Like Scott, I used chatgpt for a proof. It gave me something convincing but wrong.

Still, it led me to a 1964 theorem about medians of sums of Bernoullis. And to fast algorithms for computing many power sums at once.

Below was my first attempt. See if you can find the bug.

The word "macroscopic" always confused me. This is like a W state, not a cat state, right? Do you know of any good discussion of this point?

The money pays for research. If those contracts stop, the research stops. Yes private donations and industrial funding will still exist but the total amount of research will go down.

Apple has to pay college-educated employees more. And colleges give training that's more general and more externally legible than you'd get from a company, thus raising the employees' market value more. So I see your point but it's not at all clear that this is a "subsidy".

Endowments are used more for research than undergrad education.

Thanks Earl! I'm glad you enjoyed it. We really found qDRIFT and your later paper with Berta+Wan inspirational and we think there's a lot of room for more use of those ideas still.

"why" is always tough because there's no objective answer but the dirac plate etc are meant to illustrate that the fundamental group of SO(3) is Z_2, suggesting its universal cover should map to SO(3) via a 2-1 map. see also
math.stackexchange.com/questions/11...

School closures were hard on kids, not only for test scores. I'm guessing you haven't talked to many parents about this topic?
Maybe a necessary evil, but certainly not a trivial cost.

It's even more impressive without the !.

That's what all physicists hope for more than anything else.

Selling exceptions is lucrative.

Yeah, it is definitely cooler than its symmetric cousin.

I don't find this claim too offensive. Yes they're no better at sending cbits but they're more powerful in other ways. "Richer information" would be better than "more information" but also raises more questions.

craphound.com/category/una...
It's more DRM than AI, but then again "AI" in most of these examples just means "algorithms."

There is of course a Cory Doctorow short story on this theme.