This time four dimensional world on this surface is two dimensional on some curve, lying can be one dimensional so forth.

And we have a tendency to believe that low dimensional things are easier, certainly easier to visualize and highly mission things that mysterious some kind of buffalo because sometimes high I dimensional objects are easier on dhe.

A problem can be solved by lifting the academician coming down to the dimension.

So here's an example.

In point to the beginning of the slow re draw three circles R B three circles, but different sizes and different positions.

Let's say they're all overlap with one another.

You have three of them large, middle on small sizes.

Any pair of circles, for example, large on middle intersect in two points here, here, and you can connect those two points by a core.

The common chord.

So like that on because they're three pairs of circles, you can connect all of them large on the middle.

Connect middle and small connect on snow on large connect, so you have three lines that appear now.

In general.

If you throw three random lines they just pass through each other, but they don't meet in the point any.

What are the chances that they meet exactly one common point village?

But in this case, if you start from three circles and if you do this construction, it turns out that those three course meeting in exactly one common point that is quite mysterious.

How do you make sense of this?

Is that an accident?

No, it's a theory.

You nervous?

It happens for any three circles that the Intersect one another.

You draw those course automatically on forever.

Every eye in the university's happens, so there must be a reason you clearly have three circles on this sheet of paper, which is a two dimensional world.

But instead of thinking of these circles, let's lift them into the three dimensional space.

Think of these as pictures of steers a scene from above.

Let's suppose that you have a large sphere here on the medium size here, here and there, like bubbles, and they're so the magic spheres, which can enter each other.

They collide, but they can enter each other.

Let's say that their centers are all on the same height, so if two spheres and th other the Intersect.

They meet each other along some common circle like this, which is vertical and similarly, if there's 1/3 sphere, which is small, enters the middle and that's fears.

Then, in a small one meets the medium sphere on small sphere meets the large sphere along some circles as well.

So you have circular arcs along which those three spheres enter each other on intersect.

And if you take a top view of this, a bird's eye view the picture that you get well look like this, you can imagine three kind of bubble like spheres entering each other right on Dhe.

Remember, their centers are all on the same horizontal plane at the same height, so the kind of very nicely entering each other now, clearly, if you take a view from the top, those are circular arcs, which kind the move like this.

Like a long values like that on they die, all of them into a common dimple in the middle, and in fact, this is a bird's eye view.

But if you look at the whole thing from underneath, you see from underneath, those three arcs are coming up like that, and they'll meet at the dimple, which is pointing up like this.

So there's that the emperor at the top and import the bottom like this.

And if you take a view from the top of those to the the most look super pose and that's what you see.

And so you see those three lines, the actually projections.

Or, if you like, the apparent lines off the actual circular arcs, which meet at a single point.

If you imagine it, everything's transparent, you get back.

This picture in that was, those three circles are supposed to be actually spheres scene from the top on those two spheres meet along that circle, which looks like a line because we're looking at it straight down from the top.

Those two circles on those two circles meet, and they all sort of meat in a single point.

So by lifting the two members of a problem to three dimensional, so the more free ambient space where you can move around more freely and you can sort of go up and down, you simplify the program and infected improvement became easier and obvious.

In fact, there's no more problem can just see this experience has a very nice application.

I've recently moved from England to California.

Well, California is very sunny, wonderful people, and the weather is sunny and so are people, but also eat on earthquake territory.

That doesn't surprise me because I always come from Japan, another earthquake country.

The filming of an earthquake is a rare event, even in Japan, where such disasters are only too frequent.

Fact.

California in Japan, both of them belonged to what is called the Ring of Fire that surrounds the Pacific on the Pacific Plate.

In all, directions are entering under continental plates On.

In doing so, they rub underneath and then suddenly everything vibrated.

That's why we're alone, full of earthquakes.

Now.

My wife, who's English, is not used to earthquakes.

And so she was very, very worried before we moved back in October, to be precise, attentive October 9 and 2017.

So this was shortly after we arrived.

We were playing with a little child, that little baby in our living room, and then we felt an earthquake.

My wife got that bit scared.

It was a small tremor, but very, very perceptible one.

But then, as soon as we felt this.

I started counting one, 23 and my wife looked at it for her.

Puzzled by this and I count it up to six or seven.

And then we felt another tremor.

And I said so.

I know this is not such a large earthquake, and the center is about 40 kilometers away.

We don't know which direction, but we're about 40 kilometers away on the fact that we've had only this.

That means that he was a small tremor, probably magnitude, I don't know, four or five at that distance and so forth, and she was very puzzled by this on dhe.

This was done because of the folding mechanism.

You probably are familiar with how, in a thunderstorm you see a flash of lightning and afterwards, a little late that you hear the rumble of thunder flash followed by rumble on.

By measuring the delay between the lightning on the rumble of thunder, you can estimate the distance to where the lightning struck.

Lightning is off course.

Emitting light and light travels extremely fast.

It's not even its speed, but it's very, very fast.

It can go around escape of going around the earth, for example, or the whole of seven and 1/2 times per second, so it's very, very fast.

So for that kind of distance, you can recommit its basically infinite.

So you get the light from lightning insomnia.

See, where is the sound from?

The thunder takes time to travel because sound travels at what, three or 400 meters per second, that kind of speed.

So if you count the number of seconds that the sound is delayed with respected arrival off the right light, then multiply that by 300 or 400 meters per second will give you the distance to the lightening spot meters.

So you know you count for example three seconds one, 23 seconds and boom that.

Then you hear the rumble of the thunder.

Well, that means that you are probably 901,200 meters about that one kilometer away from where the lightning struck on.

So it's exactly the same with earthquake.

Absent the calculation, it turns out that when the earth shakes, that's the ass quick.

It sends out various kinds of waves all over the place, but they're two very prominent waves.

One of the waves works us like this say that this part is shaking on that part because it expands, compresses the next part off the earth and then bounces back because Earth is a little elastic on.

Then that bounce compresses an expert and expands complex, so you get this kind of compressive wave.

A pressure wave which travels like this on the shake is in the direction of travel like that.

That's called a P wave or pressure way for primary wave.

All of them stand for peace.

Another kind of wave, it's called she away for secondary wave on DDE.

That works because when the Earth is shaking, that kind of shake in trains also drugs the next part of the Earth and then goes like that and that shake.

So the rubs against the next.

But and then it goes like this.

So the shake is happening in a direction perpendicular direction of travel, where, as in the previous case, he was going along direction.

So that's called the S Wave on the 1st 1 has got a P wave P primary secondary on as prime on dhe on secondary indicate P wave travels faster, and that's kind of intuitive rate for something as strong and as robust as Earth.

Probably this kind of wave is much faster and this is a much softer mode.

So s wave travels slower the speeds off p and s waves very a lot.

In fact, they tend to increase as you deep into the going into the depths of the earth.

But roughly on the surface, T wave travels at six kilometers per second on P s wave at around three kilometres.

Bastard, there are variations, of course.

So here is how you can calculate.

Let's say that you are feeding enough quake.

Thank you.

Yeah, with your baby.

And then there's the place which is shaking somewhere down there.

Okay on.

Let's say that the distance between the absent and you is distance D and I'm going to express it in kilometers on days a P wave that comes on DPI way.

It kind of comes shakes like that and then it's wave which comes but more slowly.

How much earlier this P arrive and how much later?

Zit, this s arrive Well.

P takes distance.

Divided by six kilometers to arrive, it's wave takes a little longer distance divided by three kilometers approximately so the difference between them will give you the delay.

Time in seconds.

That's good.

So that's the common fact that 1/3 minus once 1616 isn't it?

So you get this equals 16 times the is and the delay in time.

So it shows that the distance you can estimate is approximately, I say approximate.

Because of those numbers, approximate obviously is equal to six times the number of seconds a day, and that's in kilometers.

So this is incentive seconds.

In other words, the rule of thumb is when you feel the P wave arrived.

The first shake by the A P Wave is traveling like this, and if you think about this picture, it's going to shake you horizontally, right?

Because if, for example, if the absent is right there, it's coming in like that.

So it's going to shake you horizontally and its way, which arrives a little later, is going to shake you like this, so it's going to shake you usually in the vertical direction.

So the fact that matter is, and this is something that is known to many Japanese troops who grew up in an environment like this that you are first shaken horizontally and then the vertical shake arrives.

By the way, another digression is that he usually this wave is slower, but it tends to carry a little more energy if you're near the center.

So we are worn in Japan when we were growing up that when you feel a horizontal shake, you should be a little care for you will be take cover, go to some a secure ground because you might expect in a few seconds a big vertical ship.

You should be prepared for this, but anyway, so the rule of thumb is when you're a few that P waves arrive yourself counting one second, two seconds, three seconds.

You can't have many seconds.

Multiply that number seconds by six on.

That gives you the distance of the epicenter in kilometers.

So in my case last year I counted 67 So I estimated there were six times 6 36 60 cents 42.

So it's about 40 kilometers away, and I looked up at the database off The American Geological Survey on bingo at the rec center was a bit too t east of sample, say, and he was exactly at 40 kilometers from here.

So that works while you're counting.

Are you also running for cover?

Know I wasn't because he was a small shake and I felt that he was Sami from experience.

Okay, by the way, the baby sleeping very beautifully handed Nothing when my wife was worried.

Now what does he have to do with this serum?

Everything has to do with this.

So they're those seismometers that record earthquake events and recording.

You know how at what time the shape came and so forth all over the place on DDE.

What this does is that if you measure the delay between the arrival of P wave An s wave at one location, you know the distance from that measuring the location to the extent there in kilometers as we've just shown.

But you don't know in which direction it can be anywhere.

On the in fact, remember, the earth is not flat.

It's not a two dimensional universe.

It's actually ah whole sort of physical thing with the ground underneath.

So absent that could be anywhere on the spherical surface, not in a circle spherical surface of radius that we can estimate so we don't know where we're not.

However, this film shows that if you take three measurements, you can determine the accent because this absent must be on the spot that is constructed by this.

You see, that's the picture off the hemisphere, if you like, which is extending into the earth and seen from above your CD Secularism on That's another.

So the distance estimate from, say, this center were decides me with this place on finally another one.

So if you have three measurements off story Sizemore, three locations you can from those three measurements determined.

Absent there.

Now you know how to draw it, how to do a circle around each instrument because how to dough, Ah, sphere and each instrument by this formula.

So each instrument that records the first wave on second wave and it can also record automatically the delay in seconds, multiplied by six that are actually speaking, defines the kilometer on.

That's the radius off this thing that you draw so automatically you can draw this on the intersection of those three course will be that point.

I should probably explain that it's very strange in the two dimension picture, because this point is not at the radius, apart from the center of the circle that it's not on the circle.

But remember, this point is actually only an appearance.

32 dimensional projection off a three dimensional picture.

It's actually a point which is underneath on top.

In this case, of course, it's natural to take the point underneath off three spheres that are entering each other on the intersection of the three spheres.