ANPA Conference 23 — Session I

0:00 That's a neighborhood that does not include young. I don't know. I don't know about that. T1, this is T0. T1, T1 means that both and T2, or usually known as Hausdorff, is the these are the three actions of separation of but let me dwell a bit on the construction of sorting because it's very interesting Okay, how can we end up with a pulse as a replacement of the region? Okay, for every x in the space, which is to be replaced, defined as lambda x, 3 to the intersection of all u in the covering, such that x belongs to u. So, what is this lambda x? It is the smallest open set in the sub-topology generated by the open cover that includes x. And define the following relation between the points of x based on this. We say that x, y, y, y. Right? Okay. One can verify directly that But this relation is what is called a pre-order. That is to say it is reflexive and trussive. Right. Then, reflexive and trussive. And the question that one can ask is, when that pre-order can be converted into a partial order? Well, otherwise to say, with this pre-order,

2:30 So you can define the following topology. The topology generated by the basic open sets of the following. The topology is on the topology, right? Y, B, set of O, Y, which is Y. Right? These are the basic open sets. But the reason we're doing all this isn't very often. Just wait, just wait. Not a half an hour. No, no, no, no, not at all. So what will convert that relation, defining this topology, to a partial order? Well, it is fair to say that two points will be indistinguishable or equivalent relative to the organ covering, of course. And we're going to the equivalence relation we are going to write like that. We cannot distinguish relative to the open covering of the underlying space. We cannot distinguish these two points. Then, the space, the structure, next, not equivalence, so we quotient the space with the equivalence class, consisting of equivalence class, then that is a partial order. is that dysmetic reflexive, reflexive dysmetic and transient now, that would be just an exercise if we could not in what sense do we contend to that this is an effective replacement of this discrete replacement the equivalence class is relative to that equivalence relation well, there are some powerful there's a very powerful theory originally due to Alexandrov well the construction was beautiful check but but Alexandrov provided the proof and for saying okay what one can do one can enrich one's covering that is to say

5:00 include in the open cover including the open cover more and numerous more more open sets. And that, of course, will result in another cover, which is a refinement of the first cover. We'll wrap it like that. Right. Now, the limit theory tells us the problem. Limit used here, tongue-in-cheek, there's no topology on the space of all topologies, But limit as n, this is called actually an inverse limit. It's a categorical column. Limit as n goes to infinity u n, which I will write like p n. p n is by short and salivary from the post and extracted relative to the u n open cover. Limit as n approaches infinity, p n, which that is to say let us put it in quite physical as I refine my measurement as I include more and more numerous more as I localize as I employ more energy higher power of resolution of the of excess point events at the limit of infinite power of resolution, infinitely small covering subsets of X, covering the points of X, at that limit, which is, again, this is not meant to be a limit of a sequence, because obviously there's no topology on the space of water. What kind of limit is it? Huh? What kind of limit is it? It's called a projected limit. It is called a projected limit, and projected limits, this system's opposites are nets. are nets, of course, or in their systems, of course, that they have a unique limit, of course, a unique up to isomorphism. But this, up to homomorphism, is homeomorphism equivalent to x, the infinite. So at the limit of infinite, we finally recovered that. Now, still. You started to say something, and I really want to be at the end of this. What was it? You were very excited. You said this last line here. You were talking then about how it applies to physics. I guess how it applies to physics. Again, in the interpretation of the net,

7:30 is that one applies to higher resolution. No, you get to higher resolution. Then and then. And what? No closure. No, no. Again, this depicts that, for instance, to see if there was a parameter about these discrete spaces, if we could relate this to a spectrum of an algebra, as I intended to do, but I don't have time. Obviously, this could be a sign that observable does energy. And what, essentially, if N is something like EN, is parametrated by something in a spectrum of an observable EN, then what this tells you is exactly a non-pragmatic limit of infinite energy resolution or localization do we obtain the continuous space yes you need more and more and more energy to get higher and higher resolution but soon in order to achieve that resolution you double up all the energy in the universe so there is there is a cut off you mean from cosmological Yeah, it won't let you have it. Yes, of course. So that's why I call it non-pragmatic. You see, these are, in some sense, the real structures. These are not. These are obtained by the regions are the real structures. Certainly, this is not. Because by construction, you see that as you employ more energy to localize, only at the infinite energy of resolution do you recover? But let me associate with these PNs, some algebras. So PNs are pozos, right? You can associate with PNs. And the instrument in algebra of the PoSET, as a vector space, is defined to be . Choose a field. Now, I'll choose to be a good processor. Thank you. It's fancy.

10:00 Of... Now, just, I want to say this. However, a few people want to give you 15 minutes. Do you want to give me 15 minutes? Have a coffee break. If you want, please. What price can we pay for this 15 minutes? Coffee break. Yeah, I've been fine, given there's a distinct absence of coffee. Discuss it all with coffee. Of course there's no coffee. It has no rhyme. Oh, of course. Oh, what is this? And the product, of course. What administration? Let me employ some other notation. I'll derive what this is. It's not a whole time. These are also the post-it you can write, and they get a rhyme. you can define that to make product. Who is responsible? Is this what you do? Somebody like this, Richard. What can you do? You're still there. What? Why all this? How I see it. So the algebra is found by the arrows of the composer and subject to that closure under this product, it's called the incidence algebra on the game of the composer. Now, there's a part in a series of papers, one and myself, in collaboration, has shown that actually there's a very rich algebra, very rich differential structure, for incidence one can define a certain new potent differential operator, one can do some nice homological operations with those incidence algebras. That's not the point that I'd like to emphasize here. What I'd like to emphasize is that as the inverse systems or net of poses in Sorkin's scheme the continuous topology, that is the C0 structure of the manifold, we have shown with Roman Zapatrin actually that an inverse system or net of their corresponding incidence algicals not only produces at the limit the continuous

12:30 structure, but also the differential structure. So we can recover, we can represent at the reticular level even smoothness. We have an abstract I would like to speak about the Afan specialization, the categorical reality between posits and the algebras, because what Stanley asked is a continuous map between two posits, like those obtained from Sorkin's algorithm, does it give rise to a homomorphism of their associated incidence algebras. And the assertion is right. So PCS, he's proved that. Stanley. Ah, you see here, I called it Rota also. Incidence algebras were much older than Giancarlo Rota, but in the context of combinatorics, they were first applied by Giancarlo Rota. And Stanley is a student of Giancarlo Rota. You probably know that your camera is not with us anymore. OK, I mentioned this bonus, that they are discrete differential manifolds, in a sense of the max and the left-waste, and at the limit we recover this smooth structure as a bonus. This is my penultimate slide, which I go to very quickly. I define some objects which are called planetary space-type sheets at the point level as the process are substitutes for the continuous topology of the underlying space I define some objects which are effective approximations of the commutative algebras of coordinates living on that space which are called the spaces space-time sheaves. They are sheaves of continuous functions living on this having a space-places, this finite terry topology of spaces. I will not go into discussion on what a sheave is. A sheave is a local homeomorphism.

15:00 I was discussing yesterday how there is currently a big fight between the French and the German mathematicians. I mean, the Germans are assigned, they say that the originator of the ideas of Schieffs is Weierstrass. As far as Weierstrass, but the French say, no, no, the Schieffs are Schieffs appear for the first time into the works on the air. And subsequently, they were championed by Jean-Claude Steyr. You're saying the introduction of Schieffs is what creates the boundary operator, or is this separate? yes all right and finite a space-time seems of the omegas and again an inverse system of such finite a space-time chiefs and at the limit of infinite refinement that gives us the the co the co homological the dual to the power operator which is okay the exterior differential which is a effect sub-sheet morphisms of the sub-algebras of these linear subspaces. I didn't have time to tell you that these, of course, are graded differential spaces, but, okay. I have an problem with all of this. I mean, this is algebraic anthropology, and, okay, it describes relational possibilities, okay, between various abstract objects. The criticism of the use of the manifold in physics is about really an operational concept. You have to say, if I want to explore a manifold observationally, what procedures do I use? And I divide it up in some way. And the way in which I divide it up is limited by the machinery I have and the way I record Now, these divisions then have to be looked at, the method of division, then has to be looked at as an operation, and the properties of the manifold are largely the operational procedures which the observer carries out. they're not really they're almost subjective you see what I mean so the subjectivity

17:30 to refine theoretical exploration of the algebraic topology of what space might be misses the point because what space can be is only what you can observe by means of your procedure so you say what is my procedure what am I doing a completely different philosophy than he does. Yeah, I know. Yeah. I'm perfectly aware of that. So I don't know how fair it is to him. Because it's another, you have to say, a structural and use as operational. That's right. That's right. It's accessible to that. The question of what's possible. It shows you that from a criticism, a very just criticism, of the physicist's use of a manifold in such theories as the general theory of relativity and so on. I would like to make a contact with what you're saying because even here I employ a certain, certainly not in the original sense, as you said, the actual procedures of determining what's, I think this operationality one has to focus, I'm using an abstract notion of the operationality which is, I think it's more in line with Heisenberg rather than original. Yeah, there's a great temptation to refine it with all the points. Are you using algebra? Yes, I know. So the algebraic operations is perfectly fine. Einstein did this. He refined it very fast. Yes, sure. In time, in fact, he did so. The operationality of general relativity rests heavily on the fact that you're employing equal calibrated rulers, and synchronized blocks, and these are, this provides the operational background. Yes, but they also tended to forget at certain points that that was what was going on, so that you ran into various abstractions, the singularities, for example. You had to do the mathematics, you didn't really have any choice, but one needs to stand back from it and say, what does it really mean? Okay, we are going to conclude with a radical change of physical interpretation of order as topology to order as causality that sort of came out. There's no point in you rushing to stop us. The coffee doesn't seem to have arrived. I was promised that it would be here by about five minutes. Okay, of course I'll say it. Go on then, forever.

20:00 I'd like to do with some project that occupies me now. So my research now is essentially based on two quite ambitious questions that I'm not sure I'm able to answer. But is there an intimate relation between the logical structure of the world at quantum scales and its causal chronological structure at quantum scale? Has the latterly supposedly determined the numbers we use for interior gravity? One is this. the second one is how much from the differential geometric can we carry through the first I'm looking I'm trying to apply some categorical means what is the theory called topos theory in collaboration with we're applying ideas and concepts and results from topos theory to quantum gravity and the second one in collaboration with we are we are applying his theory of vector sheeps. And we have gotten some quite interesting results about this question. But I would like to also, with all due respect to the physicist, this deserves all the respect, I would like yesterday, like Peter said, said, well, I do not apply algebra as an algebraist would do. I do not take algebra. as the problems arise I think about and do whatever I can but so by no means one should say oh I'm applying topos theory to quantum gravity there are specific problems questions we are trying to resolve here so we should not fall prey to Woody Allen's you know I have an answer can somebody please tell me the question physicist always poses the question before gravity theory, it's a possible theory, but what would it be? I mean, what would it be? There's no unanimous, there's no unanimous. Oh, but a theory, oh. Okay, from a particle physics point of view, it would be something like to give us some spectra from there for the graviton, that quantum of, say, the gravitational field, of course, it's of enormous importance for cosmological. Do you have to be a theory which would say something about world that we haven't actually observed yet because we haven't tried. It would invite us to look at something we haven't looked at. Let me close with Einstein's, with some prophetic words by Einstein because I think this quotation

22:30 is great. And he says, one can give good reasons why reality cannot at all be represented by a continuous field. From the fundamental phenomena it appears to follow with certainty that a finite system of finite energy can be completely described by a finite set of numbers, quantum numbers. This does not seem to be in accordance with a continuous facetime theory and must lead to an attempt to find a purely algebraic theory for the description of reality. However, nobody knows the basis of such a theory. Okay, this is the meaning of relativity, appendix D, published after his death. This one. And also very recently, because this is at the end of his life, he said that, but also, curiously enough, 1916, he writes to a student of his school. You have correctly grasped the drawback that the continuum brings. If the molecular view of matter is the correct, that is to say the appropriate one, That is to say, if a part of the universe is to be represented by a finite number of points, then the continuum of the present theory contains too great a manifold of possibilities. I also believe that this too great is responsible for the fact that our present means of description miscarry with the quantum theory. The problem seems to me how one can formulate statements about a discontinuum without falling upon a continuous space-time as an aid. The latter should be banned from the theory as a supplementary construction, not justified by the physical essence of the problem, a construction which corresponds to nothing physically real. But we still lack, unfortunately, the mathematical structure. How much have I already plagued myself in this way of the manifold? and he says, he adds an algebraic theory of physics is affected with just the inverted advantages and weaknesses, aside from the fact that no one has been able to propose a possible logical schema for such a theory it would be especially interesting to derive something like spatiotemporal from such a schema I cannot imagine how the axiomatic

25:00 framework for such a physics would appear and I don't like it when one talks in dark apostrophes. But I hold it entirely possible that the development will live there, for it seems to me that the state of any finitely space and limited system may be fully characterized by a finite set of numbers. This seems to speak against a continuum manifold with its infinitely many degrees of freedom. The objection is not decisive only because one doesn't know in the contemporary states of mathematics in what way the demand for freedom from singularity in the continuum theory limits the manifold of solutions. This is the conclusion of my talk. And this, of course, thanks are due to David Finkelstein, to Basil Hailey, to Chris Ayshom, to Jim Landek, Tassel Magnus, Chris Morgin, Steve Selesnik, Freddy Van Oestein, Roman Zatagin, and, of course, Keith Bolden, I don't know about the group for, for making all this possible. Thank you very much. Thank you. Thank you. A couple of things. First one, because I quickly decided that, well, came to the conclusion that talking on a hoop is a damn good discipline, so it's going to be slightly negative. I wasn't really quite sure what I was going to talk about this year because I've been working on the same thing for a long time now, and I suppose I've decided to talk about and do what I'm going to do because things have moved on a fair amount in the past year the way we're now analysing the state and so on and so forth. And I'm beginning to get the glimmings of an idea of what's going on behind what I'm going to talk about. But I'll give you a quick background to all of this, to the data analysis I'm going to describe. And my original interest was in ways of implementing what we're pleased to call Marx's principle, which for me meant more or less what Tony was where's Tony by the way? he was talking to me two minutes ago anyway for me it effectively meant that without the universe being populated by objects or whatever the notions of space and time had no meaning whatsoever so I formulated the question is it possible to have a globally inertial space and time

27:30 associated with a non-trivial distribution of material? Of course, in terms of general relativity, this question, this makes no sense whatsoever. Because as soon as you have material, populated and universally, you have this curved manifold of business. So that was the question. Is it possible to have a globally inertial space and time which is associated by a non-trivial method distribution? I mean, stuff there. Ah, real, you mean? Real, yeah. So, I said we're a very simple model to deal with this question. I won't go to the details of it. But essentially... Excuse me, how does this impinge on your earlier statement that without a matter there was no meaning to a space-time continuum? Oh, well, the point being, the simplest as an inertial one. Globally inertial one. Okay? That's all. So, could you have this simplest conception of a space-time continuum, which is a flat one, associated with a non-trivial method distribution? Okay? So, I'm pretty much of the idea that really there is no such thing as a space and time continuum anyway. that somehow or other space is perhaps discreet and somehow in time is discreet. So I just don't really know. But the way I went about this was to set a formless continuum, no structure whatsoever, and to populate it with objects whose only property was innumerability. And then went on. And it turned out that the final answer to this question is, yes, it is possible to have a globally inertial space and time so long as the material distribution is fractal dimension two. Now, the interesting point about this is, in fact, when astronomers look into the universe and try and decide what the distribution of large-scale structure is, after medium scales at least, there's pretty well agreement now the material is distributed fractally. we're more or less quasi-fractically, with dimension D equals 2.

30:00 But there's a great argument about what happens thereafter, because the big-bang cosmologists want everything to become uniform at big enough distances. It isn't at all clear what goes on beyond the median distances, simply because estimates of distances beyond a certain point become purely dependent upon your interpretation of redshift. So, yeah. But anyway, to median distances at least, seems that there's a conjunction between this deduction from a simple analysis and what we actually see. Right, so this was very pleasing. What does fractal dimension 2 mean? It simply means that the amount of material at a given volume goes up, as I say, the square of the radius, rather than the cube of the radius. So that implies that galaxies are flat things? Well, not really. No, I'll talk to you about it. and homogenous universe is at the fractal d equals 3 in other words the amount of material that goes over to the bottom but of course there's no real evidence for the universe going to be homogenous right? the big bankers will say yes we actually do observe what is agreed is that at the medium distances at least we do have this apparently d equals 2 around the universe is it a little more? than 2 well you see figures put up to 1.9 and 2.1 snap on I would expect you see that if you made random errors in your counting and your partition of the space random errors on measurements tend to raise dimensionality of fractal systems I wasn't aware of that the figures you see quoted at a fairly modest range is between, as I say, 2.9. What distance would that be exactly? Oh, frankly. No, I didn't. Around about 200 mega parsecs. Which is... I can work it out, Wade. Anyway, now, next stage is when we write down a theory of gravitation, no matter what we're doing, what particular viewpoint we're taking, with assuming some kind of locally flat environment

32:30 and then we perturb it with some point source. And we write down our equations, and that's our equation of gravitation. So, of course, the structure of your gravitational theory depends very much upon what you mean by an inertial background, the one within which you're operating. So inertial background, which is necessarily associated with the d equals 2 to 2 material must necessarily give rise to gravitational theories quite different from, shall we say, Newtonian gravitation or GR. That's what happened. So I was keen to see how gravity came out of all this, how it worked and I've got a theory. And when one considered simply spherical point source perturbations, then you had a theory which you couldn't really tell from the predictions of ordinary theory. And since ordinary theory works superbly for spherical point-source perturbations, then there's no way of telling the part. So I then moved on. What systems out there do we know a lot about? Or what do we know most about? And what we know most about, in terms of information, is the spiral galaxies. made a simple model of a spiral galaxy basically it's the cylindrical distribution of material and wrote down the equations for that and so on but of course one has to put into that what's the actual material distribution best reflects what you actually get in a spiral galaxy well I had a fairly small sample of about 25-30 objects for which I had information on hydrogen distribution of these spiral galaxies. And it turns out that if you forget about the bulge component... Oh, by the way, I forgot to say, yes, it's an important point. The model assumes perfect cylindrical symmetry, whereas spiral galaxies have a spherical bit in the middle and then a cylindrically symmetric disk. So when we want to look at the data, So you have to have somehow some means of abstracting the bit in the middle, the spherically spectrum problems with it. Well, if you do, when you look at the distribution of hydrogen and disks of galaxies, you find that the density goes off pretty well as 1 over R squared.

35:00 Of course, there are fluctuations above and below this, probably due to the lumpiness of galaxies. But as a statistical statement, you can say, fairly reasonable exactitude, that 1 over R squared is how hydrogen at least drops off in the disparate galaxies. So you can feed that in as the mass model into these symmetric. Do you mean the density of the galaxies? The density of the hydrogen in the disk goes off as 1 over R squared. Or in a disk. Just 1 over R squared. So you feed that in and then out comes... The density falls off in the square of R squared. Yes. Yes. Of hydrogen. Just so you don't lose me now. You're talking about the density of a galaxy, right? The density of a gas in the disk of a galaxy. So a galaxy has got a specific density. Right? You can measure the density of hydrogen in the disk of a galaxy. Yeah, and this galaxy is less dense than this one and this one. No, no, any given one. Any given one. Oh, I see. Any given one, you measure the hydrogen densities across the disk. any galaxy, any given one, any spiral galaxy, you'll find it goes off as 1 over r squared. There's a lot of random noise in all that. You might find it's 1 over r to 1.5 It goes to be from the centre. When you take a large number of these, you'll find that induced physical averages that they can spot on 1 over r squared, very, very close to that point. So, feed that as a model into an idealised disk. And when you get out, there's a lot of what you find the circular velocity that is the radius which is rotating in the disk particles in the disk going round and round and round go as a power ball that's the radial displacement in the centre that's a constant and that's a constant and these will vary different between galaxies so these are things you determine phenomenologically so you get this result here you also get out the materials move in logarithmic trajectories logarithmic spiral trajectories that's also the consequence of moving what do you get

37:30 that an object moving moves along the trajectory like this and that would be the theta well, lambda b in lambda just consequence so you get, that tells you how move in the disk. Now, that was actually quite an interesting... This particular one was... I say exciting was exciting because, in fact, ever since from the very first time that people identified spirals in galaxies, it was very quick to realise that in fact these spirals were very well described as logarithmic spirals. So this came out as a good confirmation of what we actually see. The question was whether rotational velocities really behave like that. Now this sounds quite a tedious potential exercise coming up but in fact this is where the excitement comes in. Excuse me just again, your alpha here in this thing, that one, yes, presumably only if that's some particular value does it rotate as a solid disk. Well, in fact, the alpha varies in practice you find it very similar for a large sample of galaxies you'll find in the alphas the one is the solid rotation pretty well these are very rare objects most of them there's some evidence that somewhere in the middle of these galaxies they rotate as a disk the galaxy in the middle between the centre and the periphery. Has anyone heard of that? I'm not sure. That it varies from that logarithmic kind of rotation in the sort of mid-range. Some of them do. Well, these are simply... These are idealized galaxies that have confirmed there were large numbers of objects, that sort of thing. You can always find individual ones which behave quite differently from this. But as a statistical statement, these are good statements. Do you put the size of this thing in as a parameter? The size? Yeah, because this problem is... I mean, there's a problem here, right? Because if you just let it go out, then you've got pieces that are moving passages in line.

40:00 Yeah, well, there is a problem here, yes, become logical, okay? But if you try to formally put that into the equations... Yeah, that's right. But there are banded conditions. This is about a problem I'm not going to look at very closely. How does it actually merge into the background? It's not something I've spent any time worrying too much about. Anyway, I thought at the time, this is simply going to be a routine data analysis, seeing whether this kind of structure here does actually fit what you see. I wasn't very by the prospect that I went on with it. Just to give you an idea of what these astronomers routinely measure these rotation curves and this is what typical these four typical ones. What you have here on the bottom this is simply angular displacement from the center and this is measured velocity in kilometers per second so typically you get this kind of very noisy profile than typical. So that's the kind of data you're working with. Now, the model was set up for an idealized spiral, that is one without a bulge. Nearly all galaxies have bulges, but they're very rare ones, which appear that normally at all, they're extremely rare. So one had to have a mechanism of taking away that part of the data which referred to what what's happening in the centre. But, of course, it had to be a black box technique which one set up just worked automatically without any records from me. There's no, it had to be purely objective. So... Because of the segmenting of it? Yes. Yeah, that's right. Partly of that, but also one didn't want to be accused of filling the source. Right. Now that actually, that transpired to be an extremely important technique. I'll come to that in the end, and crucial to the end of my talk. By the way, I forgot to say, what I'm going to be presenting is, what I now see is evidence circumstantial against the notion of black holes in the middle of spiral galaxies. I'll come to this in a minute. The notion of a black hole,

42:30 the standard notion of a spiral galaxy these days is that the central bulge contains, always contains, a black hole, which is in there. In some sense, it's responsible for the bulge. Yes. Well, not responsible for the bulge. The bulge is basically created by an input material, and on the inside you get this... Is it only about the spiral galaxies? No, no, it's supposed to be all galaxies. Now, the evidence I'm going to present to you, I'm going to suggest that... it's very difficult to understand this, this phenomenon I'm going to be talking about, If, in fact, we do have black holes in the middle galaxies. And if we don't have black holes in the middle galaxies, then we can at least begin to get a grip on maybe what's going on. Right. Right. So, before I started off the... Well, okay, first on the data. Where's all the data going? I had no data at all. I just had these models. the first was a small sample of about 25 or 21 objects measuring in fact the first published set of rotation and I simply just to see how the analysis would go I put them through this model to see how the data looked through it in terms of this model and it all came out very well and one of the crucial things which came out was that there seemed to be a very strong correlation between the A and the alpha which was unexpected in itself, and won't talk about that at all. And that correlation actually formed the basis of a large amount of work which went on in this. But as a subsidiary observation, I noticed on this very small sample that the A parameter which came out of analysis seemed to fall into one of the four distinct bins, values, very close to certain values. That's very interesting. when I've done the large product analysis I'm interested in currently I'll go back and have a look at this so I spent the next 18 months doing the main product analysis I'm interested in confirming just to see whether this is a good model and not the spirals which it turns out to be and then I came back to this interesting observation was it nonsense or really was there any enemy to it

45:00 and it relies crucially upon me on my ability to subtract from this data the bit which corresponds to the bulge. So for the moment, take it from me that I can do this. Well, it was quite a job tracking down large amounts of data because whilst the data is there, it isn't actually available. It isn't published in the journals because it represents large volumes of numbers and so on. Anyway, I tracked down the existence of a sample of 800 or 900 of spiral galaxies with rotation curves measured. Now, one of the problems with the rotation curve, and this is actually relevant to the talk, is that astronomers, they simply measure strength across the disk. so across the disk you will actually see a set of points like that and like that so that's the displacement across the disk that's the velocities this would represent the stuff coming towards you that would represent the stuff going away from you these are basically double ship measurements when you have a galaxy it's also got a global redshift step onto it global redshift, then you have these doppler redshifts, and also, you're not entirely sure, and also galaxies are tilted towards you, the realists of the medion, there usually is some of this, so you have to make corrections for that, and so on. And then you have to make an estimate of what is actually the global redshift involved here, which is not obvious. That really involves in determining of the object is, which you can do roughly, but it's not easy to do accurately enough that it's thought about. Well, I had this large sample. It turned out that an Italian that came from Australia, an Italian pair of astronomers, were interested in the internal dynamics of galaxies. So they'd set to take the 900 objects and then a very accurate, what astronomers do having measured this people are interested in the dynamics they what we call foam the rotation curve and they get estimates for the global redshift

47:30 to subtract out of the is that measurements estimates for the superimposed out on that to get to it if you look at these you will see that half the in this comes from the fact you've actually got the measurements from two parts of the disk superimposed on each other and that's called the process of foam and that's quite difficult it's quite it's easy to do it um if you're very interested in very rough answers but it's not really accurate two italian guys had done the job for me okay so the first thing i had took it, put it right through my machine doing nothing to the data except subtract the central core problem. And these, these black bars were my predictions based upon analysis of the very small sample. This is a histogram, by the way, of the calculations of log A 900 objects, that's the frequency, and these are the log-a values. And those are the predictions based upon the analysis of a very small sample, and at first we've noticed this potential effect. And you can see that, well, there's hardly any argument about whether that prediction is manifest in the live sample. Because it is, and it's more or less spot on. What is the frequency of the frequency of? Of occurrence. Frequency of occurrence. It's a histogram. It's a histogram. It's a histogram, yeah. Right, so I didn't have a clue what it meant. When I got this diagram, I believed the result. But what it meant, I just couldn't begin to imagine what it might mean. Except that it was fairly important for us to physics. We got this published quite easily, amazingly. then of course if you're fortunate enough to make this kind of discovery of physics this kind of thing which happens I believe it's a really great thing this is and I felt very fortunate to come across this week I was obliged to show that it existed in further samples because nobody's going to just take the one sample and change the whole group of uastrophysics so the chase was on there for more data

50:00 and it turns out there were only five samples, five large samples available in the world I got four my first problem to briefly touch on was the Italian guys had done a very large labour intensive job of folding these rotation curves in an accurate fashion And I even thought this was small, but I hadn't realised. So I then tracked down another large sample of 1,100 objects, which was much further away than this sample. This sample, well, roughly 70% more distant than that sample, which implies less accurate than so much. I got the raw data. Then I discovered that the Italians had done this, this folding job, by hand, and it had taken two of them a year. I can't do this this is ridiculous so I spent 18 months writing software to do this so the next diagram just for comparison purposes is my software's job on this data so I'm going to represent I'm going to indicate these particular things these centres well it can do it looks rather messy because the other diagram is a bit noisy that's mine, the dotted lines are the actual Italian piece so you see the software essentially does what the Italians did in a much cleaner way so that had a tool here to work on new data, that's the point next sample I'm missing out all kinds of details here as you can probably imagine the next sample came from the same astronomers in the first place but has not been through the Italians so I had to put this through my own software reduction routines completely independent sample well from the same astronomers but different objects the dotted lines of the piece in the previous slide So there's absolutely no doubt that these peaks are real on the data.

52:30 So now, of course, one begins to worry, well, maybe, you know, the same astronomers, perhaps they were doing something really funny, which has created these peaks as artificial star effects. where I couldn't see how it could be simply because if I didn't apply my black box routine of subtracting the central cores out then you didn't get these results. So if they were doing something then somehow or other they were doing it in a very subtle way which had only affected what you saw on the disk rather than the whole object. David, I'm sorry, I'm even reminding as to why you need to extract the central cores. Because the model on which this is based based upon the notion of a pure disk galaxy. With no numbers. Okay. So the only way I can check it is against pure... So in a way that's a theoretical model to which it's been fitted. So the problem now was the data reduction has been done in two ways. One's by the Italians and one's by the minds. So we can cut out the data reduction as a source of this. But we still have only one set of astronomers implicated in this. And maybe they're doing something like that to make all this happen. So then I tracked down another set of data, a much smaller sample. American astronomers, or Canadian, in fact. These are southern sky spirals. These are northern spirals. It's a much smaller sample. We put it through the same software reduction. There's the dotted lines. that this is the dim end of spiral objects, and there are very few in a sample, this particular sample. So we can discount that, but apart from that, these three peaks are reproduced essentially perfectly. Just to make sure, you do mean intrinsically dim? Yes, intrinsically So now what I have is objects from independent astronomers, independent telescopes, two different data reduction techniques. And then I fell upon the fourth sample, that's three samples,

55:00 we've got one more sample. Now this sample is interesting because the objects concerned here are five times the distance of the ones we've been looking at here. And in fact, five times the distance, generally speaking, means far less accurate. But these were made, these were observed with a huge mirror at Mount Palomar, so much bigger instruments than the ones used for previous ones. So even though they're far more distant, that's what you get. The dotted lines are the central lines of the original diagram. So, I convince myself that I'm looking at some kind of real phenomena here. Somehow or other, these log A parameters fall into these discrete classes, so long as one is careful to abstract the effect of a bulge from the data. And the alphas and the A are correlated. Yeah, and they're very strongly correlated. but when you do error analyses you find that the errors involved in these are about five times the errors involved in these so you're about to say of course does this have a similar the error is sufficient that it is there to be completely washed out so I've convinced myself that this is a real effect but what does it mean? and I you know for the past five years I've been completely bemused by all this and just swinging around trying to just get a hand on it you know talk with my strong friends what is the evidence of Black the business of Black in the center of Galatians I'll come to that And that depends upon how I go about abstracting the effect of the central object on galaxies. And how do I do that? What I do is I say, well, OK. If the power law is a reasonable description of what's happening with this, then when you take the parallel and fit it to the whole lot of the data, then you should see a poorer fit in towards the middle, and you do add it towards the disk.

57:30 So all I did was, the way the algorithm works, is you fit this to the whole set of measured philosophy points and you simply look at the fit of the innermost point to the to this. And if it's it shows high leverage or large deviation from that if it doesn't conform within certain parameters which is defined in the black box you dump the point, repeat the process ask the same question of the new inner most point and keep doing that until the last inner most point fits this model and you stop this process that's the black box technique, the question is I mean, it works in this context, but is there any objective evidence that it's a good method? And that's the interesting point. Well, astronomers measure all kinds of things like black disks. And one of the things they measure are luminosity profiles across the disk. In other words, light intensity. They count photons. So they get this light intensity measurement across the disk. and there is a commonly used magic called an 83% light level meaning the diameter within which we see 83% of all the light dimity by the galaxy within a certain wavelength so it's an objectively defined parameter and it's got nothing to do with this I had the idea, well if my black hole process does have any kind of objective underpinning then one would expect the diameter of the hole that you've cut out if that's a physical thing then it should be correlated with some other outer diameter measurement of the galaxy so the outer measurement of the galaxy is a total is 83% isotope so you're saying it could be correlated with the diameter By some independent process, exactly. Big galaxies have people in their little galaxies. Now that's the rubbish. That was the way I thought about this in the first place. But we'll come to that.

1:00:00 Okay, this is it. What you see in this first one here. What you see is this optimal radius is this 83% measurement. The radius contains 83% of all the light in the wavelengths measured. This R-min is the size of the hole that I've got before I've been anything. This R-min on this slide is the least measurement, the innermost measurement on the data I've got as it comes. So you see there's no particular evidence of any correlation between this and this. The next slide shows what happens when I apply this whole cutting routine, if you like. And that diagram becomes that diagram. So you see immediately there's a carbon correlation imposed between that one and this one. Yes, but you're calculating the luminosity of the rest of it. The one when you've taken it out. Well, in fact, I've done it both ways. In fact, what you take out is very little light associated with it as it happens. Most of the light is actually in the disk. Right. I don't have it in both ways, but you just can't tell. That's for the... That was for the first sample. The same diagram... The same two diagrams for the second sample. These. That's the raw data as it comes. essentially no correlation between the innermost point and this radius put it through the black box business and you get obviously a very strong correlation now imposed on the data and the third sample there's very few points here so it's not quite so striking that's before data reduction and that's after the data reduction you can see it it's not quite so striking because of the far less points I haven't done the analysis for the very last sample so the point here then is But originally, that simply confirmed me in the belief that the technique I was using to take out the effect of the bulge,

1:02:30 as I saw it, was an object to be just violent. Now, originally, I thought that what I was doing, the way I interpreted this, and I was what you said, was, in essence, that's how I thought of that. That's a disc, and there's a bulge. I was effectively, as I thought, literally cutting out this object here. So what I had left was essentially an estimate of the radius of the bulge. Or else it's simply a tracer for it, anyway. And I didn't do any work on that to justify that statement. That's simply something. Anyway, finally, maybe I should have to look at this more carefully. So look at it more carefully. And there are ways of estimating Bull's radius from these light profiles that you can answer. I won't talk about how that is, it's a little detail, but you can do it. And it turned out there's zero correlation between my radius, whole radius, and estimates of these Bull's radiuses. In other words, this R-min on my diagrams is really, it's not a tracer, it's a torch. And in fact, I should have realised this earlier on because I actually know anyone. There are many examples, by no means, just because of the public, it's a minority, but there are easily found examples of galaxies with very large disks and little pinhead cores. So I shouldn't realise that perhaps. So, this also must be found. And this is where the black object is. this R-min is strongly correlated with this R-optical now R-optical is definitely a physical parameter that means that my R-min is definitely a physical parameter what can it represent it can't represent the bulge because I've done the analysis and showed there's no connection so it's not a measure of what's there in the middle of the galaxy maybe it's a measure of what's happened in the galaxy in the recent past which implicates what's in the middle as some kind of engine

1:05:00 but if it's a black hole of course when things fall into that when things fall into that black hole effectively they're not affecting the outside world at all ok you get strong radiant you get strong beaming out of the things, but you're not getting massive effects into the disk. Now, if this R-min is being caused, in some sense, by what's in the middle, it also means that the whole disk is, because R-min is the same as R-opt, it's a tracer for it. So it's saying that the whole disk is somehow implicated in what's going on in the middle. But it has a black hole, and you have a problem. Because there's no way that that can create this big disk. Because once that is in the inner black hole, it's then lost. But it is a very intense gravitational field. Yes, it's a very intense gravitational field. But we're talking about, it looks like we're talking about disk creation here in a way. And that's the problem. Now this is only circumstantial. It's a very arm-waving argument. and I've just come to this way of viewing things fairly recently simply because no ideas I just cannot begin to get a grip on this unless I think along these lines so what I'm saying is that there's a definite real phenomenon here in spikes which fundamental rest of physics what? fundamental rest of physics It's very hard to understand how they can arise on the basis of standard gravitational theory. The standard theory is simply how the dust is falling in to create the bulge. In fact, astrophysicists are convinced they can understand that. If they understand bulge creation simply by inflow of dust and the standard theories of gravitation, they're not sure about this creation. Of course, all that's based upon standard GR theory, which has black holes in the middle of all these things. And it's that which makes all of this, I think, extremely hard to understand. So I'm suggesting this is the first evidence, the first clear evidence, that there might be a huge question on the ways we view galaxy formation and, by implication, the way galaxy works.

1:07:30 And that's it. Thank you. Questions? Three years ago, you gave a talk where you were questioning the gravitational constant. Me? I don't know. I was shocked at the end of it. There were questions to be there coming up about the gravity. Yes, yeah, I think that was it. I was probably talking about, you know, I started off talking about relating global inertial space-time with fracture 2. I'm talking in detail about that. Is that another prong of this? Yeah, that's what came before all this. It was all that work which led me into this. In other words, these discoveries have come. And there's no room sort of in the standard picture for some sort of resonance effects like you see with the wounds and wounds, which could produce this conversation. Well, people have suggested this too. The problem there is, get a resonant effect on a given disc, and you might well, in any given galaxy, might well have, shall we say, eigenfrequency, any modes of which you can fall into. But why should those modes be the same across all galaxies? That's the problem with that particular. There is a possibility, isn't that? But there's some kind of, if you're bearing in mind the sphere of geosizing, the back is a composite of stars and dust and stuff, but there's some kind of capture process going on. I'm thinking of the rings of Saturn. And those rings do very, I don't know much about it, but I understand, very complex dynamics, some of which is chaotic. and there seems to be kind of capture processes where small satellites create a ringlet and capture it around it I don't know whether the rings of Saturn conform to any sort of simple arithmetic

1:10:00 electrical structure or anything like this, but it might be the case. It seems unlikely to me that someone could analyze this and show it was on the back of the cut kind of thing. You'd probably have to do some kind of big simulation. It seems to me that's a very small one percent. Yeah, it's the same resonance, but I think it's the uniformity of the resonance. It's not that good, but the simple interpretation seems to be that there's not just one kind of core, but several different kinds. Well, OK, I did get beyond this. I think this answers your question. The question is, OK, if you do away with black holes in the middle of galaxies, once you have that, you've got so much rather trapped in the middle, you can't possibly create these disks in this country. it seems to imply that the this seems to imply that somehow or other this creation is coming from the middle to me if you don't have black colours what we do know about galaxies about star galaxies for sure is the the centers are occupied by incredibly dense compact objects that's for sure I'm simply saying but they're not necessarily black colours because it seems to me that this is consistent with the idea that the whole disk has access to all these materials. It's ours. It's a very odd way to become a picture of this. Once you have very dense compact objects, you're into the realm of condensed matter physics. And in condensed matter physics, you have all kinds of covariance effects given. I envision a situation whereby the initial formation of the spiral galaxy, the spiral galaxy, you have this bulge thing, no disk. It's a very compact object. So you say they exist? No, I'm not saying this. I'm putting this forward as a possible arm-waving process. how galaxies might evolve. So you have this very complex, very compact, dense, non-black hole object.

1:12:30 And once the parameters within it, which define what it is, are certain thresholds, it explodes and creates a disk around it, carrying all its angular momentum. And that's one phase in the evolution. The process repeats itself, a new voltage builds up, just crosses some threshold, explodes again to create quite different characteristics. And the uniformity across lots of galaxies has to do with the idea that these catastrophic explosions only happen in very tightly defined parameter regions. So what you're really seeing is the statistics reflecting these distinct catastrophic problem may be that the gravity calculations are not being done properly, because if you think about the sheer size of these things, I mean, if the one in the middle hiccups, the gravitational wave is going to take thousands of years to get to the middle or the outside, if you see what's happening. Of course it will, yes, but in terms of the galaxy's lifetime, that's very short. Well, that's Yes, that's true. But that then has to affect the way matter moves and so on. Well, one of the, one of the, okay, I didn't actually, I implied it in what I said. When I first started doing this, it was thought that there was very little radio movement. and now it's become clear that in fact there's quite a lot of radial movements and in fact I do have a model for the radial movement in this but the radial motions are so small our measurements aren't good enough to test the model. It's quite clear that there's substantial radial movements So they're not So then you have to ask where do these motions come from? So that again that speaks of action, events. Aren't there any nuclei without arms? Yeah, there are. There are, hang on, you've got the arms. Oh, sorry, no, I thought you meant arms without nuclei.

1:15:00 Well, that's why there are... There are very distant objects measured in with the Hubble Space Telescope. Supposedly proto-spiral galaxies where you see very strange morphologies with cores, and they're supposed to be all the formation of galaxies. The standard interpretation near the start would be You mean elliptical? Yeah, I'm just referring entirely to an elliptical galaxy. What about globular clusters I mean you know the fact that I don't know a lot about this is there any angular momentum in a globular cluster or is it just no it's a huge amount of angular momentum in a globular cluster sorry a huge amount of angular momentum in a globular cluster and does it move like a sphere no it's all over the place it's spherical it's spherical which means that the stars in them go in all directions it's like a mist like a cloud it's not a there's not an is evolving to the ellipses and then the ellipses involved in the ellipses with the one with the bulge. If the bulge, if the part of the bulge forms after the disk, then it's pulling material in and it will spin up say that again your concept was that you started with a bulge and built a disc now having built a disc it's still possible for the bulge to pull in some of the matter it's also still falling in anyway If it does that, given that the disc has an angular momentum, the bulge will spin up. And if the bulge spins up, I guess you get a different kind of instability. It's extremely complex, I agree. You know, that might produce stripes for all I know.

1:17:30 Okay, now maybe... Well, I'm in great... I'm in great plan. next person is he who is a new person he's from Oxford and he's talking biologists I would like to say a few words about The talk actually is a kind of autobiography of how I want to be here. So, well basically I did a, I've got a doctorate in Zoology from Cambridge, and in that thesis I developed some ideas on hierarchies, applying them to Eucharist and Theory. So that hierarchies would resolve some of the problems in Eucharist and Theory. But I felt that the next step was to relate that to some ideas in physics. I really had no idea how to do it. So it's basically through meeting Keith that I've got some ideas about how to do it. So that's what the talk's going on. Does that make sense? I suppose the reason I got into computing was probably because I couldn't take research any further. So I got a job in a software company. That's why I do it now. So I'm going to start with talking about evolution and some nice bits of zoology. So in the business this is the issue of evolution. So classic examples of Darwinian evolution. Two examples there. Changes in the proportion of dark and light varieties of the peppermoth. This was during the Industrial Revolution, when trees got covered in soot, so the dark varieties weren't spotted by birds. The light varieties became rare. Now, since we've got clear air, the light ones become more common again, because the bark is lighter.

1:20:00 The other kind of paradigm example is the proliferation of finches on the Galapagos Islands. They think probably from one ancestral species and we end up with lots of different finches on different islands, different sized beaks with different feeding styles. Now I would say that they're basically micro evolutionary changes. so you've got it's just changes within a population or you've got proliferation of populations which though similar no one wins a breed but basically we've got variations on a theme if we consider another example a different example Take the multicellular animals. They divide into two groups, radiates and bilateradians. Jellyfishes, an example of radiates, so they have a rotational symmetry about the vertical axis. Flatworms are the first bilateral aliens, so they've got a reflectional symmetry on a horizontal axis, just like that, basically. So we've got two quite different body patterns here, different basic symmetries. So, thinking about how those would evolve, we're talking about a process of macroevolution, which is the origin of new body patterns and new ways of life. So, that's like the problem, because you've got these two different modes. so evolutionary theories

1:22:30 and of course the flat worms have no more bones than the dentures is that true? they may be called after but they don't have any bones oh no they're definitely not called out they don't even have a body cavity at that stage but you know they share that bilateral symmetry with us probably more nutritious too so evolutionary theories can be classified according to how they resolve the issue So Darwin's theory of transformation is basically saying that microevolution is nothing more than the accumulation of many microevolutionary events. So evolution takes place gradually. The metaphor for this is the order of succession of changes that occur during a particular developmental stage. I consider a human life basically is one elemental stage because we don't really have any kind of metamorphosis so JVS how they, for instance when people would ask him how could intelligence evolve would say, well it evolves in every lifetime for a human being gradually we presumably heard it from Charles Darwin I've heard of Richard Owen. I don't know if you do. First director of the British Museum of Natural History, contemporary of Darwin, political opponent. Basically, most people thought you synonymise Darwin with evolution. Owen's an opponent of Darwin, therefore Owen of creations. It's basically the way it's gone. It didn't occur to anyone to actually think that he might have his own theory of evolution, which was contradicting Darwin.

1:25:00 So he had a theory of metagenesis. microevolution then is the origin of new things upon which microevolution changes simply variations so microevolution is the interesting thing and that goes in about changes about changes yes and the metaphor for that was was a life cycle where you have different stages I've got an example. Massive biology. Larry. I think the lens is not parallel with the screen. No, it's still pretty damaged. Do you have to teach at the university for many years? if you can drop the reflector see the lens isn't parallel to the screen at all you look at it from here it's all over the place I tell if it's life cycle metaginesis then is the sequence of stages pick out two to begin with, the polyp and the reducer. So the polyp is the sessard stage, fixed rock. Is this the development of one particular animal, or is this a number of animals with different characteristics? This is a life cycle of one animal. It's used as a metaphor for how we think evolution could take place. Yes, but also they might be literally a mirror of that. Yeah. The earlier stages showing the earlier evolution. Yeah, I'll say something about it. So a fixed phase, a free-swimming phase, Medusa, which is the jellyfish that we know.

1:27:30 And the planula in between. that was actually suggested in between was considered as maybe a precursor so we could break the metagenetic cycle at a particular point and initiate a whole new so that's the kind of basic problem that we're dealing with these two different modes, continuous and discontinuous. So what I want to do is to try to introduce a picture that's going to help us result in it. It's a picture of hierarchy. Now, this comes from an essay that David Berman wrote towards a theoretical biology series of conferences in the late 60s, early 70s. Now he talks about two movements in a hierarchy, horizontal movement is, if you consider the subsystems alone, the various functions that they carry out each level, but then the vertical movement is the flow of information up and down between those subsystems. So the example he gives is a government. Think of different departments, sub-departments. Now, consider as, well, say, Ken Ligamson commissions a report on congestion in London. So that's a very precise instruction coming up at the top of the hierarchy. That gets sent down, the hierarchy, and is basically spread out into a number of different instructions to many different people.

1:30:00 So rush about collecting different forms of information. Exactly. So it could end up being a particular person standing on a particular street corner, recording how many cars going through. And then it has to go the other way. And then it has to go the other way, exactly. Come back up, the upload flow is basically abstracting out that information, selecting what's relevant, and then the report ends up on Pendleton's desk. Nice and compact form. So, that's quite an intuitive kind of idea of hierarchy. I'm curious to know what Boehm was reading at that time, because it has a lot in common with Arthur Koestler's model of hierarchy, which came out a couple of years earlier. It's based around this idea of the Holon. The Holon is both part and whole. So nice quote, no man is neither, he is a Holon. And it has this metaphor of Janus, Janus being the Roman god of always. Well, the heroes of the January is named after him. So he has two faces facing to the old year and to the new year. So a whole lot of his Janus face and looking inward, looking down, sees himself as this whole, self-contained. Looking outward, he can actually see himself as a dependent part of a larger home. So... So suddenly I remember you asked what one was reading at the time, when I was looking at one of the letters which he was writing, actually he was specifically referring to the picture for this... Yeah, so, right, if they're looking outward there, they're sending information back to

1:32:30 up so they're scanning information from further down digesting it generalizing passing it up they're looking inward they're giving instructions so they're triggering things processes further down spelling out and as it goes further down that instruction will be spelt out particularized yes so he talked about scanners and triggers So what then goes on to talk about two different ways that this hierarchy can change. We've got changes that take part of the ordinary function activity of the hierarchy. These are basically adaptations to local conditions, restoring equilibrium. so it's talking about functions in time it's localised it's continuous but basically it's habitual so we're just bestowing basically the habits this is so well talking about it it is can I just ask how many stages do you imagine there are to this hierarchy I don't know you're just talking about two at the moment You know, there's this one, there's this one, there's that one. Well, there's every level, but has anyone with one, an outer direction? At each level, there's possibly one above and one below, and then the one above has one above that one. Yeah. Go on my line, you'll get a fractal. you all got the first one the second one is a very interesting one because it's changing the structure of the hierarchy itself so we've said that each subsystem can no longer adapt to the local conditions so we need to establish a new regime of adaptability by reorganizing the hierarchy now this is like a sudden flash

1:35:00 understanding more, which is interesting because Kerstler talks about flashes of understanding and Bowen has a similar idea here, so that in a sense it takes no time. It's just like that. Is this Kerstler's book on creation? The actor creation? That's, it's the Dosen machine I'm talking about. Oh, yeah, it's true, actually, a flash of understanding probably does talk about it in the actual creation, right? And it's non-local, the change is affecting all the hierarchic ones. It's a discontinuous change, you know, we were doing that, now we're going to do this. And it's a creative change, because you can't deduce what we're doing now from what we were doing before. This is a reorganisation of the whole way of doing stuff. Yeah. Very sloppy, right? But this was a very odd span. Since, please. I don't know if you did it all day. Right. I'm talking softly. No, no. I don't mean you. I mean the rotation. Well, that's my stick on there. So, we can actually apply this. This is a model of an evolutionary transition. And what we talk about as a species, then, quasi-equilibrium, space-time, functional, developmental hierarchy, that's a bit quasi-equilibrium, so space-time, so it's localised in a particular geographical space, particular geological time. It has a consistent adult form which emerges through consistent development, which I'm calling a developmental hierarchy. So basically, it's the idea that species are stable and then undergoes some patients. I don't understand that, for example. It's only the time that's changed. I just don't understand. What does that mean?

1:37:30 Well, the idea from the previous slide is that you go from one organization to another. Oh, okay. Yes, but in such a functional way, as you had it all in the previous slide, one can understand it. But evolution, I think it has to take time. This is quasi-equilibrium, right? Even the species is changing, but over a long period, only changing a little bit. Now, I don't understand this saltation. Yeah, you need these trees. Now, jump. Is it? Yeah, if you were to flip. it's a sudden regrouping in the hierarchy it simply doesn't change this dumb species which exists it takes some time but this species must change it doesn't help if you think about the unfolding of a genetic program The reason why I didn't understand saltation is the word timeless. It should be sudden, not timeless. Timeless means nothing is happening. What you're really saying is it happens all of a sudden, that's it. Bang, done, finished, gone. So, sortation means a quantum jump, as it were, is it? That's where I'm heading. Ah, okay. Well, I'll just stick with this. Because I, well, it's quite important for what Ben says. I think it's an awful word. No, I think it's a non-physics word. It's a non-physics word. We mean understanding this stuff, but just correct it for now. It's better than pointlessness. More pointless. See what I'm trying to do with it, and then tell me whether it's so good or not. Would you move the slide up, please? We need to come with a stooge to do this.

1:40:00 So he didn't want to say instantaneous because in biology nothing is instantaneous. He means that it was that . I'm saying time is not relevant to that change. But timeless has a completely different meaning. It doesn't mean that it is instantaneous. Are you going to explain why you use the word? So, we're talking about, you know, species reaches its limit of adaptability and there's a transition to a new regime of adaptability to a new species, which after, you know, after we adjust on that, hierarchy settles down to a new... Yeah, that transition happens suddenly. So, because if it doesn't, the species dies out. Yeah, I'm going to say it's either changes or... Here makes a definite correlation of quantum transitions here, and regards the quantum state then as a space-time functioning of some hierarchy, and the quantum transition then is a timeless change in the structure of the hierarchy. A change for which time has no meaning. And again, he talks about the state as the system trying to adapt to to its surroundings and if it's unable to do so it then changes to another state. In that transition it takes a while for the hierarchy to settle down and get into this new mode. So I think I want to try to justify my title. There's another one, too. In 1940, Schrödinger proved that there was absolutely no way genetic material would be stable enough to pass on the third generation's characteristics, the third generation, for example, given the usual laws of thermodynamics and the way things did all about.

1:42:30 and he showed that the necessary stability was actually a quantum stability in the atoms of the molecules of the genetic material and he didn't know about DNA but he did work out that the only way he could do it was by quantum mechanics getting that stability for it to hold together for that length of time that sounds Well, I think precisely because he didn't know about DNA, he had an argument. The point is that every cell has a copy of the DNA, so it's by redundancy and error correction. Oh, sure. Yes, but fair enough. They did show there was a stability effect. So to summarize two kinds of change, I would say, we have a habitual creative change, see, the habitual change is just another event in the chain to determine mechanically worth where the normal space-time function is a creative change, I would say the break in the change is the origin of a whole new change of events, so that the normal space-time functioning is disrupted. So if we're looking from the framework of normal mechanical space-times, it appears paradoxical, this creative change. It appears it's non-legal, non-forzable. In essence, this is a timeless process that dominates and regulates the time process.

1:45:00 anything really new and creative has to come in timelessly. The order of time is then what carries the creative change forward to a complete realization. So that flash of understanding, that split in the vertical hierarchy, the flow of information, time has come relevant to that. The realization of that change occurs in time. So we have a discontinuous change between two space-time functions. So I think microevolution occurs in time and is continuous, gradual. I would say it's a timeless evolution. Time is not relevant to it because it's a change in structure of the hierarchy. So it's a creative change. It has to change quickly because the species are under stress and they don't change quickly or select quickly. They're done for. but you also have to find a different kind of equilibrium I'm very bad at names I probably forgot the wrong name but there are things Burbage Shales what are those shales that are about 600 million years old Burgess that's right they had the most extraordinary forms seemingly appearing all at once with legs on top of them and forms that you just don't see now and somehow those disappeared suddenly didn't they or some of the forms did and the rest carried on. People have talked about this that you can see you get a whole series of macroeoceanic events creating a pool of species and then you've actually got a selection among those species among those new things, new body He synthesizes even Jacob's idea of that formative explosions which he put in against the continuous idea of movement. Yeah, yeah, I think this is, I mean, this is probably maybe a bit more wonderful. You, you are more.

1:47:30 Maybe. Contrary to equilibrium is his theory. But that's kind of saying that, I mean, yeah, I wonder. I mean, I actually gave Alice the title of the slide for evolutionary transitions and thought, well, am I reading too much into Google? Because is he just saying that there are phases where my evolution goes faster? Yeah, that's always been an antibiotic. But he sees a species as this kind of stable equilibrium thing, you know, that stable equilibrium structure, the elemental hierarchy, he sees that the species is defined by a certain... Well, if it's not on the stress, it doesn't need to evolve, so it doesn't change, and it stays as it is for a long time. So, yeah, basically you've got these set of development and strengths, and it stays there. You always got the strengths, as you know. So, because my feeling then is that if you're a key to macroevolution, is to understand this idea of timeless change, this idea of timeless evolution. and so what Bohem suggested for quantum theory was that what had been called time in Schrodinger's equation wasn't time at all, it was actually this timeless order frownter talking about how the timeless aspect of the hierarchy changes. So, he leaves this strange idea in this essay, and that's where I was stuck at, thinking what does this mean? How do we do this for four years? Well, it's not so strange. I mean, you can write down Shreddinger's equation with the state version. And the time then cancels out. So what you're left with is an eigenvalue equation which says the eigenvalues and eigenstates of the energy satisfy these conditions. Now, you know that when you've got to that state, because the time has cancelled out, that this

1:50:00 is a steady state. And if you don't disturb it in some fairly drastic way, you can just sit there. If you disturb it, you have to bring in another system. So the original Schrodinger equation doesn't apply anyway. And then you've got to decide what measure of time will I use and how will I describe the interaction with the performance of change. And very soon but he's got this brilliant idea of a term he's used it several times quayside equilibrium what exactly do you mean by that? I suppose it's not equilibrium what? it's famous term That's why I don't know. No, no, later on. Later on when we . He called this out the implication parameter. Huh? And then... And it's part two of my talk. Oh! Is it the end? No, no. It's part two. It's where... But what I want to do at the beginning of part two is just to take a bit of agreement and get to play a game. I've just got the hierarchy game. So, I suppose I should just ask you to shut your eyes. That's interesting. But then the answer goes again afterwards. Think of a beautiful place. Think of the living things there. As many different kinds as you can. How big are they? And how long do they live? Well, out there is a very nice place to think about. So, what do you find? A few suggestions. Take a soil sample and a microscope, you might find that the soil bacteria is a matter of micrometres long, and that only lives for a matter of minutes before it reproduces. A human being, one to two metres, It's a matter of decades. That's what they reproduce?

1:52:30 Yeah. Yeah, this is like the philosophical model of the war. Having this from a bacteria when it reproduces, is it the same one that was learned before? So I'm saying it's not a tree. Once it's reproduced, it's finished its life. A tree is tens of meters tall, lives for centuries. So, what's this telling us? What it's telling us, I was saying, it's telling us about scale. We're finding many different things living at different scales. And what that means is they have different potent dimensions of space and time. so this is the size and the longevity that I was talking about these are total dimensions of space and length a choice of scale then is a choice of a particular space-time order this links it with another idea that Boe had by order you mean sort of size extent, duration all those things and the idea of moments so entities of scales have different potent moments. So the moment for a bacteria would be a minute, say a year or a decade, for a tree than a century. Now that's actually quite weird if we start to say that, we're saying that the passage of time is different in different scales. So, what it's actually is cumulative time. Because, you know, as a human observer, I'll understand the processes occurring to, say, the bacterial or tree in terms of my current moment. So I think the tree is very slow, and the bacteria is very fast. But I'll create this cumulative time through this perception of the other levels. It's really an artifact if we're trying to collapse those altogether. There's another feature of this, isn't there? So that if a creature lives a very long time, as a macropagic,

1:55:00 it cannot make a great many incremental changes of evolution in a given ailment. So that if it lives for too long, it can't adapt very quickly to the kind of stress which doesn't completely ruin it it simply keeps on nudging and says look you've got to change the weather's changing the planet's changing, you've got to change now if for example human beings all live for 10,000 years we probably wouldn't be here we wouldn't have been able to adapt fast enough mmm so which is why we've got building and so let me get the way and that goes with scale as well and brain size so how does the brain size again that would be another aspect of it I have a question I have a question of the moment And would you regard it as semi-timeless or something like this? Well, it's time to come to take up . Is it a general time of this particular? But it is time. It seems like it is either blind time or it's the time to procreate or some constant factor times that. I don't know why you mean big word, but it's not wrong. In Shakespearean, it's the seven stages. The seven stages of man. Now, they're each shot in enlightenment, but a significant change takes place. Yeah, but I think there could be some reoccurrence of happiness by this differentiation between the moment and the human human. No, I mean, it's just seeing that. I wanted to bring a moment into this that has to visit the job of time. Bringing the idea of moments is to try and bring the idea that time classes differently at different scales. So, you know, small scales can come more quickly.

1:57:30 Large scales can come more saving. How much more time do you feel you need talking about time? It's open Because we're not in late That's sign 13 I've got 19 slides 19 slides How many additional ones? Six additional Six slides About half as much again In minutes How much I had so far Well I said it because of all the questions If you listen quietly I'll read it one slide with six in the middle. Let's do it now. We'll read it one slide. We mean the idea of a metamorphosis. Well, yes. That's my one equation. it's a sort of less of an equation more kind of a philosopher's stone pass things over it given a set of potential spatial dimensions E we can specify a transformational metamorphosis which turns E into a different set of potential spatial dimensions E prime we said that E prime straight to E. E prime are complementary, incompatible, since an observer cannot adopt both scales simultaneously. And I would say that a series of such transformations is an iteration of only the scales in the hierarchy. So basically stepping down levels with each So it isn't just a dog's life goes through roughly the same phases as a horse's life, but on a different time scale. It's not just that. So, that introduces, I would say, another picture of hierarchy, which is basically what

2:00:00 Keith has been telling me about. So, this is the theory of Tera system by removing a layer of components, mainly the intersection network, but the interface between adjacent systems. So, this is the kind of thing that end up with I being the intersection layer, X being subsystems. So, I'd say this is actually equivalent to the first picture that I came the program produced where the subsystems are a horizontal movement and the intersection network then is the vertical movement the flow of information and i'll also say it's equivalent to the person's picture the next bit that keith did was to show that khan's picture was the same jessel's picture so that information about any subsystem is held in a holographic form at its surface, that is, at the intersection. So all that one observer needs to know about a torn subsystem is the information on the surface and closing that subsystem. And you can switch this around as well. So similarly, an observer within the torn system, what it needs to know about the outside world is the whole surface. So I'd say the holon is a homographic surface through which information enters into cards so that kind of makes the link with the first half of the talk So, think of, take a system and make a series of TAS disconnecting a subsystem step by step. a series of tears is a series of transformations of the system matrix of this form

2:02:30 so the succession of transformations I've got a very quick thing here it was referred to by David Bowen as an ordering away a folding and by Jess and Westgate as a logical system so I'm saying the scale of the analysis is the choice of a particular at a particular degree of involvement, but it's basically a number of tears is an application, a number of applications of events, a number of unfoldings. So, I hope is this provides us with a way forward. If we base this transformation M on a new folding parameter, respecting, representing successive steps, which is the way I interpret it as well. That's what's done in the algebraic process. Our transformation equation becomes equivalent to the Schrodinger description of quantum transitions. Schrodinger's equation can be thought as specifying at least in a serious criterion. This is the conclusion that people have understood so what we've done. If you've replaced manifest time, the Schroding's equation, by this unfolding crampton, which is called Tao, to make the link with what Poeum was predicting in that essay. So I feel that that has the ability to capture this idea of timeless evolution that we need to talk about to understand macroevolutionary changes in body plans and new ways of life. I feel that that's the right philosophy of nature that evolution needs. And there is this implementation. As I find, it's really a bit of a post-script in a way, That's a kind of homage to Bow, I suppose, to make this one a kind of homage to Kirsten. Reading Slendon's latest book struck by chapter 12 on the holographic principle.

2:05:00 And these are kind of paraphrases or quotes from what he says there. The most succinct description of the system is the evolution of the image of the system projected onto the surface. So any surface is a channel of information between the surface. Now this is exactly what we were talking about. It's a holon, there we are. So any surface can be treated as a holon. The world is a network of holographs, each of which contains only within information about the relationships between the others. That's the kind of model of the world, the holographic principle. And I'd like to paraphrase that as to say that the world is a hierarchy of columns to make person apparent. And that's the end. Are there any other holons besides human beings? Well, I'm saying, basically, first of all, the way I was talking about what you've got holons were. So you would say human beings, kidneys, cellulose, nuclear. I'm saying that you can simply designate a surface through which information flows as a holon. What I mean is, are there any supernatural holons in the Leibnizian sense? you know I'm thinking about what Bohm thought he was implicitly I think kind of religious I'm not suggesting that there are I don't know what's being said it's a whole of something like with an interface, not with a window, but with an interface? Yeah, that's it. That's why I know Simone is quite

2:07:30 leaning to vibrance, so it would be possible to refresh the windows, which are not there. Any more questions? The hierarchy that I was telling you about last night, actually I was infected by two and the hierarchy I was describing was the same hierarchy. And for those of you who have heard me over the years, one way to describe what I was doing was trying to find an objective criterion for what constitutes a holon. In other words, how do you know a holon when you see one? And this corresponds then sort of to Eddington's definition of a particle, or a particle, a sort of carrier of certain parameters, a carrier of certain parameters between interactions. You're thinking of how long this is positive? Well, a particle is an example of a whole. Ah, that way. Yeah. I wonder what concerns things how long it's been. Well, they carry their own structure, right? Yeah. A particle is a difficult thing to deal with, you know? I think that a whole lot is more like an atomic system than it's on. I mean, if you're going to do hierarchy, then you've got to play the same part of the art. I think you can go a long way before you start dealing with particles. I don't see any difference. But if you go, you can play a photon with a particle. You can do it. You can talk about the particles. You can talk about the particles. The particles are things that exist on the hologram or in the hologram. the tearing. That's where the particles are. We're talking about material systems. If you say that, then you have disallowed particles to do that. You could potentially level the ground and say, there are all these things. He's conserved a lot of these transactions. I think those belong to the holograms, what he described as the holograms, the surfaces.

2:10:00 Well, because a young man has got sort of a park in a jaguar in it, because he, you know, sort of a park is simple, unfamiliar, the jaguar is familiar, I think, but complex, but then he seems to be saying, here you've got different levels, and there are different levels of complexity, which is my figure would be that you can't say that there are certain levels of simple numbers, you've got to have to complex them all the way down, so you can't sort of say that. Well, if you argue you sort of shift the layer, I guess you could do it. My argument is that if you're going to build hierarchy, then the actual hierarchy of construction It has to be in the Senate because that's what we can't really say. So I'm grateful for the rest of the time that we've got an end to that break, right? So you can discuss it with us. Thanks again. And we have four o'clock. Thank you. Well, I too often speak in the first person, except where I want to make a contrast with the received opinion. But, well, it's directed to the eternal task of getting from CH, the combinatorial hierarchy to normal physics. It's prune d'apri is the particles with the interaction strength as our firm starting point, the guideline, and we're not forcing it into the classical mode at all. Moreover, the dynamical ideas, concepts, charge, mass and the rest of it, have to appear naturally if we've made our bridge satisfactorily and not to be taken over from Newtonian physics as they are in quantum quantum physics. Well, so, okay.

2:12:30 Well, I'm after what you might call a blow-by-blow account of what it is to be a particle. We've got an algebraic structure which has been tossed around for many years to which we attach importance. Now we want to say what the algebra actually means in terms of things out there in the world. Program universe years back was a real attempt to find this meaning. I would say that the proponents of program universe back then were afflicted by a sort of philosophical cold feet. If you ever ask them whether they really believed the world was like that, whether those things went on in the world, this is only a model. And so the argument went on. I mean, I can tell why he did describe that in the very future. Well, in addition, I'm aiming to build on parallels of our algebra with that of Peter Rowlands and Don Culler, who much were referred to for brevity as R and C. We think we can benefit from the extensive connections with the experiment which they claim and thus fill up this connection with conventional, fit with ordinary physics. Of course in order to do that we have to establish that there is really a correspondence between in what we're saying and what they're saying. Right, well, the bare bones of the argument are, firstly, that we're hoping to reach a representation of a typical elementary system in interaction with a statistical background. In fact, a high energy particle of some sort. Now, that statistical background It's what we always suppose in the combinatorial hierarchy. We start with unknown things and we proceed by a process of discriminating against things that are known and build it up that way, build it up that way.

2:15:00 But there is always presupposed an unknown in which there are things going on that you don't know what they are until you perform this process. it's not a problem, it's not a, it's not nothing, there's something really out there and the shape of the things out there will determine our experiment, what we find in experiments. Right, now there's the interaction with the statistical background, and we're supposing which gives us the information that we've got to build up some concept of the particle and its stability we shall find is due to the structure of the discriminatory closed subsets which an idea you'll be familiar with and I shall mention it again anyway but the things which are closed under the construction process will naturally appear in the physical world and on that stability stability of whatever particles we try to find. And that stability is therefore threatened all the time. Perhaps we could say we have to maintain that stability against outside intervention, rather than statistical background. Well, now, this is how we want to use the hierarchy out of it. At every stage, there's a constant flux of new elements coming into the known picture. In addition to that, there's a process going on within the picture that has been built up, corresponding with the interactions between the elements themselves. So everything is in this state of flux. and the stability, which we should define using groups and so on, will be achieved against that. But something's going on inside all the time. So there's a beginning about what we're actually saying, we're actually saying that the algebra stimulator describes a flux

2:17:30 of processes going on all the time. Now, I should say that this initial flux creates a framework into which the later elements can be fitted, so that we've always got something there in terms of the hierarchy, we've got elements and they may be at different stages of the hierarchy, different levels, they can be increased, they will accrue by a reason of the interaction and they can be removed. This is an important thing, the possibility of removing it. Otherwise, for a long time, we just thought in terms of a process which we're on building things up which would happen very quickly and we didn't quite know what to do then to perhaps start the way over again. But we've got to support, our model's got to be that there is this continual removal of things that have already been put there in addition to their new things being created. If we don't have that, how can we imagine the changes with nothing to compare with what is new with what's gone at all? Now this framework is not the same as our statistical background. The framework is in the area of what has come to be established, what is known. The most important use of this framework will appear when we can identify with these hierarchy Now, Clive has written an extensive first section to this paper, in which he really does a very nice build-up of the processes of the, I should say, the steps by which this argument has gone through in history, and it's too long for me to try and do it now to read it out, which I would otherwise do, but we shall, when this paper is printed, we shall, it will appear there as a an improvement to this abbreviated thing that I'm doing now. So in general it's a more complex level which behaves as the framework for the operations which are going on at every simpler level. And you'll remember that the point about this construction is that one element at the more complex level specifies or defines the closure of a discriminately closed subset in which

2:20:00 the operation, the transformations are going on. So, and there again, we can speak of changes in the occupancy of one level, which is an if it's useful to have, if and only if there's something which can tell us there's something there but it doesn't have to be there, and for that you need a framework, and the particular form we give to that is that there should be a higher level. Right, well... Now, if you would like to demonstrate that the CHS that's a common problem hierarchy does provide the means for us to do this, to provide this flux on this increasing occupancy of sites and reduction of them. Excuse me, Clayton, you wrote CP, clear. Yeah. Did you mean that? Well, I did say it. I said it too quickly, actually. I should have thought of a comment over the hierarchy. Yeah, C8. Well now, right from the very early days, the occupancy or non-occupancy of sites is a principle which occurred in our earliest algebraic thinking with the quadratic group. These elements simply existed or did not exist. When Frederick came along, he wrote them as noughts and ones and strings, and the situation then became in one way rather less clear, because you didn't know whether these noughts

2:22:30 were symbols or what algebra they carried with them. In fact, it was, in fact, ambiguous and took a lot of sorting out. They are, in fact, what you might call existing symbols and correspond to them with a thing either existed or not existing. And just to look forward a bit, we will find that in R&C, it's a very important principle but not one can be attached to each of his charges and to each of the quaternian elements. And they there do indeed also mean existence or non-existence, either the thing has that in it or it doesn't. well so in the common historical hierarchy we put it on the biblically in the beginning known or unknown entities become known and we recognise equal entities that gave rise for sets of equal entities which is a set of equal entities we get a label I personally prefer to depart from the scriptural emphasis and simply say they're labeled and start there also there has to be a signal to indicate that the incumbent element is not new and that nothing is created so those are the logical beginnings and they will define discrimination without any being committed to the park of roads nor one string representation I point out at this stage that in those days, and from long after, we assumed that the cometitility of an incoming element and the thing that was used to discriminate it against, indeed that was proved in our book Combinatorial Physics, but it happens that it was wrong. It was a special case we were looking at, and it has become very important to generalise and to allow that these are not symmetric, they are, and the process is not equivalent

2:25:00 if you reverse it, it's not commutated, and for reasons I'm not quite clear about, this began to be called Aspect, but not a very good word. So, okay, to sum up, I speak of firstly the continual flux of discriminations inside the constructed hierarchy, and second, the need to have something stable enough to define a particle in the face of this flux, and this is presumably a set of elements which persists at least for a number of steps. can be disrupted by interference from the background about which we know nothing and which can throw a look at all sorts of things, so you have to allow for that as well. These statistical ideas will, as I see, become increasingly important as we manage to get nearer to an actual interpretation of the scheme in terms of actual physics. In other words, particular interest attaches to changes which have some kind of regularity, and of these again those which can be represented by groups will be important, and so we get the picture of the groups as a sort of algebraic engine which keeps things ticking over or indeed racing along. You probably think this is very crude, you may think it childish, but that is for me what groups are. It's what groups are for. The children often inquire what things are for, like what is an elephant for? That seems the question should have an obvious answer. I remember I was instructed in America that the question, what is a chemical plant for, had one answer. A chemical plant is to make money. Anyway, who was it to generate this activity and to describe the limitations on it? Well now, I describe an innovation. I'll call it the world outside. This is quite a recent accretion to our thinking. It seemed obvious enough, but it represents a major change.

2:27:30 We had always supposed that the things coming in from the statistical background were elementary. And it followed that there was nothing in the universe of any significant structure except our own construction. A solipsis picture, if you like. And a bit troubling, you know, it seemed to run counter to what should be. Well, then we realised this again, as it was arbitrary, thinking explicitly about the statistical background, what we said was that there could be anything out there like pigs and cows and sheep, and in particular there could be structured things of exactly the kind we were studying, and what more natural to suppose than that it was populated at least to some extent, by things like the hierarchy that we've already been building up. And therefore the thought arose, well, perhaps these can come straight in, and they can be especially right for them to be discriminated against things in the hierarchy, and this will produce changes at all levels, which removes the very objectionable part of the picture, knowing that you had to start more than the one that wouldn't build up. According to this new picture, interactions can take place anyway. The stimulation from the outside can take place at any level, with any complexity of things, and whole lumps of things can get transferred in that way. When these things are outside, then indeed will be correctly equipped to engage in discriminations with what we've already labelled. Can I ask you something, Tad, are you saying that the hierarchy can start at any level? I can say that the interaction from the outside, the external background, can happen at any level. And that gets rid of the solitist universe, I mean, one mustn't allow one's, when things get out of hand, you mustn't start picturing, imagining yourself having all sorts of knowledge about these things outside. It remains the case that you can only find out what's there by the very process that we're talking about. Nevertheless, it's not a solitist universe

2:30:00 just to reiterate the warning we may be in a universe in which we have a knowledgeable sort of things other than ourselves but we must remember that this expression otherness means what it says and no more, in particular would be quite erroneous to refer any sort of spatial distribution, we mustn't start thinking that these things However, that very thought stimulates because you think, well, then we've got a statistical build, we've got statistical information about the rate at which different kinds of things accrue. Perhaps these can be the first stage in our building up of a spatial picture. Perhaps they can. I mean, that is on the cards. And I can see a fruitful use of statistical methods, perhaps like those to get its refinements of the fine structure constant calculation, to start introducing those notions of spatial configurations and the dynamics resulting from those configurations. As long as you don't believe those constructions of this at all along. When I mentioned about the first process through which the constructed assembly gets depleted to more or less extent, and it's rid its significance to finding a kind of stability, this has become particularly important when we find the need to fit in anti-mix, that's the state of being an antiparticle, I'll use the word entities for convenience, and derivatively from that, of course, there's signs of charge, because it will have been very evident to you that my entire dependence upon the existence, the non-existence, doesn't immediately answer these. You can't just say we've got places in the configuration, they will have physical properties, or they may be negative or positive. Those things are undefined. The old, I mean, the normal way of working is, of course, I suppose, that you can bring the whole classical apparatus with you all the time, whether you've defined it or not.

2:32:30 For far, say it's anathema, you can't. You may have to do that specially. Now, I'll come on, actually a bit later, I'll be going. What is the term deems to be? How about Paul? Yeah, what I meant was how long is it since we started? We started with Paul. We started after, okay. A bit after. At least half an hour more. At least half an hour more. Oh, okay, that should suffice. So, as soon as two different elements come in, they can generate a whole hierarchy. But this whole hierarchy, which is the framework for future elements, has to be generated gradually by the flux of discriminations. I might pretend to say they're all there in potential, but actually that isn't a very good way of speaking. speaking, you seem to need the mathematicians to know whether they're impotential or not. So what happens next? How does the hierarchy cope with our requirements of the divena talking about in a sometimes slightly poetic manner? Well, I've glossed over this. Suppose if you've K and K dash, two elements, and both are known. Well, in the case of, I call it discrimination of these K and K dash, we're nothing to rule. And we have one situation. And we need to dispose of that. In the other case, I'll cut here and I can go back to it. In the one case, the original framework is emptied by one element and in the other case, it's filled up by one element, so we get the possibility of increasing and decreasing

2:35:00 I may get fussed about this because this was never appreciated. We never thought of these terms. I think the work on, even on the program universe, was one of the best is you had one construction, and it went to completion, and then you stopped. I don't know if that agrees with you, Mike. We didn't have any mechanism for getting rid of things. No, no. And so I just remind you that the 0-1 principle has to be pushed further yet, things like an active charge of properties because it must be brought in under the 0-1 data. And the answer to that will depend on the anti-particle picture as I shall show your data. Well, now I'm going to make a direct connection with the work of John, Peter and John, RMC, in an effort to find a bridge from our radical construction of the particle concept. I particularly refer to their paper, the Dirac Algebra and SU-5 symmetry, but also to other papers of theirs, particularly one where they deal with the Higgs mechanism. I will see by no means follow an ironic approach, and in fact they arrived at their theory using the usual, I was going to say naive, particle concept. However, they've introduced certain pieces of mathematics which appear to make the best sense when viewed as a part of a freestanding combinatorial scheme I should do my best to show that and indeed what's more that their basic structure of group algebra bears a strong correspondence with ours therefore I ask your indulgence and theirs in treating the combinatorial structure which we see in the RNC as something separable from the you don't have a good idea of this and standing in its own right as a

2:37:30 It's very difficult to do that because that's not the way they present it, and as I say, I'm asked their endowment in trying it. However, if one could do that, it might put R&C in a position to work backwards and derive results in conventional theory, which otherwise they have to assume. Well, our beginning point of our connection with Arden C is a use of quarks and quark colours. I'm going to... It's just about ten views of the sort that you can do it, I guess. Yeah, it looks all right. Um, I'll take it. These are the interaction screen both of those chargers, this is the electromagnetic chargers, this is the electric, I don't like them that way round. How do you, Professor Robert? Oh, it's Peter, this is the director. This is, I really think that's called S, because my mind works that way, and this is from Europe's. Now, I call these quarks, these are quark colours, they are the descriptions of quarks,

2:40:00 They're not quarks themselves, regardless of the pumpkins, they are not quarks yet. But this is a table which puts, let's see, things, the colours, the coloured quarks, which can be associated with these interaction strengths. and in which these are the simplified form, or the oversimplified form, of the co-efficient center put in two returning groups. So that the use of cork colors is a sort of vital intermediary or interlingual between particle identification and the structure that represents the dynamics. And because these are the coefficients of the fraternity group, I imagine that these are, these represent my engine, you know, they represent the transformations between these things, the possible translations of the different kinds of closures that you can get from speaking of. And there's an enormous scope there, tying it down is a very good work. So one is to read this, say, as a function, as a mapping, one is to read this table as a function, as a mapping, say, w argument b equals to r. It's a changing mapping. It is a mapping, yes. It also has a dynamic element to it. Yes, yes, yes.