Sep. 1st, 2011

In calculus class, the teacher outlined a problem with two yards of specific sorts of shapes, the idea being to enclose the maximum area with a given amount of fence. After a while, he asked what areas people had gotten. Mine was more, so I said so. He said I had the wrong answer. I maintained that my answer was correct, and I could prove it. Sure enough, he called me up to the board to show everybody. I started by drawing the diagram – with the two yards sharing a section of fence. As soon as I drew that, he knew what I had done. He pointed out that no-one had attempted that approach in all the years he had taught the class. He also pointed out that the problem was much harder to solve that way. Heh heh heh.
My mom was going back to school to prepare to re-enter the workforce, and we ended up deciding to take the same math class. After a few weeks, the teacher called us both in. She explained that she was a little curious how we did things. We always sat together, and had the same surname, and when she'd hand out a test, she'd get back a lot of copies of essentially the approach she'd just taught, and two oddballs, from us. At first she thought we were copying from each other, but then she noticed our solutions were not only unrelated to what she was teaching, but to each other.

For example, she pulled out our most recent test, which contained a problem involving proving that the four points provided were the corners of a square. I had done something involving line lengths and reciprocal slopes. My mom had shown that the diagonals were the same length and perpendicular. Whereupon I pointed out that this didn't constitute a proof of squareness - unless the diagonals were perpendicular bisectors, you could have a figure known as a "kite", not a square. The teacher was boggled she hadn't even seen the flaw in the reasoning, but let my mom keep the credit for her answer.

When I was working at the particle beam lab at the University of Maryland, I learned not to say whether I knew how to do something, just assume that I could learn how. One of the researchers asked me to create a high voltage pulser with a high voltage output with a very short risetime (less than a nanosecond).

This was a tall order, so I went to hit the books. It turned out that there was a special tube designed for just such a purpose, known as a krytron. This was an obscure beast, which actually used radioactive nickel to keep the gas in the tube partially ionized, ready to switch at any moment. It had originally been designed for firing explosives in nuclear weapons, and had been classified. But this was an advanced lab and had accumulated a great assortment of oddball parts. Some time spent asking questions and rummaging around actually managed to produce a krytron.

This was a little thing, about the size of a peanut. I built a charged transmission line setup, with the tube switching it into a 50 ohm load, and ran the thing at a few thousand pulses a second with a sampling plugin to an oscilloscope to fine-tune it and measure the actual risetime (which turned out to be an astonishing 370 picoseconds or so).

So I went to show the finished apparatus to the researcher, only to find out he had basically given me the assignment as a prank, figuring a young college student who wasn't even in his research program wouldn't be able to solve such a difficult and arcane problem. He'd also given it to one of his EE grad students, who'd assembled this huge board with a chain of "avalanche" transistors in series to do the switching. It took about ten minutes between pulses, and would fry the transistors every dozen cycles or so. My board had run for hours at thousands of pulses per second, and was still on the original tube.

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