1 00:00:16,460 --> 00:00:21,900 I'm going to tell you today about a natural phenomenon. 2 00:00:21,900 --> 00:00:30,010 That I've been enthusiastic about for many years. 3 00:00:30,010 --> 00:00:36,010 I hope that as I proceed, you will find it interesting in a number of different ways, 4 00:00:36,010 --> 00:00:42,160 but one way in particular is that it involves connexions between the phenomenon I'm going 5 00:00:42,160 --> 00:00:48,670 to describe and other matters in physics and mathematics and connexions are important, 6 00:00:48,670 --> 00:00:54,370 and I want to begin by quoting my very distinguished late colleague Charles Frank. 7 00:00:54,370 --> 00:01:02,660 Physics is not just concerning the nature of things, but concerning the interconnectedness of all the natures of things. 8 00:01:02,660 --> 00:01:14,310 Connexions are not just optional extras, they're an essential feature of our intellectual landscape as mathematical and physical scientists. 9 00:01:14,310 --> 00:01:22,020 Now, this emphasis on phenomena would not have pleased Einstein because he wrote, 10 00:01:22,020 --> 00:01:27,030 I'm not interested in this phenomenon or that phenomenon, I want to know God's thoughts. 11 00:01:27,030 --> 00:01:35,100 The rest is mere detail. But today it's worth pointing out that Hooke had a different opinion. 12 00:01:35,100 --> 00:01:41,190 The truth is, the science of nature has been already too long made only a work of the brain and the fancy. 13 00:01:41,190 --> 00:01:49,260 It's now high time it should return to the plainness and soundness of observations on material and obvious things. 14 00:01:49,260 --> 00:01:53,610 Now they're both right and they're both wrong and in their scientific practise, 15 00:01:53,610 --> 00:02:01,170 neither of them was consistent with the opinions that I've just quoted. 16 00:02:01,170 --> 00:02:04,920 This is the phenomenon. It's a tidal wave travelling up a river. 17 00:02:04,920 --> 00:02:09,690 Here's one on the in Brazil. It's called the Paraka. 18 00:02:09,690 --> 00:02:17,850 Here is our local one on the River Severn in England, and here is also the River Severn in England. 19 00:02:17,850 --> 00:02:23,040 And here is the Silver Dragon on the canting river in China. 20 00:02:23,040 --> 00:02:29,340 More about these later. Now for. 21 00:02:29,340 --> 00:02:39,590 A long time, as I said, I've been very enthusiastic about this local phenomenon, I've been to see it many times and for a few years I've. 22 00:02:39,590 --> 00:02:44,530 Been speaking about it to non-technical audiences. 23 00:02:44,530 --> 00:02:52,780 But in the last months, I have a theory of the phenomenon, and I wouldn't be true to my craft if I didn't describe that to you. 24 00:02:52,780 --> 00:03:01,360 So the talk today is a sandwich, the bread in the sandwich is the public lecture and the filling is the little bit of theory. 25 00:03:01,360 --> 00:03:10,540 So those of you who are not mathematical scientists, if you get lost during the theory part, don't worry, the public part will come back. 26 00:03:10,540 --> 00:03:19,590 OK, now it's a phenomenon of the tides and. 27 00:03:19,590 --> 00:03:29,010 It occurs on a number of rivers in the world where the you have a gently narrowing estuary open to a tidal ocean. 28 00:03:29,010 --> 00:03:36,060 In this case, it's the Bristol Channel. Here is Bristol. There are 29 Bristol in the United States. 29 00:03:36,060 --> 00:03:46,320 This is the Bristol in the European Union, and the board happens upstream up near Gloucester. 30 00:03:46,320 --> 00:03:51,510 So I'm zooming in and I'm zooming in and I'm zooming in. And here's a few kilometres and here's Gloucester. 31 00:03:51,510 --> 00:04:01,020 So this is where the bore is at its best. As I said, it's a tidal wave and you need to understand a little bit about tides in particular, 32 00:04:01,020 --> 00:04:07,020 why there are two tides each day, and it's surprising how many people, even physicists sometimes get this wrong. 33 00:04:07,020 --> 00:04:12,120 So let me explain why, because you know, the tides are caused by the moon and the moon is on one side, not the other. 34 00:04:12,120 --> 00:04:17,130 Well, here's a a quick and dirty way to think about it, but it's right. 35 00:04:17,130 --> 00:04:25,470 The force on the water on the moon's side is is greater than on the solid earth, 36 00:04:25,470 --> 00:04:30,330 and the force on the water on the far side is less than all the solid Earth. 37 00:04:30,330 --> 00:04:39,330 But the solid earth is not fixed in a cosmic vise. Whatever that would mean, it's falling freely under the gravity mainly of the Sun, 38 00:04:39,330 --> 00:04:46,470 but also of the Moon, and that falling freely cancels out the gravity on the solid Earth. 39 00:04:46,470 --> 00:04:57,360 That's Einstein's principle of equivalence, which I was astonished to discover a thousand years earlier in when reading the Arabian Nights. 40 00:04:57,360 --> 00:05:03,930 It's about Sinbad the bird rows and rows till I thought I was about to touch the Vault of Heaven. 41 00:05:03,930 --> 00:05:09,090 Then suddenly it dropped so swiftly that I could not feel my own weight. 42 00:05:09,090 --> 00:05:11,550 Principle of equivalence, exactly. 43 00:05:11,550 --> 00:05:17,880 So the force that raises the tides is the difference between the force of the water and the force on the solid earth, 44 00:05:17,880 --> 00:05:22,830 and that's outwards in both directions. It's the gradient of the tidal force. 45 00:05:22,830 --> 00:05:28,020 And for technical people, that's an inverse cube force, not an inverse square. 46 00:05:28,020 --> 00:05:36,060 There are two tidal bulges. And as the Earth rotates, it moves under each one of them every 12 hours. 47 00:05:36,060 --> 00:05:42,180 Now, this tide raising force explains another thing when you hear that the tides are caused by the moon. 48 00:05:42,180 --> 00:05:45,900 You think why the moon? I mean, it's the we go round the sun, not the moon. 49 00:05:45,900 --> 00:05:52,170 We wobble a little bit, but basically it's the sun's gravity. That's the inverse square, the inverse cube. 50 00:05:52,170 --> 00:05:55,920 The moon's gravity dominates, but not by much. 51 00:05:55,920 --> 00:05:59,250 The sun tide is about half as big as the moon tide. 52 00:05:59,250 --> 00:06:05,910 This begins to explain the complexity of the tides at different times, of course, when the Sun and Moon are in line. 53 00:06:05,910 --> 00:06:12,780 The tide is high, but then the Moon's orbit is inclined relative to the Earth's orbit. 54 00:06:12,780 --> 00:06:19,560 So when this in line happens along the line of intersection of these two orbits, the tide is stronger still. 55 00:06:19,560 --> 00:06:21,390 Both orbits are elliptical. 56 00:06:21,390 --> 00:06:30,900 And so when these first two things happen, when the Moon is closer to the Earth and the Earth is closest to the sun, the tides are higher still. 57 00:06:30,900 --> 00:06:36,900 And these are substantial effects. And that explains why the tides vary a great deal. 58 00:06:36,900 --> 00:06:42,150 These the ball happens more and more dramatically, the higher the tide. 59 00:06:42,150 --> 00:06:50,130 And so it's very variable. There are about 20 years worth seeing. 60 00:06:50,130 --> 00:07:01,560 Now what about the wave aspect now the tide, the bore is the tide coming in as a breaking or other kind of, as I'll describe, later wave. 61 00:07:01,560 --> 00:07:08,880 Now, normally that doesn't happen on the seashore. The tide comes in gradually over six hours and goes out gradually over six hours. 62 00:07:08,880 --> 00:07:14,070 But why then does it concentrate as it as it goes upstream? 63 00:07:14,070 --> 00:07:19,590 For the same reason that the wind waves that are more familiar that you see on the seashore? 64 00:07:19,590 --> 00:07:25,530 They steepen and break. And this is for this reason. 65 00:07:25,530 --> 00:07:31,950 Here's the here are the waves travelling upriver, and you could think of this on a small scale waves on the shore. 66 00:07:31,950 --> 00:07:40,050 The maximum wave speed is a square root of gravity times the depth, and that's faster, the deeper the water. 67 00:07:40,050 --> 00:07:47,910 Now here's what I call poor person's nonlinearity. The crest of a wave is in deep waters and the trough of a wave, 68 00:07:47,910 --> 00:07:54,990 and so the crests overtake the trough and the waves steep and eventually might break with the ball that sometimes happens. 69 00:07:54,990 --> 00:08:09,090 Usually not quite. OK. And so that's why this phenomenon occurs a stretched out the River Severn between sharpness and Gloucester. 70 00:08:09,090 --> 00:08:16,650 That's about 50 kilometres. And here's the normal flow drops about 10 metres during that distance. 71 00:08:16,650 --> 00:08:22,530 But when the ball comes in, here's the tide. The bore is the beginning of the tide. 72 00:08:22,530 --> 00:08:29,730 So after the ball passes, the river flows upstream, it flows backwards, but it's still flowing downhill. 73 00:08:29,730 --> 00:08:35,100 Because the tide is still coming in, it takes about an hour for the full tide to pass. 74 00:08:35,100 --> 00:08:40,350 The ball is the beginning of the tide. So that's the basic phenomenon. 75 00:08:40,350 --> 00:08:48,180 And here are some pictures as a book by Fred Rowbottom about the tidal bore, which as my late, 76 00:08:48,180 --> 00:08:56,430 sadly late colleague who is an expert on the bore hole Peregrine said about this book, It's just not quite wrong. 77 00:08:56,430 --> 00:09:05,080 Okay, but it's actually a good book. You learn a lot about the history of tidal bores and so on from it. 78 00:09:05,080 --> 00:09:12,030 That's the first slice of bread. No, I'm going to tell you. 79 00:09:12,030 --> 00:09:20,160 About this bit of theory that I've done recently, and I want to describe the communist type of bull, which is an unduly bore. 80 00:09:20,160 --> 00:09:22,020 So bits of the ball are breaking, 81 00:09:22,020 --> 00:09:33,600 but mostly it's an undulating wave of a particular shape which moves fairly rigidly upstream for many for several tens of miles. 82 00:09:33,600 --> 00:09:39,690 And it's that shape that moves upstream that I, as a theoretical physicist, want to describe. 83 00:09:39,690 --> 00:09:48,150 Now there is a literature on theory of bores, and it uses a navy stokes equation, nonlinear equations, and it's largely computational. 84 00:09:48,150 --> 00:09:55,410 But I wanted an analytical formula, and that's what I'm going to describe, and I have to be careful with a disclaimer. 85 00:09:55,410 --> 00:10:03,930 Here we see the shape again and here, here again. It's what Nigel Goldman felt the physicist calls a minimal model for the shape. 86 00:10:03,930 --> 00:10:15,750 And what is that? That's. A theory that most economically caricatures the essential physics without necessarily claiming quantitative accuracy. 87 00:10:15,750 --> 00:10:18,500 So I just want the shape, and anyway, it's a natural phenomenon. 88 00:10:18,500 --> 00:10:24,350 It varies as the river bends and as the as a depending on what's on the bottom and so on. 89 00:10:24,350 --> 00:10:32,150 So you're never going to get a precise analytical description. But I want to capture the essence of what you see now. 90 00:10:32,150 --> 00:10:43,160 So here's the boar travelling upstream there it is viewed from the point of view of the land you standing on the land. 91 00:10:43,160 --> 00:10:47,990 This shape is moving past you. And here's the tide coming in below. 92 00:10:47,990 --> 00:10:51,500 And usually the river reverses as the boar arrives. 93 00:10:51,500 --> 00:10:56,990 It's one of the most dramatic things to see this river that's been flowing down reverse itself. 94 00:10:56,990 --> 00:11:02,630 The water flows the other way rather fast, actually for quite a bit, for quite a while. 95 00:11:02,630 --> 00:11:11,090 Well, as a scientists will appreciate, if you want to describe something that doesn't change, it's best to go into the frame, which is at rest. 96 00:11:11,090 --> 00:11:18,560 So you move with the ball and that's the that's the the ball frame moving upstream. 97 00:11:18,560 --> 00:11:25,250 And the aim is to calculate this profile as a function of distance in that moving frame. 98 00:11:25,250 --> 00:11:29,090 OK. Well, there are two aspects to it. 99 00:11:29,090 --> 00:11:33,770 One is completely standard, and I'll run through it very quickly. It's not original at all. 100 00:11:33,770 --> 00:11:37,300 It's called stand is called hydraulic jump theory. 101 00:11:37,300 --> 00:11:41,780 And basically the bore is a difference between two heights of water. 102 00:11:41,780 --> 00:11:46,220 And it's a front that moves along. I want the details of that front the beginning. 103 00:11:46,220 --> 00:11:49,880 Let's just think about the conditions before and after. 104 00:11:49,880 --> 00:11:57,230 And it's based on two ideas conservation of water. What is in compressible and Newton's law to a volume of water, 105 00:11:57,230 --> 00:12:02,720 which is which includes all that, all the interesting stuff we're going to discuss later. 106 00:12:02,720 --> 00:12:11,660 And the result is it connects the down flowing speed and depth of the water upstream 107 00:12:11,660 --> 00:12:17,650 to the incoming tide speed and depth downstream in terms of one single quantity. 108 00:12:17,650 --> 00:12:21,800 You know, we like to describe things in as few quantities as we can. 109 00:12:21,800 --> 00:12:26,450 And the fewer parameters, the better the theory. And it's the ratio of depth D1. 110 00:12:26,450 --> 00:12:37,670 That's the depth, the larger depth of the tide before the bores passed downstream and upstream before the ball comes by. 111 00:12:37,670 --> 00:12:41,720 That's the lower distance D0. So this thing is greater than one. 112 00:12:41,720 --> 00:12:46,610 And how much greater than what it is determines how strong the ball is and tidal bores, 113 00:12:46,610 --> 00:12:53,180 I say both greater than one, and it's roughly speaking the boys under the kind I'm going to describe. 114 00:12:53,180 --> 00:12:59,690 Theoretically, if our is less than about 1.5 and above that, it's turbulent. 115 00:12:59,690 --> 00:13:07,790 Most tidal bores in the world, and they're about 50 or 60 of them of the angular kind. 116 00:13:07,790 --> 00:13:13,850 By the way, the UK has more tidal basin any other place in the world. 117 00:13:13,850 --> 00:13:18,050 Apparently there are 16. I know about four or five of them. 118 00:13:18,050 --> 00:13:23,480 I haven't seen them all. But there are more. 119 00:13:23,480 --> 00:13:27,740 But another, for example, in North America, there are only two. 120 00:13:27,740 --> 00:13:33,380 It's really interesting, and I'm not quite sure why, but I have some thoughts about it. 121 00:13:33,380 --> 00:13:40,910 Now there's an important implication of this first little bit of theory, and it's based on the idea, 122 00:13:40,910 --> 00:13:45,140 which I mentioned really the maximum speed that waves can travel on water of depth. 123 00:13:45,140 --> 00:13:51,680 The is a squirt of g times D. Now what is this implication upstream? 124 00:13:51,680 --> 00:13:59,160 That's ahead of the ball. The flow speed is faster than the maximum speed that waves can travel. 125 00:13:59,160 --> 00:14:05,730 So waves cannot travel upstream away from the bore downstream that's behind the bore. 126 00:14:05,730 --> 00:14:06,930 The speed is slower. 127 00:14:06,930 --> 00:14:18,300 The waves can travel in both directions, so the front of the bore is a horizon separating regions where waves can and can't travel upstream. 128 00:14:18,300 --> 00:14:23,830 And that's my first connexion. It's the basis of an analogy with horizons in relativity. 129 00:14:23,830 --> 00:14:26,520 This isn't relativity, it's fluid mechanics. 130 00:14:26,520 --> 00:14:37,200 There is a large subject of developing over the last 30 years of fluid mechanical analogies to phenomena that occur in the theory of gravity. 131 00:14:37,200 --> 00:14:41,340 Einstein's relativity I'll tell you my opinion about that. 132 00:14:41,340 --> 00:14:52,680 None of those analogies tell you anything interesting astrophysical or about black holes, but they do lead to interesting fluid mechanics. 133 00:14:52,680 --> 00:14:59,040 Now, the common feature here is because, like all analogies, it's partial. 134 00:14:59,040 --> 00:15:05,610 The common feature is waves associated with horizons, and here it's a white hole. 135 00:15:05,610 --> 00:15:12,660 Upstream that's away from the ball is into the hole where waves cannot travel, 136 00:15:12,660 --> 00:15:19,560 but they can travel into the front, which is out of the hole, into the horizon and onto the other side. 137 00:15:19,560 --> 00:15:27,730 So it's the analogue analogy is with a white hole that's standard hydraulic jump theory. 138 00:15:27,730 --> 00:15:36,520 But I want to go beyond that, describe the shape of the undulations. And it's based on this. 139 00:15:36,520 --> 00:15:44,830 There is what's called a dispersion relation for many, many waves of all kinds of linear waves, which. 140 00:15:44,830 --> 00:15:53,710 This, to some extent, is you specify the frequency, I'm calling it Omega as a function of the wave number. 141 00:15:53,710 --> 00:15:58,000 The wave number is one divided by the wave length. 142 00:15:58,000 --> 00:16:05,630 So different waves travel at different speeds. And in this particular case is standard shallow water. 143 00:16:05,630 --> 00:16:17,230 There's shallow water because the the waves, which we're going to describe are longer than the depth and the slopes are rather gentle. 144 00:16:17,230 --> 00:16:24,610 There's a standard formula which I will not derive. It comes from fluid mechanics applying Newton's equations to fluids. 145 00:16:24,610 --> 00:16:31,600 It involves the tangent of the of the depth, which depends on position in this case and the wave number and his due. 146 00:16:31,600 --> 00:16:33,160 These are gravity waves. 147 00:16:33,160 --> 00:16:42,490 Now the group velocity, which is the velocity with which disturbances travel, is the derivative and as a function of wave number, it has this slope. 148 00:16:42,490 --> 00:16:46,870 There's a maximum which I've told you already squirt of g times a depth, 149 00:16:46,870 --> 00:16:53,740 and that's four zero K. That's the longest wave, so the shorter waves travel more slowly. 150 00:16:53,740 --> 00:16:58,060 OK, so that's the first ingredient of this theory, 151 00:16:58,060 --> 00:17:06,910 but that's for water on waves that isn't flowing and our water is flowing even in this moving frame where we move with respect to the bore, 152 00:17:06,910 --> 00:17:10,630 the water is still flowing through that stationary shape. 153 00:17:10,630 --> 00:17:17,020 Now there are four steps in this bit of theory, which I'm going to quickly outline you need to transform, 154 00:17:17,020 --> 00:17:26,340 and it's essentially the Doppler effect from the frame of the water to get the frequency in the frame of the moving bore that we're working in. 155 00:17:26,340 --> 00:17:35,190 We're interested in the ball near the front and for long waves, so we make as one of our common tricks in theoretical physics, 156 00:17:35,190 --> 00:17:41,010 we make an approximation we can expand that more general formula. And and here it is. 157 00:17:41,010 --> 00:17:45,720 This is a frequency in the ball frame and it involves various things. 158 00:17:45,720 --> 00:17:51,300 It involves the the depth at the front and it involves the slope at the front. 159 00:17:51,300 --> 00:17:57,360 Both quantities of which we're going to find later. Then there's a third thing. 160 00:17:57,360 --> 00:18:03,000 We want a steady profile. Nothing is changing. So the frequency is zero. 161 00:18:03,000 --> 00:18:08,550 That's an analogy with what in some branches of condensed matter, physics is called a soft mode. 162 00:18:08,550 --> 00:18:16,320 OK. And then finally, there's another trick, which is this We want to find this depth. 163 00:18:16,320 --> 00:18:18,870 We want an equation that it satisfies. 164 00:18:18,870 --> 00:18:28,110 And to get an equation from a dispersion relation, you do exactly what Schrodinger did when he found his way of equation in quantum mechanics. 165 00:18:28,110 --> 00:18:33,630 You replace the wave number by a derivative, and I won't explain why that where that comes from. 166 00:18:33,630 --> 00:18:38,970 But when you write simple formula for simple travelling waves, it becomes clear. 167 00:18:38,970 --> 00:18:46,320 So this is now an operator acting on this depth that we want to find. 168 00:18:46,320 --> 00:18:48,360 As I say, it's an analogy. 169 00:18:48,360 --> 00:18:58,320 So the profile is a zero energy I state of the water for technical people, and this is what in quantum mechanics will be a Hamiltonian, 170 00:18:58,320 --> 00:19:03,390 which is what determines the structure of the system you're interested in here. 171 00:19:03,390 --> 00:19:08,310 It's shallow, flowing waves on shallow water. 172 00:19:08,310 --> 00:19:14,340 Good well, and not just one little technical comment before I give the answer. 173 00:19:14,340 --> 00:19:19,110 You say this involves x k in case an operator, the order matters. 174 00:19:19,110 --> 00:19:28,860 Now this is common throughout quantum physics and wave physics is that the order, which operations act makes a big difference in everyday life? 175 00:19:28,860 --> 00:19:36,060 Of course, this is very familiar. You know, you put your socks on before you put your shoes on and not the reverse. 176 00:19:36,060 --> 00:19:42,540 It's obvious that operations don't, as we say, don't compete with each other. 177 00:19:42,540 --> 00:19:46,590 And so how do you deal with that now in quantum physics? It's a known problem. 178 00:19:46,590 --> 00:19:54,270 And actually, given a Newtonian dynamical system, there isn't a unique way to get a quantum system that corresponds to it. 179 00:19:54,270 --> 00:20:00,210 You have to use physics to determine one of the ambiguities, which is this ordering. 180 00:20:00,210 --> 00:20:10,460 But. In quantum physics, it doesn't actually usually matter enormously, it gives certain corrections to choose one ordering or another. 181 00:20:10,460 --> 00:20:16,820 This case is unique in my experience, if you don't choose the right ordering, there's only one. 182 00:20:16,820 --> 00:20:24,650 You can't describe a bore. A bore is something where from this theory, the water has different heights on the two sides. 183 00:20:24,650 --> 00:20:32,120 If you don't use the right ordering, you get waves that are of the same height on both side tsunami as an example of that, 184 00:20:32,120 --> 00:20:36,650 where the waves are the same height waters, the same height on both sides. 185 00:20:36,650 --> 00:20:43,400 So uniquely, the ordering is specified by the fact that you're wanting to describe a bull. 186 00:20:43,400 --> 00:20:52,400 And here's the answer I'll just tell you the answer. The depth is, well, the depth before the bore passes. 187 00:20:52,400 --> 00:21:00,740 And then there's this parameter ratio of depths. But then there's is scaling function and what it is, it's an integral. 188 00:21:00,740 --> 00:21:05,720 If those of you know, integrals are is the interval of something called an area function. 189 00:21:05,720 --> 00:21:10,800 I'll talk about it later, but I want to just show you the picture. So here's a picture. 190 00:21:10,800 --> 00:21:23,600 Now this is the shape and. In this minimal model, Angela Balls are a stretched version of this shape, and the stretching is this L, 191 00:21:23,600 --> 00:21:32,420 it's a skill to scale and what it is, it's the depth at the ball, which is basically it's here, never mind the one third. 192 00:21:32,420 --> 00:21:38,780 We come to that later. And here's the slope at the at the origin there. 193 00:21:38,780 --> 00:21:45,860 So this tells you this is the basic theory. Now it's not enough. 194 00:21:45,860 --> 00:21:51,140 And there you have to apply certain self consistencies, which I won't have time to go into. 195 00:21:51,140 --> 00:22:01,100 But from that you get for results. The first is the depth, the depth at the picture, in the ball frame. 196 00:22:01,100 --> 00:22:12,510 The depth is is where this the natural origin point of this little function is one third of the way up between the. 197 00:22:12,510 --> 00:22:17,490 Before and after depths of the waters, one third of the way up, that's the first result. 198 00:22:17,490 --> 00:22:23,640 The second result is that the maximum slope again depends just on this parameter. 199 00:22:23,640 --> 00:22:28,350 And it's a number which comes from theory of every function doesn't matter what. 200 00:22:28,350 --> 00:22:31,410 And here it is very precise theory. 201 00:22:31,410 --> 00:22:40,910 The slope in degrees as a function of this ratio of depths before an hour, well when the depth ratio is nearly one, there's hardly any border at all. 202 00:22:40,910 --> 00:22:44,040 The border is very shallow. This slope is very shallow. 203 00:22:44,040 --> 00:22:52,560 Beyond the range of where this theory will work, it's still only risen to about 30 degrees is a rather gentle, rather gentle slope. 204 00:22:52,560 --> 00:22:56,770 Then what about the quote wavelength distance between the first two maxima? 205 00:22:56,770 --> 00:23:00,420 That's a dramatic thing you see. Is this these first two waves? 206 00:23:00,420 --> 00:23:06,750 Then they get closer and closer and closer. And again, it depends only on this ratio. 207 00:23:06,750 --> 00:23:10,380 And here's the picture for very gentle pause. 208 00:23:10,380 --> 00:23:20,190 This wavelength is enormous, and that justifies this gentle, linear wave approximation. 209 00:23:20,190 --> 00:23:25,980 And then as the ball is stronger, the wavelength gets smaller and smaller. 210 00:23:25,980 --> 00:23:35,400 But it's always large in any relevant region compared to the depth, which again justifies the shallowness that we're that we're using. 211 00:23:35,400 --> 00:23:40,110 And then there's the steepness, which is this I've defined it this way. 212 00:23:40,110 --> 00:23:51,790 It's the ratio of the. Contrast between the maximum depth and the minimum depth at the first minimum, divided by twice the wavelength. 213 00:23:51,790 --> 00:24:01,610 There also is this function. Now this completes the theory that one has every feature of the bore in terms of this ratio of deaths. 214 00:24:01,610 --> 00:24:10,930 Now, physics is an experimental subject, and I wanted data for which I could compare this theory. 215 00:24:10,930 --> 00:24:14,770 It's very hard to find reliable data. 216 00:24:14,770 --> 00:24:19,210 First of all, because it is a natural phenomenon, the numbers fluctuate enormously. 217 00:24:19,210 --> 00:24:21,190 I'll show you the best I could find as well. 218 00:24:21,190 --> 00:24:33,460 The Good Book by Hugh Burchard songs the notion there's a tidal engineer, and he gives data for this precise quantity as a function of this ratio. 219 00:24:33,460 --> 00:24:37,420 And he gives the data for a number of different pours. 220 00:24:37,420 --> 00:24:42,130 Some of them are natural balls, and some of them are laboratory balls. 221 00:24:42,130 --> 00:24:46,780 I make no apologies for what you're going to see now because the numbers fluctuate enormously. 222 00:24:46,780 --> 00:24:50,590 There we are. However, it could be. 223 00:24:50,590 --> 00:24:56,620 It could have been that this theoretical curve, which is what I'm showing you here, could have been way above. 224 00:24:56,620 --> 00:25:04,300 It could have been way below. But it isn't. It goes through this rather inadequate, but inevitably inadequate data. 225 00:25:04,300 --> 00:25:09,370 So I'm quite pleased with this. That's the that's the the theory. 226 00:25:09,370 --> 00:25:13,720 OK. One little tiny bit of oh, OK. 227 00:25:13,720 --> 00:25:17,050 So so the outcome is what is the bore? 228 00:25:17,050 --> 00:25:25,910 It's a zero energy organ function of a quantum Hamiltonian, a soft mode, a white whole horizon, and it's related to airy functions. 229 00:25:25,910 --> 00:25:28,750 And I got to tell you a little bit about every function. 230 00:25:28,750 --> 00:25:35,680 Some of you here who know me know that this is one of my favourite objects in theoretical physics. 231 00:25:35,680 --> 00:25:48,950 It's ubiquitous. It's ubiquitous because as Airy himself in 1838 realised, it describes what waves do near the singularities of the theory of rays. 232 00:25:48,950 --> 00:25:58,630 Now we see that mostly in most clearly in optics, a rainbow is a caustic acoustic is the singularity of ray. 233 00:25:58,630 --> 00:26:04,900 Optics is where focussing occurs. It's a line where that comes from with with raindrops drops. 234 00:26:04,900 --> 00:26:13,690 I don't have time to tell you, but if you see a rainbow on the meteorological conditions where all the raindrops are similar in size, 235 00:26:13,690 --> 00:26:18,250 which happens about a third of the time, then you can see interference fringes. 236 00:26:18,250 --> 00:26:24,490 These are wave effects and they they describe this characteristic, airy function. 237 00:26:24,490 --> 00:26:31,090 Now the tidal bore, I didn't describe that, but in a way this front is a kind of caustic. 238 00:26:31,090 --> 00:26:35,980 It's of caustic in space time. I don't have time to explain that, but it is. 239 00:26:35,980 --> 00:26:40,570 So here you're looking with your eyes, you can see an airy function. 240 00:26:40,570 --> 00:26:45,550 There are several in fluid mechanics other than the. 241 00:26:45,550 --> 00:26:53,620 The tidal bore tsunami is an example, which is the tsunami is built on this function undulating, 242 00:26:53,620 --> 00:26:57,850 convoluted with the structure of the earthquake that causes it. 243 00:26:57,850 --> 00:27:04,000 And there's a lot one could say about that, but it's another talk. 244 00:27:04,000 --> 00:27:09,460 You're all familiar with this v shape behind a swimming duck or a ship. 245 00:27:09,460 --> 00:27:14,440 Well, this is a caustic of the rays of the water waves and. 246 00:27:14,440 --> 00:27:25,060 It has always the same angle, it's about the arcs on one third, it's about 19 degrees, the half angle, and that comes from the physics of water. 247 00:27:25,060 --> 00:27:28,000 This is now deep water, not shallow water. 248 00:27:28,000 --> 00:27:39,490 If you are in a small boat, for example here and a big boat passes by with this, with this with its V shape. 249 00:27:39,490 --> 00:27:49,210 Eventually, the V-shaped will catch up with you. It takes longer than you think because the group velocity with which this group approaches 250 00:27:49,210 --> 00:27:54,610 you is half of the phase velocity of the waves within the group that you naturally see. 251 00:27:54,610 --> 00:28:02,350 But still, it will catch up with you. And then as this crosses passes you, you in little rock up and down. 252 00:28:02,350 --> 00:28:05,170 Now this is a caustic, so this is an airy function. 253 00:28:05,170 --> 00:28:13,180 So you then feel in your body the undulations of the area function every time you're in a small boat, in a big boat passes by. 254 00:28:13,180 --> 00:28:23,380 Very good. And here's an example of a picture where you see both of them because the wakes of these surfers interact with the undulations of the ball. 255 00:28:23,380 --> 00:28:28,330 So here you see both kinds of a phenomenon. 256 00:28:28,330 --> 00:28:35,560 A couple of little digressions. Before we get back to the bread, there's an empty bore. 257 00:28:35,560 --> 00:28:42,350 Tiny ripples. You have to include surface tension, as well as gravity that modifies the dispersion relation here. 258 00:28:42,350 --> 00:28:48,610 Surface tension in a particular way. It surface tension this term dominates for short waves. 259 00:28:48,610 --> 00:28:55,840 That's large K and in particular, if the wavelength is less than a couple of centimetres ripples. 260 00:28:55,840 --> 00:29:05,480 In other words, and then something interesting happens. This square root of g times, the depth is still a limiting velocity. 261 00:29:05,480 --> 00:29:12,050 But now it's the minimum, not the maximum. And that means that the short waves travel faster. 262 00:29:12,050 --> 00:29:24,050 So when you see when it's raining and you see water cascading down in films of water cascading down the pavement, they form groups within each group. 263 00:29:24,050 --> 00:29:28,520 You see, the undulations are ahead of the group, not behind the group. 264 00:29:28,520 --> 00:29:35,480 As with tsunamis and as with tidal bores, and you can see that ripples ahead. 265 00:29:35,480 --> 00:29:44,570 You can see that when with a faucet, the tap is on on onto the onto the sink. 266 00:29:44,570 --> 00:29:51,410 And now you see these waves, which are ahead of the of the main of the main structure. 267 00:29:51,410 --> 00:29:57,290 You have to think a little bit to fit that into. The framework that I've been describing is a kind of A. bore. 268 00:29:57,290 --> 00:30:03,890 Now another digression, which I can't resist telling you one other tidal phenomenon sort of related, 269 00:30:03,890 --> 00:30:10,550 but not really, but which I saw recently is in the Gulf of Corey reckon. 270 00:30:10,550 --> 00:30:22,220 Now, the Gulf of Corey Reckon is a place which near Glasgow, which has huge waves and a whirlpool associated with the flood tide and the ebb tide. 271 00:30:22,220 --> 00:30:27,890 Now here we are, though his Glasgow and and his Jura and his Scarborough, 272 00:30:27,890 --> 00:30:38,040 and it's between them that you get this gulf of Corey reckon the most dangerous place to sail in around the UK and. 273 00:30:38,040 --> 00:30:44,130 Here it is, again, Scarborough and his juror, and I just want to remark down here is Barnhill. 274 00:30:44,130 --> 00:30:53,670 It's where George Orwell escaped after the war to write nineteen eighty four and he was with his young son and they went sailing in. 275 00:30:53,670 --> 00:30:59,610 This Gulf of Korea reckon at the wrong time and capsized and nearly came to grief, 276 00:30:59,610 --> 00:31:06,930 though very lucky to be rescued anyway because of the structure of the bottom. 277 00:31:06,930 --> 00:31:15,300 There's a pinnacle underneath the interaction of the flood tide and the ebb tide with that causes huge 278 00:31:15,300 --> 00:31:24,150 whirlpools and huge standing waves away from this sort of a kilometre or so a mile or so where this gulf, 279 00:31:24,150 --> 00:31:31,630 the water can be very calm. And I was there a few a few months ago. 280 00:31:31,630 --> 00:31:37,170 You can. There are few boatmen licence to take tourists through this. 281 00:31:37,170 --> 00:31:41,700 They know what they're doing. You should never try to sail yourself. 282 00:31:41,700 --> 00:31:46,230 It's the world's third biggest whirlpool area without boats. 283 00:31:46,230 --> 00:31:49,560 What happened was that the the pilot would see a whirlpool. 284 00:31:49,560 --> 00:31:58,360 There could usually three or four of them and see a whirlpool and sails into it and turn off the engine and you slowly go round and round and round. 285 00:31:58,360 --> 00:32:02,870 Kind of lovely thing and huge standing waves. 286 00:32:02,870 --> 00:32:11,400 You can be 10 metres high. They weren't on the day that we went there, but it's kind of really, really wild, wild standing waves. 287 00:32:11,400 --> 00:32:22,950 Now, just one thing before I get back to the bread, we embarked on this for this tourist trip, the place a little bit north of Corrie, I reckon. 288 00:32:22,950 --> 00:32:28,650 And there were two boats our boat, another boat for the same company, which had a television crew on it. 289 00:32:28,650 --> 00:32:34,260 And I got talking to the guy there who seemed to know a lot about tides. 290 00:32:34,260 --> 00:32:38,490 And I said to him, You know, it's quite a dangerous place. 291 00:32:38,490 --> 00:32:42,330 George Orwell nearly came to grief with his young son. 292 00:32:42,330 --> 00:32:46,530 He said, Yes, I do know I looked him. I you George Orwell son. 293 00:32:46,530 --> 00:32:53,280 He said yes, and we've been in correspondence. He's a retired engineer, slightly younger than me. 294 00:32:53,280 --> 00:33:00,480 He was two and a half at the time. He just about remembers it. But now he often he lives somewhere in Warwickshire, 295 00:33:00,480 --> 00:33:07,050 but he has a house up there and occasionally takes groups of people in commentates about this tidal bore. 296 00:33:07,050 --> 00:33:10,560 So this is kind of a very unexpected encounter. 297 00:33:10,560 --> 00:33:19,500 Now, every year, I buy the tide tables from Victoria Arrowsmith Brown, whose company has been produced, 298 00:33:19,500 --> 00:33:30,450 whose family have been producing the tide tables of the Bristol Channel since 1835, and I've just received the other day the ones for next year. 299 00:33:30,450 --> 00:33:40,110 And this contains the tides from navigable navigation, the interesting place on the Bristol Channel and the relevant places the highest one. 300 00:33:40,110 --> 00:33:43,500 Upstream it sharpness. There it is. 301 00:33:43,500 --> 00:33:53,430 And you look at the tides that sharpness and when the tide is sharpness is more than nine metres high, then there will be a bore higher up. 302 00:33:53,430 --> 00:34:00,690 It won't be nine metres, it will be one or two. But that's the algorithm. And then you can predict and it's very useful, just a comment. 303 00:34:00,690 --> 00:34:10,620 The tides in the Bristol channel, where the Avon near Bristol moves out into the region, where the two bridges are the second highest in the world. 304 00:34:10,620 --> 00:34:14,970 So that's why this phenomenon happens farther up the tide range. 305 00:34:14,970 --> 00:34:19,140 There can be 17 metres, a huge tide range. 306 00:34:19,140 --> 00:34:29,130 OK, now there's a lovely book by a French surfer, Antony Koller, called mascara owned lunar, 307 00:34:29,130 --> 00:34:34,410 which contains some lovely pictures, some of which I'm going to show you. Here's the seven. 308 00:34:34,410 --> 00:34:38,970 Actually, it's sort of turbulent, but you also see the undulations. 309 00:34:38,970 --> 00:34:42,930 Here are some boat people. OK? 310 00:34:42,930 --> 00:34:47,520 By the way, it's much more magical to visit at night. 311 00:34:47,520 --> 00:34:51,090 There are fewer surfers, almost no service and fewer boats. 312 00:34:51,090 --> 00:34:56,520 And there's always enough light from Gloucester or from the full moon, which happens to be a full moon. 313 00:34:56,520 --> 00:35:05,370 And then the magical thing is that you hear the ball coming before you see it and you can't predict exactly when it's going to come. 314 00:35:05,370 --> 00:35:11,970 It's not like an eclipse. The reason is that when it comes and how big it is depends not only on the height of the tide, 315 00:35:11,970 --> 00:35:17,700 but on how much wind there is, how much water there is in the river, on winds in the Atlantic and so on. 316 00:35:17,700 --> 00:35:28,560 So you can predict about half an hour. And he's got a convenient table of if when the tide is high, it sharpness. 317 00:35:28,560 --> 00:35:36,390 When do you see the bore? Different places it, and that's kind of as useful. 318 00:35:36,390 --> 00:35:42,800 There are a number of different. Is that the good to visit? He also shows pictures on the Amazon. 319 00:35:42,800 --> 00:35:49,250 Now every year I visit an institute here, a physics institute, 320 00:35:49,250 --> 00:35:55,490 but it's never quite at the right time to see this ball on a tributary of the Amazon, and it's a very dramatic thing. 321 00:35:55,490 --> 00:35:59,870 It's called the poor roka, and I've got some rather lovely pictures from him. 322 00:35:59,870 --> 00:36:03,080 You see the scale of it there to get there. 323 00:36:03,080 --> 00:36:06,870 It's not easy. You have to go to Belgium and you've got 15 hours on a riverboat. 324 00:36:06,870 --> 00:36:11,840 It's a long I. I've never done it in India. 325 00:36:11,840 --> 00:36:18,830 On the Hughley, that's the barn. Hughley is a distributor of the Ganges near Calcutta, and here we are. 326 00:36:18,830 --> 00:36:28,760 Here we see Calcutta. Here's the Jubilee coming down. And here's an old picture This is where the barn comes. 327 00:36:28,760 --> 00:36:33,110 Somebody is measured the profile. It doesn't always look like this. 328 00:36:33,110 --> 00:36:42,710 Sometimes that you quite quickly get to something. It's almost horizontal, which is the depth I call one before I've been to see it once. 329 00:36:42,710 --> 00:36:48,830 And it was actually not the best day we were taken to the wrong place, the wrong side. 330 00:36:48,830 --> 00:36:55,760 And all we saw was that there was a gentle swivelling of or rocking of the boat on the water. 331 00:36:55,760 --> 00:37:00,470 It wasn't as dramatic as I'm going to show you now. So here we are. 332 00:37:00,470 --> 00:37:05,510 That's connect about that. Do that. 333 00:37:05,510 --> 00:37:17,450 You'll see a lot of mud coming up, but it dredges a lot of mud from the riverbanks up bottom. 334 00:37:17,450 --> 00:37:27,680 Is. It comes at about 10 or 12 miles an hour, so you can see it in a number of different places. 335 00:37:27,680 --> 00:37:58,920 If you want, if you want to drive from home one to the other. It was, I think, a rather fanciful picture. 336 00:37:58,920 --> 00:38:06,180 I don't know if the person who drew that had ever actually seen it, but since I haven't seen it at its best there, I can't really comment. 337 00:38:06,180 --> 00:38:12,390 But I want to read you something about the bomb. This curl, the ball commences. 338 00:38:12,390 --> 00:38:19,110 Huguely points the place where the river first contracts itself and is perceptible above Huguely town. 339 00:38:19,110 --> 00:38:26,370 And so quick as its motion that it hardly employs for hours in travelling from one to the other. 340 00:38:26,370 --> 00:38:34,140 Though the distance is nearly 70 miles, Calcutta sometimes occasions an instantaneous rise of six feet. 341 00:38:34,140 --> 00:38:42,630 And both here and in every other part of its track, the boats on its approach immediately quit the shore and make for safety to the 342 00:38:42,630 --> 00:38:47,460 middle of the river in the channels between the islands at the mouth of the Makena. 343 00:38:47,460 --> 00:38:53,640 This height of the border is said to exceed 12 feet and is so terrific in its appearance 344 00:38:53,640 --> 00:39:00,390 and dangerous in its consequences that no boat will venture to pass at spring tide. 345 00:39:00,390 --> 00:39:08,490 When I read you this because of what he writes next, the hugely porous, fearsome as it could be, 346 00:39:08,490 --> 00:39:17,430 is but a ripple compared to the can tank bore the greatest of tidal pulls between the river and the city walls, which are a mile distant. 347 00:39:17,430 --> 00:39:21,060 Dense suburbs extend several miles along the banks. 348 00:39:21,060 --> 00:39:28,620 As the hour of flood tide approached, crowds gathered in the streets running at right angles to the can tank. 349 00:39:28,620 --> 00:39:35,340 But at a safe distance, I had the pleasure of visiting this can tank bore. 350 00:39:35,340 --> 00:39:40,290 A few years ago, and I want to tell you a little bit about it. 351 00:39:40,290 --> 00:39:44,970 So here it is. It's inland from Shanghai. 352 00:39:44,970 --> 00:39:56,460 Here's Shanghai. It's called the Silver Dragon. That tidal bore, and it's near the city of Hangzhou, the historic and beautiful city of Hangzhou now. 353 00:39:56,460 --> 00:40:06,030 Just to give you an idea of the scale where we see the boar on our River Severn, it's about 50 metres wide here. 354 00:40:06,030 --> 00:40:12,810 The boar, it's about three kilometres wide where our River Severn opens out into the Bristol Channel, 355 00:40:12,810 --> 00:40:18,360 where you get the very high tides where the bridges are. It's a few kilometres across here. 356 00:40:18,360 --> 00:40:23,970 It's 40 kilometres across a very dramatic. Not quite the longest bridge in the world. 357 00:40:23,970 --> 00:40:29,280 There's a new one near Hong Kong, which is longer just recently opened, but it's very spectacular. 358 00:40:29,280 --> 00:40:31,740 There's a hotel in the middle where we stayed. 359 00:40:31,740 --> 00:40:41,010 OK, now and every day we were taken twice two times a day for three days during this period of high tides. 360 00:40:41,010 --> 00:40:47,910 To see the ball at slightly different places along the river, it's a local attraction. 361 00:40:47,910 --> 00:40:55,110 It's actually President Xi Jinping quoted in one of his G-20 speeches. 362 00:40:55,110 --> 00:41:00,400 All kinds of entertainers are there clowns up and down policemen? 363 00:41:00,400 --> 00:41:05,850 Why? Because some foolish people jumped into the boat several years ago and they were killed. 364 00:41:05,850 --> 00:41:10,890 It's catchy, dangerous, and many people are watching it. 365 00:41:10,890 --> 00:41:15,120 One hundred and twenty thousand was the estimate when we saw it. So here it is. 366 00:41:15,120 --> 00:41:20,250 We were in a little cafe just above everybody, but we could see the boar beginning to come in. 367 00:41:20,250 --> 00:41:26,310 Here it comes by, and here's the wave as it passes the turbulent boar, not an Angela ball. 368 00:41:26,310 --> 00:41:30,840 I want to show you this movie that that I took just to make a comment. 369 00:41:30,840 --> 00:41:39,630 This will go out of shot. But when the ball was passed by, the water level is about this second story of this. 370 00:41:39,630 --> 00:42:14,180 And here you can see people standing. You get the scale. We can just see the far shore far away, several kilometres distant. 371 00:42:14,180 --> 00:42:47,460 And that. And the transition from this smoothly laminar flow down and the turbulent flow upstream is very striking. 372 00:42:47,460 --> 00:42:51,840 I'll just show you a picture that we took at night of just a comment. 373 00:42:51,840 --> 00:42:56,310 I mean, we stood at a place which we thought was good and we could see the ball coming. 374 00:42:56,310 --> 00:43:01,800 And then suddenly motorbike cable, there were policemen screaming at us to get out of the way. 375 00:43:01,800 --> 00:43:03,540 You got to take your car. 376 00:43:03,540 --> 00:43:10,540 They were right because where we were, the water overtopped and we wouldn't have been killed, but we would certainly have been flooded in the boat. 377 00:43:10,540 --> 00:43:15,880 The car would have been flooded to a depth higher than its wheels, so we were very grateful. 378 00:43:15,880 --> 00:43:52,640 So we stood somewhere else which to where I took this picture from. It would go out of focus and then come back again and again a lot more. 379 00:43:52,640 --> 00:44:00,280 Now. Right. 380 00:44:00,280 --> 00:44:08,350 This gives you an idea of the scale because it, by the way, here a boat safely out of the way, it's the way they do it and again, time river. 381 00:44:08,350 --> 00:44:19,090 And look at the size of the people. There they are. Now I want to show you a rather beautiful wave effect that we saw there. 382 00:44:19,090 --> 00:44:25,750 Here's a little bit of the river and the bow comes in and part of it hits this jetty. 383 00:44:25,750 --> 00:44:30,460 That's this bank that's poking out. And there it is. 384 00:44:30,460 --> 00:44:39,130 And you therefore can expect that there will be a reflection. Now, I was aware of this because the first time I saw the boat, some of you, 385 00:44:39,130 --> 00:44:45,280 my mathematical people, will know the name of Ed Lorenz, who's one of the pioneers of chaos theory. 386 00:44:45,280 --> 00:44:48,640 He didn't like to travel much from America where he lived. 387 00:44:48,640 --> 00:44:55,300 But he was persuaded to visit Bristol and give a talk, provided it was scheduled for the day when there would be a bore. 388 00:44:55,300 --> 00:45:02,470 So we took him to see it. We drove to several places and the highest point where you can see is a place called Maze Moor, 389 00:45:02,470 --> 00:45:06,400 etc. Of course, the closest to Oxford, it sits almost on the A40. 390 00:45:06,400 --> 00:45:15,190 Not quite so. You can drive from here very easily, but just upstream from there is a weir which stops it before that, where was built. 391 00:45:15,190 --> 00:45:19,930 I think in the thirties, I'm not sure the ball went up as far as Worcester, but not so. 392 00:45:19,930 --> 00:45:22,180 We wondered if you would see reflected bore. 393 00:45:22,180 --> 00:45:28,210 And sure enough, after about 15 minutes, we were standing on the bridge where we could see the this little ripple came down. 394 00:45:28,210 --> 00:45:35,740 Now I'll show you a more dramatic one. So here's the poor approaching and then it hits the wall. 395 00:45:35,740 --> 00:45:40,390 You're standing on the wall. It's it's safe there and then it interferes with its reflection. 396 00:45:40,390 --> 00:45:46,840 There it is. So this is a reflection. Travelling backwards, interfering with the ball, travelling forwards. 397 00:45:46,840 --> 00:45:57,520 Very good. The rebels in France, several of them on the scene at Caldbeck in French word Islamist go mascara. 398 00:45:57,520 --> 00:46:01,060 That's the title of the book by Alan Anthony Colau. 399 00:46:01,060 --> 00:46:06,340 They're actually two books now, and they used to be a famous book at Caldbeck. 400 00:46:06,340 --> 00:46:14,800 It no longer exists because they dredged the river to help navigation that destroyed it, by the way, with the seven war. 401 00:46:14,800 --> 00:46:16,510 There's endless talk. 402 00:46:16,510 --> 00:46:24,790 I mean, going back more than a century about using the energy of the incoming and outgoing tides to generate electricity with the tidal barrage would, 403 00:46:24,790 --> 00:46:26,440 of course, kill the Boer. 404 00:46:26,440 --> 00:46:37,810 And if that were done, it's estimated that that would supply about seven percent of the UK's electricity needs, which is pretty substantial. 405 00:46:37,810 --> 00:46:45,230 But of course, there are environmental considerations and it's Britain, so things almost never happen anyway. 406 00:46:45,230 --> 00:46:52,150 Caldbeck Here's some old pictures there is a ball of masquerade which you can visit, 407 00:46:52,150 --> 00:46:59,500 which we did, and you see pictures on the walls of the Boer in those days. 408 00:46:59,500 --> 00:47:09,010 Here we are again. This is a again, I suspect, a slightly fanciful picture from the popular astronomy book by Claude Flannery on a 409 00:47:09,010 --> 00:47:14,620 famous astronomy book translated into English around the turn of the previous century, 410 00:47:14,620 --> 00:47:21,940 for which I want to read you two statements. 411 00:47:21,940 --> 00:47:29,560 One day after being present at Caldbeck, after this always curious spectacle of the Boer on the sand, 412 00:47:29,560 --> 00:47:33,400 I returned on foot where it was overtaken by countrymen, 413 00:47:33,400 --> 00:47:41,320 with whom I entered into conversation on my asking him what he thought and what the old people of his family thought, 414 00:47:41,320 --> 00:47:49,090 the phenomenon in which they had observed for so many years. I do not know, he replied, how the wise men explain it. 415 00:47:49,090 --> 00:47:55,630 But for us, it seems to be nothing else than the well known antipathy between salt water and fresh. 416 00:47:55,630 --> 00:48:03,910 They're not of the same character, you see. But this is certain that the freshwater falling into the sea worries the salt water, 417 00:48:03,910 --> 00:48:10,690 with which it finds a difficulty in mixing well in the salt water ends by becoming angry. 418 00:48:10,690 --> 00:48:17,350 It accumulates its anger and every evening, especially the equinoxes, when it's already naturally furious. 419 00:48:17,350 --> 00:48:23,800 It resolves on hunting the freshwater, sending it back with great velocity. 420 00:48:23,800 --> 00:48:29,230 I assure you, sir, that this region is much simpler than the attraction of the Moon. 421 00:48:29,230 --> 00:48:35,860 Now, I'm not reading this in any a spirit, a contemptuous spirit, because, you know, 422 00:48:35,860 --> 00:48:40,180 if you don't have physics, you think of whatever you can and fresh water, it's a wrong theory. 423 00:48:40,180 --> 00:48:45,940 But still, we know in physics there are wrong theories which turn out to be very useful. 424 00:48:45,940 --> 00:48:57,220 OK, so that's that's one. But now I want to read you another one which goes back to mythology and the origin of the word sin. 425 00:48:57,220 --> 00:49:07,750 The sin nymph of Ceres and daughter of Bacchus walking one day on the seashore was seen by Neptune's old monarch of the waters, 426 00:49:07,750 --> 00:49:12,850 who delighted with her charms set out to follow her. 427 00:49:12,850 --> 00:49:19,270 He had already reached her when Bacchus and Ceres invoked by the nymph and being unable otherwise to save her, 428 00:49:19,270 --> 00:49:28,510 metamorphosed her into an azure river, which ever since has borne her name and as every year on its banks, joy and fertility. 429 00:49:28,510 --> 00:49:37,060 Neptune, however, has not ceased to love her, though she has preserved her aversion to him twice a day. 430 00:49:37,060 --> 00:49:43,630 He pursues her with great bellowing. This is the Harvey Weinstein of mythology. 431 00:49:43,630 --> 00:49:48,910 Each time the Sun escapes into the meadows and goes back towards its source. 432 00:49:48,910 --> 00:49:52,300 Contrary to the natural course of rivers, 433 00:49:52,300 --> 00:50:00,340 it's always interesting to see how natural phenomena are reflected in different cultures from the one we happen to have now, 434 00:50:00,340 --> 00:50:06,300 where we use physics now to finish why? 435 00:50:06,300 --> 00:50:09,590 What's the deepest reason to be interested in the book? 436 00:50:09,590 --> 00:50:16,720 Well, there are a number of reasons I've described you various connexion with quantum physics with horizons and the like. 437 00:50:16,720 --> 00:50:29,020 But what is the. Most fundamental aspect of the goal of physics is unification now know unification is connecting unexpected things, 438 00:50:29,020 --> 00:50:37,030 and everyone is familiar with Maxwell's unification of in the middle of the 19th century, 439 00:50:37,030 --> 00:50:43,540 where he showed that electricity and magnetism and light are all part of the same phenomenon a great unification. 440 00:50:43,540 --> 00:50:47,860 Now, of course, we try to unify gravity with other forces and so on. 441 00:50:47,860 --> 00:50:52,630 It's easy to forget that the first unification was Isaac Newton, 442 00:50:52,630 --> 00:51:00,430 who told us that gravity that holds us down and holds the Earth in its orbit and the moon and pulls the tides is the same force. 443 00:51:00,430 --> 00:51:04,120 This was a fantastic discovery and the great unification. 444 00:51:04,120 --> 00:51:14,770 When you see this tidal bore before almost before your eyes, you're seeing this unification of Newton because the tides are pulled by the Moon. 445 00:51:14,770 --> 00:51:22,630 The whose orbit, of course, is determined by gravity and the water is held down by the solid earth, which holds us down. 446 00:51:22,630 --> 00:51:26,410 So really, this unification becomes immediate. 447 00:51:26,410 --> 00:51:39,790 So it's a really lovely thing to see and contemplate. You can read a little about this in two papers one before I made the theory. 448 00:51:39,790 --> 00:51:43,540 It's a little travelogue about the Silver Dragon visit. 449 00:51:43,540 --> 00:51:47,350 And then there's the theory, which was published earlier this year. 450 00:51:47,350 --> 00:51:55,630 The first of these is in my book, which has at least one reader. 451 00:51:55,630 --> 00:52:22,519 No, thank you.