Have you read the novel Flatland? If you haven’t, maybe you should, since this book sets out the idea of the multidimensionality of the space and presents it in an unusual way.

More particularly, the protagonist of the book called “A Square” is a creature from a two-dimensional world, where everything is a plane, just like a sheet of paper. One day he is visited by another character, “A Sphere”, from a three-dimensional world (just like our own).

A Square can’t imagine what the 3-D world looks like until A Sphere takes him from Flatland to Spaceland. From there, A Square can see his world and family just like we see cartoons on the TV. The only problem is that two-dimensional creatures look disgusting because from Spaceland you can see their insides, since their skin has the shape of a square and does not cover their sides.

Then A Square wonders if a four-dimensional world is possible and what it would look like.

In theory, it is, because there is no reason that could deny the possibility of the existence of space with as many dimensions as you can imagine. But no one can easily imagine, let’s say, a 10-dimensional world and the physical laws it would be ruled by.

But the question is: can the worlds with different dimensionality really interact with each other?

The answer is no because they are ruled by different physical laws. In fact, A Square would have never been able to see his world from Spaceland since Flatland can interact only with forces of two-dimensional space. In order to see Flatland, the 3-D light from Spaceland should be able to interact with Flatland. But it is impossible since the objects in Flatland can’t reflect light or let it through.

Remus Gogu in his book Book Riding. Creative Readings and Writings in Physics and Psychology writes, “If objects from Flatland could interact additionally in two distinct ways, then Flatland itself would become a 3-D world and its citizens would cease to exist because their organs would be exposed to outside forces (just as you would miss the skin on two sides of your body).”

However, the novel raises another interesting question: what a world with 4 and more dimensions would look like?

Let’ begin with understanding how we perceive our three-dimensional world. In reality, we see in 2-D, just like when we watch a movie on the TV, except for the fact that we have a better perception of angles and distance due to the structure and position of our eyes.

You cannot actually see the world in 3-D; when you look at a box in front of you, you may observe a side and a bit around the corners and edges, but you can never see all sides of the box at once”, writes Gogu.

Thus, a 4-D creature would see a 4-D box as a complete 3-D image with some enhancement on edges and corners. Just imagine, wouldn’t it be amazing to see all the six sides of a box simultaneously with no cameras or mirrors? If you can’t imagine it, don’t worry; no one can! That’s why A Square couldn’t figure out what the 3-D world looks like until he visited Spaceland and saw it with his own eyes.

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