Exploring the Fourth Dimension: Venturing Beyond 3D Spaces

Anything can come out of a 4D pocket, but what does the 4th dimension look like in the first place? I think we have all wondered this question. We exist in a three-dimensional world. It is a world of length, width, and depth, and those of us who can only perceive three-dimensional space are told that it is impossible to fully understand the four-dimensional world.

However, we can think about the 4-dimensional world and become familiar with the 4-dimensional world. In this article, I will show you how to use "expansion diagrams" to feel like you understand the 4th dimension a little better.

First, the dimensions are like this. You may have learned about expansion in elementary or junior high school. To expand means to lower one dimension.

• 0 dimension = point

• 1 dimension = line

• 2 dimension = surface

• 3 dimension = 3 dimensional

When a 2-dimensional figure is expanded, it becomes a 1-dimensional line.

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When a 3-dimensional cube is expanded, it becomes a 2-dimensional surface.

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Going in this vein, if we expand a 4-dimensional cube, it becomes a 3-dimensional cube. So, it is difficult to draw a 4-dimensional cube, but we can recognize its expansion. This is the right figure. (The colorful colors are for the sake of clarity.)

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As you can see, the expansion of a 4D cube is said to be a combination of eight 3D cubes like this. In the 4D cube before expansion, a to a, b to b, and c to c, in the expansion below, are spatially connected before expansion.

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I want to say "What?". It is not intuitive, but that seems to be the case.

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Salvador Dali published "Crucifixion (Corpus Hypercubus)" in 1954. This depicts the development of a four-dimensional figure.

Photo: Dali Crucifixion hypercube

It looks like a cross between 4-dimensional space and religious significance.Other than that, the 4th dimension has been a source of inspiration for many scientists, mathematicians, and artists. What we know to be there, but don't understand, stirs people's spirit of inquiry. The concept of the 4th dimension will continue to fuel our imagination.

References

• Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas by Edward B. Burger, Michael Starbird.