What Exactly Is A Tesseract?

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:

avengers tesseract

The Tesseract, as shown in the Marvel Cinematic Universe. (Photo Credit : Avengers movie / Marvel Studios)

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.

The moment you realise that the tessaract is a real concept in geometry meme

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.

Wall E 2d vs 3d image

Notice how there is a sense of depth in 3D, but not in 2D. (Photo Credit : Pixabay)

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.

Original version of the animated 8-cell

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.

Square cube tesseract 2d 3d 4d

Notice the shapes in 2D, 3D and 4D.

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.

So you think a 4d cube cant exist just because you cannot visualise it in your head thats cute meme

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.

3-D net of a Tesseract

3-D net of a Tesseract. (Photo Credit : A2569875 / Wikimedia Commons)

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

  1. University of Pittsburgh
  2. Harvard University
  3. University of Illinois Urbana-Champaign
The short URL of the present article is: http://sciabc.us/DEeAj
About the Author:

Ashish is a Science graduate (Bachelor of Science) from Punjabi University (India). He spends a lot of time watching movies, and an awful lot more time discussing them. He likes Harry Potter and the Avengers, and obsesses over how thoroughly Science dictates every aspect of life… in this universe, at least.

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