I've been doing lots of logarithm problems, the old-fashioned way using the log tables and sometimes the slide rule. It takes an entire page of scratch paper to work out just one of them, since there might be four or five different numbers each one with its own logarithm which has to be added, subtracted, or multiplied, then turned back into its anti-logarithm, i.e. the number which would be the answer to the whole computation. I am constantly having to "reverse" negative logarithms into the difference of two positive numbers or vice versa, after I find their mantissa on the log table and interpolate it.

I get most of these problems wrong. Maybe all of them wrong. When I trace my many steps back through the log table and the reversing of negatives, it always comes down to one arithmetic mistake, somewhere. An 8 instead of a 9. A negative sign instead of a positive. And then I re-do the calculations, and check them not only against the answer that appears in the 1958 book (at least for the odd-numbered problems) but the answer that my calculator gives me. Wrong again. Write a frightening red X over the wrong answer and start all over again.

OK, I'm a little obsessive. Maybe more than a little. I close doors that are left open. I want things to be neat and lined up. I perceive the world as a maddening mess of details, all of them clamoring for my attention at once. And maybe I'm not very good at ordinary arithmetic. But I want to know that I am doing things right. I want to master these archaic mathematical tools, once I have taken them up, even though calculators and computers now have probably irrevocably taken the place of hand-computing by tables and slide rule. Yet I am defeated, again and again.

I experience a kind of anxiety as I progress in mathematics. Ahead of me now are places I've never been, mathematics I've never, ever worked before, full of arcane Greek letters and forbidding symbols. It looks to me like magic, like Things I Am Not Meant To Know. If I fail in the small workings, how can I attain the Great Work? I remember that this quest is something I have taken on myself to do. No one is making me do it. There is no usefulness to it, no engineering or scientific career waiting for me if I do well and persevere. I am not a fresh young thing dreaming of doing research and making new world-shaking scientific discoveries.

Nevertheless, there may come a time when I actually will need to know what
-0.8619 to the minus fourth power is. (With only a log table and no calculators or computers available, which is the least probable part of this possibility.) I guess I'll do some more of these logarithm problems. Sooner or later I'll get one right.

Posted at 2:37 am | link