After learning to find the common logarithm of a number in the tables of my 1958 book, I'm now learning to interpolate between logarithm entries to find the log of a number that is between the integers they cite in the table. There's a four-stage process to this which is too tedious to relate here. It's done in reverse to find the antilogarithm, or the number that's associated with the logarithm.

Of course, nowadays, you just look up the damn number on the calculator. Which brings me to a peculiar matter of practice when using the 1958 book. In 1958, no one had hand calculators. They had slide rules, or nothing but pencil and paper. I don't have a slide rule. When I started working with the 1958 book, I asked the question: should I do the problems in 1958 without a calculator, since students in those days didn't have them? Perhaps, for the sake of authenticity, I should work only with the tools that the students in 1958 had. For some of the subjects, such as polynomials, I didn't need a calculator. But when the answers were numbers, calculating was necessary, and I quickly realized that if I spent my time working all these multiplications and divisions out on paper, it would take me a long, long time. Not to mention that it would drive me crazy. So I used my calculator, a futuristic gadget solving problems from 46 years ago that were meant for guys with slide rules, or lots and lots of patience and time. So much for authenticity.

Even so, my style of doing math tends towards the stepwise, detailed, and sequential. I'll do all the problems in a set rather than skipping them as I used to when I was in school. I don't know whether this is the right way to do math. For all I know, the geniusboys who learn calculus on their own at age 11 do only two or three of the problems in a set, or perhaps none at all. If I had as much talent and energy as those young mathletes, I'd already be doing differential equations, rather than picking my way through logarithms.

When I do my math (or physics), I am approaching a vast field with a tiny little focus. When I read the weblogs or articles or biographies of scientists and mathematicians twenty years younger than I, they already know more about math, physics, and computer programming than I will ever know. It does not console me that I know more about art and how to draw and paint than they do. There is no comparison in power and complexity or knowledge and craft. If I look too far ahead, I feel overwhelmed, and have no idea where to go or what to do next. That's why I keep my focus low and small; this way at least I can do something. Doing those problems, one after another, is like trying to cut a lawn using a scissors.

I can't help wondering. Will I ever really get to calculus? Will I learn more than Newton's laws of motion? Will I ever learn to do even the simplest computer programming? Will I ever do a physics experiment, even the kind that kids do in middle school? (I never got to do anything like that in school.) And don't even let me think about WHY I'm doing this. Ambition isn't a pretty thing, especially in a lady of a "certain age." And if I think about what use I could possibly put this study to, that's even more dispiriting, because there probably isn't any use for it. So it's better not to think about it, and go on snipping, one little green problem at a time.

Posted at 3:17 am | link