What form of the universe is there?

When you look around you may seem like you live on a flat plane. After all, so you can walk a new city using a map: a flat piece of paper that represents all the places around you. This is probably in the past some people believed that the earth was flat. But most people know that now is far from the truth.

You live on the surface of a giant area, the size of the ground like a beach ball is a few bumps. The area of ​​the area is two possible 2D spaces of the aircraft, ie you can walk in two directions: north and south or east and east.

What else can you experience possible space? So other gaps around there are 2D? For example, a giant donut surface is another 2D space.

Through a field called geometric topology, Mathematicians like me Learn all possible gaps in all sizes. Trying to design Safe Sensor Networks, mine information or use Origami to place satellitesThe main languages ​​and ideas are likely to be topology.

The uniform of the universe

When you look around the universe you live, it looks like 3D space, like the world’s surface 2D space. But if you looked at the universe like the world, the world, the 2D beach ball can be a giant 3D version of the surface or a more complicated place like something more exotic.

Although you don’t need topology to determine what you live in something like a huge beach ball, it can be useful to know all possible 2D gaps. A century ago, mathematicians have understood All 2D gaps possible And many features.

In the last few decades, mathematicians learned a lot about all possible 3D gaps. If we do not have a complete understanding of as we do for 2D venues, we do know a lot. With this knowledge, physicist and astronomers may try to determine what 3D Space People Actually Live.

The answer is not completely known, there are many Interesting and surprising opportunities. If you consider the time as a measure, the options are becoming more difficult.

To see how it works, say a comet to describe the place of something in space – you need four numbers: you need a number to describe his position and describe the time when it is in this situation. These four numbers are what makes up the 4D space.

Now you can think of what 4D gaps are and which of these gaps are experiencing.

To topology in higher dimensions

At the moment, there is no reason to think of taking into account the venues of the sizes of the four, because it is the highest imaginary measure that can describe our universe. But one branch of a physique string theory Indicates that the universe has more than four sizes.

There is also a practical application of thinking about higher sized gaps robot action planning. Suppose you try to understand the movement of three robots moving around a factory floor in a warehouse. You can put a grid on the ground and describe the position of each robot with the coordinates of X and Y. Since each of the three robots requires two coordinates, you will need six numbers to describe all possible positions of robots. You can interpret the possible positions of robots as 6d spaces.

As the number of robots increases, the size of the space is growing. Factoring in other useful information, such as obstacles, makes the gap even more difficult. You should learn high-sized gaps to learn this problem.

There are countless other scientific problems that high-sized gaps appear the movement of planets and spacecraft try to understand “Form” of large databases.

Tied in knots

The study of a problematic type of topologists can sit in the other.

For example, if you hold a knotted loop, you have 1D cavity (wired loop) in 3D space (room). Such loops are called mathematical knots.

This The study of the knot First came out of physics, but turned into a central area of ​​topology. They are important for scientists to understand how 3D and 4D spaces and researchers have a delicious and delicate structure Still trying to understand.

In addition, there are many applications variable between nodes string theory In physics DNA recombination In biology section In Chemistry.

Which form do you live?

The geometric topology is a beautiful and complex topic and there are still countless interesting questions to answer about the gaps.

For example, Smooth 4D Poinsaré think “The simplest” asks for what is the 4D space of the 4D The respect of the slice of tape Aims to understand how the knots in 3D venues are related to surfaces in 4D spaces.

Topology is currently useful in science and engineering. In all sizes, it will be invaluable to understand more secrets of gaps, and understand the world where we experience and solve real world problems.

John EtnyProf. Mathematics, Georgian Institute of Technology

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