9 January 2008 by John.

When I first saw integration techniques in calculus, I thought they were a waste of time because software packages could do any integral I could do by hand. Besides, you can always just use Simpson’s rule to compute integrals numerically.

In short, I thought symbolic integration was useless and numerical integration was trivial. Of course I was wrong on both accounts. I’ve solved numerous problems at work by being able compute an integral in closed form, and I’ve had a lot of fun cracking challenging numerical integration problems.

Many of the things I thought were impractical when I was in college have turned out to be very practical. And many things I thought would be supremely useful I have yet to apply. Paying too much attention to what is “practical” can be self-defeating. Pragmatism is impractical.

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9 January 2008 by John.

I ran across an article recently comparing the performance of a 1986 Mac and a 2007 PC. Of course the new machine would totally blow away the old one on a number crunching benchmark, but when it comes to the most mundane benchmarks — time to boot, launch Microsoft Word, open a file, do a search and replace, etc. — the old Mac pulls ahead slightly. Software bloat has increased at roughly the same rate as Moore’s law, making a new machine with new software no better than an old machine with old software in some respects.

The comparisons in the article resonate with my experience. I expect administrative tasks to be quick and number crunching to be slow, and so I’m continually surprised how long routine tasks take and how quickly numerical software runs.

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