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WARNING: the following contains references to mathematics and may involve actual instances of calculus.
During Magic 101, my one (required) semester of college physics, the professor assured me and my fellow history and lit majors that there was no such thing as calculus in the real world.
For the most part, that works for me. But every now and then something reminds me that I’m only seeing part of the universe. Take yesterday, for example, when I read Stephen Wolfram’s blog post on “Computational Knowledge and the Future of Pure Mathematics”. Stephen is hands-down the most brilliant person I’ve ever met, and arguably one of the smartest people on the planet. (Caltech PhD at age twenty, he was the youngest recipient of the MacArthur “genius” fellowship in 1981.)
In addition to being the creative force motivating Mathematica, one of the premier computational software tools out there, Stephen is also one of the best writers I’ve ever encountered. Of course, his essay is (literally) mostly Greek to me, but his clean, elegant prose is also uniquely accessible to math-less luddites and former English majors everywhere.
Math, especially pure math, says Stephen, is essentially a way of using a language to tell a story. But his description of that might also be the most perfect description of the writing process I’ve ever seen.
I’ve been doing language design now for 35 years—and it’s the hardest intellectual activity I know. It requires a curious mixture of clear thinking, aesthetics and pragmatic judgement. And it involves always seeking the deepest possible understanding, and trying to do the broadest unification—to come up in the end with the cleanest and “most obvious” primitives to represent things.
He has other points to make, of course. I liked his consideration of whether math, especially pure mathematics, is science or art. “If it’s science, then being able to make more theorems faster is surely good. But if it’s art, that’s really not the point. If doing pure mathematics is like creating a painting, automation is going to be largely counterproductive—because the core of the activity is in a sense a form of human expression.”
And as a side note for sci-fi and fantasy writers (not to mention fans of Star Trek and Dr. Who), he even asks about the trope of the computer “…going off and doing math by itself”. Wolfram speculates, “I would expect that in time the computer will be able not only to identify new structures, but also name them, and start building stories about them. Of course, it is for humans to decide whether they care about where the computer is going, but the basic character of what it does will, I suspect, be largely indistinguishable from many forms of human pure mathematics.”
So… okay, then. It sounds like I don’t need to worry about HAL, the murderous computer from 2001: A Space Odyssey, telling me, “I can see you’re really upset about this. I honestly think you ought to sit down calmly, take a stress pill, and think things over.” Instead I’m reminded of one of my favorite classic sci-fi stories, “The Last Question”, which involves a computer designed to consider entropy and the eventual end of the universe. Even after all human consciousness has died out and space and time no longer exist, the computer whirs on, assembling and considering data until finally answering the question nobody is left to ask. The last line of The Last Question is “LET THERE BE LIGHT!” And there was light—”. (Asimov, Isaac. The Last Question. Science Fiction Quarterly. November 1956)
Kassandra Lamb said:
Okay, my head is about to explode. All I can say is that if I’d had someone like this guy teaching my math classes in high school, I might have actually listened to him.
Sorry I’ve been MIA from all your lovely posts for a while, Barb. I was on vacation (i.e., unplugged as much as possible), and then got lost in editing land for a couple weeks when I got back. Missed you!
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barbtaub said:
I never had a classroom teacher like Stephen Wolfram. As far as I know, the only degree he ever got was the PhD, and I doubt very much that he spent much time in any classroom.
Hope you had a terrific vacation, and welcome back!
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sknicholls said:
When I took algebra in college I was 30 yo and 18 yo kids were whizzing past me. I had to drop out and take a remedial class. Then I had two algebra classes I passed with ‘B’s because I had a tutor. Then I hit chemistry. At first I didn’t have a clue and got a ‘D’, but I had a kind professor who refused to give up on me and took the class again (we had to have ‘C’s or better). That led to five more chemistry classes I passed with ‘A’s. I had learned a new language. If I didn’t know algebra, i would have never learned chemistry, and without that, human anatomy and physiology…so I can’t say I never used the math I learned. As a nurse I used it every day. As a writer, I’m not sure? Plot dynamics?
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barbtaub said:
Getting me through algebra and then college took the concentrated efforts of a large group. The (marginally) successful technique we finally settled on was to have my father explain something in engineer-speak to my mother, and then she translated it into English-major for me. Apparently, lots was lost in the translation…
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Danielle Lenee Davis said:
But, isn’t it interesting how struggling through something like that led to a rewarding career? I struggled through Pascal (years ago) and 18-year-old kids were zipping through it. It wasn’t until the semester was half over when the professor told me most of those kids had Pascal in high school. I felt a little better about it then. I worked my butt off and ended up with a C, but the next programming class I took was easier. If I hadn’t stuck it out I wouldn’t have the career that I have today. I don’t know what I’d be doing.
As far as math goes, I never went higher than Trigonometry. And didn’t want to! 🙂
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The Regular Guy NYC said:
Ugh. Math. I had the most boring teachers and wanted to be anywhere else than in their classes. No wonder I now work in ad sales and media.
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barbtaub said:
I think you’re right about how important the teacher is. My youngest daughter had a dynamic young woman for a teacher, and absolutely adored her math classes. She’s now an engineering undergrad.
I never had Stephen Wolfram for a teacher and can’t really picture the alternate reality where that might have occurred. But his company has contributed far more to the teaching of mathematics than any one classroom teacher could hope to accomplish, and he certainly deserves the credit for that.
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susielindau said:
Geometry was my nemesis. Sounds like an amazing teacher!
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barbtaub said:
Dear Math, I am getting sick and tired of being asked to help you find your X. She’s moved on, dude. Deal.
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Kassandra Lamb said:
SNORT
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