Recent content by Cantab Morgan

According to the Youtube comment, you have it backwards. The weighted ball moves out, and the floating ball moves in. What to believe?

Why do you contend that the flashlight will not roll? Of course, a real flashlight will not, but in your thought experiment, the flashlight with frictionless wheels will enjoy an impulse from the light.

I learned to love the subject from Gelfand and Fomin.

I can't tell whether you are joking or whether you think being pedantic contributes meaningfully to the discussion. (But I think my restaurant bill actually does rely on arithmetic working.)

Yep. They rely on the Radon-Nikodym theorem to do their image processing.

That's either a totally brilliant or terribly misleading way to model the collision. I'm not smart enough to tell which. It seems to me that the ball energy is conserved (assuming the collision is elastic) because none of its kinetic energy is transferred to the wall. If the wall had less...

Are you actually proposing that a simple mechanical system violates energy conservation? Or are you merely suggesting that the "pendulum energy" is just one place in the system where the energy lives, and it moves around among the parts of the system? (Or something like that.)

Ah yes. Much simpler to consider the work being done by the pivot than to consider the forces needed to keep the pivot/ceiling moving at constant velocity. Nice!

George Polya's How to Solve It is a classic. I've also heard good things about a book titled How to read and do proofs. And, what I'm about to suggest may sound strange but... Consider learning to program. There's a discipline of thought that comes from programming that may help your brain...

MIT's Open Course Ware (OCW) is pretty cool.

I think it only appears not to be equivalent because the ceiling is given infinite mass. In any real situation, the ceiling will oscillate a little? The idea that inertial reference frames (in a Galilean/Newtonian universe) are not equivalent is just too unpalatable for me. I suspect that...

Why not? Measure theory is needed to make your MRI scanner work, too. As Wigner pointed out, math is unreasonably effective.

Quite a few years ago, I attended a lecture given by John Kenneth Galbraith, and he was asked what he thought of all the advanced math that was coming into Economics. He said he approved, because it would keep the undiligent out of the field. Petek is correct. Measure theory is integral...

Wouldn't that be a solid? Elastic recoil is not required to conserve momentum, it's required to conserve mechanical energy. If a wad of putty collides with something and sticks, momentum is still conserved. (But it gets warmer.)

LOL! I hope I'm not derailing the thread, but Newton probably didn't mean for his third law simply to mean that F_{12} = - F_{21} as we commonly summarize it today. Elsewhere in Principia he applies it a bit more powerfully, anticipating D'Alembert's principle.