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Explaining the different dimensions

I normally avoid the first person when writing an article or essay, but in this case I need to begin with a personal story. A year into my studies at Humboldt State University a mutual acquaintance showed up at my friend's apartment while I was visiting and regaled us with his synopsis of a lecture on dimensions he recently attended. I do not recall what the class was, and I'm not even sure I remember the student's name, but I will never forget that conversation. Prior to that day, I had not given the concept of dimensions my full attention, even though I had previously encountered the topic in math, science and science-fiction.

The discussion we had that day about dimensions was not significantly different from the usual lecture on the first four dimensions, the point, the line, the plane, and the volume. The debate that followed was prompted by discussion of four-dimensionality. I got caught up initially in the numbering conflict; having just discussed four different dimensions, the "fourth dimension" being volume. Once the proper numbering of the dimensions was reestablished (0, a point; 1, a line; 2, a plane; 3, a volume) along with the accepted rule of progression (once an initial line is established, each new dimension lies outside of and perpendicular to the previous dimensions) we returned to addressing a four-dimensional object.

In specific, my acquaintance asserted that it was not possible to visualize a four-dimensional object. I conceded that it would be difficult to represent, graphically, but not impossible. Having an artistic background, I had thought immediately of the representation of depth in drawings (a two-dimensional environment.) I suggested that a representation of a four-dimensional object could be visualized in the mind. I suspect he took me too literally, because he objected, claiming, "The only way you could imagine four-dimensions is if your mind got warped into the fourth-dimension!" My immediate thought was, "Maybe it has."

Since that day, I have given a lot of thought to the concept of dimensions, and the ways that dimensional concepts have been (or can be) applied. To date, the best example I have ever found for a four-dimensional object is the mind. The mind not only creates its own space (defines its own space, I should say), it contains the three-dimensional image we use to interface with reality. The mind's ability to encompass dreams, memories and images of different times and places, real or imagined, and to jump between


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