Wednesday, January 04, 2006


Today's cool word is "Surcomplex", as in "surcomplex number". Surcomplex numbers are to surreal numbers what plain-vanilla complex numbers are to real numbers. The name combines "surreal" and "complex", and I can think of lots of everyday situations where this word would be a perfect description.

As you may have noticed with the stubby little Wikipedia article referenced above, there's not a lot of info on the net about these babies. And I've seen nothing at all about "surreal-hypercomplex" numbers, which would seem to be a logical extension of the idea. With the use of something called the Cayley-Dickson construction, you can go on indefinitely, creating ever-more-hypercomplex (and ill-behaved) numbers. It's interesting to note that the number of dimensions of a number created this way is always going to be a power of 2, which suggests a sort of parallel with the binary-tree way that surreals are constructed. Well, it does to me, anyway, but then I'm a computer geek, not a mathematician, and besides, by no means are all mathematicians happy with Conway and his surreals (you'll want to read a few posts in the thread to get the gist of the argument). Anyway, a surreal-style tree that also gains dimensions on the way down is quite an interesting thing to comtemplate. At omega, assuming the analogy holds this far, you'd start encountering weird beasts like numbers with an infinite number of dimensions. Just try to imagine that for a moment. And each dimension a surreal number, possibly infinite or infinitesimal. Wheee!

I'd hope there'd be no way to use something as esoteric as a surcomplex number to design a new kind of bomb, but you never can tell. GH Hardy took a great deal of pride in the notion that his beloved number theory was of no practical use to anyone, not foreseeing the rise of math-intensive cryptography. Now, cryptography clearly isn't a bomb, and has lots of wholesome, nonmilitary applications, but in this day and age it's also safe to assume that numerous large numbers have been factored using the Cheney algorithm, which is to find someone who already knows the factors, and torture them until they cough 'em up.

Speaking of Cheney, here's another fun article about his (and Rummy's) longstanding love of surveillance and hatred of Constitutional government. Meanwhile, the talk radio / think tank / conservative blog echo chamber is full of the usual suspects, each trying to outdo the next in heaping scorn on outdated and subversive notions like search warrants, habeas corpus, the ban on cruel and unusual punishment, freedom of speech. We're told again and again that anyone who still believes in that old-fashioned stuff is a commie pinko liberal who hates America and loves the evildoers. I ask again, what's this country coming to, when to be considered a "true patriot" you're expected to abandon, and actively oppose, the entirety of the country's founding principles?

Well, actually today the wingnut universe has other, more immediate concerns, namely yesterday's UN-imposed ban on trade in wild caviar. Here's one example of the conservative hysteria this is evoking. This story's got everything. The UN, which they hate, and have all sorts of fun conspiracy notions about. The environment and endangered species, which they're also 100% against. Left-wing-inspired "persecution" of poor innocent rich folks who just want to enjoy their bland, salty fish eggs in peace.

Interestingly, we have a similar fishy situation here in Oregon, except with sea urchins instead of sturgeon. People are often surprised that sea urchins are commercially fished along the Pacific coast. It's not like you see them at the grocery store, or even in seafood markets on the coast. No, they're all exported to Japan, where sea urchin eggs are a delicacy. They only started catching the things here in the early 70's, and the sea urchin population seems to have been in a steady and ongoing decline ever since due to overfishing. What makes this even more fun is that the urchin population started out at an unnaturally inflated size, due to the prior local elimination of its main predator, the sea otter. And when the urchin population explodes, the little beasties mow down the coastal kelp forests that provide shelter to numerous species of fish, hurting those populations as well. So some might argue that overfishing of sea urchins is good news for kelp and fish. Well, until the population crashes, which is something fisheries of all types are prone to do, and then there aren't enough urchins around to keep the kelp in check. Then I suppose the answer to that problem will be some kind of anti-kelp herbicide, or an ongoing Federal kelp mitigation program at taxpayer expense.

Here's a pic of a sea otter eating a sea urchin.

Here's an even cuter sea otter picture. Awwwwww.....

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