More on the History of the Calculus

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When I wrote earlier this week about Archimedes, I didn’t get into why I found the Nova piece so remarkable. I loved it in part because I remember the “aha” I had as a youngster when I got the notion of integration – of summing across a series of infinite slices.

Malcolm Tredinnick wrote to point out that this is in fact something that’s been invented multiple times – Egyptian and Chinese methematicians had at least part of the insight as well:

…. Some of the ancient Egyptian scrolls (two
famous ones are the Rhind — or Ames — papyrus and the Moscow papyrus) included various mathematical algorithms and puzzles. These included things like computing the volume of a pyramid. My recollection is that historians are not completely sure *how* the Egyptians discovered some of their algorithsm; just that they did write them down.

The Chinese, on the other hand, wrote down their working as well as the conclusions. They also knew how to compute things like the volume of a pyramid, which they did by repeated dissections and then taking the leap that the infinite series of dissections converged to something sensible (that was really Newton and Liebnizs’ breakthrough: they realised both that there was a question to be settled about the convergence of such series and they provided reasonably rigorous answers). The Chinese also appear to have come up with an early version of approximating a circle with succesively more sided polygons and computing the area that way. Archimedes did it better than they did, though.

Malcolm’s right when he points out that we should be careful not to “look through rose-colored historical glasses” and infer more about their early insight than is warranted. But it’s still cool.

(More here.)

Archimedes Palimpsest

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Saw a cool Nova episode this evening on the Archimedes Palimpsest, which had some fine storytelling leading us into the tale of how Archimedes, at something like 200 BC, prefigured the calculus.

He was using sums of infinite numbers of slices of non-trivial three-dimensional geometrical objects to calculate their volume. Smart guy. But the intriguing storyline of the Nova piece was how Archimedes’ work was lost, wiith what appears to be the surviving copy of his “Methods” torn apart and copied over by some dumbass monk around 1200 AD who needed paper to write his prayers on. Imagine, the Nova people suggested, how Renaissance science would have been accelerated if they’d had Archimedes to draw on.

update: Reader Ryan points out the delicious accidental pun – “to draw on”. I can’t claim credit. I’m a terrible punster.

Yet More Hurricanes and Climate

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Ross Gelbspan is speaking in Albuquerque next week, so I picked up a copy of Boiling Point, and this morning I chased down the references associated with the little discussion of a couple of weeks ago over on Chris Mooney’s blog about hurricanes and climate change.

Gelbspan’s key reference for his assertions about a growth in extreme weather under greenhouse climate change is Trends in U.S. Climate during the Twentieth Century, by Tom Karl. The paper’s relatively noncommittal on hurricanes (“Recent studies indicate that even if significant greenhouse induced warming were to occur, it is doubtful whether increases in tropical storms would be detectable due to the large natural variability in these storms.”) but gives a good account of other issues related to variability, which is to me the really interesting climate change issue.

It’s a bit dated – a lot’s gone on since 1995 – but still an interesting read.

Hitchcock

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When we first moved to Albuquerque, the video store within walking distance of our apartment had a Hitchcock section. This was a perfect solution, because otherwise where do you file the Hitchcock movies? Horror? Mystery? Comedy? Romance? Over time, we trekked through most of what they had, but Hitchcock made a lot of films, so we’ve still not even come close to seeing them all.

When in doubt at the video store (there are so many bad movies, choices always pose such risk) one can always pick up a Hitchcock and rarely be disappointed. Saturday night: Stage Fright. Marlene Dietrich was delicious.

Racin’ in the ‘Hood

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It was a perfect way to end my season.

I’d planned to make the Moriarty time trial two weeks ago my last race, but then the Nob Hill Crit popped up as a late addition to the schedule, and I couldn’t resist – a bike race in my own neighborhood, where I could just hop on the bike at home and ride over!

It was a lovely course, a triangle through the residential neighborhood on the north side of Albuquerque’s Nob Hill, which is the best urban walking neighborhood in town. It’s lovely little post-war bungalows, narrow tree-lined streets. Some folks watched from their front porches, lots of folks drifted over from the Nob Hill shopping district (they were having a chile cookoff there) to watch. They had a kids’ race, which even had tykes on tricycles. There was a terrific “A” race, with some of the fastest racers in town.

Racing in a neighborhood was sweet. Per my usual crit performance, I got lapped twice in my race (the “B” race), but I pretty much expected it given that two women’s national road racing champions were there at the start line, plus a lot of the guys who I know are faster than me. Once I got dropped by the main field, I picked up a workmate and we had fun. The last corner of the triangle course’s turn, off a downhill into the front straightaway, was wide open and fast, and every time I headed into it I popped up into a higher gear and accelerated, getting lower and faster each time. It was fun.

I came in 10th this year in the beginners’ division of the annual state road racing points series, third in my age group, which was pretty satisfying.

Mom and Dad and Lissa came to watch the crit. They’d never seen me race before. Having them perched in lawn chairs on the sidewalk clapping for me each time I came through the front straightaway was a gas.

It was a perfect way to end my season.