greetings, aliens and earthlings. This is not an episode of Earthlings 101, your crash course for alien visitors, but a series of three shorter videos about something that seems to confuse earthlings and aliens alike, the shape of the universe. What was that? Most earthlings and aliens don't understand space. It's not what they think it is. People assume that the universe is infinite and flat. But actually, from a non-acglidian, non-local viewpoint, it's more like a big ball of wimbley wobbly, spacey, wastey stuff. And the shape of this big ball, that's what this three-part series is all about. When we talk about shape, we are basically talking about two things, topology and geometry. Geometry is all about distances, angles, areas and so on. Topology doesn't care about exact angles and distances, it's about which zones are next to each other. For example, when you deform a square, you change the geometry, but not the topology, as long as you don't trip it apart, create holes, or glue parts together. For the sake of simplicity, let's neglect the expansion of the universe and only consider a snapshot of the universe, that is a slice of space time. Unfortunately, I don't know with certainty what the actual shape of this slice is. All research on cosmotechnology is classified as secret of defense by the central galactic bureaucracy. So, I can only discuss hypotheses, different possible models of the universe. Basically there are three kinds of models, spherical, flat, and hyperbolicle. Today we will talk about flat models. Flat or not, there are a lot of misconceptions about the universe around. The universe also on the other hand might be finite, somewhere out beyond where we can see there might be an edge. No, hang. A finite universe and a universe with an edge are two wholly different things. No, gawth. Curved space doesn't mean that the universe curves through an embedding hyperspace. It only means that the laws of geometry are not what you would expect. It doesn't expand into anything, it just expands. So, within the limits of our observational capabilities to these days, we think that the universe is flat, so if you go out in one direction, you probably shouldn't return the way you came. So, no, the universe does not appear to be closed, and you probably never see the light coming up behind you. No, Derek. A flat universe isn't necessarily infinite, and can contain straight lines that lead back to their origin. To be honest, that's just stupid. So, what does finite universe mean, anyway? It means that the universe has finite volume. In other words, you need only a finite amount of hydrocassive to inundate the whole universe. No edge, on the other hand, means that when you explore the universe, you won't suddenly run into a wall of nothingness. An edge. But isn't that the same? When there is no edge, you can just fly on and on, and boldly go where no man or alien has gone before. And when you do so, you see more and more volume, so the total volume must be infinite. Right? Wrong. Because when you fly on long enough, you might eventually find yourself in known space, you might even return to your home planet. In other words, space may bend into itself. To understand this, let's look what happens in two dimensions. Like many alien races, earthlings have gone through a stage in history when they wondered about the shape of their planet's surface. Some imagined an infinite surface, whereas others believed the surface had an edge. Eventually they found out that both were wrong. There is no edge, but the surface is finite, when you sail away into one direction and keep sailing in a straight line, you will eventually come back to where you came from. The reason is, of course, that earth is a sphere. Finite surfaces without edge can easily be understood by three-dimensional beings. But how would you explain them to two-dimensional creatures, like the flat snails from Regulus 3? Flat snails can only think in two dimensions, but they have a highly developed portal technology. A flat snail portal alters the topology of surface by gluing different parts of a surface together, for example to opposing sides of a square. When a flat snail leaves the rectangle on one side, she enters on the other side, like in a video game. Topologically, this is the same thing as a cylinder. Let's call it a video game cylinder. What would a video game cylinder look like from the anderia? Flat snails can't see very far, but if they could, they would see an endless series of images of the same space. A bit like what you see when you stand between two parallel mirrors. What happens when you glue the other two sides of the square together, as well? Now you have the loopy video game effect into directions. A far-sighted flat snail inside would see her own image repeated in a grid pattern. Topologically, this is a torus. The surface of a donut. So, let's call the double loopy rectangle video game torus. The important point is that you don't need the third dimension to define a cylinder or a torus. All you need is portals, to glue the edges together. And once the gluing is done, you can forget about the portals and just enjoy your seamless yet loopy video game environment. A flat snail that grew up on this torus would be used to the fact that she lives on a flat, finite, somewhat loopy surface, without edge. No need for portals or bendy space, not to mention this sociable third dimension. But what about the universe we live in? Is it so unthinkable that our universe is similar, only in three dimensions? Why shouldn't it? Is there any reason why the universe has to be either an occludient space, or embedded in a higher dimensional occludient hyperspace? But back to two dimensions. Let's toy around some more with surfaces and portals. For example, what happens when we glue together two sides of a rectangle, but with flipped directions? Well, we get a mebius strip, a surface where each round trip makes you flip orientation. When you glue the other pair without flipping, you get a climb bottle. When you flip both pairs, you get something called projective plane. Now, we are not limited to rectangles, though. We can, for example, take a parallel diagram and glue opposing edges together. Geometrically this is a skewed torus, topologically it's the same thing. A flat snail sitting inside would see herself repeated in a skewed grid pattern. What happens if you take a hexagon and glue opposing sides together without flipping? Well, a flat snail inside would see the herself in the same pattern as before. So this is just another way to construct the same skewed torus. Let's go back to the video game torus. Can't we do a similar construction in three dimensional space? Of course we can. All we have to do is take a cuboid in space, and link opposing sides with portals without twisting anything. If some space fairer happens to be trapped inside, he will find himself in a three-dimensional video game space where he comes back to his origin when he flies long enough along one of the axes. He won't even notice the portals, he would just experience an universe that somehow repeats itself. This is called a hyper torus. Just like our video game torus, the hyper torus is flat, which means that the rules of school geometry still hold for very large objects. In part two we will define more precisely what this means. Did you see what we just did? We constructed a flat universe with finite volume, but no edge. Something hank and Derek thought was impossible. Such a universe looks exactly like infinite flat three-dimensional space, except that it repeats itself like a hotel wall paper in three directions. Some earthling scientists think that the hyper torus is a possible shape of the universe. No edge. Yes earthling, no edge. But the hyper torus is not the only flat finite model. For example, you can obtain another model by turning the top portal by 90 degrees. This is called the quarter turn manifold. A third variant is the half-turn manifold, obtained by turning the top portal by 180 degrees. Remember how we constructed a torus with a honeycomb pattern? You can do the same with a hexagonal prism to get the hyper torus. Now, you can rotate the top gate by 60 degrees to get the one-sixth turn manifold, or by 120 degrees to obtain the one-third turn manifold. There are overall ten models for a finite closed flat universe, six orientable and four non-orientable ones. What does non-orientable mean? It means that the universe is like a mebius strip. When you make a round trip, you might come home mirror inverted? This is called an Alice universe. For you, your planet will be mirror inverted? Also, as electrical charges a matter of orientation, the planet and everything on it will consist of antimatter. But the ten finite, closed, flat models are not the only possibilities. In part two and three we will see other curved models for the universe, like the hypersphere or the point-carry space. We will also talk about evidence that may help finding out which model is correct. Of course, the crash course frailian visitors continues. What do you think? Should I alternate between the crash course and nudge episodes, or rather finish this mini series and then continue the crash course? Tell me your preference in the comments below, or on my Twitter account, or my Facebook page. Thanks for watching. Like if you enjoyed it, share if you really enjoyed it, subscribe if you don't want to miss my next videos, and as always, don't forget to be alien.