I'm going to tell you today about a natural phenomenon.
That I've been enthusiastic about for many years.
I hope that as I proceed, you will find it interesting in a number of different ways,
but one way in particular is that it involves connexions between the phenomenon I'm going
to describe and other matters in physics and mathematics and connexions are important,
and I want to begin by quoting my very distinguished late colleague Charles Frank.
Physics is not just concerning the nature of things, but concerning the interconnectedness of all the natures of things.
Connexions are not just optional extras, they're an essential feature of our intellectual landscape as mathematical and physical scientists.
Now, this emphasis on phenomena would not have pleased Einstein because he wrote,
I'm not interested in this phenomenon or that phenomenon, I want to know God's thoughts.
The rest is mere detail. But today it's worth pointing out that Hooke had a different opinion.
The truth is, the science of nature has been already too long made only a work of the brain and the fancy.
It's now high time it should return to the plainness and soundness of observations on material and obvious things.
Now they're both right and they're both wrong and in their scientific practise,
neither of them was consistent with the opinions that I've just quoted.
This is the phenomenon. It's a tidal wave travelling up a river.
Here's one on the in Brazil. It's called the Paraka.
Here is our local one on the River Severn in England, and here is also the River Severn in England.
And here is the Silver Dragon on the canting river in China.
More about these later. Now for.
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.
Been speaking about it to non-technical audiences.
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.
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.
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.
OK, now it's a phenomenon of the tides and.
It occurs on a number of rivers in the world where the you have a gently narrowing estuary open to a tidal ocean.
In this case, it's the Bristol Channel. Here is Bristol. There are 29 Bristol in the United States.
This is the Bristol in the European Union, and the board happens upstream up near Gloucester.
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.
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,
why there are two tides each day, and it's surprising how many people, even physicists sometimes get this wrong.
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.
Well, here's a a quick and dirty way to think about it, but it's right.
The force on the water on the moon's side is is greater than on the solid earth,
and the force on the water on the far side is less than all the solid Earth.
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,
but also of the Moon, and that falling freely cancels out the gravity on the solid Earth.
That's Einstein's principle of equivalence, which I was astonished to discover a thousand years earlier in when reading the Arabian Nights.
It's about Sinbad the bird rows and rows till I thought I was about to touch the Vault of Heaven.
Then suddenly it dropped so swiftly that I could not feel my own weight.
Principle of equivalence, exactly.
So the force that raises the tides is the difference between the force of the water and the force on the solid earth,
and that's outwards in both directions. It's the gradient of the tidal force.
And for technical people, that's an inverse cube force, not an inverse square.
There are two tidal bulges. And as the Earth rotates, it moves under each one of them every 12 hours.
Now, this tide raising force explains another thing when you hear that the tides are caused by the moon.
You think why the moon? I mean, it's the we go round the sun, not the moon.
We wobble a little bit, but basically it's the sun's gravity. That's the inverse square, the inverse cube.
The moon's gravity dominates, but not by much.
The sun tide is about half as big as the moon tide.
This begins to explain the complexity of the tides at different times, of course, when the Sun and Moon are in line.
The tide is high, but then the Moon's orbit is inclined relative to the Earth's orbit.
So when this in line happens along the line of intersection of these two orbits, the tide is stronger still.
Both orbits are elliptical.
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.
And these are substantial effects. And that explains why the tides vary a great deal.
These the ball happens more and more dramatically, the higher the tide.
And so it's very variable. There are about 20 years worth seeing.
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.
Now, normally that doesn't happen on the seashore. The tide comes in gradually over six hours and goes out gradually over six hours.
But why then does it concentrate as it as it goes upstream?
For the same reason that the wind waves that are more familiar that you see on the seashore?
They steepen and break. And this is for this reason.
Here's the here are the waves travelling upriver, and you could think of this on a small scale waves on the shore.
The maximum wave speed is a square root of gravity times the depth, and that's faster, the deeper the water.
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,
and so the crests overtake the trough and the waves steep and eventually might break with the ball that sometimes happens.
Usually not quite. OK. And so that's why this phenomenon occurs a stretched out the River Severn between sharpness and Gloucester.
That's about 50 kilometres. And here's the normal flow drops about 10 metres during that distance.
But when the ball comes in, here's the tide. The bore is the beginning of the tide.
So after the ball passes, the river flows upstream, it flows backwards, but it's still flowing downhill.
Because the tide is still coming in, it takes about an hour for the full tide to pass.
The ball is the beginning of the tide. So that's the basic phenomenon.
And here are some pictures as a book by Fred Rowbottom about the tidal bore, which as my late,
sadly late colleague who is an expert on the bore hole Peregrine said about this book, It's just not quite wrong.
Okay, but it's actually a good book. You learn a lot about the history of tidal bores and so on from it.
That's the first slice of bread. No, I'm going to tell you.
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.
So bits of the ball are breaking,
but mostly it's an undulating wave of a particular shape which moves fairly rigidly upstream for many for several tens of miles.
And it's that shape that moves upstream that I, as a theoretical physicist, want to describe.
Now there is a literature on theory of bores, and it uses a navy stokes equation, nonlinear equations, and it's largely computational.
But I wanted an analytical formula, and that's what I'm going to describe, and I have to be careful with a disclaimer.
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.
And what is that? That's. A theory that most economically caricatures the essential physics without necessarily claiming quantitative accuracy.
So I just want the shape, and anyway, it's a natural phenomenon.
It varies as the river bends and as the as a depending on what's on the bottom and so on.
So you're never going to get a precise analytical description. But I want to capture the essence of what you see now.
So here's the boar travelling upstream there it is viewed from the point of view of the land you standing on the land.
This shape is moving past you. And here's the tide coming in below.
And usually the river reverses as the boar arrives.
It's one of the most dramatic things to see this river that's been flowing down reverse itself.
The water flows the other way rather fast, actually for quite a bit, for quite a while.
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.
So you move with the ball and that's the that's the the ball frame moving upstream.
And the aim is to calculate this profile as a function of distance in that moving frame.
OK. Well, there are two aspects to it.
One is completely standard, and I'll run through it very quickly. It's not original at all.
It's called stand is called hydraulic jump theory.
And basically the bore is a difference between two heights of water.
And it's a front that moves along. I want the details of that front the beginning.
Let's just think about the conditions before and after.
And it's based on two ideas conservation of water. What is in compressible and Newton's law to a volume of water,
which is which includes all that, all the interesting stuff we're going to discuss later.
And the result is it connects the down flowing speed and depth of the water upstream
to the incoming tide speed and depth downstream in terms of one single quantity.
You know, we like to describe things in as few quantities as we can.
And the fewer parameters, the better the theory. And it's the ratio of depth D1.
That's the depth, the larger depth of the tide before the bores passed downstream and upstream before the ball comes by.
That's the lower distance D0. So this thing is greater than one.
And how much greater than what it is determines how strong the ball is and tidal bores,
I say both greater than one, and it's roughly speaking the boys under the kind I'm going to describe.
Theoretically, if our is less than about 1.5 and above that, it's turbulent.
Most tidal bores in the world, and they're about 50 or 60 of them of the angular kind.
By the way, the UK has more tidal basin any other place in the world.
Apparently there are 16. I know about four or five of them.
I haven't seen them all. But there are more.
But another, for example, in North America, there are only two.
It's really interesting, and I'm not quite sure why, but I have some thoughts about it.
Now there's an important implication of this first little bit of theory, and it's based on the idea,
which I mentioned really the maximum speed that waves can travel on water of depth.
The is a squirt of g times D. Now what is this implication upstream?
That's ahead of the ball. The flow speed is faster than the maximum speed that waves can travel.
So waves cannot travel upstream away from the bore downstream that's behind the bore.
The speed is slower.
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.
And that's my first connexion. It's the basis of an analogy with horizons in relativity.
This isn't relativity, it's fluid mechanics.
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.
Einstein's relativity I'll tell you my opinion about that.
None of those analogies tell you anything interesting astrophysical or about black holes, but they do lead to interesting fluid mechanics.
Now, the common feature here is because, like all analogies, it's partial.
The common feature is waves associated with horizons, and here it's a white hole.
Upstream that's away from the ball is into the hole where waves cannot travel,
but they can travel into the front, which is out of the hole, into the horizon and onto the other side.
So it's the analogue analogy is with a white hole that's standard hydraulic jump theory.
But I want to go beyond that, describe the shape of the undulations. And it's based on this.
There is what's called a dispersion relation for many, many waves of all kinds of linear waves, which.
This, to some extent, is you specify the frequency, I'm calling it Omega as a function of the wave number.
The wave number is one divided by the wave length.
So different waves travel at different speeds. And in this particular case is standard shallow water.
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.
There's a standard formula which I will not derive. It comes from fluid mechanics applying Newton's equations to fluids.
It involves the tangent of the of the depth, which depends on position in this case and the wave number and his due.
These are gravity waves.
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.
There's a maximum which I've told you already squirt of g times a depth,
and that's four zero K. That's the longest wave, so the shorter waves travel more slowly.
OK, so that's the first ingredient of this theory,
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,
the water is still flowing through that stationary shape.
Now there are four steps in this bit of theory, which I'm going to quickly outline you need to transform,
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.
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,
we make an approximation we can expand that more general formula. And and here it is.
This is a frequency in the ball frame and it involves various things.
It involves the the depth at the front and it involves the slope at the front.
Both quantities of which we're going to find later. Then there's a third thing.
We want a steady profile. Nothing is changing. So the frequency is zero.
That's an analogy with what in some branches of condensed matter, physics is called a soft mode.
OK. And then finally, there's another trick, which is this We want to find this depth.
We want an equation that it satisfies.
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.
You replace the wave number by a derivative, and I won't explain why that where that comes from.
But when you write simple formula for simple travelling waves, it becomes clear.
So this is now an operator acting on this depth that we want to find.
As I say, it's an analogy.
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,
which is what determines the structure of the system you're interested in here.
It's shallow, flowing waves on shallow water.
Good well, and not just one little technical comment before I give the answer.
You say this involves x k in case an operator, the order matters.
Now this is common throughout quantum physics and wave physics is that the order, which operations act makes a big difference in everyday life?
Of course, this is very familiar. You know, you put your socks on before you put your shoes on and not the reverse.
It's obvious that operations don't, as we say, don't compete with each other.
And so how do you deal with that now in quantum physics? It's a known problem.
And actually, given a Newtonian dynamical system, there isn't a unique way to get a quantum system that corresponds to it.
You have to use physics to determine one of the ambiguities, which is this ordering.
But. In quantum physics, it doesn't actually usually matter enormously, it gives certain corrections to choose one ordering or another.
This case is unique in my experience, if you don't choose the right ordering, there's only one.
You can't describe a bore. A bore is something where from this theory, the water has different heights on the two sides.
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,
where the waves are the same height waters, the same height on both sides.
So uniquely, the ordering is specified by the fact that you're wanting to describe a bull.
And here's the answer I'll just tell you the answer. The depth is, well, the depth before the bore passes.
And then there's this parameter ratio of depths. But then there's is scaling function and what it is, it's an integral.
If those of you know, integrals are is the interval of something called an area function.
I'll talk about it later, but I want to just show you the picture. So here's a picture.
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,
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.
We come to that later. And here's the slope at the at the origin there.
So this tells you this is the basic theory. Now it's not enough.
And there you have to apply certain self consistencies, which I won't have time to go into.
But from that you get for results. The first is the depth, the depth at the picture, in the ball frame.
The depth is is where this the natural origin point of this little function is one third of the way up between the.
Before and after depths of the waters, one third of the way up, that's the first result.
The second result is that the maximum slope again depends just on this parameter.
And it's a number which comes from theory of every function doesn't matter what.
And here it is very precise theory.
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.
The border is very shallow. This slope is very shallow.
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.
Then what about the quote wavelength distance between the first two maxima?
That's a dramatic thing you see. Is this these first two waves?
Then they get closer and closer and closer. And again, it depends only on this ratio.
And here's the picture for very gentle pause.
This wavelength is enormous, and that justifies this gentle, linear wave approximation.
And then as the ball is stronger, the wavelength gets smaller and smaller.
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.
And then there's the steepness, which is this I've defined it this way.
It's the ratio of the. Contrast between the maximum depth and the minimum depth at the first minimum, divided by twice the wavelength.
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.
Now, physics is an experimental subject, and I wanted data for which I could compare this theory.
It's very hard to find reliable data.
First of all, because it is a natural phenomenon, the numbers fluctuate enormously.
I'll show you the best I could find as well.
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.
And he gives the data for a number of different pours.
Some of them are natural balls, and some of them are laboratory balls.
I make no apologies for what you're going to see now because the numbers fluctuate enormously.
There we are. However, it could be.
It could have been that this theoretical curve, which is what I'm showing you here, could have been way above.
It could have been way below. But it isn't. It goes through this rather inadequate, but inevitably inadequate data.
So I'm quite pleased with this. That's the that's the the theory.
OK. One little tiny bit of oh, OK.
So so the outcome is what is the bore?
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.
And I got to tell you a little bit about every function.
Some of you here who know me know that this is one of my favourite objects in theoretical physics.
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.
Now we see that mostly in most clearly in optics, a rainbow is a caustic acoustic is the singularity of ray.
Optics is where focussing occurs. It's a line where that comes from with with raindrops drops.
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,
which happens about a third of the time, then you can see interference fringes.
These are wave effects and they they describe this characteristic, airy function.
Now the tidal bore, I didn't describe that, but in a way this front is a kind of caustic.
It's of caustic in space time. I don't have time to explain that, but it is.
So here you're looking with your eyes, you can see an airy function.
There are several in fluid mechanics other than the.
The tidal bore tsunami is an example, which is the tsunami is built on this function undulating,
convoluted with the structure of the earthquake that causes it.
And there's a lot one could say about that, but it's another talk.
You're all familiar with this v shape behind a swimming duck or a ship.
Well, this is a caustic of the rays of the water waves and.
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.
This is now deep water, not shallow water.
If you are in a small boat, for example here and a big boat passes by with this, with this with its V shape.
Eventually, the V-shaped will catch up with you. It takes longer than you think because the group velocity with which this group approaches
you is half of the phase velocity of the waves within the group that you naturally see.
But still, it will catch up with you. And then as this crosses passes you, you in little rock up and down.
Now this is a caustic, so this is an airy function.
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.
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.
So here you see both kinds of a phenomenon.
A couple of little digressions. Before we get back to the bread, there's an empty bore.
Tiny ripples. You have to include surface tension, as well as gravity that modifies the dispersion relation here.
Surface tension in a particular way. It surface tension this term dominates for short waves.
That's large K and in particular, if the wavelength is less than a couple of centimetres ripples.
In other words, and then something interesting happens. This square root of g times, the depth is still a limiting velocity.
But now it's the minimum, not the maximum. And that means that the short waves travel faster.
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.
You see, the undulations are ahead of the group, not behind the group.
As with tsunamis and as with tidal bores, and you can see that ripples ahead.
You can see that when with a faucet, the tap is on on onto the onto the sink.
And now you see these waves, which are ahead of the of the main of the main structure.
You have to think a little bit to fit that into. The framework that I've been describing is a kind of A. bore.
Now another digression, which I can't resist telling you one other tidal phenomenon sort of related,
but not really, but which I saw recently is in the Gulf of Corey reckon.
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.
Now here we are, though his Glasgow and and his Jura and his Scarborough,
and it's between them that you get this gulf of Corey reckon the most dangerous place to sail in around the UK and.
Here it is, again, Scarborough and his juror, and I just want to remark down here is Barnhill.
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.
This Gulf of Korea reckon at the wrong time and capsized and nearly came to grief,
though very lucky to be rescued anyway because of the structure of the bottom.
There's a pinnacle underneath the interaction of the flood tide and the ebb tide with that causes huge
whirlpools and huge standing waves away from this sort of a kilometre or so a mile or so where this gulf,
the water can be very calm. And I was there a few a few months ago.
You can. There are few boatmen licence to take tourists through this.
They know what they're doing. You should never try to sail yourself.
It's the world's third biggest whirlpool area without boats.
What happened was that the the pilot would see a whirlpool.
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.
Kind of lovely thing and huge standing waves.
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.
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.
And there were two boats our boat, another boat for the same company, which had a television crew on it.
And I got talking to the guy there who seemed to know a lot about tides.
And I said to him, You know, it's quite a dangerous place.
George Orwell nearly came to grief with his young son.
He said, Yes, I do know I looked him. I you George Orwell son.
He said yes, and we've been in correspondence. He's a retired engineer, slightly younger than me.
He was two and a half at the time. He just about remembers it. But now he often he lives somewhere in Warwickshire,
but he has a house up there and occasionally takes groups of people in commentates about this tidal bore.
So this is kind of a very unexpected encounter.
Now, every year, I buy the tide tables from Victoria Arrowsmith Brown, whose company has been produced,
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.
And this contains the tides from navigable navigation, the interesting place on the Bristol Channel and the relevant places the highest one.
Upstream it sharpness. There it is.
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.
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.
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.
So that's why this phenomenon happens farther up the tide range.
There can be 17 metres, a huge tide range.
OK, now there's a lovely book by a French surfer, Antony Koller, called mascara owned lunar,
which contains some lovely pictures, some of which I'm going to show you. Here's the seven.
Actually, it's sort of turbulent, but you also see the undulations.
Here are some boat people. OK?
By the way, it's much more magical to visit at night.
There are fewer surfers, almost no service and fewer boats.
And there's always enough light from Gloucester or from the full moon, which happens to be a full moon.
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.
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,
but on how much wind there is, how much water there is in the river, on winds in the Atlantic and so on.
So you can predict about half an hour. And he's got a convenient table of if when the tide is high, it sharpness.
When do you see the bore? Different places it, and that's kind of as useful.
There are a number of different. Is that the good to visit? He also shows pictures on the Amazon.
Now every year I visit an institute here, a physics institute,
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.
It's called the poor roka, and I've got some rather lovely pictures from him.
You see the scale of it there to get there.
It's not easy. You have to go to Belgium and you've got 15 hours on a riverboat.
It's a long I. I've never done it in India.
On the Hughley, that's the barn. Hughley is a distributor of the Ganges near Calcutta, and here we are.
Here we see Calcutta. Here's the Jubilee coming down. And here's an old picture This is where the barn comes.
Somebody is measured the profile. It doesn't always look like this.
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.
And it was actually not the best day we were taken to the wrong place, the wrong side.
And all we saw was that there was a gentle swivelling of or rocking of the boat on the water.
It wasn't as dramatic as I'm going to show you now. So here we are.
That's connect about that. Do that.
You'll see a lot of mud coming up, but it dredges a lot of mud from the riverbanks up bottom.
Is. It comes at about 10 or 12 miles an hour, so you can see it in a number of different places.
If you want, if you want to drive from home one to the other. It was, I think, a rather fanciful picture.
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.
But I want to read you something about the bomb. This curl, the ball commences.
Huguely points the place where the river first contracts itself and is perceptible above Huguely town.
And so quick as its motion that it hardly employs for hours in travelling from one to the other.
Though the distance is nearly 70 miles, Calcutta sometimes occasions an instantaneous rise of six feet.
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
middle of the river in the channels between the islands at the mouth of the Makena.
This height of the border is said to exceed 12 feet and is so terrific in its appearance
and dangerous in its consequences that no boat will venture to pass at spring tide.
When I read you this because of what he writes next, the hugely porous, fearsome as it could be,
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.
Dense suburbs extend several miles along the banks.
As the hour of flood tide approached, crowds gathered in the streets running at right angles to the can tank.
But at a safe distance, I had the pleasure of visiting this can tank bore.
A few years ago, and I want to tell you a little bit about it.
So here it is. It's inland from Shanghai.
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.
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.
The boar, it's about three kilometres wide where our River Severn opens out into the Bristol Channel,
where you get the very high tides where the bridges are. It's a few kilometres across here.
It's 40 kilometres across a very dramatic. Not quite the longest bridge in the world.
There's a new one near Hong Kong, which is longer just recently opened, but it's very spectacular.
There's a hotel in the middle where we stayed.
OK, now and every day we were taken twice two times a day for three days during this period of high tides.
To see the ball at slightly different places along the river, it's a local attraction.
It's actually President Xi Jinping quoted in one of his G-20 speeches.
All kinds of entertainers are there clowns up and down policemen?
Why? Because some foolish people jumped into the boat several years ago and they were killed.
It's catchy, dangerous, and many people are watching it.
One hundred and twenty thousand was the estimate when we saw it. So here it is.
We were in a little cafe just above everybody, but we could see the boar beginning to come in.
Here it comes by, and here's the wave as it passes the turbulent boar, not an Angela ball.
I want to show you this movie that that I took just to make a comment.
This will go out of shot. But when the ball was passed by, the water level is about this second story of this.
And here you can see people standing. You get the scale. We can just see the far shore far away, several kilometres distant.
And that. And the transition from this smoothly laminar flow down and the turbulent flow upstream is very striking.
I'll just show you a picture that we took at night of just a comment.
I mean, we stood at a place which we thought was good and we could see the ball coming.
And then suddenly motorbike cable, there were policemen screaming at us to get out of the way.
You got to take your car.
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.
The car would have been flooded to a depth higher than its wheels, so we were very grateful.
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.
Now. Right.
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.
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.
Here's a little bit of the river and the bow comes in and part of it hits this jetty.
That's this bank that's poking out. And there it is.
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,
my mathematical people, will know the name of Ed Lorenz, who's one of the pioneers of chaos theory.
He didn't like to travel much from America where he lived.
But he was persuaded to visit Bristol and give a talk, provided it was scheduled for the day when there would be a bore.
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,
etc. Of course, the closest to Oxford, it sits almost on the A40.
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.
I think in the thirties, I'm not sure the ball went up as far as Worcester, but not so.
We wondered if you would see reflected bore.
And sure enough, after about 15 minutes, we were standing on the bridge where we could see the this little ripple came down.
Now I'll show you a more dramatic one. So here's the poor approaching and then it hits the wall.
You're standing on the wall. It's it's safe there and then it interferes with its reflection.
There it is. So this is a reflection. Travelling backwards, interfering with the ball, travelling forwards.
Very good. The rebels in France, several of them on the scene at Caldbeck in French word Islamist go mascara.
That's the title of the book by Alan Anthony Colau.
They're actually two books now, and they used to be a famous book at Caldbeck.
It no longer exists because they dredged the river to help navigation that destroyed it, by the way, with the seven war.
There's endless talk.
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,
of course, kill the Boer.
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.
But of course, there are environmental considerations and it's Britain, so things almost never happen anyway.
Caldbeck Here's some old pictures there is a ball of masquerade which you can visit,
which we did, and you see pictures on the walls of the Boer in those days.
Here we are again. This is a again, I suspect, a slightly fanciful picture from the popular astronomy book by Claude Flannery on a
famous astronomy book translated into English around the turn of the previous century,
for which I want to read you two statements.
One day after being present at Caldbeck, after this always curious spectacle of the Boer on the sand,
I returned on foot where it was overtaken by countrymen,
with whom I entered into conversation on my asking him what he thought and what the old people of his family thought,
the phenomenon in which they had observed for so many years. I do not know, he replied, how the wise men explain it.
But for us, it seems to be nothing else than the well known antipathy between salt water and fresh.
They're not of the same character, you see. But this is certain that the freshwater falling into the sea worries the salt water,
with which it finds a difficulty in mixing well in the salt water ends by becoming angry.
It accumulates its anger and every evening, especially the equinoxes, when it's already naturally furious.
It resolves on hunting the freshwater, sending it back with great velocity.
I assure you, sir, that this region is much simpler than the attraction of the Moon.
Now, I'm not reading this in any a spirit, a contemptuous spirit, because, you know,
if you don't have physics, you think of whatever you can and fresh water, it's a wrong theory.
But still, we know in physics there are wrong theories which turn out to be very useful.
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.
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,
who delighted with her charms set out to follow her.
He had already reached her when Bacchus and Ceres invoked by the nymph and being unable otherwise to save her,
metamorphosed her into an azure river, which ever since has borne her name and as every year on its banks, joy and fertility.
Neptune, however, has not ceased to love her, though she has preserved her aversion to him twice a day.
He pursues her with great bellowing. This is the Harvey Weinstein of mythology.
Each time the Sun escapes into the meadows and goes back towards its source.
Contrary to the natural course of rivers,
it's always interesting to see how natural phenomena are reflected in different cultures from the one we happen to have now,
where we use physics now to finish why?
What's the deepest reason to be interested in the book?
Well, there are a number of reasons I've described you various connexion with quantum physics with horizons and the like.
But what is the. Most fundamental aspect of the goal of physics is unification now know unification is connecting unexpected things,
and everyone is familiar with Maxwell's unification of in the middle of the 19th century,
where he showed that electricity and magnetism and light are all part of the same phenomenon a great unification.
Now, of course, we try to unify gravity with other forces and so on.
It's easy to forget that the first unification was Isaac Newton,
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.
This was a fantastic discovery and the great unification.
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.
The whose orbit, of course, is determined by gravity and the water is held down by the solid earth, which holds us down.
So really, this unification becomes immediate.
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.
It's a little travelogue about the Silver Dragon visit.
And then there's the theory, which was published earlier this year.
The first of these is in my book, which has at least one reader.
No, thank you.