Category Archives: Mathematics

Too Much Time On His Hands

And now for something completely different — an estimate of how fast the signal of the Beacon of Gondor propagated:

After the first signal is on fire, Gandalf sees the next signal only 6 seconds later. WHAT? The guys (or gals) at the next station must have just been sitting there staring and waiting for a signal. Oh, it was probably like 40 years since the last time it was used. I guess you can do stuff like that if you don’t have youtube. But wait, the more I think about this, the more upset I get. I am ok with invisible rings, flying dragons, glowing swords and stuff. However, it is beyond the bounds of reason to expect me to believe that some guys are sitting way on the other mountain with a hair-triggered lighting mechanism. Six seconds. Seriously.

[Via Geekpress]

Fact Checking The EPA

I was doing a little research on the mess, and wanted to get some data on the Gulf. According to the EPA, it has a volume of 642 trillion gallons. This seems off by three orders of magnitude to me (that is, I think that its 642 quadrillion gallons — 1015th, not 1012th — which is what a trillion would be).

My calculation is based on the stated area of 600,000 square miles (which seems reasonable to me), and average depth of 1600 meters (why do they have to mix their units?), which is about 5100 feet. Multiply the square miles by 5280 squared, and you get about 17 trillion square feet. So the volume has to be three orders of magnitude more than that, and it’s another order of magnitude (7.5 gallons per square foot) when you convert to gallons.

Am I off, or are they?

Yeah, I want these people to be in charge of regulating carbon emissions (including, no doubt, my exhalations).

[Update late afternoon]

Why do I care, you ask? Because people are saying that with the new estimate of the leak rate, this is the equivalent of “n” Exxon Valdezes per week, where n varies with the commentator. But the Gulf isn’t Prince William Sound. Based on the number of 11,000 square miles affected in Alaska, and an average depth of a thousand feet (generous, I think — the deepest point in sound is 2000, and most of it is a lot less, even when you get out around the Kenai Peninsula), I get a ratio of volumes of on the order of 300, so we’d need a lot of Exxon Valdezes to make it comparable to that disaster. I don’t know whether the warmer temps of the Gulf make things better, or worse, though.

Logical Fallacy

In a review of a movie trailer (and a forties movie reviewer) by Lileks:

Let me just go on record as believing that it is not a good or necessary thing to make comedic action movies about 12-year-old girls who shoot people in the head. Because this is what I think of when I read a quote about the loss of dignity and importance – the way a culture, not individuals, loses its sense of dignity and importance by finding opportunities to leach the innocence from anything previously regarded as sacrosanct.

The comments on the HotAir thread are full of the usual scoff-talk – why, comics were once considered corrupting to children! Elvis was forbidden to be seen from the waist down! Piano legs were covered by Victorians! Christians chopped peeners off Roman statues! and so on. If there was once a standard now seen as silly and puritanical, it must mean our current standards are the same.

This is the same fallacy as that engaged by someone who, in response to a critique of his loony ideas cries, “They laughed at Einstein, too!” To which the rational rejoinder is, “They also laughed at Soupy Sales.” It’s an unjustified extrapolation, and a more robust defense is required.