Apparently we really ought to call "algebra" bijaganita, since that's its name in Sanskrit, and they're the people who invented it as a separate field. I mean, as long as we're randomly borrowing names, as if the field wasn't well-known in the West (really everyone whose math is more advanced than simple arithmetic does algebra all the time). The Europeans adopted the Arabic name for it because of the work the Arabs were doing with it...but the Arabs got most of it from the Indians.
What's less well-known, I think, is that the last eight or so of Euclid's books are very seldom touched on in our mathematics; I don't have the background to judge but I've heard he actually had a sort of prototype calculus. So did some of the Hindu mathematicians.
What's always bizarre, to me, is when people actually contrast the architecture of the New World favorably with that of Europe. I have the utmost admiration for the social organization of the great American civilizations (Olmecs, Maya, various "Teca" peoples, the mound-builders, and the Inca), though a lot of it was accomplished through Prussianist or even Stalinist measures; my admiration for their art and philosophy has no such reservations; but their architecture is just not impressive. Do you know what a Mesoamerican "pyramid" (really a ziggurat) basically is? It's a pile of rocks. Yes, the rocks are cut very neatly, and arranged quite efficiently; there is certainly know-how involved in hauling them up there to make the thing so tall. But do you really mean to compare the tiny little stone temples at the tops of those pyramids, however big the pile of blocks it's sitting on, to Notre Dame de Paris or St. Peter's Basilica?
The New World lacked the wheel except on toys—and I'll concede that the lack of horses was a factor, but they also didn't have dog-carts or rickshaws, and that's just odd. More, they lacked the arch; those Maya lintel-doorway thingies aren't even close. The dome, the great achievement of Roman architecture? Forget about it.
All these thoughts were occasioned, in part, by someone saying something about how Firefly's setting just assumes society won't change. He's right—I have complained of that myself—but then he said that technology changes culture, even such factors as average intelligence. Though I won't deny that tech can have an effect, he seemed to be implying that technology can make people smarter.
As they say in these barbarous environs, lolwhat? It took a lot more intelligence just to do bookkeeping in the Middle Ages; if you don't believe me, I dare you to compute your income taxes this year using Roman numerals instead of Hindu-Arabic ones. Our math is not a sign of greater intelligence, a superior science; it is an algorithm, that is a technology. As I said before, all technology, all civilization in general, functions to remove greatness from the equation. If anything, technology would change society by making the average person dumber—by letting the average person be dumber. My dad's a math teacher, ask him what effects calculators have had on his students' knowledge of, oh, say, fractions.
The fascinating thing is, in a rightly-ordered society, this would all be to the good. I may be a snob but I'd rather have everyone be able to understand me when I talk; even I like people too much to want them to think I'm talking gibberish. If we could really put technology at people's fingertips to explain concepts or define words mentioned in conversation, I know I'd spend a lot less time backtracking when I talk to people. But in order for it to work at all, for such a thing to sell, people have to understand that it's bad not to understand things—and, instead of just, first, feeling bad, and second, ignoring the thing they don't understand so they won't feel bad again, they should want to understand things.
And I really think our culture has just given up on that idea. Why? Really, shouldn't something like I mentioned, that'll define words and concepts in real-time, be as uncontroversial as artificial legs or eyes? Ignorance is a disability; it should be compensated for like any other. Why are so many people content to lie around, intellectually speaking, until they get mental bedsores?
3 comments:
Hear hear! I like that thought, that ignorance is a disability. You definitely have a talent for summing things up in concise, memorable ways.
I contest this thesis. In particular, this bit:
"Our math is not a sign of greater intelligence, a superior science; it is an algorithm, that is a technology. As I said before, all technology, all civilization in general, functions to remove greatness from the equation."
First off, with regard intelligence, intelligence as in the raw processing capacity of human brains probably has not changed all that much over a few hundred years. That's a function of genetics, and that doesn't alter that fast.
You mention about Roman numerals vs. Arabic, though better Indian, numerals. This switch did not remove "greatness" -- our genetics didn't change, remember? -- it doesn't reduce intelligence, rather it means less intelligence has to be devoted to baser tedium, i.e. manipulating numbers, and frees it up to be used for more complex things. The computer you use to post these arguments would likely not have been possible were such tedium still in place. What it does is let you put mental resources toward more complex things, by simplifying away all the little niggly bits. Manipulating Roman numerals doesn't make you "greater", it means that much more of your education time is spent on small things, not more complex things, and that much more time is spent manipulating numbers, as opposed to doing more sophisticated things with those numbers.
Cognitive capacity was not different, but it was apportioned differently.
Maybe it "took a lot more 'intelligence'" to balance a book, but that's that much intelligence taken up, that could not be used to, say, discover string theory or explore the rest of the Universe, and uncover what wonders may lurk therein.
Technology simplifies the stuff of the "greats" of before, allowing the "greats" of the present to make things the past "greats" couldn't even dream of. That is, with the basic stuff simplified, the exertion of the same amount of mental power that the greats of the Middle Ages or whenever exerted creates Space Shuttles, whereas back then it created a cathedral, or Damascus steel, because all that basics stuff is offloaded and so more complex stuff can be loaded.
The people in the Middle Ages did not have more intelligence, rather they expended more of their intelligence on simple tasks. That doesn't make them "better", it just makes them more effortful. You don't do "better" arithmetic with Roman numerals; you just expend more mental effort.
And...how is that contesting my thesis? From where I sit, it looks more like you just repeated my thesis.
The gist of your argument is "place-value is a labor-saving device, making the rest of thought easier by requiring less effort", yes?
Well that's exactly what I said, in the argument you claim to be disputing. What did you think "it's a technology" meant?
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