Four-Dimensional Vistas

The Fourth Dimension has been an interest of mine since I was a child. I’m not sure when I first heard about it, but I still have my coverless copy of “Geometry of 4 Dimensions” by Henry Parker Manning that I bought in a used book store. (I wonder why it hasn’t ever been reissued by Dover?) Maybe I heard about the fourth dimension in some science fiction TV movie, or in some mathematical survey book like “Mathematical Snapshots” or “Mathematics and the Imagination”.

Once I tried to explain to my best friend about my newly discovered insight how a hypercube could be folded up in four-dimensional space from its so-called three-dimensional net consisting of eight cubes, just as a regular three-dimensional cube could be folded up from its two-dimensional net of six squares. This 3D net somewhat resembling a cross is famously seen in Dali’s “Crucifixion (Corpus Hypercubus),” although I probably didn’t refer to this painting in my explanation.

I’m not sure who came up with the take-away message from my exposition, but it remains clear in my memory that the “junk in the middle” of the hypercube was a piece of the fourth dimension, just as the faces of a cube enclose a piece of our normal third dimension.

I recently came across Claude Fayette Bragdon, architect, author, draughtsman, stage designer, and mystic. At first I was interested in his drawings found on-line. His book “Four-Dimensional Vistas” started off with a good if overly wordy introduction to the concept of the fourth dimension. But then he suggests that many esoteric concepts such as the meaning of dreams, reincarnation, past-life regression, prognostication, ESP, etc. could possibly be explained by higher dimensional space or even higher dimensional time.

Even though I initially found many of these hypotheses too far-fetched for my tastes, I still found some interesting ideas to mull over in this little book.