The Fourth-Dimension - Beyond Visualization

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Min Khant Okkar

Introduction

We are living in a 3-dimensional world with a 3-dimensional vision where we can see the length, width and height of an object. But, what if we had a 4-dimensional vision? What will be our new experiences? Let’s have a deeper look into it. First, we need to understand what dimension is and what exactly we are experiencing.

The dimensions we can see

When an object is moving away from you, you will be able to tell it is by seeing how it is getting smaller for every distance it moves. When it is moving towards you, you will see it is getting bigger and can tell that it is moving towards you. But what if the object is moving away from you and at the same time, it is expanding in size, proportionally to the distance it moves. Thus, when it moves away, it will look like it has the same size and distance as its initial from a point of view.

This suggests that a 2-dimensional vision will be seeing what's called an ‘illusion’. The reason why it is mentioned as a 2-dimensional vision is that from the point of view, it is only possible to see the length and width—no depth. As aforementioned, the size changes as it moves inward or outward. However, when a 3-dimensional view is acted upon the movement and the 2-dimensional object, the 3d view can see how the object is moving or expanding.

This means that we humans— with a 3-dimensional vision—-can see the actual situations in a 2-dimensional world in such a way, that a 2-dimensional vision can see what’s happening in the 1-dimensional world. This comes to our senses that we are not seeing the world in the way it truly is: we are seeing only a part of it.

The 4th dimension

What can the 4-dimensional vision see?

Accordingly, 4-dimensional visions can see the true happenings in our 3-dimensional world. For example, they will be able to see what humans cannot see at one glimpse; they will be able to see through humans; buildings; etc.

What is in the 4-dimensional world

Since in the 1-dimensional world, there is only the length in which a thing can move either inwards or outwards, and length and width in the 2-dimensional world, and length, width and height in the 3-dimensional world, we can say that there is another measurement in the fourth dimension. With width being perpendicular to length and height being perpendicular to both of them, the fourth measurement is similarly perpendicular to all three above.

Taking into account that a 2d world is made out of an infinite amount of 1d lines, a 3d world is made out of 2d planes. In such a way, a 4d world is made out of 3d blocks. However, if the blocks were stacked on each other like legos, that will just make another 3d object. Thus, the way a 4d object is formed is beyond what we can visualize. It will be like visualizing a state of matter that does not exist.


A Tesseract


However, researchers have discovered a 4d object called a tesseract. In our 3d world, a cube has 2d squares on its sides and produces a 2d shadow. In the 4d world, the tesseract has cubes as its sides and produces a 3d shadow. As aforementioned, it is difficult to imagine a higher dimensional world.

Resources

[1] “From 2D to 3D”, Stack Exchange, July 2017 https://math.stackexchange.com/questions/216847/why-is-it-that-i-cannot-imagine-a-tesseract#:~:text=Now%20the%20answer%20to%20your,then%20interprets%20those%20two%20images.

[2] C. Yan, K. Zhou, S. Yang, Y. Shi, “Four-Dimensional (4D) Printing”, September 2021 https://www.frontiersin.org/articles/10.3389/fmats.2021.757479/full

[3] C. Benedek, Z. Jankó, C. Horváth, D. Molnar, “An Integrated 4D Vision and Visualisation System”, July 2013 https://www.researchgate.net/publication/262288444_An_Integrated_4D_Vision_and_Visualisation_System

[4] T. English, “Understanding the Fourth Dimension From Our 3D Perspective”, May 2017 https://interestingengineering.com/understanding-fourth-dimension-3d-perspective#:~:text=To%20summarize%20our%20understanding%20of,perpendicular%20to%20the%20previous%20three.

[5] Tesserect image, Wikipedia https://en.wikipedia.org/wiki/Tesseract

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