Four-dimensional 'nonsense'

Thinking In Four Dimensions

            Height, width, and depth are three very important dimensions that allow us to judge shapes on a three dimensional plane. Through seeing this we are able to measure the surface area of an object, and/or its distance between another object. If we had no depth, and could only see the height and width of things, then we would constantly be bumping into everything! So that third dimension is a very important factor. Using it I will explain why hypercubes are not truly four dimensional, and I will show what one will look like on a geometric plane.

            Albert Einstein in his Theory of Relativity said that Measurements of various quantities are relative to the velocities of observers. Velocity is a measurement of change, which happens over  time. If the quantities were to be our three dimensions of height, width, and length then the fourth dimension is velocity which we can say is time. What we have now are geometric shapes named "Hypercubes" which are said to have four dimensions. There are many Hypercubes that can be made, but a 'Tesseract' is one of the most simplest of the shapes. A Tesseract is a cube with a cube inside of it creating a total of eight cubes within itself. In short, it is cube-ception:

            People have put this in a three dimension simulation of where it rotates within itself which in essence would give it velocity, however on a two dimensional plane the shape remains stagnant, and a cube could also be rotated on a three dimensional simulation. In a two dimensional plane, as you see above, it only becomes an exploitation of depth to create an object within itself. So I believe that it is not a true four dimensional shape.

            A four dimensional shape will have to be something that does not remain the same in any plane of conception. So I formed a theory that a four dimensional shape could be drawn if our perception of it was constantly changing. One way this could work would be to draw it as a paradox like the "Penrose Stairs" drawing. So after a long night of critical thinking, simple line drawing, and lots of erasing, I was able to place a four dimensional shape on a two dimensional plane:

            As you look at the shape your vision of it teeters between it being a cut out of four squares connecting to each other, and a cube. It fails to make sense of how it would exist in three dimensions, but you perception keeps adjusting itself to try and make sense of it. This constant change in perception of the shape gives it that fourth dimension of velocity. And through this knowledge we can create a hyper four dimensional shape:

Which creates a total of eight four dimensional shapes, like the Tesseract does with making eight three dimensional shapes.

            I feel that modern math has missed conceived what four dimensions really look like. Hypercubes are only an exploit of surface area in three dimensions. True four dimensional shapes maintain constant change over time which gives it velocity. And velocity is relative to the other quantities being measured. This is my understanding of 'outside the box' thinking and I hope this inspires you to think critically about how dimensions are formed.

Works Cited

Einstein, A. Relativity: The Special and General Theory, New York: H. Holt and Company (1916     (translation 1920)), Print.

Ernst, Bruno. The Eye Beguiled: Optical Illusions. Benedikt Taschen. 1992, Print.

T. Gosset: On the Regular and Semi-Regular Figures in Space of n Dimensions, Messenger of         Mathematics, Macmillan. 1900, Print.

Hanson, J.R. International Journal of Mathematics Education in Science & Technology.    Harrisonburg:  Taylor & Francis Ltd. 2014, Print.

Grosse, Harald. Communications in Mathematical Physics. Munster: Springer Science &      Business Media B.V. 2014, Print.

DeVito, Jason. Differential Geometry & its Applications. Tennessee: Elsevier Science, 2014. Print