Cause and Effect

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Dean Dad asks

Why do so many states require only two years of math in high school?

[…]

We have anecdotal evidence that suggests that students who actually take math for all four years of high school do better in math here than those who don’t. We also have anecdotal evidence that bears crap in the woods. Why the hell do the high schools only require two years of math?

And there is followup at Uncertain Principles

There is a lot of discussion, so I may have missed someone raising the following point:

People who take four years of math and do well are probably good at math. Whatever distribution of students took the math for two years, I’d bet that it’s not the same as the distribution who took it for four. I’ll bet the players who go out for (pick your sport) do better at that sport in gym than the players that don’t, because you tend not to pursue and enjoy an activity if you suck at it.

The discussion seems to be dealing more with the other reasons why schools don’t require four years of math. I can ignore that for a moment and still assume an ideal case not limited by the availability of teachers or caused by bureaucracy. To me, the proposed solution embedded in the rhetorical question is not the head-slap obvious conclusion.

Blackbird Singing in the Dead of Night

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The Ultimate Spy Plane

One nit:

Created as the ultimate spy plane, the SR-71, which first took to the air in December 1964, flew reconnaissance missions until 1990, capable of hurtling along at more than Mach 3, about 2,280 miles per hour—faster than a rifle bullet—at 85,000 feet, or 16 miles above the earth. It is the fastest jet-powered airplane ever built.

Mach 3 is about 2280 mph … at sea level. But it varies with density altitude, so at 85,000 feet, it’s about 2000 mph. The speed of sound, i.e. Mach 1, is not a constant of nature — it’s defined by the conditions (as opposed to the speed of light, which is c in a vacuum)

(S)Poof!

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Another video, reminiscent of the viral popcorn-popped-with-a-cellphone video I discussed a while back

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And, in fact one of the response videos is with popcorn

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Also one involving toast

Objections: One is electrostatic. Matt has been discussing static charge distributions recently (here and here) and it’s very important to note that he’s discussing charge distributions on conductors — the charges can easily rearrange themselves. But in these video examples, the people and the targets are not conductors. So while you might build up some static charge on a person (in a very questionable display of boys gleefully rubbing other boys with balloons. Not that there’s anything wrong with that, if that’s who you are, balloon-fetish-freaks). A discharge to another insulator just isn’t going to send the energy where you want it to. A small discharge will even out the potential difference, and you’re done. A full discharge needs to be to a conductor, preferably a grounded one.

Speaking of sending the energy, how much energy are we discussing here? I’m not sure how much energy it takes for an eggsplosion, but I’m guessing we’re talking well above a few Joules. Accounting for my slight overestimation of the water content in the earlier popcorn analysis, it probably still takes somewhere north of 10 Joules of energy to pop a single kernel. Can we get anywhere close with static charge?

The energy stored in a capacitor is 1/2 CV^2. The capacitance of the human body is a few hundred picofarads. Let’s be generous and say it’s 2,000 picofarads (pico is 10^-12). How much of a potential difference do we need for 10 Joules? Do the math — it’s 100 kV. A few kV makes for a painful spark when discharging to a doorknob. A 5 mm spark between conducting spheres happens at about 16 kV. A realistic spark leaves us at significantly less than a Joule of energy.

Spoof