Category Archives: Math

Supply, Demand, Yada Yada Yada, I Learned Some Economics

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The Economics of Seinfeld

For example, The Bottle Deposit is tagged as arbitrage, fixed costs, incentives, variable costs

Kramer and Newman hatch a scheme to arbitrage bottles from NY, where the deposit is 5 cents, to Michigan, where the deposit is 10 cents. They can’t figure out how to make the costs work; gas is too expensive (variable costs), and there’s too much overhead (fixed costs of tolls, permits, etc.) with using a semi to haul the bottles in volume. Finally, they hatch a scheme to use a mail truck, which lowers their variable and fixed costs to zero.

Rush Hour, Anytime

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Traffic simulator

I think the ring road is the most accurate; it shows the density fluctuations that appear and is a good match to actual traffic. The other situations have left out some details — I’ve noticed that when a lane closure is upcoming, where people will change lanes varies greatly, even when traffic in both lanes has slowed to a crawl. When that happens, you’re supposed to go all the way to the merge point, and then merge, but many people will force their way into the other lane well before, and some people will simply not let a car into the gap in front of them. In the uphill grade I didn’t see much of the behavior I observe on I-81 in northern Pennsylvania: a truck going 55 mph passing another truck going 54 mph, and screwing a long procession of cars behind them, all of whom want to (and can) do at least 65.

Still, it’s a simulation, and I see there’s a “politeness factor” slider, which I presume controls letting people in rather than someone in the simulation flipping a virtual bird or honking a horn.

Stretching that Hit

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Winning the World Series with math

To figure out just how critical the turns are, Carozza did a calculation comparing the straight-line path with a circle around the bases. A path that follows a circle turned out to be a whopping 25 percent faster.

When Carozza presented his calculation at a colloquium talk in the math department at Williams College, Stewart Johnson, one of the professors in the audience, got intrigued. The circular path is so long that it can hardly be the fastest, he figured. So what path is the fastest?

Johnson ran a simulation on his computer, tweaking the circular path in tiny ways to make it shorter and faster, until no more tweaks could improve it. The result was surprisingly close to a circle, both in its shape and its speed: It swung nearly as wide and was only 6 percent faster than Carozza’s circle.

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“This cries out for an empirical test,” Winston says. “It would be easy to do. If it holds up, God, that goes in the New York Times sports section.”

Bette Davis Eyes, Karl Malden Nose

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Strange Maps: 468 – Crime Topography of San Francisco

San Francisco’s iconic topography – with grades of up to 31% – is as much a tourist attraction as its cable cars or the sea lions at Fishermans’ Wharf. But the city’s hilliness is more than just ankle-biting eye-candy. Its elevation, mainly in the city’s centre, is responsible for a 20% variance in annual rainfall throughout its eastern and western precincts, with bay-fronted neighbourhoods in the east also significantly less cold, windy and foggy than those facing the ocean.
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These maps present San Franciscan peaks and troughs of a different, less savoury kind. Although the information they convey is as real as the city’s actual orography, these infographics express incidence of crime rather than elevation above sea level. By mimicking cartographic methods of height demarcation, the mapmaker has hit upon a visually very arresting method to frame raw crime statistics in a geographic context.