe as bringing itself into being by a process that is ultimately logical, which somehow justifies my...

7:30 The use of logical paradox in order to produce this oscillatory system because there are two reasons. First, I don't see any other engine which would, like logical paradox, produce true, false, false, and true, and this oscillation would be possible and actual. And on the other hand, it is allowed by good people like Peirce to do that. So that's why I would like to start with this logical structure and only after that I would try to algebraize it. There are some attempts with the algebraization, but nothing is done, so today I will talk only about this logical structure. Epimenides. The Epimenides paradox. So you've not gone much further. I just wanted to have it written. I already said everything about it, so that the second level paradox would be not the oscillation between true and false, but the oscillation between... The formal logic, the logic of actual, the logic of excluded middle, and the logic of possible, which is either inconsistent or modal, so some kind of opposite logic to the logic of formal. So that is just the formulation of the seven paradigms. That's it. So we can go further. I said everything. If we go further...

10:00 Further on? If we go further on. Now we arrive to the third part of the talk. The similarities between features of tetrahedron and main characteristics of mind and love. So what are these main characteristics? Mind is a dialogue between incompatible logics and examples are like rational consciousness is a dialogue between hemispheres over left and right hemisphere and the whole mind is a dialogue between righteousness and self-consciousness. If we take the Sabdele-Kauffman equation, this one, they have produced the solutions of these non-linear equations, which are regular, chaotic, and what we call biotic solutions. That's our Kauffman, not the other Kauffman. This is our Kauffman. Stuart Kauffman's metaphor patches I dropped. But Lou Kauffman, that is Lou, yes. And he wrote a few papers on that. Concentrating on these biotic solutions. He mentioned even that if the heart starts to beat regularly, in this paper he mentioned, in 24 hours a human being will be dead. So there must be some kind of quasi-chaotic, not chaotic, but biotic thing. So what I'm saying here is that life is on the border. And then it reminds us the oscillation between actual and possible and the borderline between these two.

12:30 So you can go further, again further. I just wanted to mention Physics, what Wiesel Haile once said, that a gun is very easy, it's chaotic, it's no correlations whatsoever, the crystal is also very easy, because the correlations are too long and it is, again, border, easy to explain, but things like Ising model, for instance. That is a really hard thing, when the correlations are only with neighbors, and this is again this borderline between chaos and order. According to Maturana and Varela, life's major feature is recursive self-creation. Tetrahedron reflects this property, but there is another property of life which it reflects. Life is a process on the border between order and chaos, so we have already mentioned that. One of the examples is Galvan. In tetrahedron, chaos is represented by paradoxical logic and order by homologic. And process on the border is represented by oscillation between the two logics. According to mathematician Yuri Lutman, mind is a dialogue or a visual translation of two incompatible, untranslatable parts. The novelty comes from ambiguity of translation. Obviously, if this is a magical statistic of mind, tetrathema reflects it.

15:00 At least that's what I think. Then we can go further. Models of social systems due to Luhmann, some symbiotic models due to Peirce, biosymbiotics or theoretical biology, as they call it. All these models also contain the major features of tetrahedron. So preference, both existence and negation of paradox, and the two levels of polarity. If we want a general theory of organization, theory of change and movement, theory which includes not only manifest but non-manifest, not only explicit but also implicit in terms of form, not only actual but also possible in a unified structure, the problem is a good place to start. So the description of resemblance of tetraton and the foundations of various levels of organization of nature is only a hint that tetraton could be useful in the alternative natural philosophy models. The way to prove that tetraton could be the basic element of the worldview is to algebraize it and try to derive quantum mechanics and self-organize criticality. I mean, it looks like these two things are incomparable. Quantum mechanics is really something. But self-organized criticality is also quite an important phenomenology. It describes accurately the biotic processes. With this 1 over f noise, which is compared to the living systems, and they include Dow Jones, for instance, to the living systems, or all the earthquakes, somehow, because they behave like a living system. And this is really the first quantitative description of these things. And Gerbach, when he started this self-organized criticality, his first few papers in physical robotics and in nature, they've been quoted like two and a half thousand times. So, I mean, it's really something. It's comparable with Weinberg's alarm.

17:30 Electroweak papers. So it is really the self-organized criticalities that are organized and I think that it is quite natural to try to derive the self-organized criticality from the algebraization of tetrahedron. Really? Yeah, yeah. So if we go back. So what are the problems with algebraization? I think that the main problem is that in algebraical structures, the projectors which correspond to the process of actualization, they are there. All the time, everywhere, Heisenberg algebra, projectors are there. But what is this diprojector which returns us back to the space of possible? That is so far unclear. And that's why I don't know how to go back to possible through the algebra. But I've been talking to Lukalkman about it. And it looks like yesterday he said that we might try to investigate this possibility. So some hope appeared. I cannot say anything. I mean, he is, from my point of view, a genius in these things. So maybe he will invent some algebra which will represent this logical structure. And then it would be a kind of spin-like system which could be used to... I mean, he is using temporary algebra, yes, to produce the... Speed-fall-like systems, yes? It was like a year ago. So, things like that should be tried.

20:00 Okay, basically that was it. Thanks very much. Questions? Why do you not think this is already known? The methodology of the renormalization of J.T. Wilson specifies material phase balances. Basically, you take the Hamiltonian and you map it onto itself until you find the stable and unstable points. So it's certainly a sort of reverential process, and the more complicated structures that we get, the more and more different kinds of phase transitions. You know, you may even get some very special phase transitions in water. I mean, it does appear that there's a certain amount of evidence. The key is that I think that from the basic principles we should be able to derive not only Schrodinger equations but also the things like full normal oscillate or projections or similar things or maybe even the theory of time operator which so far doesn't exist. So if it really doesn't exist... At least the explanation of the projection and the measurement, which is a little bit non-existent so far, should be done together. It's like Hopf-Linck, in my opinion. If you put the Schrodinger equation from the same principle, from the same algebra, you should be able to obtain a polynomial projection postulate.

22:30 Again, self-organized criticality is not reproduced from the world. So many things which I think should be easily derivable from it, they are not. So that's why I don't think that this is already done. Maybe I should talk to people who I believe are in Basel-Karabakh, Lukavkin and Andarski, if the quantum mechanics is already derived. But how I can judge, from the 1980s Lukavkin produced a lot of papers which look like attempts to produce algebra. From which one can produce quantum mechanics? So, he's done a lot, but he didn't derive quantum mechanics yet. And yesterday he told me that we are missing something important, so that quantum mechanics couldn't be produced tomorrow from the algebraic exercises he is doing. So, there must be something. I was thinking he was showing me, and I don't know if he's shown you, some of his virtual knots that he's been working on, and it seems to me that there's something in that, which is very much knots. Absolutely, absolutely. In these three-coloured, three-coloured knots... There is this logic of, kind of logic of paradox, and instead of dichotomous, tropotomous, when two produce one, for sure, there is something, but, and something still is missing as he judges, and I think it's up to him to judge, because he knows more of these things. Yeah, I think there may be... There may be some fundamental difference between things like the Schrodinger equation and some of these emergent things that might come from self-organized criticality. Because, for instance, you can derive the Schrodinger equation just by examining the normal translations and velocity transformations that we are aware of in normal space.

25:00 You know, just normal, non-relativistic stuff. If you try to do quantum mechanics in Galilean space, it turns out that the only way to do that is to create ray representation because it turns out that momentum commutes with boost generators. You're not able to produce... Well, I won't go into the technical details, but what I'm saying is that it's the space-time symmetry that gives you things like the Schrodinger equation, but not to the calculus. First, let's produce space-time, okay? From the field of abstracts, okay? And then, if we produce space-time, then we're all ready. Have you done any algebraic work on this logic? Yes, I've tried, but nothing I can show here. And I need a kind of preparation and some insights from Lukács, because there are so many papers. And when I'm trying to do something, like 70% of what I'm trying to do comes from his papers. I feel that he knows something which I am missing obviously, but he knows. So I need some help from him because it turns out that when I am trying to obtain something like that, I bumped into his papers which give me some answers, but not all of them. Is anybody else is working on it? Because you said there are conferences. Yeah, but these conferences are the conferences of magicians. Aha, so you won't have the progress. It's not algebraic. It's figuratively logic. All right. I see two times C2 that tetrahedron. I think that's amazing. It was a good thing. Yeah, yeah, yeah. What about the... Maybe not the sort of original, but in this direction.

27:30 What about the correct... Wave function, especially in its nil quantum form, zeta for wave, etc., plus and minus e, plus and minus p. Maybe, but this is already somehow, let's take algebra and produce something from it. I don't want to start from algebra, I want to start from something which will produce the space-time for us. And then, it's algebras and everything. In fact, once you produce space-time, those things will come, because the Racket equation likewise comes out in space-time. So all of them, you can do any representation, they are transformed in space-time, whatever your particular state is. So, indeed, it is just what you're trying to do. I think it's time to thank them. Well, there's twistor theory and, uh, I didn't see anything. Of course, I don't know. This has got a pin in the carry. That's mine. Is it? It's part of the most expensive one we've got. It wasn't? Perhaps it's this one here. This is yours, Peter. Is this yours? I'll take that, shall I? Yeah. We'll take on these.

30:00 Open brackets, absence of a, first brackets, relationship between thermodynamic and psychological aerosol. This is hopefully going to be quite a tight and easy talk because the argument I'm going to present is almost embarrassingly simple. And the only reason why I feel it's so much worth doing it is because it's all going against the point of view that I constantly come across physicists putting forward. So, and having actually spent some time looking into the actual basis of this particular argument, I can rather scientifically say that not only does the argument not work, but the inferences lead to the complete opposite of these kinds of conclusions. So the basic arrow of time problem, there's a whole number of arrow of times. The problem being there's lots of different systems and lots of different situations where we see manifest temporal asymmetry, which we can describe as an arrow of time. And the error of time problem really has only come about since the advent of statistical mechanics as an explanation for thermodynamics because of the idea that then all, everything, is actually ground into a form of micro-physical dynamics which is time-reversal invariant. So, I mean, until that came along, you could quite easily in 1850 believe that there was something very fundamental about the temporal relationship we see around us.

32:30 And the fact that our psychological perception goes along in the same direction as, say, the entropy increase of the universe wouldn't necessarily seem to be anything that requires explanation because it would just be a manifestation of fundamental asymmetry in time. Since the fact that the thermodynamic error of time problem occurs, you have the tendency of entropy to increase but not decrease. There is a quite important tendency there to take into account fluctuations, and the best explanation of this is through the initial condition hypothesis. In fact, I think it would be safe to say at the moment it's the only explanation that physics currently has. It's possible that the fundamental microdynamics might have a time asymmetry. There are certainly indications in high energy physics for a time asymmetry or invariance. Nobody really seems to believe even that time reversal non-variance is the right kind. There's also the suggestion of wave function collapse, but I argue that, for a few years ago, that definitely isn't the right kind of temporal asymmetry to produce thermodynamic asymmetry. But the initial condition hypothesis is just really a brute force insistence. The past was in the laboratory to say, damn it, because we actually have no way from We can then, of course, the thing is, because of that just chibber and forcibleness, we can quite easily consider worlds in which entropy is decreasing. And the way we do it is we impose a final condition for practice. We leave the past open and we just insist that the future is actually going to be in a low entropy state. And all the same probabilistic reasoning that produces a tendency for entropy to increase. Then it gets completely turned around and we have a universe in which there is a tendency for entropy to decrease. Now it's not clear what it would be like to live in such a universe. The psychological arrow of time causes physicists a lot more pain when we try and avoid talking about it. It's a bit harder to characterise, but generally it goes along the various points of view.

35:00 We remember, we have knowledge of our past, but we don't have knowledge of our future. We can act in ways that changes what happens in the future, but we don't seem to be able to act in ways that can change what happened in the past, unfortunately. And another thing is the concept of transience, that this being that we are right now situated in a now, this now is actually moving, it changes. By the time I say now, it's actually become some other now. But that movingness of the now is actually always in one direction. The thing is, once you've actually not got fundamental time asymmetry in there, there are other areas of time as well, but once you've removed fundamental time asymmetry, the question is, is the justification for all these different areas of time the same? It's easier to write what it would be if two areas, if they pointed in different directions. We'd remember a past which entropy was higher, we'd move into a future which entropy was lower. Is that possible? The question actually is, is such a thing possible? Is it ruled out? For a physicist to actually attempt to answer this question, there's lots of arguments one could make that actually simply go beyond the thing of physics. And the whole area of philosophy of consciousness is a very deep and sophisticated area. But I'm coming from just a physicist's naive type of structure to be able to look at this. And, as a physicist, I need to then be able to relate mentally to the physical. And that's what physicists do. They try to give the substance to it, to the idea, I substitute a computer for a conscious being. It's their favourite trick. They will always do this. Because they know how computers work, and they don't know how conscious beings work. Now, the first argument for doing this is based upon the Landau's principle, which is involved in thermodynamics of computation. Well, you're at the University of Turing Machines. Anything involving the University of Turing Machines definitely would be a good answer. You could also include probabilistic Turing Machines, I think it would be covered by my maths principal, or at least I pretend to generalize my maths principal.

37:30 I think Landau's Principle is felt to hold for quantum computers... It's a principle. It's a principle, so therefore it's a hypothesis. It's not established. The status of Landau's Principle in the literature is actually an issue, yes. There are papers that tend to derive it from first principles, it's been there quite a bit. But I will have something to say about it. The universe is a symbol, a connected entity. In order for it to be able to carry out measurements, it has to have a measurement standard. The measurement, the measurement, the measurement, the only measurement standard available to it is the arbitrary, is the arbitrary fixed phase of its wave function. You cannot have measurement without having a measurement standard. And the measurement standard can't be observed because there's nothing to, there's nothing to, there's nothing to, All other measurements have to be measured against them. And that's what causes all the times to be of a similar nature. Also, I don't accept any of your arguments. I'm really not sure what part of my argument you haven't accepted, but for the sake of argument, I can say that I'm an Italian friend of classical physics. That would make you happier just to say that... Well, but there is no classical physics. I believe we will go through quantum mechanics, but we are involved in a very large amount of argument as to exactly how one should interpret quantum mechanics, and I think I'd like to remove that, because that's the whole point of the lecture. But that's your own indulgence that I've actually been able to proceed as if we are arguing classically. Because certainly the arguments that I'm going to present and argue against are arguments that I've presented in class. Are you going to give us a hint of the language of physics? I will, thank you. The second argument that I'll just summarize is that an analogy between memory and correlation, and information correlations. And so this is really just sort of introducing what structure the choice is going to be.

40:00 I'm going to say, they're not really dubious in that the premises are debatable. And a sound that the conclusions don't actually follow from the premise, but in some cases, or even untenable, that the premises imply the opposite of the standard conclusion. This is actually an example of some of the quotes that physicists have produced on this. So, consciousness is the hard problem. Physicists usually, as I say, model the mind as a computer. And then they use the thermodynamics of computation to give computers their own time. That's about the name of a paper that was published on this topic just last year. I'm going to search for a couple of quotes to actually say this is the actual example. Hawking, Stephen Hawking, in a conference on the physics of time asymmetry says, A computer's record records something in memory and the total entropy increases, as computers remember things in the direction of the time in which entropy increases. When the universe's entropy is decreasing in time, computers' memories will work backward. There are steps very daily that we see. If we were in that final condition hypothesis, computers would not, their entire perception time would simply be reversed, so they would still remember the low entropy and move into the high entropy. So the perception would just simply reverse around. Not necessarily. I mean, I think what Hawking is trying to say here is that actually a computer by its very operation causes it to generate heat and give off entropy and create entropy increases in its operation. But once you've entered into the environment, you've killed the boss, but never mind. And, yeah, so, I mean, Shulman is saying slightly different. Shulman is this a faker in 2005. Of course, the computer's there all the time. In which he's saying, computation requires the reversible processes of regeneration, and he then talks actually about, he actually gives a summary of what Landau's principle is, the system enters a new macrostate, a microstate of energy, that somehow, in the process of particular operation here, it forgets what happens, and in the forgetting of it, it...

42:30 There's a lot of information and this is associated with the production of heat energy. Assuming that, it's about as far as Schumann actually goes with it. The thermodynamic justification of this is the thing called Landau's Principle, which is being described as the basic principle of the thermodynamics of information processing. As far as I've been able to tell, every single argument that I've found physicists putting forward for psychological and thermodynamic paradigm going together, they have basically The rest of the Landau's Principle. So, what is Landau's Principle? As I say, the other one is remarkable. The most popular expression of the Landau's Principle, currently stated by Caves, Carl Caves, who works in quantum information, he says, to erase a bit of information in an environment at temperature T, requires a dissipation of energy greater than or equal to KT log 2. And greater than is actually where the irreversibility comes in. Slightly stronger, the philosopher Jeff Book expresses it as, a logically irreversible operation must be implemented by a physically irreversible device which dissipates heat into the environment. Now, case ties explicitly to the erasure of a bit of information, and Book talks about a logically irreversible operation. These are operations which, the definition of a logically irreversible operation is one where the output state cannot be used to uniquely identify what the input state was. So an example of that would be the n-gate. If you have an n-gate and the output of the n-gate is zero, you can't actually tell which of the three possibilities would be in the whole state. And an inclusion. Some computational operations are logically irreversible, say the n-operation, and these must be thermodynamically irreversible, and they give up heat, crazy thing to do, KT loves it. So, putants have an hour of time, that's all. I'd like to get to that, but it might just turn out like that. Just a question about the EPB 2001. If you were an auxiliary device with an AND gate,

45:00 which generates lost information, then you have a reversible process. So that can be part of a reversible process. When you say you put an auxiliary gate with the AND gate, do you mean you save the input? We could put it that way, but no, you produce the auxiliary information that's required to fill in the bit that isn't in the results. If you keep the information that went into it, then you have to avoid it, but if you don't, if all you do is you have the output from the input, that's all you have, there's no way you can reconstruct it. Indeed, but if you run this diagram next to it, that holds the other information, you've kept yourself the option to run back again, which means that you've only done your part of the universal process. One of the things that many of these quotes have never been shared in the 1970s is that any logically irreversible process could be read as a reversible process, whereas a propagative or amplification process in a noise environment cannot be reversible, and that's the distinction that seems to me to be true. There's sort of an underlying assumption that if we're talking about the entropy, we're talking about the entropy of everything. Can I have local entropy increasing and say global entropy decreasing? So the arguments are not including that type of situation, I assume? The assumption would become the usual kind of assumptions in statistical mechanics, where you have an environmental heat bath at some temperature T, a large environmental heat bath at temperature T, and then the computer and anyone interacting with the computer is simply part of the system, and the heat being given up is being dissipated into the environmental heat bath. So this is the entropy of the whole universe? Yes. So the entropy of the system itself... So there can't be homogeneities because it would happen if it's the entropy of the whole universe, the whole universe has to be sort of uniform. Well I wouldn't necessarily say the whole universe, I'd say the environmental feedback. I don't think I would necessarily need to include the whole universe to be able to treat the Atlantic Ocean as being a very large feedback. But the argument of Landau's principle is that in fact the heat given off has got to be

47:30 Can I ask why? That was a really hard one. Basically, in a simple situation, really, so it's kind of... Through phase space. No, you'll put... Turn the whole pattern around. Yeah, it's just to start... One more, and then it will be... This one is mine. Okay, so the argument, the very, very quick argument for why iron house principle works is that it's a suggestion that, A, you've got degrees of freedom of the environment, B, this is a very simplified explanation and it's been very criticised, and that's one of the reasons why there's a lot of argument over this particular explanation in the literature, and I believe a lot better explanation could be done, but I took me 70 pages to do it, so I'm going to present the simplified version. You've got degrees of freedom of the environment, say, if we keep that in this direction, and your logical processing system, which is here, where it's got some degree of freedom, where this region represents state 0, this region represents state 1, and so if the system's initially named, say, state 0, or possibly even state 1, with equal probability, then the probability distribution over that state space fills those two boxes. That all because it's equal probability of one bit of information. Now, when you perform an operation called Landauer Eraser, where you erase this one bit of information, you go to a situation where you have, the system has to be in the zero state. And in that case, well, by Learfield's theorem, it's got to have decided twice as much space in the environment to give that.

50:00 But if it's an environmental heatback, then we happen to know that the only way you can actually increase the entropy of an environmental heatback is by checking energy into it. So you've actually had to increase, you've doubled the volume of the environmental heatback you're occupying, which means you've increased its entropy by k log 2. And the only way you can do that in a heatback, anyway, is to actually increase the heat in it by kt log 2, at least. Because, of course, that's in an ideal process, but if you have a non-ideal process, then you're going to actually use more than that. So that's Landa's principle in induction. Now, is that okay with you? I think that's more to explain why it's a problem, because... It's lost on me anyway. The problems are very myth-making, and they're about definition of terms. I'm not trying to alternate, but maybe you can decide, because it seems simpler to me, but I don't know if it's right. Okay, the minimum entropy change you could have would be a two-state system, and so the thermodynamic weight would be two. Because, you know, if you're in one state system, the thermodynamics really want. And so the associated entropy would be K log 2, right? And then a heat bath. The reversible entropy change would be K delta S, which is the KT log 2, and so that would be the heat change in that particular situation, and then by the second law of thermodynamics, it has to be greater than or equal to the reversible ones when it's equal, and then greater than if it's not reversible. The information here is the maximum amount of information you can represent from 10 to 1 is 1 bit, because the channel information of that is maximum although if it's not half of it then the channel information has to be 1 bit. But if the probability there is not uniform then the channel information of that is less.

52:30 And that's exactly why what you're doing is both classical and quantum. It does not matter. You're just counting. So it really doesn't matter whether it's classical or quantum. You're just counting. The second thing that has been criticised is that it assumes that the second law of dynamics is true, and unfortunately Landau's principle for a long time has been bound up in the argument about Maxwell's demon, and when you're discussing Maxwell's demon it's not an obvious thing to assume that the premise of your argument is that the second law of dynamics is true. So you end up in charge of secularity of your reasoning. I would suggest that, I think you can actually justify this from pure statistical-mechanical reasoning that says on average the entropy generation, the heat generation, is at least KT log 2. So with that simple qualification you can fix all those problems. I'm actually now going to talk about exactly why this very, very simple argument doesn't, I'm going to say actually, because it's completely opposite, doesn't work at all. I mentioned logically irreversible operations. These are operations where you can't identify the input state uniquely from the output state. An example of this is this reset operation where you've got 0 and 1 and you get as an output 0, which is sort of the most primitive one. Reset to zero. An example of a logically reversible operation is the NOT gate, because the output's one and you need the input for zero, and the output's zero and you need the input for one. So you can linkstrip the input from the output. And in fact you can build, basically, all of deterministic, universal, Turing machines from just those two combinations. Plus the identity operator. No, you can't do that. I'm sorry. You need other computational primitives in order to build the machine. You need unit wires, you need unit wires and you need exchange operations.

55:00 You need to physically embody it, of course. But you can from this... Well then you can't build the machine until you physically embody it. You have to assume other components. You can build it and then... I couldn't find them. You can construct a physical system that embodies these operations, gates that embody these operations, and combinations of those gates can do anything a universal Turing machine can do, because you can construct a man's gate from these plus the identity. But you can't build a machine, you can't build an actual... You build a machine out of systems which physically embody these operations, it's not really... You need other physical, you need other logical primitives to actually do that. You need a physical system that embodies the operation. I'm not sure what exactly is wrong with the others. So it's not just the operations which count, it's the thermodynamics of the physical embodiment that you have to take into account as well. Yes, the manner. And that's what you're saying. And they say you're assuming that information comes in bits and information doesn't come in bits. I say information, I refer to Shannon information, by definition. You may have a different version of information, but that isn't the version of information that I'm using in this talk. You just say the information does come in bits. I mean, you've got about even two. No, no, I said that information comes, there's a generalisation of information, information is holographic and continuous. Now, one of the things these operations have is that they're logically deterministic operations, which is sort of the converse of logically reversible, which means that logically deterministic operations, given the inputs, you actually can say what the output is going to be, which the input is 0, the output is 0, the input is 1, the output is 0. 0 after 1, 0 after 0. This seems almost a trivial thing to say, because almost all the operations were really used to go like this, but you can actually have other operations that are logically indeterministic. These are ones where the input, these are one-to-many operations. Now, they're not the usual to come across, but this one, flip a coin, is actually quite important because it's a random number generator, and if you've got a universal Turing machine with this one, there exists a class of problems called the bounded probabilistic polynomial problems that the computer can actually solve faster by having this game. It can debate any combination of these guys.

57:30 You still have those as well, I think. Oh, you still have those. Oh, you still have those. In fact, this gate can then actually go up to these gates as well. But you can't build that gate as any combination of these gates. If you don't mind, I'd like to remind you of the Turing machine. Turing machine. A universal Turing machine is just the standard model of a universal computer that works on classical information processing. So can you build a Turing machine that does random numbers? The universal Turing machine is generally deterministic, so you need to actually equip it with this additional gate to create what's called a probabilistic Turing machine. Now, there's some... I've had people argue these aren't really logical operations, which is a matter of definition. What's involved is it's actually quite easy to build them, as I said. 5 volts to your PC? Yeah, these are actually being marketed. There is random number generators being marketed, quantum random number generators even, that use wave function collapse to generate a random number. When you actually include, for logically deterministic operations, we can sort of define an operation by a truth table. For indeterministic operations, it's a bit more complicated. We have to actually define it by a conditional probability. Now, in the case of a deterministic operation, these are all strictly either 0 or 1, and that's how we can tell the operation is deterministic. If we have a distribution over the input states, then we can define what I call a reverse transformation, called the reverse transformation, simply by this. And this is just standard probability application based.

1:00:00 But, essentially, given any one of these operations, and then taking a distribution over the input states, I can define another operation and this also falls into the category of those operations that can be constructed out of those. The reason why I call it the reverse is because if you have that as the input and you operate on that and then you operate on the output of this with that, you get back to this. You don't necessarily get back to the original state you started off with because if you have indeterministic operations you can't guarantee it by definition. But you will get back the same probability distribution over the output states as you had over the input states, which of course means the Shannon information is going to be the same. It should also, hopefully, be easy to see that the reversal of a reversal is just a derogatory operation. In general, such an operation changes the Shannon information by a certain amount, and you can calculate... If you look at those, you get out probability p, and you look at the change in channel information, and when you actually run all the arguments of Landau's principle, the statistics documents before it, you find it just simply generates this delta q is greater than or equal to minus delta h k t dot 2. Delta h is the measure of the channel information, it doesn't have to be discrete, it can be continuous. So if that helps, probably not. So this can be an even block. It doesn't have to be actually an integer. And just to sort of illustrate this point, these are examples of the reversals of these primitive operations. The not gate just becomes the not gate. It's its own reversal. The reset to zero becomes the coin. The coin becomes reset to zero. And the complete randomization just stays complete randomization. And what's most nice about it, if we were to build a physical system that implemented this and ran it, And then we would take the exact microscopic dynamics, including everything, heat back the whole universe, because now we're talking about thermodynamic time reversal.

1:02:30 If we were to take the exact time reversal, including all the microdynamics, and consider that as an operation, we would actually find that it converts. You would actually then have the reversal, because you've just got all the same operations going across. This is going to be key. There are key postulates that underlie the argument that connects the computer. First of all, this is the assumption that I think a lot of people want to make. Mental state super beings are logical processing states. This is the sort of essential assumption of what the idea of modeling the mind as a computer is to say that I don't know if everyone's familiar with what a super being is. I will not. Okay, supervenience is a term they invented in the kind of mind and matter debate as a way of avoiding saying other things because the general way, they wanted to be able to say that the mental state has some relation to the material state because it's well established that there are physical correlates of consciousness states, that there are certain physical states that seem to be very correlated to the occurrence of mental states. Lundy really disagrees over this point. Oh, it's in correlation. You've got lesions of the brain that are doing lesions of things. Yeah, yeah, okay. Yeah, okay, never mind. It feels a little bit more as though you're saying brain state rather than mental state. No, specifically this is mental state, because this is specifically about the issue of what a consciousness feels like. The actual consciousness. Because that's what they're trying to actually say. There's the argument is that well if you change the physical state does the mental state change and if you have a different mental state it must be a different physical state and there's a sort of wanting to actually say that well maybe if you move a few atoms in my head then my mental state will be exactly the same. I wouldn't feel any different. I wouldn't be having any different emotions of course. But if I'm having different feelings and if I'm having different emotions...

1:05:00 And finally, I want to say that my mental state is different, and really that my physical state ought to be different as well. But without actually committing oneself to the idea that my physical state is causing my mental state, or determining my mental state, or that my mental state is somehow reducible to my physical state, instead it's just the relationship is that A supervenes upon B if a change in A means there must have been a change in B. So the mental state supervenes the physical state if and only if a different mental state must be accompanied by a different physical state. So this is about what they didn't want to avoid saying. It's the very, very weakest thing they could say about talking about the physical correlation of consciousness. This is a stronger statement than that. This is the one that goes on. It's not just the physical state, it's about computing. Saying the mental state supervenes an illogical processing state. This has to be more than just what the actual logical state is seeing. It actually has to be the logical operations acting upon it. So this process of being in some state and having a logical operation acting on it, and if this can be modeled exactly like a computer in a functionalist approach to the mental state, I'd use it. This is actually all there is. If you've got the logical state and the logical operation acting upon it, that's what gives rise, that's what actually defines the mental state supermeans upon this. Consciousness is just something that comes out of a very, very, very complicated big computer. So this is a serious constraint on what it means to... what consciousness is. Yeah. It's a very serious constraint. I mean, there are a lot of people in the consciousness debate who do not agree with this statement. So it's not... So basically, your computer doesn't have a separate mind. It's just a... it's a... You don't assume that there is, that you can do things in your mind quite separate from in your brain. I don't think so. It's everything you think has a representation. It actually has a reflection. A representation. Yeah. There's a reflection in both states, right, mental and physical. This doesn't commit oneself to actually believing that...

1:07:30 You can believe there is actually something different, something extra to it than just the actual physical state that the mental state is. But if that mental state changes, then the logical process state must have changed. That's what's important. Do you have to mention mental states in this at all? Can't we just talk about computers? Because I mean I think we're just committing to the numerological power from that even before the others. Well I don't think we should be committing to this position. This is a position that, all I'm asking is, some people are committed to this position. I can't agree with it. Why don't you think we should do the logical operation rather than just the state? A logical state actually, when you actually look at the physics of a logical state, there isn't, you can't identify a logical state. It's only actually as it transforms that it actually has any significance. I suppose that it's latent. And it's unique canonically labeled. Then I do a mental state, I can change one mental state, which is a huge logical path difference from another mental state, and I can do it practically instantaneously. So why should the two suit the people? It's only if you haven't got to the mental state that you want to transform to in your mind. Using your mind as a computer, but then you want to verify that you want your brain then to carry out the action, you then get it to carry out the logical, the logical operation, and the two things, the two things, the two things are quite different. I'd like to avoid kind of getting into the details of the different minds of matter. I think just, what do I know about the different parts of this argument? This is a point of view that some people believe. I'm not going to actually try and defend it. I'm actually going to suggest there's reasons to doubt it. But it's certainly a position that some people hold. Now, if you believe that the mental superglue is on the actual information state itself and not the logical transformation... Then it actually also supervenes upon the combination of the two. That's actually one of the things that, when you start to think about it, if A supervenes on B, then A also supervenes on B and C, because if A can't change without B changing, then B and C has got to change, because B changed.

1:10:00 And the second thing that people want to believe at the same time is that the psychological area of time has to be in the same direction as the thermodynamic area of time. It's simply because if it's not, then they've got to find another explanation for the psychological arrow of time, other than the initial condition hypothesis. And once you've got the Hamiltonian dynamics and the initial condition hypothesis, it doesn't really leave much space for finding another arrow of time. The argument then for logical processes against an arrow of time from Mandel's principle, A implies B. Again, Q and B. That's the argument. Very, very simple. Now the problem. Consider a sequence of logical transformations of information that corresponds to a succession of mental states. So this is according to someone who believes these statements aim B. I don't know what these logical operations are, but whatever the logical operations are that this computer that embodies the mind goes through, and these are the states, the possible states for this operation. So we've got, I may have just used here as a label that equals. We've got the state of I minus 1, the logical operation of it, all that kind of state, and it brings you to I. And you have logic operation I that brings it to I plus one. So we're just moving forward in time thinking, and this has to be accompanied by this conscious perception of this moving foot now going in this direction. We can always construct the reverse operations because we've got everything we need. The problem is that the solution shouldn't help. It might be very interesting and difficult to do in practice, but in principle it's possible. We can construct this. And in principle, we could build that. And, in principle, we can build that in our entropy-increasing universe. So, and the punchline, of course, is, so now we build that, and then from the exact time reversal of the macro-physical trajectory of the second system in the incoming system,

1:12:30 at the exact time reversal of L-sides L, this produces that, but it's in an entropy-de-increasing universe. And, of course, now if you believe A, then you believe that the mental state is super-B. So, if you can't believe the logical processing states, then you must believe that you've got consciousness moving along in that direction, because these two logical processing states are identical, and if the two logical processing states are identical, there cannot be a difference in the mental states, otherwise mental would not supervene on the logical processing states. But this is a natural decrease in the universe, so you can't possibly believe that both mental states supervene upon logical processing states and the thermodynamic area of time. And the mental error and the psychological error type have to point in the same direction. You have a contradiction. That's more or less the actual main and close line of the talk. Well, that's it then. Are there any questions? I think he's only got just a little bit to go, so I thought you'd see if this looks like a sort of a final statement. There's actually a second thing about the issue of, there's another additional attempt to do it which involves memory as correlation, but this is the actual name as well. Similar to the result, isn't it? And, well, I'll just say, right, okay, there's one thing I would add. It's about Landau's principle, and this problem you'll make it. What about this argument? What about this? Well, the problem is that this principle is derived from the assumption that entropy increases in time. This inequality is derived from the usual statistical and mechanical assumptions. And these assumptions go like this. Systems are initially uncorrelated, generally interactions and correlations develop through the microscopic degrees of freedom, and these get lost into the environment. Well, these are compatible with the initial condition hypothesis, but they're not compatible with the final condition hypothesis. Obviously. So if we have an entropy decrease in the universe, We have a different type of phase of analysis. Systems have to be initially highly correlated at the macroscopic level, and as they interact, these correlations disappear, and this loss of correlations causes the appearance to eventually decrease, and what's more, these lock uncorrelated systems. Systems don't re-interact with the uncorrelated volumes. This is the normal assumption they don't have.

1:15:00 So the end correlation just disappears and more correlations come out of the environment to cause the end of the decrease. And then when you try and rewrite Landau's principle from the first one, then of course he turns around, obviously. Can I make sure I put it around something? Let me be clear. Have you finished what I've written? Fantastic. I've got to say I've always had a... There's a couple of points that seem to come out from here that are reinforcing the way I figured that you meant to, I think, anyway. But one of them is sort of... ...sneaky sort of relativity that seems to be exactly behind entropy anyway, sort of, you know, it's how much do you know about the system is somewhere at the basis of it, rather than what is the state of the system to me, if you understand, and that gives room for certain leakages, which I think can lead to a kind of reversal, but I noticed also, and it may be related, I wonder if you could comment, early in your delivery, you showed a simple inversion of the mapping. To show that there was a symmetry about them. Whereas it seemed to me, and that's a Shannon interview that you were quoting, it struck me that you were talking about, yes you were talking about, yeah that's right, there's a simple math in there. Whereas it seems to me, I could be wrong of course, but it seems to me that there is... A presumption there that the level of the relativity of the entropy is being held constant, whereas in fact, if you do sort of a coherent analysis of it, so that you were tracking through the information, then that symmetry kills some of the information that's concerned. Do you understand what I mean vaguely by that? No, you don't, obviously. Furrowed brows, Peter. You've taken a sort of an objective frame of reference in order to create that reversal, that symmetry, whereas the reality is a bit like the same. You're saying that the chaos you're creating is dispensed with out into the universe, and in fact if you track it all on conditional basis, then you're going to get a very different thing from some sort of objective.

1:17:30 I mean, there's a number of things. These are operations that one can... Well, the probabilistic, I mean, these ones... I mean, the source of this probabilistic step can, again, occur in a number of different ways. The sense of probability there has got an objectivity in it, which seems to be dangerous. If you're working classically, then really any sort of this that really does the job is picking, somehow, degrees of freedom from the environment, like the population and stuff like that, and then of course you need to learn more about it, but the question of whether there are such microscopic correlations is... One of those things, if you actually find a source of such microscopic correlations that's reliable, let me know, because we've done Max's Dean. Well, yeah, sure. That reversibility theorem which I sort of raised early on, if you somehow can keep track of what that change was, then you're in a position to wind back, which means it's not on that basis of an objective platform. I mean, the initial conditional hypothesis only generally sort of works because... You've got this repeated asymmetric assumption that, as you're doing these operations, microscopic correlations develop in the environment, and they're lost. Now, I mean, if you actually just look at Hamiltonian flow, the fine-grained Gibbs entropy is constant when you're at Hamiltonian flow. If you've got a military system, and there's sort of resonance, and you get it right, then the downtime can bounce back again, sort of thing. I just want to say, a lot of the time, a lot of the time we think correlations are getting lost, they're just becoming more subtle, like, you know, like the black hole evaporation, some of the recent major, you know, we've shown that.

1:20:00 The correlations don't really get lost. It's just a lot harder to see them because you have to have collected information over the entire history of the evaporation, that kind of stuff. So it's practically lost, but not in principle lost. So some of those arguments, you know... These are problems with the thermodynamic areas of time, aren't they? I'm very unhappy with the initial condition hypothesis as a search. These are some of the reasons why. Of course, if the dark energy, the simplest dark energy ideas are correct, or it really is a cosmological constant, we did this paper, of course that means that there's a horizon outside of us, and that means that the entropy is actually finite. As soon as you have finite entropy, that means you have a finite number of states. As soon as you have a finite number of states, If you're thermodynamic and going through the states, eventually you'll recycle. That's called Poincare invariance. So in fact, if dark energy is purely cosmological constant, the universe as a whole will undergo Poincare invariance. So it's a non, I mean it actually, it happens in a time of e to the s, or e to the s over k basically. So it's a long time before our Poincare invariance will happen, but still the universe as a whole in the simplest, in the simplest terms. We'll undergo a pump-array recurrence in the time associated with the decelerators, which is about 16 billion light years or something like that, but my original point, still you can have regions in the universe as it's undergoing the pump-array recurrence, where entropy is locally increasing, and so I'm not sure, I think that may be a little... The key in the argument in that even though the universe as a whole is undergoing a local negative entropy fluctuation, that that bubble, that little small region could be undergoing still continuous, you know, still a forward, increasing entropy.

1:22:30 What are the probabilities of these fluctuations? I mean the general way in which we calculate the probabilities of fluctuations is Given the initial condition hypothesis, and even the larger the fluctuation, the less likely it becomes, of course, if you want to question the initial condition hypothesis, then you can even put other conditions on it, just as arbitrary as that, in which you can map around the probability of fluctuations occurring. The question is really, I'm not sure... Oh, my question is mainly, I think most of your arguments, in fact all of your arguments sort of had a uniform, and all I was saying is you can still have regions of non-uniformity where entropy and error goes opposite directions, and it's very difficult. One of these concepts I don't agree with is the wave function of the universe. And here's why. If I have the wave function of the universe right now, well, it's gone, right? Because I just collapsed it and it's useless, right? You know, the standard quantum mechanical thing is fixed past, uncertain future. As soon as the wave function has been decoherent, it's useless. No, no, that's experimentally true. No, no, no, experimentally true is not model-dependent. There's a big difference between model-dependent. I'm just stating the experiment. The experimental fact is, once you decohere a wave function, it's irrelevant to the future of the system. In other words, the new initial state... Right? That old information is gone. It doesn't see a role. There's no longer a question that's actually that the work of the Poincaré occurrence is actually more, occurs more frequently in quantum systems. But I don't know if that's true on the cosmological scale. But finally, whether backwards in time, if it comes, it is relevant. I mean, it comes from the future and it is back there. There's going to be a wave function. You would have to have the entire universe decoherent at one time slice in order to define some wave function and then you have sub-clusters that are decoherent in different, you know, as we're talking because you and I are talking decoherent.

1:25:00 Yeah. It all depends on the concept of decoherence. Could I just make a brief remark? I've always been a strong supporter of your thesis. But there's no relationship between these two. But the matter is a lot more general. The matter is that if you see things happening in sequence, then there's a strong psychological urge that people have to say, well, there's a time which is behind, which is flowing on. Time, like an ever-rolling stream, bears all its sums away, you know? But if you abandon that picture and say, well, the way that things are formed in sequence is the ultimate fact, then of course you don't need to talk about a reason for the direction in which it goes. Sequences don't have to be an indirection. There isn't this time, there isn't that time, there isn't that relationship between the thermodynamic one of it and the psychological one of it. By simply saying, do the conditions somehow predicate that there must seem to be a direction in time? You don't have to be hanging on this idea of it. Fundamentally then, you can just take a sort of a static geometry view of it, sort of. I mean, once you've sort of abandoned this sort of very naive connection, then a lot of possibilities are open, certainly. The solution has to be more, will not be found directly in any kind of naive physical models of what's going on. It has to be found much more in natural study. Think of the actual looking at the issue of consciousness. So there's sort of a section of time. So you might find some nice models that tie it together. Acceptably, that's possible, isn't it? You won't get the philosophical answer, which you might get something where all the ends are tied up nicely. Generally possible with models, isn't it? I've got one to suggest you after the other. I really don't see how you could accept these arguments until you've done it with the complete model of thermodynamics, which is quantum thermodynamics, and the best model we have so far is the quantum kernel engine. And that introduces an entirely new factor into the nature of the thermodynamics to do with quantum coherence, unless you examine that particular model in great detail.

1:27:30 It seems that it can certainly be applied to macroscopic quantum systems, indeed to the whole universe. I don't know how to do statistical physics without quantum mechanics. There is no classical statistical physics. You really need the H bar in the phase space. Where else is dimension coming from? So, I mean, the only thing that made statistical physics... I'm sorry, I'm not talking about statistics now, I'm talking about statistical physics. The only thing that made it consistent was the introduction of harmony, I think. I think the class of this system, you can't say this is Camden consistently, but... But what do you use as the dimensional, in phase space, what do you use as the dimensional parameter of each form? Well, I'm using Gibbs entropy approach and you don't need a parameter to actually partition a phase space, all that. This DP is dimensional, so you need to divide by something in order to make something that's dimensionless, then you go from counting states into... Yeah, but that's the Boltzmann approach. I wouldn't use the Boltzmann approach, I would use the Gibbs approach. And the Gibbs approach just has a problem with the distribution of continuous space-time, using the Begman-Gergen method. Without counting? It's not counting. That means there's some unknown dimensional parameter in the phase-based and automatic dimension list because you're putting it inside a law. So it has to be a dimensionless number. Otherwise, you can't do the mathematical operation of taking a law out of it or anything else. Well, a good system does work, right? It's been used quite a bit. But when I use it, it has to be an h-bar in order to make a dimension. Even if you're doing classes, it has to be a dx, dt, or h-bar so that you can take mathematical laws. That's kind of puzzling to me because Gates wrote his book on the mathematics of mathematics. Yeah, but he certainly didn't assume that there was a dimensional constant in order to take the mathematical laws or the exponentials.

1:30:00 There are many, because you can't take an exponential of a dimensional point. I'm not sure which quantity is the question. Yeah, it's got to be a scale. How does it? Well, it's a mindset that you can't. No, it's got to be one related. You take another one of the probabilities which are dimensions. Right. And how do you get probabilities? The probability of a state with energy being occupied would be in the equilibrium e to the minus e over kt, but e over kt is dimensions. But I also think this argument does go through with the standard quantum statistical mechanics. Thank you for your attention.