The Shape of the Universe

There are many ideas for the shape of the universe. Perhaps the space is a cylinder, maybe a sphere or a funnel. But apart from this listing, what does it actually mean that the space has some shape?

The globe has no limit, but it is finite. Going all the time in one direction, after some time (rather long), we arrive at the starting point. There is no wall, there is no precipice or end of the earth. But on the other hand, the Earth has definitely finite sizes. After all, it can be observed, for example, from the surface of the Moon. The fact that something has no limits does not mean that it is infinite. Is it the same with the universe? At the moment, there is no definite answer to this question.

The results of studies of the cosmic microwave background show that the space is actually finite and closed. But… It is not about what shape the closed universe has. Whether we sit in the centre of a sphere, a cone or a cylinder, but in what form the space is enclosed. Everything that we see around: planets, stars, galaxies, it is all located on a three-dimensional surface of some figure. But this figure does not have a centre. There is only a surface, which has a degree of curvature. It will be different for a conical shape, and different for a torus. But we are still talking only about the surface. It is difficult to understand, because when we talk about the surface, we imagine a space which has two dimensions. And our world is (at least) three-dimensional. How can this be reconciled? I guess it cannot. Our brain is not able to imagine the three-dimensional space bent to any shape. But if we lived in a two-dimensional world, we would not be able to imagine spatial figures. In such two-dimensional world, a scientist talking, for example, about a balloon, which, when it is being inflated, “gains” a third dimension and becomes a spatial figure, would be as incomprehensible as… the cosmologists who are trying to figure out what is the shape of our three-dimensional space. In the two-dimensional world, a non-inflated balloon is (approximately) two-dimensional. How is it possible that this two-dimensional space can be somehow curved – two-dimensional people may wonder. Just as we, the three-dimensional people, are wondering about the curvature of the three-dimensional space.

Divination about the shape (curvature) of the space may seem an abstract, academic dispute and unnecessary to anyone, for anything. Nothing could be further from the truth. Without the information about the characteristics of the space in which we live, we will never understand either how the universe was created, or how it works, or what will be the end of it. Although in the immediate cosmic surroundings it seems that the space is flat, it is rather the same illusion as the one that the Earth is flat. On a flat surface, however, the rules applied are different than on a curved surface. On a plane, the sum of all the angles in a triangle is 180°. On a curved surface, it is not. Similarly, on a curved surface the Pythagorean theorem does not apply, two straight parallel lines can cut each other or “go apart”, and two points can be connect with more than one straight line (on a flat surface they are connected with only one). It is similar with the curvature of a three-dimensional space. Depending on the degree of the curvature and the “direction” (whether the space is concave or convex), the rules which are the foundation of modern science for us, may not be so fundamental.

In cosmology, not many things can be understood by activating the earthly intuition. Are we able to understand the curvature of a three-dimensional space at all? Can we then explore it? Some are able to switch off or drown out their intuition in some inexplicable way. Maybe they stand a chance? And at the very end. Leaving the issues of “hard science” aside, knowing the shape of the space may pay off. On a sheet of paper points A and B can be connect only with one straight line. But if the same sheet of paper is rolled up into a cylinder, the points A and B can be connected with more than one straight line. It may be possible to get from point A to point B somehow taking a short cut, maybe, instead flying on the surface of the cylinder, it is possible to pass through the middle? Who knows, perhaps the knowledge of the curvature of space will allow covering large distances in a short time in the distant future?

**dr Tomasz Rożek**

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A doctor of physics, a science journalist of the *Gość Niedzielny* weekly and an author of popular science books. Has his vblog “Science. I like that”.

dr Tomasz Rożek