The NumWorks graphing calculator

I think I was in sixth grade, when I memorized log10(2) and log10(3). Turns out, that means with a second or two to think about it, I know the logarithms of all the numbers from 1 through 10. Although, admittedly, log10(5) and log10(7) are trickier and I'd have to interpolate.

There are an amazing number of problems that can be approximated, if you know these logarithms. You can usually get the order of magnitude and sometimes one or two significant digits. That's absolutely good enough to eyeball the results for plausibility.

Also, like most of you, I know the powers of two up to at least 16 -- and probably higher, if I give it a little thought. Turns out, a lot of problems that look difficult in base 10 look really easy in base 2.

Math is all about reducing a complicated problem to a different problem that is easy. And if you memorize a small number of constants from different problem domains, then your toolbox grows exponentially more powerful. Logarithms are particularly good for this, but some of the trigonometric functions are pretty useful, too.

I distinctly remember moments in university (back, when I still needed to do lots of math), when I would arrive at an approximate answer within seconds, whereas my peers took about one minute to get the exact answer from their calculators. Turns out, my answers were always within less than 10% of theirs, and often better -- which frequently is good enough.