Saturday, December 22, 2007

Math Rant (Part 2)

[This is part 2. If you arrived here first, don't start here, you'll just be confused. Well, even more confused than if you had started with part one; so, start with part 1.]

Any sufficiently advanced technology is indistinguishable from magic.

Arthur C. Clarke said that in 1973. I find it a profound comment on the human condition. More on that in a minute, after I chat about Clarke.

This is the third of "Clarke's Laws," which are obviously somewhat tongue-in-cheek; they mathematically parallel Asimov's Three Laws of Robotics or, in Clarke's own pseudoegotistical words, "Three laws were good enough for Newton, so, modestly, I'll stop there." Naturally, soon thereafter (In 1999, specifically, so I guess that's not soooo soon.) he proposed his Fourth Law, which states: For every expert, there is an equal and opposite expert.

What a wag! Parenthetically, Asimov also ultimately outdid Newton but went the other way and added not a Fourth Law but a Zeroeth Law to his three on robotics.

But on to the point I'm creeping lethargically toward. Map this law of science/magic against current society, or most (all?) societies in history, and you'll find (*I* find, anyway) two interesting phenomena which are, at first glance, unrelated or perhaps seemingly opposite, but are, on deeper examination, inevitable lemmata of this sardonic law. That's a great word, isn't it? Lemma/lemmata. Wasn't there a grade Z movie about a "forbidden dance" called something like the lemmata? Ok, I'm just fucking with you. The dance/movie was the "Lambada." Pretty close, huh? Oh, if you're now interested in the movie, be warned by one reviewer's comment. He said: I'd rather watch Barney and friends. Ouch!

Both lemmata are, essentially, examples of magical thinking, sometimes called analogical reasoning. That sounds kinda pedantic, doesn't it? Let's stick with "magical thinking" although it might be more proletarian and more accurate to call it antilogical nonreasoning. I'm gonna digress from the usual conceptualization of magical thinking and address it in the two ways I see it in action in society.

I must admit, however, that I would like to do a lengthy post on the cargo cults because they seem to me to be a perfect example of Clarke's third law and magical thinking in human society and they occupy the same cultural region as my favorite disease, kuru. Ya gotta love a 100% fatal disease with the unique symptom of uncontrolled laughing. More on that some other time, maybe. Gives you a fresh perspective on the societal (nutritional?) value of brains.

Yes, both of these examples are part and parcel of the innumeracy which is at the root of my rant, if you consider rigorous, logical, scientific thinking in general as an adjunct of the specific of numeracy, which I'm gonna define here as being comfortable with a broad range of mathematical concepts without necessarily being a mathematician. (See the quote which closes this portion of the rant for more on this particular notion.) So what are my two lemmata?

Imprimis, all science/logic/numeracy is abstemiously abstract and meaningless to daily reality.

Secundus, science/logic/numeracy is meaningful and important to daily and long-term reality but WAAAY too complex for ordinary mortals to understand and therefore we might as well not try. Let's just leave it to those mutants who walk among us who actually understand that crap in some kind of idiot-savant gestalt.

There is no tertius, for which, I'm sure, you're zealously thanking your favorite deity. If you're currently without a favorite supernatural boojum [Also check out the use of this term in cryogenics, superfluids within a gnat's hair of absolute zero. Science is cool!], may I suggest The Flying Spaghetti Monster? I love that particular divine being. He's just so… noodly! And so appropriate here because he's a close cousin to Russell's Cosmic Teapot and Bertrand Russell is certainly a monumental figure in mathematics, if for no other reason that the fact the he penned the mighty tome, Principia Mathematica. Ya gotta have some serious testicular fortitude to write a book in the twentieth century and name it that. I don't think he ever expected best-seller status, ya know? You go, Bert!

Let's consider lemma 1. Essentially, it's all bullshit with no bearing on reality.

In ancient times, Zeno's paradox, specifically the one about Achilles and the tortoise, is the prime example of this. Infinite regression means that movement is actually impossible. You can't get there from here. Actually, you can't get anywhere. Of course, ordinary daily reality amply demonstrates (proves) that this is a silly notion. Obviously we all get up every day and move about in the world. Therefore all math is silly and mere intellectual masturbation.

The perfect modern example, for me, is the populist concept of chaos theory. Even intelligent, educated science popularizers like Crichton turn chaos theory into a universally applicable Ubertheory of Everything. Randomness rules all; nothing is predictable. It's the ultimate stochastic universe. Therefore, everything is random and learning about math/science is useless and meaningless in real life. Again, ordinary daily reality amply demonstrates (proves) that this is another silly notion. Obviously we all accurately predict coming events every day. (The sun will rise in the East tomorrow. I'll bet you a year's pay.) Therefore (Say it with me now.) all math is silly and mere intellectual masturbation.

One quick side note. Whatever else you say about chaos theory, ya gotta love it for giving us "strange attractors." Man, that reminds me of an ex-girlfriend from before I met and married the inestimable Ronnie. And who doesn't love Cantor dust? It's kinda like fairy dust but stranger. Yes, even stranger than Big G's fairy dust which I sometimes suspect is illegal in most of the Western world. Do Big G and the Logarithm Fairy count as "strange attractors?" So many questions, so little time.

And now a brief word about lemma 2. It's useful for so many things around the house and around the universe. Don’t touch that mouse! You'll want to be here for what comes next.

Lemma 2 says basically: Ok, all that math stuff is important and useful but reserved for a tiny subset of mutant humans. Regular folks can't comprehend it.

For instance, have you seen that TV show NUMB3RS? Man, those folks can figure out anything but it's all a mystery to me. Of course, while they're in their ivory tower writing arcane symbols on the whiteboard, some flatfoot cop is finding out the same thing by asking around the neighborhood. Duh!

And that "Beautiful Mind" guy, Nash. Tres bizarre, non? It's just so complex. Really? His big conceptual breakthrough, which overturned a paradigm entrenched for a coupla hundred years, resulted from an encounter in a bar with a beauteous babe and her pedestrian pals, something which any low-grade moron would understand intuitively. The Nash equilibrium. Whoa! Very significant sounding. Oh yeah, and then it took him forever to prove it mathematically. Duh!

Or quantum mechanics. How can the cat in Schrodinger's box be alive and dead at the same time? It muddles my poor, little brain. Superposition? Is that, like, having good seats at a Seahawks game? But when you open Schrodinger's box, the cat is not simultaneously alive and dead; it's whichever happens to be the case for you, your eigenstate. Cool word, cool concept (thought experiment); but c'mon. Duh!

And good old relativity. People complain all the time about how they can't understand it. However, Einstein himself used to have the easy, perfect explanation of relativity. Well, special relativity, anyway. General relativity we'll leave for another discussion. Einstein explained it this way: If a pretty girl sits on your lap for an hour, it seems like a minute. If you sit on a hot stove for a minute, it seems like an hour. (All together now:) Duh!

Einstein also famously said, "If we knew what we were doing, we wouldn't call it research." I like that one.

Ok, this is already longer than part 1; so I'll call this part 2 and warn you that part 3 is gestating. I'm taking just a bit longer than a Planck time unit with this rant but we'll get somewhere eventually.

I'll close with a quote by Bertrand Russell for your amusement:

Pure mathematics consists entirely of such asseverations as that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It's essential not to discuss whether the proposition is really true, and not to mention what the anything is of which it is supposed to be true. If our hypothesis is about anything and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

Another smartass, like Clarke and Asimov. What is it with these science/math guys?

So, lemme actually finish this part (Really. This time I mean it.) with a quote about the quotidian math experience most of us had in school and why math instruction *should* be better than the idiotic crap we all put up with. From (the name is an homage to the Gordian Knot), an interesting math website:

I hope, in time, more emphasis will be put on the abstract side of mathematics. Drills contain no knowledge. At best, after sweating on multiple variations of the same basic exercise, we may come up with some general notion of what the exercise is about. At worst, the sweat and effort will be just lost while the fear of math will gain a stronger foothold in our consciousness. Moreover, if it's possible at all for a layman to acquire an appreciation of math, it's only possible through a consistent exposure to the beauty of math which, if anywhere, lies in the abstractedness and universality of mathematical concepts. Nonprofessionals may enjoy and appreciate both music and other arts without being apt to write music or paint a picture. There is no reason why more people couldn't be taught to enjoy and appreciate math beauty.

What's coming in Part 3? What can I say? More of the same.

[Go to part 3.]

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