Saturday, April 09, 2011

Hypercubes and God

I found myself thinking today about order, possibly in response to watching cage fighting on TV, symbolically a totally disordered activity. The Mormons have a pamphlet contrasting the order of heaven with the economic chaos which they perceive to be prevalent on earth, a depressing little read. I learned that order was brought to us by 'Father Adam" from another planet, which came as something of a surprise. And yet, looking at the world through the dark glass of the media, order seems a hard commodity to acquire. Mathematics defines order in terms of predictability. There is something comforting about defining a point, then a line, then a square, a cube...and so on. Most of us stop at cubes since our sense of reality is circumscribed by the boundaries of length, breadth and height, thus for us perceptual, or better, measurable reality does not extend further. Time is a fourth reality or dimension and mathematics extends to any number. It's over-simplistic to suggest transcendence as a fifth, since we assume that it must naturally follow the fourth, which may not necessarily be either logically or mathematically 'true'. And, what follows order five, in the heavenly schema?
So, where are we so far?

These are three and four dimensional hypercubes. Let a fifth dimension be added, this time with a different rule, the four-dimensional cube is rotated, thus.

I thought this an interesting metaphor for transcendence. It makes no mathematical sense, before people throw up their hands in horror. Each cube is distorted momentarily by the action of the fifth operator - 'transcendence', causing it to appear to distort  its own sense of reality before re-forming within orderly limits, maintaining symmetry.
Instead of a candle flame to meditate upon, if this were used instead, where might it lead?


  1. Makes me think about Chaos Theory and its apparent opposite, Fractals. Of course, not being mathematically gifted, accomplished, or even inclined, the fact of connecting those two things may have given you hives. Nevertheless, I ended up mesmerized by the funny little boxes in your movie.


    What was it I was supposed to be contemplating? Oh, yes. Transcendence. Right.

  2. I think you and I ought to form SMUG - the Society for the Mathematically Ungifted.Mathematics is God's way of explaining Nature to us - 'e pluribus unum' is the ultimate expression of order from chaos. I think fractals and chaos are intimately related, as it happens.

  3. "We??" If you are "mathmatically ungifted" I am an asphasic mute. But I'm honoured that you would be willing to identify yourself with someone so numerically challenged as myself. A true friend. =)


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