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  • so I mean, this has quite a long history in that at the end of the 19th century, a guy called Edwin Abbott wrote a very famous book called Flat Land, in which he kind of explored a A flat universe.

  • It was sort of social satire rather than physics.

  • So he didn't go much into the physics of the universe.

  • But subsequent to that, various people who looked at it and, most famously, a guy called Alexander do DNI, who's a computer scientist in Canada has gone through figuring out a lot off the physics of what the universe would look like if it actually only had two dimensions, whether you could actually make it work or not.

  • Alexander Jr wrote a book called The Plane a Verse in which he actually it's a It's a story about some people who accidentally start kind of communicating with the two dimensional universe, and so you kind of explores the communication between universes and so on.

  • But it's a load of technical appendices at the end of the book about what the science behind it wasa and actually I read it, you know, in the mid 19 eighties, just after it come out.

  • Somebody gave it to me for Christmas and I was fascinated by This is one of the things that sort of inspired me about physics and actually one of the things that just sort of made me think the most When I started doing this, there's something very trivial if you were a two dimensional being living on a flat piece of paper.

  • So your little stick figure living on a stack peaks flat piece of paper and you try and lift one end of a plank up.

  • You can't do it because there's nowhere for the air to Russian.

  • You're kind of creating a vacuum by lifting the end of the plank because you got the plank resting on the ground.

  • And then there's you holding onto the plank, so there's no gap there for air to come in the way there is from the sides in three dimensions, so you can't do it.

  • You can't even pick up a plank.

  • And in fact, in this book he had these characters having to kind of shuffle their feet up and down to sort of let the area as they were, lifting one end of things in order for that to happen.

  • So it was just that trivial example got me absolutely fascinated with these things.

  • There's all sorts of stuff, like, If you start trying to think about biology exposing, you have a two dimensional being.

  • If it had a digestive tract, in other words, it has a mouth going all the way down to the bottom.

  • Then basically all fall in half, right, because there's nothing holding the two hearts together in two dimensions.

  • And so you have to come up with some clever way if you want your two dimensional beings to be able to eat and not fall in half, and so do I.

  • He came up with this idea of basically a zipper, because you can have a zipper in two dimensions.

  • And so these these creatures are kind of zipped together, and that allows things to kind of work their way down through their bodies.

  • So it's complicated world living into damage give you one more example that one more good good things, so an astronomical example.

  • But astronomy in two dimensions on space travel into dimension.

  • Turns out space travel in two dimensions is quite tricky, and that's because the concept of escape velocity doesn't exist in two dimensions that, actually it turns out that so on.

  • In three dimensions, the force of gravity drops off like one over distance squared, which means you can't go twice as far away.

  • The force of gravity is four times this week.

  • If you go down the dimensions so it's only two dimensions, it turns out the only gravity only drops off like one over distance.

  • So when you're twice as far away, gravity is still weaker.

  • But only by a factor of two rather than a factor of four certainly is.

  • Gravity is a much longer range force in two dimensions than it is in three dimensions.

  • And so that means that so in three dimensions that's this concept of escape speed.

  • You can actually fire a rocket fast enough from the earth, say, and it can actually escape entirely in two dimensions because the force of gravity is that much stronger, that much longer range.

  • No matter how fast you fire your rocket up into space, it will eventually always turn around and come back.

  • And that means firstly that actually you can't.

  • But deep space travel is very difficult, because actually you have to put huge amount of energy in to get far enough to actually get to the next planet.

  • But worse than that, it means that actually, the universe is sort of doomed because the entire universe can't achieve escape velocity either.

  • So the universe can't keep expanding forever and will eventually collapse back on itself.

  • And so there will always be a big crunch into to damage.

  • You know what?

  • A lot of people are probably under the belief that our universe is going to do that so well.

  • Life is complicated, right?

  • Firstly, in our universe, in three dimensions, it doesn't have to happen in our universe.

  • There is probably this thing called a cosmological constant or dark energy, which is driving things apart.

  • So actually, when I started thinking about this again for making this video, I started thinking, Couldn't you do the same flat universe?

  • Right.

  • If we introduce this cosmological constant, would that actually allow the universe to keep expanding forever?

  • So I talked to my particle theory colleagues who are much clever at these kinds of things.

  • Turns out that actually, general relativity doesn't work into spatial dimensions.

  • That or you can make it work, but it's very limited in that the concept of action at a distance goes away.

  • In other words, the pull of gravity outside anybody is zero.

  • So actually you can't if you live in a general relativistic universe.

  • You can't even have gravitational interactions between bodies the way we do in our three dimensional, three spatial dimensional universe.

  • So if you believe in general relativity rather than Newtonian gravity, which is what I was just talking about, then actually, you can't build a universe.

  • It'll we gravity in it, or there's no gravity in any way that we recognize it.

  • So why why bother to do this?

  • Because it's kind of fascinating.

  • And actually, you know, if you like, you can think of it sort of an exercise for scientists, cause it's good to kind of think about things in ways you don't usually think about things, and that's how you kind of try and do.

  • New science is trying to think about things in new ways, but it turns out, actually, there are two dimensional things in the real universe.

  • On the most current example is this stuff called graphene, which is this sort of single layer thickness of carbon new new type of carbon that's been discovered.

  • And it really does behave because it's only a single layer of atoms thick.

  • The electrons, as they move around within graphene, are really moving in two dimensions, which means that the physics of what's going on really is explained in terms of two dimensions.

  • So there are physical systems that off Rheal current research interest, where understanding the physics of what goes on in two dimensions is really important.

  • It's really stuck with May, the idea of these two dimensional beings trying to eat and following her.

  • Yes, and these other conundrums.

  • If there are people who live in four spatial dimensions, well, they look at us and laugh in the same way I should be things about us that we're limited.

  • What are we limited?

  • I think they probably would.

  • They would.

  • How on earth can you exist in only three dimensions?

  • It's so restrictive.

  • You know the number of things you can do in three dimensions.

  • Here in four dimensions, we can do all sorts of clever things that they can't do in three dimensions.

  • Another thing in if you start thinking about two dimensional three dimensional beings is the connections in the brain because in three dimensions, you know it's quite easy to wire things up so you can rewire all the neurons together in two dimensions.

  • It's actually a lot more complicated because things have to cross over, and you've gotta figure out how you can pass information where the wires cross over and so on.

  • And so, actually a three dimensional brane, it's probably easier to design and probably can be more efficient than a two dimensional brane.

  • Now, presumably, if you went up into four dimensions, things will get even more efficient, cause the number of ways you can think things together gets that much bigger.

  • And so presumably, you know, a four dimensional brane could be an awful lot clever and the three dimensional brain.

  • And they presumably pity us for our miserable three dimensional thoughts when they can have four dimensional.

  • I can't imagine how fourth spacial dimension works.

  • Can you imagine that?

  • Or is that well, that's that.

  • I mean, in some ways, that's the lovely thing about thinking about two dimensions because actually, if you start thinking about what how would a two dimensional being think about three dimensions.

  • That at least gives you the beginning of an insight of how can the three dimensional being start to think about four spatial dimensions?

  • But there is no force special.

  • Well, if you ask the particle theorists, they can tell you that sometimes you have 11 spatial dimensions, but most of them are very small.

  • But for practical purposes, there are three spatial dimensions that we know following the Earth around.

  • They used to be lots of science fiction stories about all three used to be a popular place to put the anti Earth or, you know, if you were an evil genius.

  • That's where you put your hidden layer because it was always hidden behind the sun as the two kind of orbit around each other.

  • We've now had enough satellites out there that have actually looked at the other side of the solar system to actually, there wasn't anything much.

so I mean, this has quite a long history in that at the end of the 19th century, a guy called Edwin Abbott wrote a very famous book called Flat Land, in which he kind of explored a A flat universe.

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B1 dimensional universe gravity spatial plank flat

Dimensions - Sixty Symbols

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    林宜悉 posted on 2020/03/30
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