Random Questions

What do people who are not obsessive ruminators do with their minds when they're not using them?

That's an honest question. I am very, very bad at turning off my swirling thoughts. Most of the time I don't mind this, because my streams of consciousness flow in all sorts of interesting directions. The result is that I am easily self-entertained, because the smallest stimulus can have me pondering indefinitely, as I drive about, stand in line, whatever. Even observing how I got from one question to another can be an intriguing exercise, if only for the suggestions of how weirdly my mind is wired.

For example:

Question: Is there a more systematic way to calculate square roots than successive approximation?

Stimulus: Trying to sleep in the backseat of my car, rather than my tent, on a camping trip. (The logic was that the seat is more padded than the ground, and I sleep in the fetal position anyway, and sleeping in the tent would involve the work of setting up and tearing down the tent.)

Thought process: Of course when you can't stretch out full length, the need to stretch your legs becomes overwhelming. So I lie in the backseat, contemplating whether to set up the tent.

But the tent I have is junior sized. I am not a serious enough camper to invest in a grown-up tent. The junior-sized tent is less long than I am tall. So, even if I got up and set up the tent, would I be able to stretch out to full length, if I lay on the diagonal?

Short answer: Yes.

But I was not satisfied with the practical, short answer. Having done the high-school geometry in my head to estimate the diagonal length of my tent floor, my mind went off on a flight of mathematical speculation and re-exploration of long-neglected terrain, including certain lacunae in my mathematical education, including the estimation of non-perfect square roots.

There must be a way calculate square roots, I reasoned, because my calculator can do it. And somebody must have programmed my calculator to do it. And they can't have programmed it to guess, check the guess, make another guess, etc., etc., etc., which is the only way I ever had at getting at square roots. Why weren't we actually taught this? I suppose by the time I was doing the kind of math that frequently involves square roots, I was also doing the kind of math that generally involved calculators. It was more important to have a sense of how exponents, etc., worked than to come up with approximate values.

This was also the stage at which it became more and more difficult for me to track with, and remember, what was going on mathematically. I got A's in all my math classes, and 15 years later I can remember how to calculate the length of a diagonal in my head. But I have no clue about sines, cosines, and tangents, or anything at all that I learned in a full year of calculus. Math that has some kind of transparent relation to practical concerns, or else logic or philosophy continues to interest me. There are many rules of geometry that I have forgotten, but I recall enough of the basics to re-derive the rules, a la Socrates in the Meno, as needed.

I had to wait until I got home and looked it up to find the answer to my second-order question. Turns out, successive approximation is the way to calculate square roots, but there are systematic ways of going about it. Just in case anyone else was curious.

Meanwhile, my mathematical musings distracted me enough from my sore legs to derail any plans to go and actually set up the tent. Doing math in one's head, however, is not especially conducive to drifting off to sleep, so I had to change the subject before my mind could catch up with my exhausted body.


Sarah said...

To "turn off my swirling thoughts," I have to direct them down well-worn, boring paths.

Like, "In what order will I complete the knitting projects I currently have started, and which new projects will I allow myself to start when?"

Or, "What is the ideal number of works-in-progress to have out at any one time, and where should they be placed?"

And, "How will I lay out my garden when I have infinite space to do so, and in what pattern will I rotate my crops?"

Thus my need for incessant thought is pacified, while my capacity for obsessive, deep thought is not indulged. And I can fall asleep.

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