Waves in the Hierarchy

0:00 Amazingly enough, we are now a few in our head. So, Michael Ranthe, fresh from Colorado Springs, not at this time, not at this time, I had a discussion with Clive, and I find out that, you know, I, being a, uh, a lonely computer scientist, I've always striven to adhere to proper, separate mathematical terminology. And I find out that these things which look like AB equals minus BA and go round and round, I mustn't call them spinners because that means relativity theory to everybody who knows about spinners. And I obviously don't, I don't mean that. But anyway, I should mention, only on a distinction between two things happening at the same time, the two things excluding each other. And I use this for at the same time, or this at the same time. And this, this is exclusion, this is quote. You can generate a hierarchy of things that have rotational essence. by those spinners. And it is a combinatorial hierarchy and Ted and Clive and I agree that it sure does look like it's the same hierarchy. But what we can figure out, because the two points of reasoning are very different. But there's no question, but that the hierarchy I get the same numbers and so on, it has the same cardinalities, and it's combinatorial in nature, and it also embodies the idea of distinction, in the same as the combinatorial hierarchy, it embodies the idea of distinction, but the distinction that I am making is, are things indistinguishable in time, i.e., they co-occur, or are they distinguishable in time,

2:30 they exclude each other. So it's, and that idea I got from him. Anyway, so you get this higher, made out of elements that have this rotational symmetry, rotational action. And And it looks to me that, okay, so you imagine this hierarchy sitting like a pyramid. Let me draw something over here. I invented all this because I wanted to do artificial intelligence. That I could believe in this start back in the 70s. And I very quickly decided that the Lisp thing and a lot of other things people were doing, I just couldn't believe in it. I started looking for something I couldn't really do. And anyway, my sort of working problem was some sort of robotics. And the idea is then that because the world is infinitely complex, it has to be a learning affair. Because you can't possibly put in everything that a girl would need to know. So it's got to be self-organizing learning. The lesson we've learned in computer science is that, in the last 20 years, it's got to be distributed. There can't be a centralized. So that leaves out anything to do with sub-D calls and that's it. From my point of view, if you are doing standard computer programming in whatever language you choose, C or 4th or Java or parallel programming. It's the same thing. It's basically the same set of underlying concepts as classical physics. So to me, sequential programming and classical physics are in one same box. And just the distributed thing and this idea of distribution with no centralization. And everybody doing their little thing all on their own, and yet you get coherent global behavior. That is the descriptive idea. And that turns out that this AI idea that's represented here

5:00 has exactly the same model of mind. It's the same mathematical form as my version of the form. So that's in the other box. So we imagine a hierarchy and thinking robotics example then, I imagine I have sensors A, B, C, and B. I'm going to have four. And these sensors can show either whatever it is it senses is present as a plus one, or whatever it is that isn't there in the environment, and that's fine. And then these get put together in various ways based on observation, and we get a hierarchy out of this. And the hierarchy is much more subtle, but I'll just point out that it's not a tree, it's a lattice. And every piece of knowledge, only a person wants to know. So, and that hierarchy is the commentator hierarchy in its own way. And I interpret, okay, so what my talk is today about if you simultaneously, if you If you imagine these things, sensors flipping as the environment changes and the impact of those sensors bubbling up, reorienting the states of these higher level nodes, that actually what is happening is that these sensors there flipping back and forth gets translated into a wave-like, back into a wave, into a wave. And so, what the bubble-up is actually doing is a Fourier decomposition of the activity on bound. And, I interpret the hierarchy and this wave-like character as being, in fact, a wave function. of Marxism. As Michael said earlier, for an earlier talk, I'm very happy to take questions

7:30 along the way that are related to, I didn't understand what you just said there, but the more philosophical questions I'd really be preferred to leave to. Mike, apropos, just to get things clear, where's the time access in the online? There's no time. What's the sequence? There's no sequence. That's just a block, is it? These sensors are just doing their thing. You've got the environment out there, this is the outside business. When you say bubble up, you are giving a sequence. Yeah, the bubble up is a sequence and that is a sequence. Yes, there is a sequence in terms of it follows the bar. Okay. And that is the same time, that's just sequence. Yeah, right. Well, even then you can't say that, I mean, it's reversible, so. It is an even time. Yeah. Quick question. What are the lines and what are the circles inside? These are nodes that work. These are sensors, and these are meta-sensors. And the lines? The lines are either bubbles up, or that's the sensory... It just shows up. It just shows paths, yes. And then if it's going to react, then the same lines go together. And so you have exactly the same, just from a software guy's point of view, it's exceedingly to collect because the nodes, it's the same piece of code. Every one of these guys is the same piece of code. And on the front side, it bubbles up. And on the back side, it trickles down. The trickle down comes out here, and then it's set up. And the sensor, it's an effect. Okay. So this is now the introduction of the sort of the conceptual situation. And for those who haven't seen it before and for those who have, the first point is that the computation that's going on here has nothing to do with numbers. It has to do, we're in the time domain And we're using a concept in computing that's called synchronization, which has to do with if you imagine two users sharing the same computer and they both want to use the printer, then one of them's got to use the printer before the other.

10:00 Otherwise, their data will come out into it and you get non-determinant. So, synchronization is not the physics of synchronization with photons. It's the act of introducing an order between two events belonging to different processes. That's the signalization. Local order. It's very local. Very local order. There's nothing global about that. And so what's going on here then is there's no data. It's a pure process. There is no databases, no records or objects, as it were, in the standard sense of the word. the state of the system is in the relative phases of where each of these things is in its code. That's it. And so, exclusion then, that a sensor is either sensing something saying plus one, or it's saying not there, those two things exclude each other. Logically speaking, they cannot occur at the same time. That's exclusion. Or in the case of the printer example, the one process excludes the other on the printer. So you took that time to say it cannot occur at the same time. Please leave the time thing out because there's two kinds of time, if you will. There's reversible time, which I tend to call flux. And then there's irreversible time, which is classical ticks. Is it possible to think of this diagram as a circuit diagram? No, I wouldn't do that. And then this idea here was actually the breakthrough idea and so I want to talk about co-occurrence because this is the place where emergent phenomena enter the world of computation. And I demonstrate it like this. I'll show you this coin here, ordinary 50-piece, and I'll show you this coin, and that's also an ordinary 50-piece, and we will, I will stipulate that these two coins are in every physical respect identical. Now, it's not a trick question I'm going to ask you. I'm just trying to make the issues as clear as possible, okay? So the question I'm going to ask is how many coins do I have?

12:30 And the right answer is I have one or I have more than one, okay? I don't have zero because you've seen one. And I could have shown you as one of the same coins twice or I have more than one coin. You don't know how many I actually might have in my pocket. So there's two possibilities. I have one coin or I have more than one coin. And I specified that they are in fact indistinguishable. So this is getting back to the introductory comments. And since there's the two possibilities, they cover the entire set of outcomes and they exclude each other logically, That is the definition of one bit of information. And the idea of information is very much like energy, it disappears in the using. So once you get the answer to the question, whether I have one or more than one, you will have received one bit of information. Any questions about that? Everybody understand? And the question I've asked you, do I have one point or do I have more than one point? I have more than one point. So you have received one bit of information. And the question is, where did that bit come from? It came from the fact that they're there simultaneously. So there is information in mere presence and that is, in fact, emergent. This is consistent with Shannon, but it's like the flip side of Shannon. I don't want to go into that discussion, but anyway. So that's the idea of co-exclusion. Then the idea of co-exclusion is to take this one-dimensional exclusion idea, the coin is there or it's not there, and combine it with co-occurrence and lever ourselves up to a higher level of perception. And the way I'll demonstrate that is we'll have two corners here. And the coin could be here or it could be there. Now we have just learned that in co-occurrence there is information.

15:00 And so we have here the co-occurrence of something here and nothing there. And we have different co-occurrence of something here and nothing there. And then we note that this state here excludes that state. And this state excludes that state. So, this state excludes that state. This state here, this excludes that, this excludes that. So, this co-occurrence-wise extends to that, okay? And what that means then is I take what I can do, what I'm actually doing then is saying that the state of this sensor over here is a one-bit process having one bit of state, okay? And this process over here has one bit of stake. And when I do the co-exclusion operation, what I do is I exchange those two onesies, say A and B, for one Tuesday. So one process with two businesses. And it turns out that if I think of these sensors used as being simple elements of Clifford Algebra, and this guy here is Clifford Algebra. So on the computer science side, we're talking about how can the robot abstract information from the environment into higher-level concepts on its own, no matter what the environment presents it with. On the mathematical side, that's being mapped into the political realm. And basically, I'm going to be talking algebra from now on, but just remember, there's a very concrete interpretation of this, and there's software that runs this way. What kind of algebraic story? What, which was algebra?

17:30 It's a Clifford algebra over... I'll get to that in a second. Okay, now just let me say, when I say hierarchy and Clifford algebra and so on, I owe a huge debt to Klein and to Ted, to Pierre for teaching me physics, to Keith for putting me on to the mathematical hierarchy thing that I'll be talking about in a bit, and to Amplan General for giving me a forum and for excellent feedback. And this work goes back in 15 or 20 years. I'm not counting the timeline before I discovered programs. So this goes back along. So, the mathematical framework, then, is these Clifford Algebras over Z3, where instead of known as base 3, but instead of a 2, I use minus 1. And the reason for this is that if you are in the binary number system, then zero is being forced to play two roles. One of the roles is zero is the opposite of one. The other role is zero, as in void. So by going, see, only computer scientists would be allowed to commit this kind of Harrison, right? Whoever heard of using base three for bits and not system one. So, 1 and minus 1 are the 0, 1 bits that you usually think of. And then the 0 is the way that I express exclusion. So, A co-occurring with its opposite, which is minus A, is 0. So, if you add two things together to get 0, then you know that they exclude each other in the synchronizational interpretation. And these algebras, perfect algebra, it's an incredible bookkeeper of symmetries. And it includes item components, that is to say, things whose square is themselves, generalized version of one times one equals one, and nil components, that is to say, things whose square is zero. So, there's some strange beasts inside the algebra, but the algebra itself, like the hierarchy that I'll use to describe, is incredibly symmetric and regular. So, are you considering finite here?

20:00 I'm sorry? Are you considering algebra over finite here? Is that straight? And what is the dimension of algebra? It's varying according to the level of hierarchy. So at this level, we have, as it were, cultural algebra consisting only of things from grade And we go up a level and then we'll have algebra consisting of things from grade two along with the grade one complex and so on. And then co-occurrence is represented by the same plus by addition. So when I write a plus, what I'm saying is they co-occur. And when I write, like, A plus B, C, what I'm saying is this sensor and this 2Z, this 1Z and this 2Z, they co-occur in whatever state they happen to be included. Oh, no, I have to draw all the lines. There's a lot of lines. There's a lot of lines. It's one of my little projects to figure out how to draw this, because when you get to three, then all of a sudden, it really takes off and gets on. Okay, and then the product, so if plus expressed co-occurrence and the product expresses change for an actual. In the sense, then, that you get from this state to this state, something happened. And what it was was you get AB to A plus A. By the way, I should mention that if you take any one of these twosies and you square it, because of the fact that AB is minus BA, you get minus 1. So you have something squared as minus 1. So really, this thing here is another way to express the square root of minus 1. And if you remember back to your higher algebra class, when you had... So here, for example, it's a state A plus B. Over here is a state minus A and B. Here's a state minus A and...

22:30 Here we have A and minus A. And then what the, what this guy does, the spinner, is every time you multiply AB times A plus B, it rotates at 90 degrees. Okay, so you have the circle and the circle is just a sine wave in this guy. Did I find that? So, when you see things being multiplied, then something's happening. When you see things being added, what you're seeing is the worst state. So now, we have this business of constructing the hierarchy. And this is where I use some very fancy mathematics, which I only... I'm strictly a user when it comes to this. If you go back a little bit, I can see that usually you get a side wave out of a kind of rotation there. Right. If you imagine a bicycle wheel with a light on it, on the rim. If you look at it in the dark, you'll light down. If you look at the wheel like this, you'll see the light going around like this. If you look at it from the side, the light's going up and down like this. But I understand that from my dynamics knowledge. But where do you get the rotation on the b? Well, if you just do the multiply, what happens is a, b, and with the anti-communativity, the next one you'll get will be a, b times a, that's minus b, and a, b times b, that's a. So actually, multiplying on a less, that's what I wrote. What kind of rotation does it change on in time? It's reversible. It's reversible. So why comes the wave? Why comes the wave? Because the wave is on a time-based thing. No, it's not real that one's happening. Let's not... The time thing is very tricky because it has to do with... Imagine I'm going to be talking about this. I think I'm logged out on it right now. I'll get to the time. It's just state changes. These are changes of fate. Fates? Yeah, it's fate. It could all happen at the same time, it could be gaining value, it doesn't have to be a time sequence. So, the way, the mathematics of this hierarchy is something called cohomology,

25:00 And what the idea is, is if I see this and I see this, then I can conclude AB. And the mathematics that captures that transition from this level to that, or if I have AB and CD opposites, I can do the same thing. So once I can use the same trick and given the second layer, I can build a third layer and so on. It's like, I use the same idea of co-exclusion all the way up and that's how this thing learns. This is learning from the AI point of view. From a physics point of view, what we're talking about actually is the mechanism by which we build the current state of the way. So you can think of it in both of those ways. So the notation for that is that the co-boundary operator operating on these, on whichever co-occurrences you have, I give you AB. And if I do the co-boundary operator on A plus B C, I get ABC. But I do it on an AB and CD, I get ABC. And the paper that's in the proceedings does this in excruciating detail. For those of you And then going down the hierarchy, you have something like ABC, and you have to split it into its pieces. You have to take it down to AB, you split that into its pieces. And that is what's called the boundary operator. And there is a formal isomorphism between the world of integration and differentiation and co-boundary boundary. Should that be, in fact, you're on the plan of the floor, it's 6, that's good. Should you have 6 meters on the first? On the second level, yes, second level. Yes, yes, you'll see that in excruciating detail in a moment. So, the algebra and co-boundary, I'll write them all. Well, they have the right properties. The boundary and the boundary is 0, the co-boundary and the co-boundary is 0, and so on like that. but the boundary of the kind of the same thing, isn't it? Oh, it sure is. But you have to expand your definition of what you mean by a boundary. Oh, probably. Which I am in great pains to do in the paper,

27:30 although the people who already think they know it, already know what this is about, cringe when I do it. But I call it a generalization. Keith calls it, I think, a mathematics. Be that as it be, it's legit. It's mathematically legit. See, this guy could be broken down into two twosies or a onesie and a threesie. Several ways. Several ways. Lots of ways. And I see it just, so if you look at it from a learning point of view, there's different kinds of situations that wind up having the same overall effect, But they are accomplished and sensed differently. What is your general definition of programming? You have to look at the paper. Just to remark on how this isn't the time. This is not the time. Yeah, but I was just reinforcing that. You said this would be accomplished in different ways. So these things do not depend on the history. You get to that product, it doesn't matter how you adopt it. So there's no time to apply that way. Well, I'd say, yeah, right. I'd say, though, that if it bubbles up one way, then it'll trickle down in the same way, in reverse. In other words, if you bubble up to this, this way, then it's not going to trickle down by A plus B to D. Is that how to say, there is a history associated with this symbol which you don't think does not cover this symbol? No, no, it's just that you have, if you will, the mapping, what happens is the current state of the surround uniquely specifies which of these are valid. And if AB plus CE is valid at the same time as A plus BCD is valid, well then you can run them in parallel and they won't get in each other's way. Let me put it in a different way then. There's an implied context in which the symbol implies this. In fact, context is not spelled out in the notation. No, that's correct. Okay, which is a problem, you know, for people watching that page. Right. Well, I look at that as an advantage. You don't have to have all these incredible details, which in a sense are not interesting, displayed in front of your face all the time.

30:00 Yeah, but they get an artist in trouble. Yeah, sure. That's the mathematical framework. Yes, I see, as I say, the paper that's in the proceedings this time does, goes through how you actually calculate this stuff and just, it's, it stems and proofs all the way through. So now, the question that, now we're actually to the content of this talk. And the thing, the idea is, how do we, I mean, first I'm going to explain it just a bit. How do we establish the value of, say, sensitive heat given the surround? I thought it was a little mathematical description, how you actually capture the surrounds value for B to get in onto the boundary. And then having done that, I want to do the same thing. I said, I'm going to measure my own boundary from this point of view. And I'm going to measure this from this point of view. I'm going to iterate this measurement idea all the way up. And my hunch, because I'm not offering a proof, I'm offering a single calculation, It looks to me like what is actually happening as you bubble up the entirety of the surround sensory depression that's what you're really getting at each level of support you can compensate. Where the highest level is the commonwealth. This is the highest level. So the boundary, there's the onesies, and I just lift the mathematical idea of measurements from the physicists, and this is the way they do it, because in quantum mechanics, when you do a measurement, they learn to their great dismay in the teens and the 20s that measurement in that is that it is not reversible. So the way they did this, the basic idea that we're going to have some sort of measurement, gizmo, algebraic gizmo, and that's when we're going to multiply that times the current state of the environment. And that's going to give us our result of the measurement plus the new environment because

32:30 Because as you all have heard many times in quantum mechanics, when you measure, you disturb the environment. So that's why I write new. And the way they do this is they, suppose I want to, suppose my environment consists only of A. And so this is my measuring tool. So we carry out the multiplication here, that's minus 1 times A, that's minus A, and A times minus A, that's minus AA, and then switching around and AA is 1, I get minus 1, minus A. And that's the new environment there, and there's my result. So when you do a measurement, you get a minus 1, that's what you're really saying when I wrote minus A, I'm asking the environment, is A minus 1? and I guessed wrong, either A isn't there at all, or it was plus, then I get a minus one back that says, sorry, I'm not going to tell you anything except you were wrong. Whereas, if I had a plus here, then this would be a plus, and I would get a plus one here, and I would say, yes, it is true. You wanted to know if A was plus? Yes, it is. But notice that in both cases, whether I guessed right or wrong, I still flip the environment from plus A to minus A. And that's the quantum mechanical disturbing the environment aspect of the measure. Now, I'm not happy with that. The reason I'm not happy with that is because I want to have the bubble off occur. But what if my robot says, well, I don't care about things. The robot doesn't react. Well, then I should allow that to be in no operation, no off. So, I came up with a, you can only call it a trick, but I like it, it's a cute trick, right? And so, what I do is I write the item potent this way. Supposing, you know, that's the negative of minus 1 minus 8, which is the one I started off with.

35:00 Now, if I multiply this out, that's what happens. 1 times 1 is 1. 1 times A is A. A times 1 is A. And A times A is 1. We're in Z3, so 1 plus 1 is minus 1. And A plus A is minus A. So this thing here, which is the negative of the, uh, I am potent, okay? Squares to the, as it were, it's the square root. It's the negative square root of this positive square root. And I call that because it's the square root of an I am potent. I call that a square root, okay? And the cute thing about the square is that when I do a measurement, See, if I can't call it a measurement anymore, you see, I'm going to use my measurement to probe, to sense the environment. Use my environment, A, look what happens, 1 times A is A, A times A is 1. So I get the result of my measuring, my probing, but I didn't change the environment. I'll only actually change the environment if I act on that and do it all. So the first of the squirts would be the triple up. The second of the squirts would be the triple down. It's only when I do the double action that I get the irreversible moment and the modification of the environment. If I get this right, do you say that you get something, you get information from the environment and I'll talk to you. That's right, but the information I'm getting is phase information. It does not matter. Hasn't it? The only, it doesn't, see, it's basically what I'm saying. See, I'm computer scientist, that means I'm a closet mechanism. In computer science, mathematicians prove theorems, physicists do experiments. Computer scientists write programs. If you're going to write a program, then you've got to say what's going to happen every single step along the way. So, I ask, where does the wave function come? How do you make a wave function? And this is the answer. The wave function is sort of like the budget of common.

37:30 You can move the money around all you like, but it's not that you spend it that makes a difference. And so the bubble up is like moving money between budgets. And the triple down is when you actually spend it. If you move around all you want, it doesn't make a difference. It's inversely. So, another way to think of it is this polling, and if you want to think of the AI thing, this is the moment in between of choice. This is free will. This is the slot. I'm not sure what people mean by the vote, but this is where it goes. when you decide to act or not. And that's what, so you're thinking of breaking the measurement process into two pieces. And the only piece I'm talking about today is the first part, just the appropriate part. Anyway, the point of this exercise was a little algebraic trick to allow me to sense it, to pull the environment, constantly sensing it, that we're in the environment And that orients the hierarchy constantly to where the environment is at. So the hierarchy is a representation of the extra state of the environment. And yet I'm not disturbing the environment. It's the only one I am. So I think that just about this entire slide here, I decided it was much better to do it on the floor. So break the, the idea of the square then is the aggregate inverse of the other, oh, it's a negative square root instead of the positive square root of the other and it breaks the measurement process into two pieces. In the first piece, it's a probe or a pole. So now we're down to the meat of the thing. We're going to probe the environment to get the phase of the onesies, and then we'll probe the onesies to get the phase of the twosies, and so on, up until we get to the top. Now I'm only going to go, I only got A, B, C, D, I'm only going to go to the fourth level. There's only going to be one inhabitant out there, namely A, B, C, D.

40:00 And there's two reasons for that. The first is that these levels, the sine when you square an entity at a level, the sines go as the powers of I. They go plus, minus, minus, plus, plus, minus, minus, and so on. So by the time you get to four, you've gone through one cycle completely. And the other reason is that I'm going to do this calculation by hand and it's any more than four, there's just too many things. So, I'm going to follow then the detailed co-boundary calculations to get the signs right because I want to orient each of the 1Ds and 2Ds and 3Ds according to the current state of the environment. That means I have to slagishly follow the co-boundary calculation rules, which I detailed, let's say, in the paper and the proceedings, to get the orientation between these guys correct. And that's what I'm going to do. And my probes, for example, if I, this is one thing taking one at a time, two things taking two at a time. So if I want to probe, say, I have two sensors, probing the two at a time, well, that's just the co-occurrence of the two probes. So I just add them together and I did minus one plus two. And the co-occurrence of three probes is being set three, one plus one plus one is zero. So when I probe, that's kind of a funny look, there's no one out there. And this is, this guy is no hope, actually. This is my candidate, or at least an important piece of my candidate for a photon. and so on with four, but that's only a small part of the possibilities. The thing with mother nature is, I've got four sensors. Let me draw the hierarchy again here. And so on. When I am going to sense the boundary, I'm not a robot but Mother Nature. Mother Nature is going to do everything all the time.

42:30 So Mother Nature is going to do the probings one at a time. It's going to do two at a time, three at a time, and four at a time. Likewise, at level two, I'm going to look at this level one, two, three, four at a time. And up here, there's going to be six of these things. I'm going to look at them, six things, one at a time, two at a time, three at a time. And I've got to add them all together. So it's a fairly lengthy computation. OK, and I'm going to forget the minus one business, and I'm going to only talk about pluses because otherwise you get proliferation of pluses and minuses and other such minor simplifications. So, I'm going to show you some tables of all these combinations, and the notation of that is this instance of measurement and area. So, how many measurements are it, and I do them at the same time. That's the measurement area. and level two. And so, for example, at level two, there's six things, taking two at a time, that's 15 different probes. Probes two at a time. And each thing that shows up, and what I'm doing that here, up here, this environment here is the one zero, because I'm measuring from the two level. Okay? So, what I will do then is I'll write down for this particular combinatorial class, I'll write down each of the possibilities, multiply by the environment, and add them all up, and finally get a sum, which will be the effective combined, all possibilities taken at one time, And this one here, this number here is mostly there for my hand calculator. This says how many times we have AB will appear in the final, in these sums, in these partial sums over here. And so if there's five of them, then I know three are going to drop out because they add to zero. There's only two. So that means the final sum is minus. So this is just a way to do the minimalism.

45:00 And so that's what I just said. We're considering the two subsets of six elements on this level, of which there are 15. And the five means that each of the two elements here occurs five times in sum. And the 15 is the number of ones, because we've got these ones here, right? They're out in front of all of them. So when the case was 15, that's 0 by 3, and that's what I said. So for level one, taking one at a time, there's only one. So the final probe is 1 plus 8. If I take them two at a time, then the environment is A and B co-occurring, and one plus A plus one plus B, and so the final probe is minus A minus A. And then, so that's two things taken two at a time, the two things taken one at a time is one at a time on A, one at B, and I add all that together, and the final probe is one. So I've taken three at a time, then it looks, uh, it can, uh, it should be an A-men, that's what A plus B plus C is. I'm taking two at a time, then 1 plus A on A plus B, 1 plus A to C on, actually B, actually A plus C, I'm sorry, one of those errors. And so anyway, add all those up, you get minus A minus B minus C. But what I'm going to do is in the final calculation, I'm only going to be interested in the maximal. And I'll take all four in all possible combinations and the resulting total probe, which is the other ones that get the cap sigma. So the total probe for level one doing everything all at the same time. Four at a time, three at a time, two at a time, one at a time. That's the final probe for level one. Now I'll run these others more quickly because it's really just the same thing.

47:30 I just want to show you enough of them to make sure you've got . So here, I'm going to take me three at a time, I have my, I have three twosies, measuring the three twosies, and that's actually no problem also. So I don't get anything out of three at a time. Out of two at a time, it turns out, and also everything else is zero. And one at a time, I get, so the final sum there is three twosies. And if I, see there's six things at level two, four things take me two at a time. So here, now I've got four things and you get this and so on. If I skip over five and I'll show you the six because that's the one that's important to us. And so... How many at level three? Level three would be four. Four things take three. But anyway, if I have six things, I have six, I get six twosies, but I take six at a time, I get zero contribution. I'm taking five at a time, then you get all these things, and that adds up to this. You're taking four at a time, that adds up to this. You're taking three at a time, you get it to zero. You're taking two at a time, that adds up to this. And finally, add them all, you get zero. For pedagogical reasons only, I'm going to use this, but it doesn't make a difference in the end, I'm going to want to square this, this is going to be zero anyway. But I just wanted to have something to show for that term. So I'm going to use this instead of zero, this appearance is safe. So this is the total profile of two. Although, in the case of six, if I had seven, it wouldn't be zero. It just happened to be zero because of six. I just noticed that there are the number of these levels of binomials. Yeah, binomials. You won't believe how binomials this is. Okay, so finally then, so if I do then level three, taking four at a time, skipping over a slide, you get this sum here. So that's the probe of level three. And the probe of level four is, of course, just probing the only elements we have. So those are the four probes.

50:00 What do I write here? I write... Good thing I wasn't wearing a prop. The probe sums express the total effect of multiple effective sentences that occur simultaneously up to getting both. Terms arise or dropouts due to plot and weight language would be destructive or destructive And the other thing I want to find out, just commented there, that it's doubly combinatoric. If we look back on one of these slides here. Now, notice, okay, first, we have the combinatorics here, five kings, five, four, three, two, and one at a time, okay? And then, if you look at this number here, one, four, six, four, one. So there's, there are two of them intertwined in each other here, you know what I mean? And of course, if you think about something that is this complicated, with this much symmetry, whatever comes out is going to be pretty interesting. If it's going to be zero, it's going to be interesting. Okay? I don't know, how am I doing? Not much. We're almost to the last slide. So that's level three. Okay, so now that I've figured out what the probes are, now I actually have to do the actual bubble-up calculation. It is a complicated business, I'm sorry, this should be a cap-signator. I got caught in the front problem here when I tried to get this stuff printed out. But anyway, the probe for level J is sigma sub J, which we just looked at. And so the probe J on level J is sigma J on level J, and that's a total sign of some things probing at that level.

52:30 The formula we're doing things then is that probe J is equal to the sum J is equal to one hat. And that's just this one hat in the calculation you see showing up on here. See, this is also the state of level J. You put a one in front as it were to get the probing effect. It's the one having that scalar there, so it's given to the probe. In fact, otherwise, we're just doing some sort of notation. So the hat means that when I show it down here, I choose I hat to make whatever scalar is in the probe go away, if I want just the state part. So it's just notation. And so, level K is equal to level going from J to K, which is the co-boundary operator from J to K of one-half times the probe of level K and level C. Now, that's the basic formula. Now, what we just do is we work backwards from four and you get this very complicated formula. All right? And then we plug in the actual values and turn the crank on this one. This is a hand calculation. I did it three times. I got the same answer all three times. So I believe it. And we have 16 possible terms in the algebra, each of which would be plus or minus. Okay? So what do you think we're going to get out of this? There's 3 to the 16th possible expressions that could be the answer, right? And so I want you to just make a little mental guess 42. This is what it looks like, okay? And we just turn the cramp on all this, right? See, and there was that, I think it should have been zero from level two, it seems to get squared, so it doesn't make it. And you gotta admit, it's a hairy calculation, okay? And so whatever pops out, if it's attractive, you can say, hmm, that's pretty improbable. Isn't that utterly amazing?

55:00 Out of 3 to the 16 possible answers, there's only two. One plus ABCD and one minus ABCD. So that's that saying is it bubbles up to plus or minus ABCD. measure what all the signs were of the original sensors, and you're going to probe that level. One thing one at a time, so if we had a level five, we're going to probe that one. So we get a score. And the point is, is that you can measure level one, all these details, but you get the same ultimate summary effect by probing the top. combine it. So this guy here, ABCD, is a totalized stand-in for all of the detail underneath. And if you think about this guy, he's got 16 phases paired off in plus and minus. So there's eight, So, you think of a four-sphere, all of that, and so it's going to take a slow time to rotate through the Earth. And that's why it's the fundamental. So, whereas the onesies are going like this like crazy, right? As soon as you're on the one, the next change is the opposite. Whereas this guy takes eight steps to get around, or 16 steps to get around. So that's why I say that's the fundamental. So, I am inclined to believe that this is a Fourier decomposition of the activity on the boundary. And I never did figure out the fast Fourier transform algorithm. It happened after I left school. You don't study that shit. You don't have to. But if somebody here knows how the FFT algorithm works, I would be very appreciative of them to give me a sketch and so on and so forth that it looks like this or not. You don't need the FFT, you just use the DFFT. Well, whatever. Which is, well, it's very simple. Anyway, I'll be interested in talking about that C. But anyway, my very strong intuition is that this is a Fourier decomposition of the hybrid

57:30 So that's the last one. So A, B, C, B, 1 plus A satisfies our squirt and idempotent criteria that separates the sense phase of the cycle from the react phase and choosing other combinations and other steps, choosing to leave some of the cost of the result in other less total, but still So, similar kind of decomposition type to the gate. So, recall that in order to be a square, one plus X, it must be the case that X, X is one, which makes X an eigenvector and the state represents an eigenstate of the system. And the importance of the eigenvector eigenstate concept is that it expresses a state of no energy expended itself. The thing interacts with itself and doesn't go anywhere. So that's the idea of an eigenstate. As you can imagine, these things are active. They're not dead data. These are processes. And the way to capture the fact that this process is stapled is that it has eigenstates. So these things are all eigenstates. And that's actually the definition of what we mean by the system is stable. And notice also that the probe string, P4 on P3 on P2 on P1, expresses that the Ivy states are nested within each other. All of which states are changing continually as the surrounding is changing. And expressing the current form of the hierarchy and mirroring the environment. It's natural to wonder what happens with more levels, say, five. To do this, we need another table like we just had with combinations of five-base sensors and the calculation grows exponentially and that's being kind. Before, there were 16 elements in the algebra and the largest level had six. I could, with help from Maxi's program, I've got an ugly language. Perl. Perl. Yeah. I knew it. The only language I've ever seen is uglier than C is Perl. Okay. But with 32 elements, some of those have over 200.

1:00:00 You know, I just can't get tested. But he is writing a new tool in Python. And hopefully, I can then really sort of exercise this calculation and find out if this stuff will hold. So, given the Fourier interpretation, I think there's every reason to believe that things will behave similarly as in their senses. That's what I had to say. What makes you think that this kind of structure could outperform neural networks, connection structures? Well, it depends a little bit by performance, but in neural networks, the learning is very slow. This, with co-exclusion, you only need to see each situation once, and that's it. And every time you present the same information, you get another level. So the rate of learning is logarithmically fast. Yeah, you can think of it from the argument point of view, too. These are the white. Yeah, these are the second controls. Yeah, correct. Exactly. If you get a misstructure. So they said that they should? They should. I mean, I think it's, you know, it's just not proof. Yeah. But I'm really quite sure. It's a question about neural networks. Let me finish that question. In the neural networks, learning is polynomial, whereas the learning here is logarithmic. And calling polynomials can be a kind of general, because it's very slow. And also, when it learns, you finally get it to do one thing, and then you have to teach it to do something else on top of that, then you disturb the first thing, whereas with this, they just slot in.

1:02:30 And then when the thing is running, most of the nodes aren't active because they're not valid at the current state. And so from the point of view, from a computational point of view, you have a zillion threads that are all running in parallel, but most of them are blocked most of the time. So actually the code runs very fast. I've run very stupid systems that have an order of 5,000 threads or so, and the response time is well under a hundred percent. Could you imagine it happening iteratively? Could you imagine it happening iteratively? Well, in a sense it is because the threads are being multi-programmed on a single CPU. but in principle, it has to run in parallel, because otherwise you don't get co-occurrence. You can't get co-occurrence sequential. The whole point of co-occurrence is that there's information in the universe that cannot be acquired sequentially. The downside of this is that the number of nodes grows exponentially, and that exponential growth factor is the reason, turning it around, that quantum computing is exponentially faster than ordinary. So to really do this in parallel, you need real parallel hardware, not simulations on a sequential PC. Well, I have a question. Running this on a sequential frequency, the response time is very good because most of the nodes are blocked most of the time because they're not active . Are you really sensing simultaneity? Well, yeah. Yeah, down to a resolution of Delta T. And that resolution really is only affected on the ground, that's the only place that makes a difference. How broad, how wide do we do the spread of co-occurrence, if that's the same sort of thing-wise? Time-wise? Well, what did you say? Yeah, well that's a good question. It has to do with how do you actually find, you know, the sensors. And that's all I know. The whole trick of this is not to put anything in by hand. You don't want to put any knowledge in by hand at all. So, the basic situation that you're in is you supply the program with a bunch of sensors and you start totally. And it's supposed to do the rest. And the question is, how do you, the chicken and egg problem is, you only want to look at the co-occurrences

1:05:00 are going to turn into co-excludents. And if a thousand censors have a thousand times 99 divided by 2, 999, that's a half million possible co-occurrences. Not all of them are going to turn into co-excludents. So how do you know ahead of time which ones to look at? And that, I want to take the time now to explain the algorithm, but you can actually do that linear time. That was my third pattern. And the basic idea is that you have a window into which you put any given flip of a sense of when it occurs. The time-based window. And the window has a few aged things as it goes into this window. And when they have been been there in delta T time, then they fall out the other way. So everything in the window is, has co-occurred to a resolution with delta T time. So you make it very, and this actually, I think, is the phase web's version of the insert, because if it's zero, then you're going to get infinite information. That's a little . some parts that I want to say a lot about Right. Well, see, I designed my own thread engine because I didn't want to be dependent on the bakeries of unique system. So, the structure system is you've got the thread engine which is designed to run tens of thousands of threads And I never deallocate to this. So you pay up front when you instantiate things. And everything's hooked up to the point, so this was linked to it. If this is self-formulizing, then I have a question, how do you keep semantics in? Semantics is as semantics does. The meaning is in the act. So it's not a separate semantic level, isn't it? No, that's not. That's the only thing. But I mean, you understand, you get this hierarchy and then you start doing co-occurrences across levels and across the circle.

1:07:30 You know, the co-exclusion idea is very general purpose. And you can co-exclude anything you have going on in the systems, you can do co-exclusion. That's what I want to tell you what's the good thing. Consciousness. Consciousness. Consciousness. Consciousness. I'm just... Well, that's great. You see, you think of semantics in the sense of consciousness, the idea of co-occurring. The idea of co-occurring is the thing that established concepts. So it could become a very autistic... So it could become a very autistic learning system, couldn't it? No. No, because it's not only dependent on the environment to have any meaning at all. It has no meaning without interacting. Thank you. Thank you. Let's go again, the fire is off. I see that as the, you know, exponentiation is like a song, you know, you can always break it down for any number of elements into something gone back into the same thing. I think the question of Dan's question though is that in this picture, syntax gives you your semantics, it just automatically generates. What I'm not quite sure is where this business of the cut between the system and the other. Has he got the holographic principle in here? Yeah, that's essentially what he's got. So that, I guess, is where the answer to the semantics comes from.

1:10:00 I'm sorry, I'm sorry, I'm not familiar. You say it's very simple, it's in the, you gave reference to a letter when she goes on. Sorry. Oh, I am sorry. I'm giving you all that a little bit. Oh, the first, the second, and the third one. If there ever would be a bigger one, that's better. Yeah. Yeah. Is equal to the anycron, minus infinity, by E, T, F, D, T, yeah. I, T, I, Omega, T, and F, T. Yeah. Okay. These form of pair because I can do the same. Yeah, right Well, you can approximate this, you can approximate the function as a Fourier series, and then trouble. And that's always true in practice, as long as you have a finite time, and you're doing the measurement. And, I mean, the number of degrees of freedom is finite, as long as the bandwidth is finite, Mm-hmm. And the time isn't our time. That's true. Right. It's okay to use, well, what you do anyways, instead of using this continuous operator for the exponential. The I-M-A-T, yeah. Yeah, you actually use these guys which are the screen operators that go around the loop like this. Right. Yeah, these. You can also exponentiate. Yeah. By the ordinary method. of an operator is defined by Taylor Swift, but because the operators have this cyclic property, in fact they end up in each one individually, you end up getting an expression. So exponentiation, instead of getting it out of the field, brings you back into it. Right, okay, now I see what's going on. Right, yes. Oh, this is a very interesting idea. even though the field of things you're talking about is actually, are actually, you know, sequences of one from zero.

1:12:30 Yeah, yeah, yeah, I see. This is where the boards and loops come in. Because you just say exponentiation, because it's what brings you back into the field. There's a very unique idea here, which is because, yeah, okay. I see some very interesting connections here with ideas in, to do with, yeah. But you can imagine doing the FFT where instead of just eating a complex number, you can use a quaternium. And that's very much the form of k dot x minus omega t, which is more of spacetime. Right, so we're getting... And you can do this discreetly. You can do the same kind of discreetly. So this, as it were, really would be your program universe with... Yeah, yeah, right. This is a little bit like what Finkelstein was trying to do long ago with his Quaternion program universe.