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Home  »  Pure Sciences


WHAT EXACTLY IS A TESSERACT?

Written by AshishLast Updated On: 19 Oct 2023Published On: 29 Mar 2018

Table of Contents (click to expand)
 * What Are “Dimensions”?
 * What Is A Tesseract?
 * Why Is It Difficult To Imagine A Tesseract?

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> Simply put, a tesseract is a cube in 4-dimensional space. You could also say
> that it is the 4D analog of a cube. It is a 4D shape where each face is a
> cube.

If you’re an Avengers fan, the first thing that comes to mind when you hear the
word “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 bright blue cube that not
only people from Earth, but also from other planets are crazy about. That’s why
all Avengers joined forces to protect Earthlings from the extraordinarily
destructive powers of the Tesseract.

But let me tell you this: The tesseract is an actual geometric concept, or
rather, a shape that exists in 4D. It’s not just a blue cube from the Avengers…
it’s a real concept.

But before we explain a tesseract in detail, let us start from the bottom.



--------------------------------------------------------------------------------

Recommended Video for you:

Play
What Exactly is a Tesseract? (Hint: Not a Superhero Stone)

--------------------------------------------------------------------------------





WHAT ARE “DIMENSIONS”?

I am sure that you have heard the terms 2D and 3D, which represent two and
three-dimensional objects of space respectively.

A dimension is only one direction you can go in. For example, if you draw a line
on a sheet of paper, then you can go in either the left/right (x-axis)
direction, or in the up/down direction (y-axis). So we say that the paper is
effectively two-dimensional, since you can only go in two directions on it.

Now in the real world, in addition to the two directions mentioned above, one
can also go in/out. Therefore, in 3D-space, a feeling of depth is added.
Therefore, we say that real life is three-dimensional.

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

A point represents 0 dimensions because it does not move in any direction, a
line represents 1 dimension (length), a square represents 2 dimensions (length
and width) and a cube represents 3 dimensions (length, width and height).

Take a 3D cube and replace each face, which is currently a square, with a cube.
And lo and behold! The shape you get is a tesseract.

Also Read: Is There Anything More Complex Than Complex Numbers?




WHAT IS A TESSERACT?

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

A 3D projection of a tesseract performing a double rotation about two orthogonal
planes. (Photo Credit : Jason Hise / Wikimedia Commons)

A square is a 2D shape; therefore, each of its corners has two lines that
separate at a 90-degree angle from each other. A cube is 3D, so each of its
corners has three lines that separate from it. Similarly, a tesseract is a 4D
shape, so each corner has four lines that separate from it.



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





WHY IS IT DIFFICULT TO IMAGINE A TESSERACT?

Since we as humans have evolved only to visualize things in three dimensions,
anything that is part of other dimensions, such as 4D, 5D, 6D, etc., makes no
sense to us because we cannot visualize them at all. Our brain cannot make sense
of a fourth dimension in space.

But just because we cannot visualize a concept does not mean that it cannot
exist.



Mathematically, a tesseract is a perfect shape. Likewise, all shapes in higher
dimensions, i.e. 5D and 6D, are also mathematically plausible.

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

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

Incredible, isn’t it?

So a Tesseract is a real concept (which is mathematically absolutely plausible),
and not just a bright blue cube, which they fight over in The Avengers.

Also Read: Why Is The Universe Only Four Dimensional?




References (click to expand)
 1. What is a four dimensional space like? - University of Pittsburgh. The
    University of Pittsburgh
 2. The Tesseract - www.math.harvard.edu:80
 3. The Tesseract (or Hypercube) - www.geom.uiuc.edu

Tags: Dimension, Euclidean space, Mathematics, Spacetime
About the Author



Ashish is a Science graduate (Bachelor of Science) from Punjabi University
(India). He spearheads the content and editorial wing of ScienceABC and manages
its official Youtube channel. He’s a Harry Potter fan and tries, in vain, to use
spells and charms (Accio! [insert object name]) in real life to get things done.
He totally gets why JRR Tolkien would create, from scratch, a language spoken by
elves, and tries to bring the same passion in everything he does. A big admirer
of Richard Feynman and Nikola Tesla, he obsesses over how thoroughly science
dictates every aspect of life… in this universe, at least.

More from this author.

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