# What Exactly Is A Tesseract?

 Listen to this post  ## Tesseract: A 4D cube

Simply put, a tesseract is a cube in 4-dimensional space. You could also say that it’s the 4D analogue of a cube. It is a 4D shape where every face is a cube.

If you’re an Avengers fan, the first thing that may come to your mind when you hear the word “tesseract” is this:

For fans of the Marvel Universe, the Tesseract is the glowing blue cube that people from, not only Earth, but other planets are also crazy for. That’s the reason why all the Avengers teamed up in order to protect Earthlings from the exceedingly devastating powers of the Tesseract.

However, let me tell you this: the tesseract is an actual geometrical concept, or rather, a shape that exists in 4D. It’s not just a blue cube from the Avengers… it’s a real concept. A tesseract is an object in 4 dimensions. But before we explain a tesseract in detail, let’s start from the absolute bottom.

## What are ‘dimensions’?

I’m sure that you’ve heard the terms 2D and 3D a number of times, representing 2-dimensional or 3-dimensional  objects of space, respectively. But what do those ‘dimensions’ represent?

A dimension is just a direction in which you can go. For example, if you’re drawing a line on a piece of paper, then you can go in either the left/right (x-axis) direction, or in the up/down direction (y-axis). Thus, we say that the paper is effectively 2-dimensional, as you can only go in two directions on it.

Now, in the real world, in addition to the two directions mentioned above (i.e., left/right and up/down), you can also go in/out. Hence, a sense of depth is added in 3D space. Therefore, we say that real life is 3-dimensional.

A dot can represent 0 dimensions (as it does not move in any direction), a line represents 1 dimension (length), a square represents 2 dimensions (length and breadth) and a cube represents 3 dimensions (length, breadth and height).

Take a 3D cube and replace each face (which is currently a square) with a cube. Lo and behold! The shape you get is a tesseract.

## What is a tesseract?

Simply put, a tesseract is a cube in 4-dimensional space. You could also say that it’s the 4D analogue of a cube. It is a 4D shape where every face is a cube. A 3D projection of a tesseract performing a double rotation about two orthogonal planes. (Photo Credit : Jason Hise / Wikimedia Commons)

Here’s a simple way to conceptualize dimensions: a square is a 2D shape; so, each of its corners has 2 lines coming off it at 90 degrees to each other. A cube is 3D, so each of its corners has 3 lines coming off it. Similarly, a tesseract is a 4D shape, so every corner has 4 lines coming off it.

## Why is it difficult to visualize a tesseract?

Now, since we, as humans, have only evolved to visualize stuff in 3 dimensions, anything that’s a part of further dimensions, like 4D, 5D, 6D etc, do not make much sense to us because we can’t visualize them at all. Our brains can’t make any sense of a 4th dimension in space. We simply can’t wrap our heads around it.

However, just because we cannot visualize a concept doesn’t meant it cannot exist. Mathematically, a tesseract is a perfectly accurate shape. Similarly, all shapes in higher dimensions, i.e. 5D and 6D, are also mathematically plausible.

Just like a cube can be unfolded into 6 squares in 2D space, a tesseract can be unfolded into 8 cubes in 3D space.

Mind-boggling, isn’t it?

So, a tesseract is a ‘real concept’ that is absolutely plausible mathematically, not just a glowing blue cube they fight over in Avengers movies.

#### References

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