WEBVTT NOTE ADDED 29 Sep 2020: This transcript is very poor. I'll try to find time to edit it, but don't know when. Meanwhile I've modified my main claim in the discussion: instead of claiming that the higher level invariants and their changing relationships CANNOT be represented in the basic co-ordinate system, I now claim that for a **controlling** subsystem the mechanisms required for using information about the higher level constructs, e.g. horizontal orientation of crane cab, vertical (angular) orientation of crane jib, length of cable suspended from end of jib, etc. are useful whereas doing planning, reasoning, etc. in a basic physical coordinate system would be intractable. Aaron Sloman ------------------------------------------------------------------------------------------- 1 00:00:00.359 --> 00:00:01.380 Aaron Sloman: Conducting now. 2 00:00:01.770 --> 00:00:03.990 Aaron Sloman: Okay, so 3 00:00:05.549 --> 00:00:21.780 Aaron Sloman: I guess I will just let you tell me what you think. Because you've you've looked at my possibly crazy ideas and I expect they made sense to you. But that doesn't mean you necessarily sort of a right or 4 00:00:23.670 --> 00:00:25.650 Anthony Leggett: Well, yeah, okay. I mean, I 5 00:00:27.090 --> 00:00:29.700 Anthony Leggett: Think it's an interesting set of ideas. 6 00:00:31.950 --> 00:00:35.340 Anthony Leggett: At a very, I should just remark that 7 00:00:36.420 --> 00:00:39.870 Anthony Leggett: And I say very much more primitive live 8 00:00:41.520 --> 00:00:42.660 Anthony Leggett: There is 9 00:00:44.250 --> 00:00:46.680 Anthony Leggett: Some literature, I believe, which 10 00:00:47.730 --> 00:00:48.900 Anthony Leggett: Argues that 11 00:00:50.130 --> 00:00:55.890 Anthony Leggett: Many of the complicated or saw some of these too complicated. 12 00:00:57.360 --> 00:01:00.870 Anthony Leggett: Structures which format. 13 00:01:02.040 --> 00:01:04.020 Anthony Leggett: in resolving crystals and so forth. 14 00:01:05.130 --> 00:01:07.980 Anthony Leggett: I'm not resolved very complicated. 15 00:01:09.090 --> 00:01:15.540 Anthony Leggett: Balancing considerations, whereas night that but purely a result of these are the stereo geometry, the 16 00:01:17.070 --> 00:01:25.200 Anthony Leggett: You know, the fact that bonds. Bonds have to be oriented at certain angles to one another and so forth and so 17 00:01:26.670 --> 00:01:27.420 Anthony Leggett: I think 18 00:01:28.620 --> 00:01:32.640 Anthony Leggett: That idea is not a sudden all completely implausible. Yeah. 19 00:01:33.750 --> 00:01:59.010 Anthony Leggett: But I think the main problem I had with what you sent me was, we start off with the system with a huge number of degrees of freedom. Yes. And then by as we're imposing these and McKenna like constraints and so forth. We cut down the degrees of freedom, but 20 00:01:59.040 --> 00:02:01.650 Aaron Sloman: also open up a new space surface, the main points. 21 00:02:02.880 --> 00:02:03.690 Aaron Sloman: Communicated 22 00:02:04.890 --> 00:02:07.020 Anthony Leggett: Okay, so you have a new phase. 23 00:02:07.230 --> 00:02:08.940 Aaron Sloman: A new space of 24 00:02:09.060 --> 00:02:10.170 Anthony Leggett: Possibilities. 25 00:02:10.830 --> 00:02:22.440 Aaron Sloman: For instance, there are now larger structures that are made of things stuck together or any rate in relationships that are in some ways constrained 26 00:02:23.220 --> 00:02:27.810 Aaron Sloman: And on the basis of those constraints, you can generate new combinations 27 00:02:28.170 --> 00:02:43.560 Aaron Sloman: And my claim is as combinations cannot be described in terms of the low level coordinates of the original system because those combinations are based on 28 00:02:44.670 --> 00:03:01.830 Aaron Sloman: Sort of high level structure things like hinges and rotatable rods and whatever constraining what portions of a set of a crane can do. And as one thing terms that changes what another can do 29 00:03:03.720 --> 00:03:08.580 Aaron Sloman: So for example, if you've got a crane with a job that can go up and down. 30 00:03:08.880 --> 00:03:18.270 Aaron Sloman: Again for a cab and the cab changes that constraints, the possible motions alters the possible emotions for the up and down gym and likewise. 31 00:03:19.350 --> 00:03:24.570 Aaron Sloman: Is no strings attached in time. So what I'm suggesting is that 32 00:03:25.980 --> 00:03:48.510 Aaron Sloman: There isn't a way of expressing those high level constraints to cover all the configurations in terms of the low level systems of coordinates. Now that needs a mathematical argument that I'm not sure I can present clearly yet, but I believe it ought to be possible, and it's 33 00:03:50.850 --> 00:03:59.910 Aaron Sloman: If that's right, it seems to me never to have been said by anybody else says, I've been searching for statements overview like that. 34 00:04:01.710 --> 00:04:03.960 Anthony Leggett: Let me just try to play devil's advocate. 35 00:04:04.230 --> 00:04:07.230 Anthony Leggett: Yes, and take a very, very simple example. 36 00:04:08.460 --> 00:04:10.980 Anthony Leggett: I have a piece of paper. 37 00:04:11.700 --> 00:04:12.150 Pencil 38 00:04:13.530 --> 00:04:17.790 Anthony Leggett: Now, so far as far as that goes. I can 39 00:04:19.710 --> 00:04:24.990 Anthony Leggett: I can draw any kind of lines or whatever I want to on the paper or no restrictions. 40 00:04:25.290 --> 00:04:25.710 Aaron Sloman: Yes. 41 00:04:25.980 --> 00:04:36.780 Anthony Leggett: Now suppose that I attached this pencil to a rigid road which is pivoted. So let's say you're, of course. 42 00:04:38.010 --> 00:04:54.300 Anthony Leggett: Then that drastically constraint was what I can do a visual work and do is to draw signals for circle. Yes, but it seems to me that in at least in the sky trivial cookies I can perfectly well express the constraints in the original coordinates. 43 00:04:56.640 --> 00:05:09.450 Aaron Sloman: I think my examples depend on changing those processes so that you set up something that constraints things and then you build on top of that something else. 44 00:05:09.840 --> 00:05:20.340 Aaron Sloman: Yeah. And then if you change one of the constraints that relative to the original set of coordinates sort of sweet everything around in a way that 45 00:05:21.930 --> 00:05:36.690 Aaron Sloman: isn't accessible that that's the sort of failure isn't accessible in terms of algebraic invariance at the lower level, you need to do it in a different using a different kind of language, you have to sort of introduce new 46 00:05:38.280 --> 00:05:46.410 Aaron Sloman: I suppose phase spaces which are defined by the structures that you've created so far and 47 00:05:48.930 --> 00:05:49.920 Aaron Sloman: If you've 48 00:05:50.970 --> 00:05:53.910 Aaron Sloman: Got a piece of paper and you start folding it 49 00:05:56.850 --> 00:06:01.500 Aaron Sloman: Things can happen that constraint later falls. I mean origami is full of things like that. 50 00:06:02.520 --> 00:06:14.220 Aaron Sloman: And I suspect I if I saw enough that I could probably make my point in connection with origami as opposed to Macondo which have many been thinking about 51 00:06:16.620 --> 00:06:25.080 Aaron Sloman: So, for example, there are origami structures where you get a kind of winged bird light thing and if you move the next wings flap. 52 00:06:26.820 --> 00:06:27.570 Aaron Sloman: And 53 00:06:28.740 --> 00:06:37.140 Aaron Sloman: depending on exactly how you have set up that thing the relationships will be different. 54 00:06:38.640 --> 00:06:46.170 Aaron Sloman: So you might have changed the the setting up of the nick in such a way that moving have it. 55 00:06:46.680 --> 00:06:54.090 Aaron Sloman: Made smaller flaps or large have left for the wings. I don't know, I'm not really an origami expert and my intuitions may be misguided. Yeah. 56 00:06:54.930 --> 00:07:05.040 Aaron Sloman: But that's the sort of thing that I think would be comparable but i i i prefer things like Macondo and Lego because they have these 57 00:07:05.400 --> 00:07:15.750 Aaron Sloman: Rigid components and I can be put together in different ways that are not rigid combinations and then you add extra set of constraints. 58 00:07:16.410 --> 00:07:26.970 Aaron Sloman: Which are rigid relative to the last set of constraints, but you can go back and change the previous set of constraints and in the newly added constraints will Otter wildly relative to the original as faith space. 59 00:07:27.660 --> 00:07:36.660 Aaron Sloman: At the bottom level coordinate system, but at a higher level. It's just a minor change of say altitude or angle of something 60 00:07:37.680 --> 00:07:43.050 Aaron Sloman: But what it's an angle relative to is now something different from what it was originally 61 00:07:44.250 --> 00:07:44.760 Anthony Leggett: OK. 62 00:07:45.960 --> 00:07:47.340 Anthony Leggett: I can totally see that. 63 00:07:48.690 --> 00:08:06.420 Anthony Leggett: The higher level language is much simpler some sentences like so simple language to express what you want some but I'm still I still have difficulty with the idea that you could have at least in principle express it in terms of the lower level, they would 64 00:08:08.220 --> 00:08:13.800 Aaron Sloman: I suspect you could with huge collections of ads and laws. 65 00:08:16.860 --> 00:08:18.840 Aaron Sloman: And some routes to, I guess, 66 00:08:21.300 --> 00:08:27.540 Aaron Sloman: But it seems to me that that description would not be usable for engineering purposes. 67 00:08:29.550 --> 00:08:33.090 Aaron Sloman: Or for the kinds of explanatory purposes that 68 00:08:35.340 --> 00:08:41.880 Aaron Sloman: One uses to show something how something works, but more importantly in the context of biological evolution. 69 00:08:42.900 --> 00:08:46.620 Aaron Sloman: It wouldn't be usable as a specification 70 00:08:47.460 --> 00:08:53.850 Aaron Sloman: That can be a starting performant point for more biological structures to be built. 71 00:08:56.490 --> 00:09:05.130 Aaron Sloman: Either during processes of development of an individual organism or through evolutionary processes which produce new types of organism. 72 00:09:06.630 --> 00:09:07.320 Aaron Sloman: Now, 73 00:09:08.820 --> 00:09:13.770 Aaron Sloman: There may be a deep flow in what I've been saying. But can you at least see the sort of intuition of got there. 74 00:09:15.750 --> 00:09:16.590 Anthony Leggett: Yeah. 75 00:09:18.570 --> 00:09:20.550 Anthony Leggett: I'm just wondering what is the 76 00:09:22.110 --> 00:09:32.010 Anthony Leggett: What is the very simplest structure that you think would effectively make appointment we presented with a pencil on I 77 00:09:34.980 --> 00:09:37.770 Anthony Leggett: Connected to the origin is another example. 78 00:09:39.480 --> 00:09:41.250 Aaron Sloman: I think it might be 79 00:09:43.440 --> 00:09:50.400 Aaron Sloman: Something like a rigid frame on a rotatable axle. 80 00:09:51.900 --> 00:09:56.880 Aaron Sloman: Which has something, it just a connected to it, which can alter its 81 00:09:59.250 --> 00:10:01.950 Aaron Sloman: Relationship to that rigid frame for instance by 82 00:10:03.480 --> 00:10:06.180 Aaron Sloman: Altering the it's positioned in a vertical plane. 83 00:10:07.260 --> 00:10:20.070 Aaron Sloman: Or something like that in their constrained way. And I'm saying that as the one constraint. The first thing changes. The other one changes wildly relative to the ritual set of coordinates. 84 00:10:21.000 --> 00:10:23.130 Aaron Sloman: And widely has to be unpacked 85 00:10:24.930 --> 00:10:33.870 Aaron Sloman: But I think you would be that I think my sort of conjecture is there's no easy way of or no natural way of doing that. 86 00:10:35.850 --> 00:10:39.000 Aaron Sloman: The in the longer term. I'm also 87 00:10:40.830 --> 00:10:43.920 Aaron Sloman: Leading up to a notion of evolution. 88 00:10:45.240 --> 00:10:53.520 Aaron Sloman: birding control mechanisms for controlling the behaviors of these multi layer structures with multiple degrees of 89 00:10:54.360 --> 00:11:04.410 Aaron Sloman: Multiple different kinds of degrees of freedom. Yeah. And then those controls structures were have to be especially evolved themselves. 90 00:11:05.130 --> 00:11:14.220 Aaron Sloman: To match were previously been involved in the physical structures and then you would have for example in organizations like animal or like humans and other in terms of 91 00:11:14.910 --> 00:11:23.010 Aaron Sloman: Animals that can learn and whatever you will have control mechanism for controlling the control mechanisms as well for extending 92 00:11:24.090 --> 00:11:33.150 Aaron Sloman: The processes. So the feeling, there is that those as the those layers of structure, get more and more 93 00:11:34.170 --> 00:11:48.330 Aaron Sloman: Remote from the starting point the difficulty of expressing in the original coordinate systems, what they're doing, just gets more and more enormous 94 00:11:48.840 --> 00:11:54.390 Aaron Sloman: But I like to be able to use a mathematical formulation, as opposed to the word enormous difficulty. 95 00:11:55.080 --> 00:11:57.240 Anthony Leggett: Yeah, actually. Yeah. 96 00:12:01.980 --> 00:12:04.620 Anthony Leggett: Interesting. And I mean, I assume that 97 00:12:06.090 --> 00:12:06.930 Anthony Leggett: There is 98 00:12:08.160 --> 00:12:14.460 Anthony Leggett: Literature in the computer science area which which examines this con Promo 99 00:12:16.830 --> 00:12:18.660 Anthony Leggett: Below the photo so but 100 00:12:20.730 --> 00:12:23.820 Aaron Sloman: I think most of the conventional 101 00:12:24.840 --> 00:12:26.460 Aaron Sloman: Forms of programming. 102 00:12:28.080 --> 00:12:32.130 Aaron Sloman: don't satisfy what I'm talking about. 103 00:12:33.300 --> 00:12:34.620 Aaron Sloman: If they use 104 00:12:36.390 --> 00:12:38.610 Aaron Sloman: Tacky constraint programming languages. 105 00:12:39.420 --> 00:12:58.680 Aaron Sloman: Yeah. Now there are some programming languages and the one that I'm most familiar with, you may or may not ever have heard of which was pop to which came out of Edinburgh. Then at Sussex. It got extended enormously. That's a programming language that has its own compiler available at runtime. 106 00:12:59.430 --> 00:13:03.180 Aaron Sloman: Yeah. And furthermore, one can use that 107 00:13:04.290 --> 00:13:10.380 Aaron Sloman: Compiler to design new languages which themselves will have their compilers available at runtime. 108 00:13:11.670 --> 00:13:21.750 Aaron Sloman: And that produces the ability to create programs which some computer scientists will hate because they cannot prove theorems about them. 109 00:13:22.710 --> 00:13:35.790 Aaron Sloman: Because how the compilers are extended at runtime would depend on what kind of environment they're interacting with for human comes along and Anthony or which problems they solve by designing a new language. 110 00:13:36.630 --> 00:13:48.420 Aaron Sloman: And the compiler for it. And I suspect that that idea was somehow discovered by evolution, long before it came into pop 11 whereas most of the 111 00:13:49.710 --> 00:14:08.490 Aaron Sloman: Sort of officially approved programming languages, rule out, things of that sort. They are too tightly constrained to deliberately prevent the kind of flexibility that I've just been talking about because it means you can't, for instance, guaranteed. 112 00:14:09.690 --> 00:14:13.590 Aaron Sloman: In the language that I'm talking about that will never get stuck in an infinite loop. 113 00:14:14.280 --> 00:14:14.730 Yeah. 114 00:14:16.020 --> 00:14:17.400 Aaron Sloman: And other thing is like that. 115 00:14:19.020 --> 00:14:36.810 Aaron Sloman: Whereas software engineers and mathematically minded computer scientists really like to be able to say, we can guarantee things and for wanting that in various engineering context. But I say enough in the context where you're trying to model biological organisms. 116 00:14:37.200 --> 00:14:37.800 Anthony Leggett: Because they're not 117 00:14:37.980 --> 00:14:38.820 That restriction 118 00:14:44.760 --> 00:14:51.480 Aaron Sloman: I can see that what I'm saying, Isn't a collection of familiar ideas to you. 119 00:14:52.680 --> 00:14:53.040 Aaron Sloman: Know, 120 00:14:55.830 --> 00:14:57.330 Anthony Leggett: Run freight in the last 121 00:14:57.810 --> 00:15:06.540 Anthony Leggett: couple of decades of my my gym reading outside really nice positivity physics been pretty thin 122 00:15:07.800 --> 00:15:16.740 Aaron Sloman: Right, but I hope that at least the Macondo example provides a kind of initially plausible. 123 00:15:18.000 --> 00:15:22.590 Aaron Sloman: Example were describing at the bottom level. 124 00:15:23.790 --> 00:15:28.980 Aaron Sloman: The constraints of you've built a few layers of structure where things can be very 125 00:15:30.900 --> 00:15:40.650 Aaron Sloman: Rigid frameworks and if you change one thing, like the angle of of one thing that can just alters the plane with something else moves up and down. 126 00:15:41.850 --> 00:15:42.480 Aaron Sloman: And 127 00:15:45.030 --> 00:15:56.640 Aaron Sloman: And that's it, simple case, but you can also make it more complicated because what may be altered at one level can alter the way something else controls and other parts of the machine. 128 00:15:56.850 --> 00:15:57.150 Yeah. 129 00:15:58.320 --> 00:16:00.870 Aaron Sloman: And and those layers of description. 130 00:16:03.000 --> 00:16:18.510 Aaron Sloman: Although, then it may be possible to translate them into infinite was me infinite disjunctions at some level, there will be useless for any engineering nervous or I would say for any biological for evolutionary purposes. 131 00:16:18.870 --> 00:16:20.580 Anthony Leggett: Yeah, that sounds 132 00:16:22.110 --> 00:16:22.740 Anthony Leggett: Sounds interesting. 133 00:16:27.960 --> 00:16:29.850 Aaron Sloman: Well, that's very encouraging to me. 134 00:16:32.280 --> 00:16:35.520 Aaron Sloman: Because I was thinking, you might be able to say no you not 135 00:16:35.670 --> 00:16:37.260 Aaron Sloman: You've missed something in 136 00:16:37.650 --> 00:16:39.630 Anthony Leggett: The counter on on the point of 137 00:16:41.010 --> 00:16:45.600 Anthony Leggett: Which you obviously take into account. I don't think I have 138 00:16:48.540 --> 00:16:49.020 Aaron Sloman: Well, 139 00:16:52.290 --> 00:16:55.350 Aaron Sloman: I don't know how you would like to 140 00:16:57.300 --> 00:17:14.310 Aaron Sloman: Proceed. For example, you may say, Well, that's very interesting. I look forward to hearing how you get on. And then you back out and I do what I can. And at some point, I might acknowledge at least your encouragement. 141 00:17:15.780 --> 00:17:16.800 Aaron Sloman: Amy, you for anything. 142 00:17:18.840 --> 00:17:25.800 Aaron Sloman: You know, alternatively, you might get some ideas which won't come immediately in a conversation like this. 143 00:17:26.100 --> 00:17:26.430 Anthony Leggett: Yeah. 144 00:17:26.550 --> 00:17:29.310 Aaron Sloman: But it might come out of a reflection, then you would like 145 00:17:29.370 --> 00:17:37.290 Aaron Sloman: To be a kind of co author, which involves your ideas and you can obviously understand why I would love to have you as a co author 146 00:17:38.580 --> 00:17:39.390 Aaron Sloman: Physicist 147 00:17:39.720 --> 00:17:40.020 Anthony Leggett: It's very 148 00:17:40.050 --> 00:17:57.900 Anthony Leggett: Kind of center, I have to say, I've spent the last couple of months and attempting to be a co author with someone who's he's actually experiment is that, apart from that he's just not as close to my field as I could possibly get have is incredibly 149 00:17:59.520 --> 00:18:02.010 Anthony Leggett: complex and time consuming operational. 150 00:18:04.830 --> 00:18:08.640 Aaron Sloman: Anyway, I won't hold you to that, but I will 151 00:18:09.720 --> 00:18:15.360 Aaron Sloman: At least continue feeling that you don't think it's correct totally crazy 152 00:18:16.740 --> 00:18:22.080 Aaron Sloman: Which for me is very encouraging. Although you might later come up with a reason why totally crazy and then i'm sure what you're telling me. 153 00:18:24.240 --> 00:18:28.830 Aaron Sloman: And I will perhaps occasionally give you the option to look at some 154 00:18:30.030 --> 00:18:36.630 Aaron Sloman: Attempt to make a more precise specification of this thing that that message I sent you. 155 00:18:38.400 --> 00:18:41.430 Aaron Sloman: Was about the 10th attempt to 156 00:18:41.520 --> 00:18:42.870 Aaron Sloman: Come up with something that's 157 00:18:43.050 --> 00:18:49.440 Aaron Sloman: Really intelligible and at least half plausible, but I do find that quite difficult. 158 00:18:51.180 --> 00:19:09.750 Aaron Sloman: And I may or may not perhaps after talking to. I have a biological collaborator, who works on has worked on various kinds of birds crows and others, and also on our anger tanks and so on. And she from her own. She goes, has also written programs and so 159 00:19:11.100 --> 00:19:15.930 Aaron Sloman: And she has actually partly spark some ideas. 160 00:19:17.550 --> 00:19:30.120 Aaron Sloman: And I think he would also be willing to be a co author, although she's so hot. Press because of pressures in her research and teaching other things going on. She's in school of bio sciences. 161 00:19:35.460 --> 00:19:40.350 Aaron Sloman: Was there anything else you wanted to ask, or say or no. 162 00:19:40.830 --> 00:19:45.210 Anthony Leggett: No, I don't think so. Right now, if I do think of anything. Perhaps I could send you an email. 163 00:19:46.620 --> 00:19:49.500 Anthony Leggett: Think if I do you think that I think perhaps I could email here. 164 00:19:49.770 --> 00:19:55.740 Aaron Sloman: Yes, certainly. And if you want to set up another meeting at some other time. Then that's also fine. 165 00:19:56.190 --> 00:19:57.120 Anthony Leggett: Okay, great. 166 00:19:57.330 --> 00:20:00.720 Aaron Sloman: Well, I'm very grateful for the time you've given us so far. 167 00:20:01.260 --> 00:20:01.590 Anthony Leggett: No. 168 00:20:01.680 --> 00:20:05.370 Aaron Sloman: I personally had the feeling that it is something very important. 169 00:20:05.970 --> 00:20:08.100 Aaron Sloman: That nobody else has actually 170 00:20:09.420 --> 00:20:15.000 Aaron Sloman: Got him, got into all over his people came close to it in different ways, including shooting, of course. 171 00:20:15.210 --> 00:20:15.510 Yeah. 172 00:20:16.890 --> 00:20:36.570 Aaron Sloman: But he, he went down a different track because he is I think thinking mainly about evolutionary reproducibility and not about controlling growth and development and behavior. And if he had asked himself. How are these mechanisms be relevant to that he might 60 years ago have 173 00:20:37.950 --> 00:20:46.620 Aaron Sloman: Come up with the ideas that I'm talking about, but with different obviously different terminology and no computer programming examples. 174 00:20:48.030 --> 00:20:48.750 Aaron Sloman: But I don't know. 175 00:20:50.280 --> 00:20:50.970 Aaron Sloman: Okay. 176 00:20:53.010 --> 00:20:54.570 Aaron Sloman: Is there anything else at this stage. 177 00:20:55.500 --> 00:20:58.710 Anthony Leggett: Now, I don't think so. I think I got here. 178 00:21:01.980 --> 00:21:02.790 Anthony Leggett: Which are thinking 179 00:21:03.870 --> 00:21:07.260 Aaron Sloman: Right. Well, what I do now is stop the video. 180 00:21:08.700 --> 00:21:09.510 Aaron Sloman: And 181 00:21:10.560 --> 00:21:19.170 Aaron Sloman: At some point I will see if it is usable. I don't know, a wizard records. 182 00:21:22.140 --> 00:21:26.640 Aaron Sloman: Both of our screens or just yours. I can only see yours and you can only see mine, I presume, 183 00:21:27.060 --> 00:21:30.630 Anthony Leggett: I can see your right now I can see myself right now. 184 00:21:31.500 --> 00:21:38.040 Aaron Sloman: Yes, actually I didn't go into the gallery view which I could have done, in which case I don't have both anyway. 185 00:21:41.940 --> 00:21:59.670 Aaron Sloman: Right when I stopped the video I thought I'm stopping the recording. I wasn't, I was good stuff. Anyway, I will, I will stop stop recording. That is what I meant to do, and I will send, send you a copy the recording. I'll put a link up somewhere. 186 00:21:59.670 --> 00:22:00.600 Anthony Leggett: Yeah, so 187 00:22:00.960 --> 00:22:02.910 Aaron Sloman: fetch it later on. Okay. 188 00:22:03.330 --> 00:22:04.140 Anthony Leggett: Okay, thank you. 189 00:22:04.350 --> 00:22:04.740 Aaron Sloman: Alright. 190 00:22:04.980 --> 00:22:06.030 Aaron Sloman: Thanks very much. Bye. 191 00:22:06.060 --> 00:22:07.020 Anthony Leggett: Okay. Bye bye.