Tesseracts and n +1

Mean Mr. Mustard and I had a discussion the other morning about tesseracts. Originally, I was talking about the local private school, but Mr. Mustard noted that it was used in a bit of science fiction. I ventured Dr.Who. He was pretty sure it was A Wrinkle in Time. We seem both to be correct. Strangely enough, the word popped up in the book I read this weekend, Alastair Reynolds' Diamond Dogs, Turquoise Days. Unfortunately, even though it contained two novellas, giving it a two-for-the-price-of-one chance to be pretty good - it was the least interesting of any of his books so far. The first novella, "Diamond Dogs", was pretty much a rehash of Cube 2: Hypercube, and Reynolds goes so far as to make his characters actually dream about that movie (piped into their dreams) on their way to confront an alien puzzle artifact. The story is less about the puzzle artifact and more about the lengths people will go through to solve a puzzle - but that angle just doesn't lift it above what seems to be a fairly "dangerous game" motif. The second novella, "Turquoise Days", is more fully a Revelation Space novella (the universe his other, better, books are set in - most of them in the tradition of grand space opera), taking place on a Juggler world - oceanic worlds where the vegetative ocean life serves as a sort of giant database of the minds of those who have immersed themselves in its waters. While it might serve to shed a bit more light on The Jugglers for those who have read his other books, it just wasn't a very interesting standalone story.

So, book review aside, where were we? Tesseracts. Four dimensional cubes. In "Diamond Dogs", one of the puzzles is to pick which object is not the shadow thrown by a lightsource in proximity to a tesseract. Apparently you need to know about mathematical nets to really get the hang of this. The idea of a tesseract is pretty straight forward - just think of a cube, now think of it sort of moving, through time (for instance, time isn't the only fourth dimension you could use) - you sort of get a "tunnel" of cubes. There's your tesseract. If that's not enough hyperobject for you, you can move on to any of the more complex hypershapes or polychorons (four-dimensional polytopes). This will lead you to the following, many of which don't even get their own wikipedia page:

• pentachoron (with 5 tetrahedral cells) (also called a "4-simplex")
• tesseract (with 8 cubic cells) (also called a "hypercube")
• hexadecachoron (with 16 tetrahedral cells)
• icositetrachoron (with 24 octahedral cells)
• hecatonicosachoron (with 120 dodecahedral cells)
• hexacosichoron (with 600 tetrahedral cells)
• faceted hexacosichoron (also called icosahedral hecatonicosachoron)
• great hecatonicosachoron
• grand hecatonicosachoron
• small stellated hecatonicosachoron
• great grand hecatonicosachoron
• great stellated hecatonicosachoron
• grand stellated hecatonicosachoron
• great faceted hexacosichoron
• grand hexacosichoron
• great grand stellated hecatonicosachoron

I'm going to use that last one for my CDFFL name next year. So. This sort of leads me back to a tour of our computing facilities for my company we had the other day where they explained that the basic approach to redundancy in most systems is "n+1" (you can see my correlation, as tesseracts are just n+1 versions of cubes). Figure out how many of something you need, and add one. Follow this advice for power supplies, backup systems, generators, everything. Thinking in an extra dimension is imperative. Mormons and TallBrad both take this advice to heart (Brad doesn't like to see just one girl kissing - he's all about great grand stellated femalekissingchorons). Presumably, this means that when they can, they'll add fourth dimension redundancy to our computing facilities, and Dr. Who or Mrs. Whatsit will suddenly appear in the middle of our facilities - I hope I'm on the tour that day.