"Surely You're Joking, Mr. Feynman!" - unam.

along, working on this mechanical computer, without any interference.
One day the lieutenant came by, and asked us a simple question: "Suppose that
the observer is not at the same location as the gunner ­­ how do you handle that?"
We got a terrible shock. We had designed the whole business using polar
coordinates, using angles and the radius distance. With X and Y coordinates, it's easy to
correct for a displaced observer. It's simply a matter of addition or subtraction. But with
polar coordinates, it's a terrible mess!
So it turned out that this lieutenant whom we were trying to keep from telling us
anything ended up telling us something very important that we had forgotten in the
design of this device: the possibility that the gun and the observing station are not at the
same place! It was a big mess to fix it. Near the end of the summer I was given my first
real design job: a machine that would make a continuous curve out of a set of points ­­
one point coming in every fifteen seconds ­­ from a new invention developed in England
for tracking airplanes, called "radar." It was the first time I had ever done any mechanical
designing, so I was a little bit frightened.
I went over to one of the other guys and said, "You're a mechanical engineer; I
don't know how to do any mechanical engineering, and I just got this job. . ."
"There's nothin' to it," he said. "Look, I'll show you. There's two rules you need to
know to design these machines. First, the friction in every bearing is so­and­so much, and
in every gear junction, so­and­so much. From that, you can figure out how much force
you need to drive the thing. Second, when you have a gear ratio, say 2 to 1, and you are
wondering whether you should make it 10 to 5 or 24 to 12 or 48 to 24, here's how to
decide: You look in the Boston Gear Catalogue, and select those gears that are in the
middle of the list. The ones at the high end have so many teeth they're hard to make, if
they could make gears with even finer teeth, they'd have made the list go even higher.
The gears at the low end of the list have so few teeth they break easy. So the best design
uses gears from the middle of the list."
I had a lot of fun designing that machine. By simply selecting the gears from the
middle of the list and adding up the little torques with the two numbers he gave me, I
could be a mechanical engineer!
The army didn't want me to go back to Princeton to work on my degree after that
summer. They kept giving me this patriotic stuff, and offered a whole project that I could
run, if I would stay.
The problem was to design a machine like the other one ­­ what they called a
director ­­ but this time I thought the problem was easier, because the gunner would be
following behind in another airplane at the same altitude. The gunner would set into my
machine his altitude and an estimate of his distance behind the other airplane. My
machine would automatically tilt the gun up at the correct angle and set the fuse.
As director of this project, I would be making trips down to Aberdeen to get the
firing tables. However, they already had some preliminary data. I noticed that for most of
the higher altitudes where these airplanes would be flying, there wasn't any data. So I
called up to find out why there wasn't any data and it turned out that the fuses they were
going to use were not clock fuses, but powder­train fuses, which didn't work at those
altitudes ­­ they fizzled out in the thin air.
I thought I only had to correct the air resistance at different altitudes. Instead, my
job was to invent a machine that would make the shell explode at the right moment, when