What’s the shape of the universe? Mathematicians use topology to study the shape of the world and everything in it

When you look at your surrounding environment, you may seem to live on a flat plane. After all, for this reason you can move in a new city using a map: a flat piece of paper representing all places around you. That is why some people in the past believe that the Earth is flat. But most people now know that this is far from the truth.

You live on the surface of a giant ball, like the Earth’s beach ball with the addition of some bumps. The surface of the ball and the plane are two possible areas, which means that you can walk in two directions: north, south, east and west.

What other possible spaces that you may live on? This is, what other spaces around you are two -dimensional? For example, the surface of the giant cake is another two -dimensional space.

Through a field called geometric dust, Mathematics like me Study all possible spaces in all dimensions. Whether it is trying to design Safe sensor networksand Mine data Or use Origami to spread satelliteLanguage and basic ideas are likely to be the language.

Universe

When you look around the universe in which you live, it looks like a 3D space, just like the surface of the Earth looks like a two -dimensional area. However, just like Earth, if you want to look at the universe as a whole, it may be a more complex space, such as a 3D giant from the surface of the two -dimensional beach ball or something more strange than that.

Although you do not need a brown to determine that you live on something like a giant beach ball, knowing all two -dimensional spaces can be useful. More than a century ago, mathematicians discovered All possible 2D spaces And many of their characteristics.

In the past few decades, mathematicians have learned a lot about all possible 3D spaces. Although we do not have a full understanding as we do for two -dimensional spaces, we do Know a lot. With this knowledge, physicists and astronomers can try to determine what 3D space people actually live.

While the answer is completely unknown, there is a lot Interesting and amazing possibilities. The options become more complicated if you consider the time remotely.

To find out how this can succeed, note that to describe something in space – say guilty – you need four numbers: three to describe its location and one to describe the time when it is in this position. These four numbers are the 4D area.

Now, you can think about possible 4D spaces and in any of these spaces you live.

Tobology in higher dimensions

At this point, it may seem that there is no reason to consider the spaces that have larger dimensions than four, because this is the highest dimension that can be imagined may describe our world. But a physics branch is called String It indicates that the universe has many dimensions more than four.

There are also practical applications for thinking about upper dimensions, such as Robot movement planning. Suppose you are trying to understand the movement of three robots that move around the factory floor in a warehouse. You can place a network on the floor and describe the location of each robot through the coordinates of X and Y on the network. Since each of the three robots requires two coordinates, you will need six numbers to describe all possible situations of the robots. You can explain possible situations of robots as a 6D space.

As the number of robots increases, the area increases. Other useful information, such as obstacles sites, makes the space more complicated. In order to study this problem, you need to study high -dimensional spaces.

There are countless scientific problems where high -dimensional spaces appear from modeling Planetary movement And the spacecraft To try to understand “Figure” big data sets.

Tied

Another type of Tobologist scholars is how the space can sit inside another.

For example, if you carry a complex episode of the series, we have a 1D space (chain ring) within a three -dimensional area (your room). These episodes are called sports node.

the Knot First of my physics, it became a major domain of Tobology. It is necessary for how scientists understand 3D and 4D spaces She has a delightful and accurate structure I am still trying to understand.

In addition, the knot contains many applications, starting with String In physics for DNA re -installation In biology to Chirality In chemistry.

What shape does you live on?

Engineering topology is a beautiful and complex theme, and there are still countless questions to answer spaces.

For example, and 4D Poincaré Guessy He asks what is the “simpler” closed 4D space, and Ribon slide guess It aims to understand the extent to which the contract is linked to the 3D surfaces in 4D areas.

Tobology is currently useful in science and engineering. The disclosure of more spaces in all dimensions will be invaluable to understand the world in which we live and solve problems in the real world.

This article has been republished from ConversationAn independent, non -profit news organization brings you facts and trusted analysis to help you understand our complex world. Written by: John Etreeand Georgia Institute of Technology

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John Etnyre receives funding from the National Science Corporation and the Elaine M. Hubbard Prize Excellence