At Educated Guesswork, my IETF colleague Eric Rescorla notes how his ears “pop” when his car is moving fast and he closes the sun-roof:
I noticed the other day that if I’m driving my car on the freeway and close the sunroof my ears pop.Now, Eric’s a scientist, so what’s the first thing he does about this?
He develops a hypothesis, of course:
After a bit of thinking, I concluded that what was going on was the Bernoulli effect: the air flowing over the sunroof lowers the pressure of the interior of the car. Then when you close it you get a sudden pressure change back to ambient pressure.
And next? Well, one has to test one’s hypothesis, right?
Initial experiments confirm this: my Polar 625SX [heart-rate monitor] has a built-in barometric altimeter. I repeatedly opened and closed the sunroof and watched the altimeter and readings seemed to consistently differ by about 75 feet. Obviously, there’s some uncertainty here because the road isn’t totally flat; if you wanted to be really sure you’d go over the same sections of the road again and again with the sunroof open and closed and measure the difference. Still, since I’m not exactly publishing this in Nature, it seems good enough for now.
Tom Lehrer, in his preamble to his song about Lobachevsky, notes that, “some of you may have had occasion to run into mathematicians and to wonder, therefore, how they got that way.” The same is true of any sorts of scientists. We’re a strange lot, to those who don’t see a need to contemplate an explanation for every little oddity we notice.
Some years ago, our work group at the office was planning to order some pizza to be delivered for a working lunch. The co-worker who organized the order came to me and said that she was going to order some set of large and small pizzas, depending upon how much folks wanted to eat. She asked me how many slices I wanted.
“I don’t know,” I replied. “It depends whether they’re slices from a large pizza, or from a small one.”
“I’ll figure that out when I have the count of slices. How many do you want?”
“But,” I persisted, “they’re not the same size. I don’t know, until I know the size of the slices.”
She rolled her eyes. “Just tell me how many slices you want.”
I said two, but I thought (and probably said aloud) that I might want more if one or both of them were small.
When my colleague left, I went to the white board. Let’s see... a large pizza was 14 inches across (7-inch radius), and is cut into eight slices. A small pie was 12 inches (6-inch radius), cut into six slices. So, for the large:
π × 72 / 8 = 19.24 square inches per slice...and for the small:
π × 62 / 6 = 18.85 square inches per sliceA slice from a small pizza is only 2% smaller than a slice from a large pie. In other words: they’re about the same, close enough as not to matter.
Of course, my co-worker knew that intuitively. I had to be the mathematician, and work it out with a dry-erase marker.