Saw the title and thought "oh, I'll bet it is at some insane high pressure or some other exotic condition". Clicked through to an image of a diamond anvil. Not disappointed.
Very fun read. There is something really enjoyable about stories of people solving the problem at hand in the most straightforward way possible, even when that means digging into all kinds of low-level details that are usually abstracted away for us.
Correction: The article states that Thomson's problem has only been solved for 2, 3, 4, 6, and 12 charges. However, in 2013 the 5-electron case was solved by Richard Schwartz. Here's the paper:
Yes, though of course here Stein is referring there to the Wolfram quote that's on slide 28 (roughly: certain kinds of development can't be done in academia) and not the condescending rejection of inquiry about mathematica's internals from earlier in the presentation.
I'm glad William included slide 10 calling attention to the hostile and insulting attitude Wolfram Research has toward mathematicians and reproducible science in general. (I think some of Sage Math Inc's other closed-course competitors likely have similar attitudes, but Wolfram Research seems to be the worst.)
"You should realize at the outset that while knowing about the internals of
Mathematica may be of intellectual interest, it is usually much less
important in practice than you might at first suppose. Indeed, in almost all
practical uses of Mathematica, issues about how Mathematica works inside
turn out to be largely irrelevant. Particularly in more advanced
applications of Mathematica, it may sometimes seem worthwhile to try to
analyze internal algorithms in order to predict which way of doing a given
computation will be the most efficient. But most often the analyses will
not be worthwhile. For the internals of Mathematica are quite
complicated."
For comparison, if you want to audit the Sage Math algorithms that your research depends upon, all you need to do is fire up a text editor (or browse their github). And you won't find any statement in the Sage Math docs telling you not to bother because you're too dumb to understand what you're reading anyway.
It's not a filter, as others have suggested, but rather a standard artifact of vacuum-tube-based television cameras that were in use at the time. (I don't know why this lecture wasn't filmed, but the extensive dark halo effect makes it clear this was shot with a TV camera. This was the early era for magnetic video tape, but I assume that's how the recording was preserved.)
Anyway, the point is that these TV cameras are based on the fact that incoming light will dislodge electrons from a thin plate in a vaccum tube in an amount proportional to brightness. A very bright spot in the image produces a shower of electrons that is more powerful than the rest of the tube (the part that detects the electrons) can deal with. The net result of this "splash" of electrons is a mild desensitization of the detection apparatus around the bright spot. This makes the nearby stuff appear darker.
You mentioned that dark spots also seem to have a bright halo, but I don't see that in the video, and it isn't consistent with the usual artifacts of these cameras. Are you sure?
This looks nice. What I'd really like to see, along these lines, is a python library for automated document metadata extraction with confidence assessment, like this: