Physical understanding & combinatorial hierarchy (partial) / Louis Kauffman: Conceptions non-associative categories (partial)

0:00 Which you could think of as sort of classical paths happening in the graph, or you take the front door over here, over here, and it becomes a quantum theory related to the graph. But it might be just stochastic processes happening in the graph. It doesn't have to be quantum theory. So you get this kind of flexibility of context when you're thinking about shifting from one diagram from one skeletal structure to another, putting bones on the structure, putting flesh on the bones, excuse me. Well, the knot theory has its own natural diagrams, crossings over and crossings under threads like this. And now this is not an obvious move, but I show it to you. You can extend some situation where you're calculating things that are topologically invariant for knots to things that are topologically invariant for graphs. And it's natural to talk about a difference like this. The difference between crossing one way and crossing the other way is represented by a graphical node. So you have an embedded graph. Now this is kind of like a commutation relation. a over b minus b over a is equal to something which is held by the graph and we want things to be topologically invariant with respect to the graphs so the key move about topological invariance with respect to the graphs would be a loop going under a bit of graph crossing could be pulled out and then it could be slid over the top okay? Okay, so there's a topological transformation that should be allowed in this situation. The point is that its consequence is something very much like the algebra structure, and I'll show you why. You see, I can write an equation. Remember, crossing under minus crossing over is node, right? So I put it in the context of this. Now, that resulted in causing this undercrossing to pop up, right? Now, I could write another equation where I pop this one up successfully, right? This one minus the up top one, and then you would have a crossing here, and you would have a node over there. You get one extra node on the right in each of these equations going around the plot lines. Four equations. Each one starts with the end of the other equation, add them up you get this one minus completely over completely over is the

2:30 same as completely under so it's zero on the left the equations will add up to zero on the left on the right you'll be going through neighbors this neighboring that this neighboring that this neighboring that and this neighboring that so i want to see what the pattern of of the sum on the right equal to zero is going to be. Now, to do that, I re-diagram the neighboring, the node, like this. So I just pull those two edges apart and put a red line between them to indicate that they touch. It's easier to see the pattern this way. For example, I take this graph and I pull it apart into one long circle and I meet one twice. One, then I get to two, then I get to three, then I get to one, then I get to two, then I get to three. And the pattern of the nodes is these two touch, these two touch, and those two touch. So I just pull it apart that way. And then these two are neighbors and these two are switched neighbors. Now, switched neighbors, you see? Let's go back to the original situation. Neighbors, and then if this node ended up here, switched neighbors. Neighbors, switched neighbors. So I get, the pattern of it is that you have a pair of neighbors, then you have switched neighbors, then you have another pair of neighbors, and another pair of switched neighbors. Of course you have to do a little fiddling of your own to see the jump I made, but then the thing that ends up summing to zero is this, in this form of a language, where I'm going from one diagram to another or the one that looks the best. And this looks the best for the following reason. It's sitting inside here is the two parallel lines minus the two crossed parallel lines. That was the bit of formalism for the Jacobi identity. So if we insert the Jacobi identity in the middle of that, we find out that Lie algebra implies that relation. C. Parallel minus crossed is node. That's a Jacobi identity. Then I'm assuming that

5:00 things are symmetrical with respect to cyclic permutation here. That's the same as saying that the structure constants of the Lie algebra are invariant in the cyclic permutation or inserting some other thing into the group. You don't want to worry about it. I just push the node over here and I see it's three node again and I pull it back apart using the Jacobi identity again, and we have the relationship. So that relationship is a direct translation of the topology, and it shows you that Jacobi identity is sitting there just underneath the surface of an object theory. So you started out with something that looked like a topological commutator, A over B minus B over A equals this whole. And you ended up actually getting the pattern of the Jacobi identity, and so getting the fact that the the algebras are actually related to things about knots. There's more to fill in to get the whole story, but it turns out that you really can do this, that if you have a Lie algebra, you can create knot invariants out of it by following this line. And it's very mysterious to me what actually is happening here, that somehow the Jacobi identity really just means that you can pull a loop out and push it back over onto the top in some way, but there's something there's something that we I mean you know people use it's a bit of technology lots of people in Mount Theory use but exactly what it really means about the nature of the algebras and the nature of commutators is not yet understood so that's a favorite of mine the point that I want to make here is that maybe I'm actually trying to sell a more informal generalization than conceptions. Because what actually happens in practice is that you keep shifting contexts in the way that is most useful to you. And you can do this and keep your mathematics making sense all the while if you're careful. and these things that we write as diagrams are actually just going up to categories that are rather arid that you can pivot from to going to another context like we did with the graph over there

7:30 so it isn't even so much the wonderful visual qualities of diagrams as these shifts of context which sometimes let us go all the way into something and then coming back into something that has more structure. So, like when you're trying to work with the combinatorial hierarchy, you're always conscious of the fact that you would like to put more flesh on the bones and see it happen and see it related to the physics, but it's more like the abstract graphs. And yet, on the other hand, it has its own concept associated with it. And you want to go from there. So you're trying to tell the stories in different directions, and so it's interesting. I think I'm almost out of time, but I wanted to show you a sequence, what? 10 minutes. 10 minutes, okay. So fine, I'll show you another example of non-associativity. This is one that we almost mentioned earlier today. Here's a little alternative discrimination system is equal to r, a squared is equal to a in this system. But a, but r times b is, anything times anything is equal to the third thing in this round of three. And if you're thinking in terms of colors, it means that if you take two colors and put them together, you get a third color. But if you take a color and put it together with itself, you get the color. And the putting together I'm illustrating here by using a knot diagram and green put together with blue gives you red. Red put together with green gives you blue and so on like that. The composition is that way. And then if you use this as a rule for coloring the diagram, the rule is three or one because of this system. And you watch what happens as you push the diagram around topologically. So I pushed red up until it met green and pushed it underneath a little bit and it turned blue. underneath a little bit and it turned green. Then I pushed the green underneath green and it stayed green. And then I pushed the green underneath blue and it turned red and it went back to there. Okay, and then I did something which is a little harder to watch. And maybe I even did it one way. I took this line which goes underneath green and red and I slid it this way so that went underneath blue and green.

10:00 See, it used to be here, from green underneath to here. underneath over here and I had to check whether the colors were working right but they are you see they went blue to red to green to green and that's okay but now it goes from blue through green to red and then from red through blue to green and the little arc in the middle turned red instead of being green because because the fact that blue hit green rather than blue hit red so So you have to check that in all the few cases that this happens, that it always does that correctly. That you only need a little local change. But a topologist on finally seeing that it does this would rejoice because he would then see that no matter how you wiggle this version of the truffle or not, it would always be colorable with three colors. And we just proved the three-color theorem for Truffle-O-NOT. Any version of the Truffle-O-NOT can be colored with three different colors upon it by doing this operation. If I give you some immensely complicated version of the Truffle-O-NOT, you might find it a little difficult to color it, but if you simply topologically slowly transformed it all the way back to the original three-color Truffle-O-NOT and then pushed the colors in going this way, you would get your coloring. So it's a coloring algorithm. If only there were such a coloring algorithm like that for maps and playing four colors, but I don't know why it's like that. This implies that the truffle knot is not knotted. That's why the topologist is rejoicing because if it were unknotted, then you could make a transformation like this and get rid of all the colors and end up on one color. But that can't be done. Every single one of these has still got three colors in it. So there's discrimination systems like that, and there are different ones depending on what not you take, but this one, but there are many nots for which this one works. The general pattern is like this. Again, non-associative product and associated diagram categories. A and B enters the product. And if you want it to be topologically good, then you need AA equals A in order to untwist that.

12:30 need ABB is equal to A, and you need, interestingly enough, self-distributivity for the third one. It's an easy calculation, and since we're near the end, I won't do it, but if you just check, if you want to shift that line down, if you want it to be compatible with the little triangle movement that I made before, then you need that the system is self-distributed, and indeed that system on the other page is self-distributed. And then, of course, you different the two compositions look. A times B and M times C looks like this, but A times BC looks like that. They're topologically not all the same. The topology is naturally not associated in this sense. And so there's lots of conceptions associated with this situation. And then And then, it's sort of curious to compare these two situations. Now I'm just making worries or wonderings that a topologist makes. You see, at this level, it's self-distributed. About underneath the surface, there is the Jacobi relation happening, the way I told you about it, right? and when you look at this self-distributivity you think well it's sort of like the Jacobi relation gone and compressed as though the operation happened in both places at once but I don't know what that means exactly sharing it with you because these things up at this level are rather natural discrimination systems nobody says they're related to the algebras but somehow there are Lee algebras lurking underneath. And I think there are Lee algebras lurking underneath the appropriate discrimination systems. So that's a speculation about discrimination systems, whether they're the ones where A squared equals 1 or the ones where A squared equals A. There's something going on here that isn't resolved in this situation that I like and probably isn't resolved in our situation either. So one more comment, simple example. Suppose that you take a square and you divide it,

15:00 or you divide it the other way. These two are different. They together form tetrahedron. The difference between these two is non-associativity. It's A, B, C, and then you have B, C here. I could put arrows, but it's probably better about arrows. And then here's A, B, C. And here's A, B, C. And then C. So of course these are not the same geometrically, but if you had a triangulated surface then you wouldn't have changed the topology of the surface you just re-triangulated it so from the point of view of topology they're equal but of course equal just means equivalent or transformable and you really want to think about transforming one way of doing it to the other way of doing it there's homeomorphism from one surface to the other the transformability is taken up in the higher dimensional picture The transform from this to that is actually the tetrahedron itself. So another move that people use to handle things like non-associativity is to keep categories, but to talk about higher categories where there are transformations between one kind of thing and another kind of thing, and they correspond to higher dimensional geometry. And then there's a lot of different kinds of algebra that comes out of matching higher-dimensional geometry to the kinds of transformations that you want. That's analogous to the fact that while you may not be able to untangle a knot in a lower dimension, you can usually untangle it in a higher dimension. Yeah, that's not unrelated. Right, right. I don't want to go into it, but surely it's not unrelated. If we went back to physics, Instead of having a product, you often have a multiplicity of outcomes. Two particles interact and there's a multiplicity of outcomes. If there's a multiplicity of outcomes, then you consider a multiplicity of interactions in some specific pattern. A interacts with B, then interacts with C, then interacts with B, like that.

17:30 Then you get a whole string of different possible things that can happen here. there's a bunch of things happening here and then for each of those you've got a bunch of things happening here so you could make a list of all the different processes that happen down the line each one could be thought of as a vector in the space of all possible processes and you get a vector space now suppose that you choose a different form of process but the same inputs and the same desired output vector space. And then you may want, it may turn out that the spaces are isomorphic as it does, say, in elementary angular momentum exchanges. And so you want to have, you want to catalog the isomorphisms between one and the other. Well, you see, from the point of view of this being one way of associating and this another and these transformations, then you're handling the non-associativity by running transformations from one form of associativity to the other form of associativity. And that's the pattern of recoupling transformations in angular momentum theory and that sort of thing. So there's just lots and lots of non-associativity floating around. And the message of this talk is that from a point of view of categories, non-associativity is okay. Why not make categories that are non-associative and give yourself the opportunity of composing things in that way and using the language. Now, given that you're given such permission, there's a big project which is to take all the different concepts in category theory and see how they work in this non-associative way. We've barely started such a project. Does anyone want to ask some questions? I have a comment plus a funny story. Okay. The comment is simply, thank you for relating your thought right at the beginning there to mine in such a clear way. I'm sorry? You talked about homology groups and things at the beginning there.

20:00 in which you related this to what I was talking about earlier on. Oh, yeah, yeah, I mean, it's short. A funny story, I think it's worth doing, but I'll have to draw something on the board for a minute. You don't want to do it, it's not this way. I was reminded when he was talking about grades, of... Keith, what do you tell me? What's the matter? So this is a braid, but it's also something that both fixes a subset, and unfixes its complement. And, well, at the point in time I was thinking, I'm going to go back to my talk, got related to this, At this point in time I was thinking about these things, I was having an ongoing dialogue with Louis Gidney by telephone. Now, Louis Gidney is a very intuitive man. Talking about these things on the telephone with anybody is sometimes difficult. with Louis there were some curious problems that came up I described to Louis that what I wanted was a braid an automorphism that took things in the DC subsets map them back to themselves and I called this a fixer, I think this relates to John Amson I think originally chose this language and the automorphism has got to take things which is which are not in the DC subset, and produce something different. Well, I'll use the same notation, but this means X is not in the DC subset, and this means that this object is something other than X. Well, I seem to be able to communicate with him about fixers, but communicating with him about unfixers produced some very strange problems of semantics. and eventually we understood what the problem was and I told Clive the story and I've never heard Clive laugh quite so much on the telephone so I'll tell you what the problem was and then I'll show you how I feel that we ought to preserve it for posterity well, Louis understood a fixer as being a

22:30 which with the way he thinks intuitively was just so wonderful and so he couldn't then translate it as being an unfixer so just to preserve this funny story of posterity, in the paper I've stelt fixer like this but actually for a long time we've wanted a word for something that was both a fixer on the subgroup and an unfixer on the complement so I think from now on we'll use this something that's better so that's the story on the stage of telling funny stories I should say when you mention J.H.C. Whitehead my memory of him a fairly rotund man was that he was a person and there aren't many of them who could at a dinner take off his waistcoat without removing his jacket he said It's possible, but when you're of the shape of whitehead, it's an achievement. Was he a bit spherical? Yeah, a bit spherical. Sabine, didn't he put on his swimming trunks without removing his trousers? Oh, yeah, same idea. It's the same pathological problem. I think you have to have been by quite a lot. Oh, he was permanently in that space. That is true for us, yes. And that's a much more subtle thing than having a correct objective representation. It's a knowledge that we actually have to live with and live through is much more complicated it's highly reflexive and highly paradoxical

25:00 well two and a half thousand years later where where do we stand you know if you just look at the kind of books about that answer the question who are we um i'll put aside the religious ones we've had somebody kind of avoid them once this morning and so that there are two there are two sorts of ways in which we talk about ourselves one is the everyday way of we are people and we have intentions and opinions and we have values and experiences and all of this kind of stuff and responsibilities. In other words, all normal everyday way of talking about people and ourselves, which is how we reflect on ourselves most of the time. And then there is the other version that comes out in pop science books that tell us who we are, which But, well, we're brains and we're DNA and all these kind of objective analytical sorts of accounts coming down to atoms in the void. And they are completely contradictory, two completely different ways of talking, you know, further apart than waves and particles. And this doesn't bother us at all. We manage perfectly well, you know, and we're quite happy to suddenly start talking about, like, washing up, and the next minute we're talking about brain chemistry, and now, you know, my serotonin levels are taking this morning, or something of the sort. It's really no problem to us. How is this possible? I mean, they ought to be, they ought to be possible, but it is, and that tells us a lot about ourselves as well. How do people, in fact, how do philosophers deal with it? Well, the traditional way is to say, oh, well, it's to do with mind and matter, it's to do with consciousness on one hand, which people take for granted every day, and physics on the other hand, which is, you know, the real stuff, the stuff that they're made of.

27:30 And these are two different, in some sense, completely two different worlds, mind and matter. Nobody, and we have not, we still haven't solved the problem of how they are related to mind. And it's an old, old problem, matter and consciousness. It's called the hard problem in these days. That's one way. That's, in a way, the kind of answer that the scientists would tend to give Neil Lappel. The scientist, or, I mean, that's if you're lucky, otherwise you'll say, all that everyday stuff is just what for, you know, and that's just, like, practical stuff, it would have to keep going. It's likely, it's all a myth, you know, and we get an awful lot of popular books explaining how there is no such thing as self and there's no such thing as values and this, that and the other. Anti-humanist tracts of various kinds come from a scientific point of view. Okay, the other way of treating this great gulf between the two ways of talking is from the people who take the more humanistic side and say, well, they're just two ways of talking. Actually, there are 10,000 ways of talking, and there are all sorts of gradations in between, and life is extremely complicated, and you can't actually reconcile all the different scientific ways of talking. They're all dealing on, they're all operating on different levels, and they're all talking about different things, and it's not two world pictures at all. It's an unlimited number. There's no real objective science. There's no more. It's all a bit relative. There are no foundations. These are the anti-foundationalists who we heard referred to earlier. and some of them will go further and start explaining why it is that anybody should ever think anything different from this and they say that trouble with these scientists is that they're obsessed with representing the world and they have to have it that on one hand there are the

30:00 representations, on the other hand, that are the things represented. And they also take it for granted that their knowledge and their minds and their truth are basically involved in the process of representation. And because by the logic, the very logic of the concept, the represented and the representing are separate, so the mind is separate from the material world that it describes and knows about. There's a kind of, this they call Western metaphysics, and it's, it comes in all sorts of varieties. You know, there's the dualistic form, and there's the materialistic form that drops the subjective side, and there's the subjective idealism that drops the objective side. They all have the basic, the same basic sort of underlying presuppositions. They're of representations and misdominated philosophy the whole time, you know, from, no, that's not true. The Greeks, it was clearly the main picture, Greek skepticism, they started off with the idea of Parmenides' appearance and reality, they're different, clearly, you only I'm sure I would like to know that. Therefore, mind is separate. And this, once you start on the idea of appearance and reality, you're off on the whole epistemological trip that divides the world into it. But there was Aristotle. Now he didn't take this view. This is, and he told me that it's impossible. for the next thousand years or more so actually you know it's quite untrue to say that western metaphysics has always been like that but since since daytime modern times it's been like that and the rest is generally written off as the dark ages when they were there was a lot of very clever and stuff there was a lot of very clever men in those days who had an understanding in many ways better than a lot of folk we see today. I'm getting a bit distracted here. Yes, that

32:30 is one way in which the humanistic people will address the scientific people. They'll say, you're just all up in Western metaphysics if you want. You have to get back to being and a few things like that and forget stop the drop this platonic idea that there is a world behind the world that um we are uh what was it the prisoners in the cave who bronnie probably doesn't know that there were um one of his his myth was that there were uh imagine these guys locked up in a cave and all they can see is shadows projected on the wall of people who walk past the cave there's some system of fires now that's all they know about the world that's how it is with us all we see is shadows projected on our retinence you know the real world is beyond us and it's and we can never ever know it you know and it's not just it's well okay we can He worked it out. It's full of things called forms, ideal forms, and lots of this kind of image, this appearance and reality, it goes with representationalism, and it's the dominant philosophy of the physicists, of course, and the mathematicians. is that they're looking for the underlying forms behind the superficial reality that meets our unreliable senses. It goes with being a scientist. You have to separate yourself from the object you're describing, the description, and the described have to be potentially independent of one another. It's as important you should be able to say things incorrectly and then you shouldn't be able to describe they can't be correct a statement can't be correct if it can't be incorrect we're not talking about kind of imprints we're talking about proper representations

35:00 right however If you follow this anti-foundationalist point of view, forget I've ranted too long about the metaphysics of representation, because actually it's pushed much too far. I believe in representation. I think it's actually the key to understanding the human mind all along. it's very easy to to get upset about the people who make it give it this metaphysical meaning and divide the world a whole world into two and divide the mind against the body and all the rest of it but don't for goodness sake throw out representation itself which is what a lot of these anti-foundationalists supposed Kuhnians pragmatists, hermoneuticists, post-modernists, deconstructionists, a whole, you know, a whole zoo of these people who want to terribly to bits because, you know, they don't like dualism. And fair enough, I can see why they don't like it. I don't like it. But if you go too far, you're left with a complete waste of relativism in which nothing makes any sense at all. and I don't know if I need to spend too much time on that because it's kind of obvious, there has to, you have to, if there is no such thing as truth, only consensus, if it's only just a matter of like getting a few people to agree with you, and that's all you can ever expect to do as well, then we're certainly wasting our time here. So, we had an initial split between everyday life, humanistic language, scientific language that seems to take all the meaning out of things, because it's all just reduced to mechanism and cause the laws and, you know, none of the human stuff that we actually live by, all the things that are.

37:30 And on the other hand, we have those two ways of looking at it. We have two different accounts of what accounts for this split. One, dualistic. The other, more holistic. and if you push either of those two to its extreme you get kind of meaningless Dawkins type productionism on one hand if you push the science too far it really just comes all men and goes out of it if you push the deconstruction too far again there's no knowledge either so obviously the task is to find some way of having it both ways most philosophers are our result there have been plenty of philosophers who have said like what makes it quite clear that this is the principal class of philosophy in modern times as a tried and bridged this unfortunately he invented the hard problem and didn't get any further than that we have to do much better than that yes a synthesis a new high level all that kind of thing and that's what I've always been trying to do I mean this gulf struck me most clearly in about 1970 or something like that in which and I tried to describe it underlying root a bit. It's changing to do with representation. And I, I mean, we hear the same sort of thing. He was talking about listening, and I said that there are underlying these two perspectives, two kind of basic attitudes. The attitude of somebody who was trying to describe the world single-mindedly and get it right and the attitude of somebody who is listening to somebody else talk and in one case you're as it were dealing with things and the other and this description of things

40:00 dealing with trying to understand people and these are completely different opposite poles of the human mind that we actually use our brains in a completely different way when we do these two things looking out at the environment trying to work out what's in it trying to master it trying to survive in it is one thing understanding other people learning to become cultural beings learning to participate etc etc this is absolute this pole we've seen in philosophy must have a deep evolutionary biological basis because we're cultural creatures. You know, we are the chief. There are two things that you have to do to survive. One, acquire your culture as quickly as you can because you've had it on your own. And the other is, of course, deal with the hazards of nature. And they're actually, they're quite different sorts of tasks because people, understanding a person who is someone yourself is a completely different sort of thing from understanding some object that you that you come across or pick up and figure out what you can do with or what it might do to you or whatever so it's not like understanding and we are hardwired to treat these two problems in completely different ways so anybody who builds up a metaphysics on the basis of the whole world view on the basis of one of these two angles, it's clear again to get into, it's not at all surprising that they end up with the kind of nihilistic dids that they do in fact arrive with, you know, and that this is effectively what we see. So, how do you bring them together? Well... A question, if I may, short one. Those two, we are listening and describing, you say Is it different that we use different areas of the mind? I am saying we are using simply different categories, or are we using different moods of knowing? No, no, we are actually thinking, in the way I see it, is a physical activity, like you orienting on the world and shouting and doing this.

42:30 there's there's there's a brain up here we deal with actions and the most the further you get right at the front are kind of really long-term plans of sort of as you move back you get to shorter I mean you know little twitches and detailed movements 10 feet you do here there's sort of this part kind of plays and then you get the output action signals going down to the body moving it. OK, that's the back of the brain, this is simplified, of course, perception. You get perception, but they are very clearly separated. Here, there'll be sensory motor perceptions of the body, and, you know, ears will be here, and eyes will be here. The more instantaneous, the more instantaneous perception is further at the back, the more kind of sequential perception is further forward. It's just that one kind of philosophy, one kind of... Understanding other people is a bit like that. Understanding the objective world, the world that's around you, is a bit like that. How is it understanding oneself? Ah, certainly. In addition, there's the hypothalamus, which is the brain's stem. The hypothalamus? The hypothalamus and the hippocampus. And there's all sorts of stuff. Yeah, but this is the most primitive part of the brain. That's true. reactions to all this experience, whether it's of people or of the outside world, centers. What they found is, this is Damasio's work in particular, who's a brain surgeon, that if that is damaged, then you cannot behave rationally with the forebrain. That is true. That is, you have to be really centered in your emotional being, you have to have that framework in order to think rationally. Yeah. And I wouldn't actually put Damasio's account, I don't know, I don't like Damasio's account

45:00 for this one simple reason that applies to almost everybody who writes about this kind stuff, is that they, what they fail to, they commit what is called the meriological fallacy, meriological fallacy, in which they treat, they treat properties of the whole, they attribute properties of the whole to the part, and in this sense, they say that the brain does this and the brain does that, and the brain thinks, and the brain, it's not, it's people that think, it's We think we are responsible, we are social human beings and we use our brains. Our brains are the method by which we do what we do as people. And almost to a man, the guys who write popular scientific works about this, over and over again commit simple philosophical blunder of attributing to the brain things that are in fact done. And therefore their attempts at explanation and their attempts at description just end up being essentially muddled and nonsensical because they haven't understood just like the basic parameters of this problem. What it is we're trying to explain, you know, just to merely say that they've replaced the old talk about the mind with talk about the brain instead. And they've somehow separated it without it being explicit. They somehow, they think, oh, we'll explain what the person does by explaining something that the brain does. In fact, no, it's the person does it, and the brain is how they do it, and the brain makes it possible. The brain doesn't cause them to do it, it's the brain is what they use in order to do it, and they do it out in the world with the rest of us. It's a serious mess, actually. I wish I could write a book to prove it. And it's not just the brain as well, I mean, it's the whole central nervous system, I mean, the heart and the GI tract all have huge numbers of neurons, and there's a lot of research and evidence now to show that a lot of the ways that we act and respond in the world are to do with the mind of the body.

47:30 we have enormous reserves of tacit knowledge we have all the sublimated experiences to do what we do no question this doesn't alter what I said in terms of the basic perspective and being able to recognise just what you are capable of the self-knowledge that can draw on one's disabilities okay yes so so that is that's that is basically the story and then up to that point now since then what have I tried what has been my intent and moving on from this contradiction between two attitudes and so on, how to talk sense about these things. Well, you've heard various versions in earlier and parts a couple of years ago. I was talking about the heart problem and I'm trying to explain how it is I describe human sapience in a certain sort of way. What it is, the kind of self-reflective activity that we are capable of, and how our understanding of other people and our understanding of language allows us to reflect in a certain way, and how any creature that can reflect in that way will be able to, if it wants, experience something like the heart problem under certain conditions it can get confused about the relationship between mind and brain it has the capacity to do that we shouldn't be surprised that we can have this experience it's part of the territory and quite difficult to argue your way out of but not impossible I've described human sapiens and how it works

50:00 how even of trying to make the narrative out of it, how it starts with... It just occurred to me, actually, that what Project Universe and Anpar's work at trying to construct the universe from first principles in a series of logical steps, I have, perhaps unwittingly, been led to do a similar thing with human sanctuaries, and I start with the idea of evolving organisms and showing how it is intrinsic to life that they have internal representation, in fact, the DNA. In order for any system to be self-reproductive, it has to contain an internal representation. Von Neumann showed this, that the DNA protein code is like a form of representation which is present in all living things. And not only that, it has to be present in all self-reproductive systems. and we can the logical pattern is quite simple I won't try and draw it up again but it's basically I say reproduction equals replication plus representation and there's a little tight closed loop that is and it's the same you see the same pattern in for example the language of bees or the use of various in human culture and you see the same pattern and then I go on like taking this little model of representation as given I go on and show how language could come how people through their ability to imitate and have that our imagination can become representational. Anyway, I'm not, I guess most, I'll just try and remind you that it's not something I want to go through all again because I've done that one. What I've been doing recently in the last year is a quite different problem, which I think is quite interesting.

52:30 I've still got time which was having more than 20 minutes yeah yeah I've got plenty of time it's good this is the alien abduction bit I want to try and having defined sapience as it were in terms of a narrative and having given the kind of representation I want to ask the question, how, what is sapiens in a long, considered in a non-anthropocentric sense? Because the story that I gave about sapiens depend on various things that are distinctively human. In other words, our ability to imitate and understand one another. Now, I think it's a more general idea than that, and that we need to have a more general account of it. partly in relation to artificial intelligence, perhaps, and the question of, or often the sort of questions that arise, independently of this piece of speculative biology that I give for how we manage to become self-reflective. So I've been performing this kind of thought experiment. How would it be if we could zap around the universe of different species. We would have the problem of deciding, this is a kind of Turing test, we would have the problem of trying to decide which species were sapient like us, and which were doing various other things that might look like it, including perhaps being technological, but were in fact not sapient and self-conscious in the sense that we are. How would you do this? And I, so I imagine these people who are called exo-ethologists, the Institute of Exo-ethology is called in when a new species turns up and they have to do this job. What would they actually do in order to decide whether these species were allowed to join the sapient league? Of course, it would go without saying that they have to be able to speak.

55:00 No, they have a lot to speak, they have to have a language, they have to, there's really, we can't cope with people, however clever, if they can't, if they haven't got a language, so they're out for a start, they don't have a sapient. then we find we look at the ones that can speak in some way now we already know that very simple automatic systems like bees can speak after a fashion they can describe the location and quality of a source of nectar and tell the others now this is there's no way they're going to be sapient even if they were very complex beads that could describe, that could send out messages relating to all sorts of different resources and hazards, and all sorts of different locations, not just simple bearings and distances, the way beads do, but you know, like they actually depict a three-dimensional space with their language. They just send out these little messages in a generally bee-like way. Now again, these are just simple Turing machines. They pick up information about the location of the resource, they process it, and they split it out as a little message. And somebody else picks up the message, processes it, and goes and gets some too. They could be very good at this, but the whole thing needs to be completely automatic. There will be no real distinction between descriptions and commands, for example. They might even do quite a fair piece of syntax on this. The exothologists looking at them could regard a piece of B as having knowledge. that one knows where such and such a resource is. We could say that piece of message has such and such a meaning. It corresponds to that place. It has semantics. They could combine little bits of information and process them. They would have bad syntax. But that would all be from the point of view of the outside observer. They themselves would be entirely automatic machines doing all this, the apparent syntax and semantics and knowledge, to then it would just be an automatic process.

57:30 So, and this is something that artificial intelligence people have come across, you know, how can we ever make the jump to it? What I say, actually, is the answer is surprisingly simple. If they behave in this way, if they live in their way, then information itself becomes a resource. And they have to start, it's no good just having know-how about first-level resources, you have to have know-how about second-level resources to it, information. You have to be able to know who's got good, what are good sources of information, who are reliable informants, what kind of information is reliable and what isn't. you are already speaking it's only natural that you should go on and evolve the ability to talk about language as well as talking about the environment in other words they're gonna move up and how does this happen well the key to me the key stage has to be when they start to ask questions it's all very well to and spit it out and respond to it but in order for information in order for the exo-mathologists to know that information is being treated as a resource in itself you have to see them asking questions and this i call i give that they will call this sissiness a new word a kind of a kind of consciousness or a kind of cognitive function uh that involves asking questions Sisticians, yes, there's a great word called, sistication, sistication is an old word for questioning, and sisticians is a new word, sistic, I mean it's the side of science, but it's repeated, it's got a built-in meta-level. which is like questions do. Questions are intrinsically meta-level communication. So, you don't have to think.

1:00:00 Yes. It's a lovely word. I'm surprised it doesn't exist. Just a quick question, just so I can have the context right. Do you feel that sapience is a digital or analog in the sense that it's something that's either on, off, or are there shades of gray? I don't know about that. I haven't thought about that. I mean, I think that sapience depends on having, should we just, I think we'll count that, sapience in us, which is the only part we know first, is that we can, we have two systems of representation. one we have a sort of sensory motor system representation which is like imagination which is like um offline simulation of of of action and perception um offline simulation lots of animals have that we in us it is actually representational because we have this hardwired ability to understand other people so that we can actually when we have the imagination of an act being performed we can both experience it from within and imagine it from without simultaneously we can flip back between the two and this ability to have it in two forms is what makes it representation in the kind of sense that I give we have that Then we also have a symbolic system, language, which represents in a quite different way. And the two systems of representation interact with one another and produce a whole lot of complex structure, including objective knowledge outside and subjective representational systems inside and the possibility of a self and all kinds of stuff. But then, I mean, I would say all life has a certain potentiality to ask questions. The simplest bacteria can ask its environment if there's food there and if there isn't food there it will set off in search of food. What we seem to have is the ability to ask ourselves questions

1:02:30 and we perhaps have only acquired, the human race may have only really acquired that to any control degree from the time of the Greeks I remember a book that Pierre once acquainted us to you know what was it I can't even remember quite what the book was. The Origin of Consciousness and the... The bicameral mind. The bicameral mind. And the bicameral mind. I thought that was always different, that's all. Let's have mine for now. To get back to the exo-ethologists, I was just like... I have this internal account of how I think our ability to self-reflect comes about, but that is strictly in terms of the narrative of human evolution. I'm now trying to give an objective account of how you would spot it in other species. Now, a point that I haven't mentioned is, of course, that the exoethologists can't understand the language of the people that they're talking to, and they don't need to understand it in order to do this. because we can interpret the language of bees it's quite simple but if we can determine that they are delivering messages they are consistently following patterns when they get a particular message then we can we can see the pragmatic effects of their ability to communicate without actually knowing the details of how they do it and that's very important because It's a very hard thing to do to learn a language, Wittgenstein says, if a lion could speak, we couldn't understand him, you know, we can only expect to understand human language. I don't think this is still, they might, once they have determined that a species were factored and given enough time, I think they could get into communication, but, you know, it would be a long and very difficult process. but you can do other things you can test they're cooperative creatures so you can set them up in situations where they have to solve problems and test their ability to communicate with one another

1:05:00 in various different situations whether they can ask for information which they haven't been given which another one has is primary they can ask where things are where things are then they are or then they are treated if they're sufficient then they're treating information on a meta level and everything the whole picture has changed the thing you would ask the thing you would now start the next series of tests would be where you introduced new objects into the situation you've got various groups using them and you will then introduce new naive aliens who would then have to ask the first lot what they were up to and they would have to arrange it so that they had to ask the equivalent of what we have in England in human language of what questions and which questions you know you give them a piece of language and you'd have to you know they would have to ask the others what this piece of language referred to or you would give them an object which had no language and they would have to ask the others what piece of language corresponded to that object you know this is like what what and which questions do which questions tend to sort of narrow down to specifics what questions tend to go out to to into abstraction they form a nice little couple actually if they if you could see had this couple then you would say ah they have semantics or rather um maybe they had it before but now they have it self-reflectively now it's it's real semantics because they they actually they have as it were a practical knowledge of what it is for a statement to have a meaning they care about meaning they regard meaning as one as a resource that they're actually out there It's as real to them as punny or whatever. Meaning is something that they seek out and therefore you can say that they are semantic creatures. They look for meaning explicitly as a goal. Yeah? Do you relate somehow meaning and self-referentiality? Are they sort of similar concepts in some respect?

1:07:30 Well, at the moment, I'm just taking the very limited sense of meaning as the way in which a piece of symbolism refers to a reality, just on this very simple operational account of semantics. when they start checking out which sentences are true or not then you say they are epistemic creatures they regard, they are concerned, actively concerned through their behaviour in whether something is true or false and whether something and who knows things and who doesn't and whether they're accurate, in other words like knowledge and truth have now become objects for them, objects towards which you can show that their behavior is directed towards seeking knowledge and truth, because they are asking questions about language, and that's what knowledge and truth. The language, the epistemic language, all the stuff that philosophers get so heated over, it's really about checking out the value of different sorts of statement and of course when you do that we were using a meta-language the language about language and if you're using a meta-language your meta-language and your language are the same language you can get terribly confused. And people do. It's really, you know, from an ethological perspective, it's not nearly as complicated as it often seems to be thought. But you have to get, you have to stand well back to see, you know, there's a lot of these problems about knowledge and truth, meaning, are really problems about communication and what you can say to people and how you manage the way you communicate with people. You don't need to worry about anything that goes on inside the head. It's all just about what can be operationally defined in terms of practical, pragmatic relations. But we haven't finished. They're not yet sapient.

1:10:00 We've got to find one. Quickly, they're not yet sapient. And it would be quite easy to imagine them actually having epistemic language and having semantic language and still being essentially mechanical, or so I believe. I won't go into the details of that. when they start off they can ask as they would be very likely to ask how questions or something equivalent something that demands descriptions of actions you know, how do you get to so and so give me, which is an answer basically to exchanging algorithms you know, that how questions, how are things done and very important and they would probably evolve as stability, these super bees and they would have made a major advance when they could because they can reproduce behavioral patterns now they can um you know action they they might in fact not even be able to imitate one another at all they might exchange all their um information about how to do things in terms of how questions it's interesting to that recursive that how questions when asked repeatedly are clearly analytical if you ask someone after how and then you ask how again then you go into it in more detail we show the sub goals and i maintain that most of science is that science is concerned with how questions it's they're analytical and they describe how things work originally they were just concerned with how people do things but now we've actually extrapolated this out into the world and we ask how things, in a disguised way, we ask how we can do things and what will happen if you do so and so. It's necessarily analytical. It always takes the meaning of it at the action, it's taken for granted. Science doesn't mostly legitimately ask why questions, it asks how questions. Why questions are not analytical. are holistic when one creature asks in order to get a creature to test whether a creature is asking why questions you have to show it like

1:12:30 a piece of an action or something which he doesn't understand and you say why are you doing that and that in other words what goal to what goal is that piece of behaviour directed or actually You find that that's not enough. If you look at why questions, you find that in order to really understand why a piece of action is being performed, you need to understand the starting point and the finishing point, and since it's very likely to be a solid goal, the wider context. Why questions suddenly open up a whole domain of activity where you describe actions in terms of their total significance within the life of the species, which is why kids at a certain age do nothing but ask why questions, because they are trying to find out how this form of life operates. you know, they want to know all the connections how, why everything is done how everything fits the way it does and as it's beaten up they will ask why questions just on and on and on you sound so you're speaking from X-Feed I just saw a wonderful kid today, I won't go on about that so actually the end of the story creature that has that can ask or perform information communication exercises that are equivalent to our which what truth and knowledge how and why how why for you know these nice little couples one analytic than the other any creature that can do that would be indistinguishable from us in in terms of sapiens. They could do philosophy, they would come up and ask us what the hell we were doing, why we had come, and why we were doing experiments on them. You probably wouldn't understand the question, but they would be able to ask them in just the sense that we would be able to ask them. And really, there's actually, there's no great complication about this, you know. Any creatures that were able to describe the world would be naturally led in order to do it properly, the questions. Their ability to communicate information wouldn't be much

1:15:00 use to them unless they had these few questions and then they would be Zapiens. Doesn't matter what goes on inside their heads, they could be robots. They'd have to be a community, of course, for this to make any sense, but they could be Geloids or what you like. I mean they don't necessarily have to that we did that's another story and so yes but that's what we do apply your criteria which events in human history with these very academic types, so demonstrate human history. No, no, but you see, this is the thing. We are, as I understand it, in human history, all that, that, those, they sound like stages, but they are, they are the kind, they're only the stages of an ethological examination. We, in fact, asked questions first and learned how to produce descriptions. And we achieved the status of beings after thousands of years of being very good at asking questions. This is what happened in our history. What I'm really asking is, how far back would these travelers have been able to identify satins in humans? Oh, I see. Ah, good. Ah, right. I don't. Obviously, we all are, everybody can ask why questions now. No, it would be, it would be, I think, we were... I don't know. We just don't know, do we? We know that 40,000 years ago, people were well into representing things. They were doing pictures and all of this kind of models and tallies and all sorts of stuff. So presumably they were representing things in language, so they were probably sapiens.

1:17:30 But I mean, it's pure speculation, really. I mean, isn't the, isn't the biosphere sapiens? And it's not of the class that you've mentioned. It got us to where we are by asking us questions. only in the best you're quite free to talk like that in a literal scientific sense and if we don't answer the questions correctly in the next 50 years we probably won't be asking them ever again and it won't care it will just reproduce something better than us listen, Peter this is philosophy that we're doing we're trying to work out ways of talking work never mind I think it's also a question of a way of listening. And I've been interested in the work of someone called Stephen Harbuner, who's a shamanic American herbalist. He's also a biochemist, he's in a position that he can outrun his looks at plants in that way, but he actually was drawn to work in a shamanic way and went around the world talking with herbalists around the world who had direct experience of plants talking to them. he's doing something else I think there's a question of maybe other forms oh yeah I mean you must sort of recognise the defined limits within which I'm working if you don't work on a problem you have to limit it quite a lot this is a kind of logical problem in a certain number of species I mean it's it's all I mean it when I say that you've discovered sapiens this is sapiens as described by these imaginary exothologists I mean if you want to describe them differently then I'll say well we have to separate sapiens on that basis from consciousness and intelligence and such like because one can readily imagine creatures which are solitary creatures which do not communicate at all but which still have a form

1:20:00 of something we would probably have to call intelligence despite the fact that they didn't actually communicate maybe you could, I have difficulty imagining that actually I can only imagine it with octopus yeah but I don't see, I think that what we experience as consciousness I didn't get onto Aristotle, but what I see, what I think we will experience as consciousness is a particular sort of self-reflective activity that involves having two representational systems playing off against one another. It's a whole complicated way of knowing yourself, which allows us to think, my goodness, I'm conscious. Yes. But what about a species of spider, which has been reported on recently, which will sit for hours gazing on a scene where its intended prey is, and it seems eventually, after a number of hours, to have worked out a strategy of how to get to that. And will sit there for hours. seemingly all one can do is draw human analogy contemplating how it's going to do it well we're very inclined to do that sort of thing so I think I'm getting you to answer my first question in steps you've already given me one part of the answer now the second part I think you can answer if you answer this question Do you feel that we are more sapient now than we were 40,000 years ago? Transphilosophia. I'm not, again, I see what you mean about, like, yeah, I mean, if I'm trying to be strict, trying to define it in strictly logical terms, then there ought to be like a couple of points of it. But evolution is never like that. Things kind of creep up on you. So there must be kind of cases that are borderline. I know you don't know. so yeah I guess actually we would think they would be pretty thick but I mean but I don't know, who knows I mean all languages, there's no question that all languages today are semantically or pragmatically as good as one another when it comes to

1:22:30 the sort of basic questions I don't know I want to close the full part of this meeting free to go to work if they want, but it can stay on if they want, and therefore this is the time to thank Adam. If someone said to me, what is clear thinking? I would say, come and listen to Adam Parker. Anyway, so. Anything else? A DVD has come into my position. Now, it refers to a man referred to as John of God. He's a Brazilian psychic surgeon. Apparently his speech are astonishing. He appears on the... All those h's are nought, but h of x and y plus h of y and x, when you swap the things over, is 7, or what Pierre used to call it. I can't remember what you call that thing which had 1s all the way down But anyway And I think that defines H No, it almost defines H completely But you also need to know that H of U plus 7 U plus 7 and B Is the same as H of U and B Yes, I think that's right So, in the next to the last line, there's an inconsistency unless you're saying x is an radical one? Sure. Is that it? Yeah. Thank you. This seven is just, when you add it on, you just turn the string of ones and noughts into the corresponding string of noughts and ones. And, you know, if you add it on to there, you get nought and nought ones. you didn't start with, as Frederick did, you did indistinguishable or something, which used to be indistinguishable. Well, I'll answer that very quickly, Peter.

1:25:00 I could develop the rest of the hour for it. I have been, in the last year and in the year before, working away at Frederick's book on indistinguishable. and there's a great deal in it which is good stuff and there's a great deal of isn't and I haven't sorted out which is which so I'm keeping away from indistinguishable that's the short answer there are there's some of the I have you got a list of the answers was it Dr Johnson told somebody his work was called the original unfortunately the good parts aren't the original parts aren't the original parts aren't the original parts obviously not doesn't that two's complement basically that kind of thing two's complement right are groups more general than operators or operators more general than groups Well, a set of operators need not be a group. So in that sense, I suppose you say they are more general. So why wouldn't you write down, whether you act special, but AA equals A? Oh, thank you. That's a good question. And this was suggested to me two or three years ago by Lewis as a better definition of discrimination. And there of course are direct links with quantum cameras. Well that really comes back to, I mean the value of this question is that it really directs me back to what I'm supposed to be talking about and what Ted has talked about and that is the nature of this process. here is things are coming into play and something has arrived already and then I have something else come into play and I want to check whether it's the same or not now if the nature of this checking operation is that A operating on A because it is the same

1:27:30 gives me A I then have to say well has it given me the same thing that I started with, or I'll have to check it and so I have to take my original A and the new A which came out of the first operation and do it again. And so on as infinitum. So that mathematical trick won't fit in with my process idea that things are coming into play and then I'm checking whether they're the same or not. so there's a discrimination system you give it a try you take a copy of A and you let them interact and nothing happens your worry is that maybe nothing happened not even the interaction process yeah I suppose that would I think that's the answer you answered the question you've done a mission I think you're there, you're, I mean, you're a long way. I'm following, I'm following Clive's, Ted's idea that we must, physical understanding comes first. Oh yes, well, I agree with this idea, but I think one's got to. Thank you.