Tuesday, December 2, 2014

The Dodecahedron & The Tesseract

After watching Interstellar, I thought a lot about the tesseract or hypercube, which I first heard about as a kid reading A Wrinkle in Time, and later encountered on Carl Sagan's original Cosmos. The subject always fascinated me, and why not? I love that I can think about something without really being able to picture it. The three-dimensional "shadow" of the hypercube is the best way to approach understanding it, if you have no math (which I don't). In fact, almost everything on that Wikipedia page I linked to above is Greek to me (in some cases, literally).

The reason I bring this up will be utterly obscure to anyone who isn't in my gaming group: the relationship of the tesseract to the dodecahedron (sort of). If you're not into Gonen's World, you can stop reading now, because this won't mean much to you. The dodecahedron - known to gamers as the twelve-sided die or d12 - has always held a place of semi-mystical significance in the fictional Gonen's World, mainly because of a story I heard when I was in third grade that stuck with me over the years. In the original Cosmos, Carl Sagan talks about Pythagoras, the ancient Greek mystic/mathematician, attempting to suppress knowledge of the dodecahedron because, through some mathematical contemplations I can't understand, the dodecahedron led Pythagoras to the fact that the square root of two is irrational. That suggested to the Pythagoreans that math couldn't explain everything and that maybe their view of the perfectly ordered universe was a bit off. Even as a third grader, that fact disturbed me. It was, perhaps, the first time I had any indication that adults, scientists, preachers, authority figures in general, might actually lie about something. In my little mind, the dodecahedron morphed into a symbol of truth - particularly, a symbol of hidden truth and secret meanings. Much later, when I began working on Gonen's World in the mid-1990s, the dodecahedron crawled out of my subconscious and inserted itself into the fiction as a powerful cultural, religious, and mathematical symbol. So those who have gamed in Gonen's World know the dodecahedron well.

Now back to tesseracts. In reading the Wikipedia article, trying in vain to understand sentences I just don't have the math for, I came across what is, to me, a fascinating reference: "The rhombic dodecahedron forms the convex hull of the tesseract's vertex-first parallel-projection." I don't know what a rhombic dodecahedron is (I mean, I read the link, but I still don't get it). I'm not sure what a "vertex-first parallel-projection" is, either. As best as I can tell, the rhombic dodecahedron seems to frame a three-dimensional shadow of a four-dimensional tesseract. That's the important point for me. It was a moment of serendipity. Two things that have lurked in my mind since childhood now coalesce. It's not important that I understand the math, or appreciate that a rhombic dodecahedron isn't the same thing as the "perfect solid" dodecahedron with twelve identically-shaped faces. What matters is that in Gonen's World mythology (fictional though it may be), the dodecahedron just got more credibility as a mystical, quasi-magical (or, as we say in Gonen's World, mathemagical) object/concept. If any kind of dodecahedron and the tesseract are connected in any way, even theoretically, I feel like it justifies or legitimizes my fictional concept of the dodecahedron all along. If, in Gonen's World, the dodecahedron is the pathway to "magical" power, maybe it has something to do with it giving the practitioner of such arts a gateway or, better yet, a control panel of sorts to operate in higher dimensions, manipulate space, time and matter, and achieve "magical" effects.

It's not necessary that the "Laws of Nature" in a fictional world be in accord with the laws of the real world. But it is nice when they're somewhat self-consistent, and that's my big discovery here today: more evidence that the dodecahedron was and is the best choice for a mystical symbol of hidden meanings and ultimate truth in Gonen's World.

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