My calculus query of the previous entry elicited at least five responses, some from Electron readers I didn't even know I had. Others were from good friends. My many thanks to everyone who has responded. What's interesting is that all of the responses basically said the same thing, though each source added some additional and useful information. I am printing these e-mails out for further study. I am now working on the next sub-chapter in the "derivative rules" section, which is the "Product Rule."

Like many people with an overactive imagination, I often have daydreams of flying, either by myself as a super-hero or with some form of lightweight aircraft like an ultralight, a balloon, or a hang-glider. I would never hang-glide or ride an ultralight in "real life," and I have no ambition to go up into space so that I could toss my cookies in zero-G. I don't like roller coasters, and have only ridden one or two. Yet in my inner world I swoop and soar like a bird. I love watching crows, seagulls, and hawks, who are the best flyers among the birds in my region. Inspired by the shamans of old, I can imagine impersonating a bird in visionary trance even though my physical body remains tied to the earth by gravity. I even like watching skiers, snowboarders, and skateboarders in their curved trajectories and parabolic flings into the air. Again, I would never do this for real, because I am prudent. The things I am "prudent" about seem to multiply as I get older.

But I don't want to be prudent about math. You'd think, because I am a visual artist, that I would be fascinated with the lines and curves and grids of visual mathematics. Sure, I like them, but it's too much like work. I feel the obligation to make abstract art out of them. That's work. But I imagine mathematics in "kinesthetic" terms as well. If you think that this "learning style" is hardly my type, maybe I surprise you. I find quite a lot in common with the temperament that webpage describes, though when I took their "inventory" test I came out as one might expect, highly "visual." But mathematics has always had a kind of physical evocation for me, even though I have never done math any other way but sitting still in front of a book or screen.

Algebra, especially polynomials, reminded me of "demolition derby" car wrecks, where you slammed things into other things to watch the parts fly off. Geometry was architecture, with some very sharp edges which would slice me if I didn't watch out. And trigonometry and classical physics, as I have described in some of my earlier Electrons, have the feel of toiling through shipping lanes, hauling large loads up and down inclined gangplanks, and loading more weight on tensile cables into the freighter for another voyage.

But calculus, the mathematics of change and motion, is more like the hawk's flight or the snowboarder's glide. I can virtually fly down or up the slope of a curve, quickly change direction, and head back the way I came. Or I can skid to a landing as I reach a horizontal limit. My virtual calculus dragonfly is free to cruise the dimensional universe of a summer's afternoon, even though it is still icy winter outside.

Posted at 4:06 am | link