Some subtle signals perhaps?

(I have no idea what y'all are using KL-divergence for, so I have no opinion about whether you should have been using it in this theorem.)

a metric, a feature sorely lacking from $D_{KL}$

I have a pet peeve around this, which is hopefully a useful comment for someone to read; KL-divergence should not be symmetric, because of the whole thing that it is. If you're using KL-divergence and thinking to yourself "I wish this was symmetric", then that should be a red flag that you're using the wrong tool!

I think it's easy for people to think, "hm, I'd like a way to quantify the how different two probability distributions are from each other" and then they grab the nearest hammer, which happens to be KL-divergence. But mathematical definitions are not for things, instead they mean things.

You should use KL-divergence when you want to measure the cost of modelling a true distribution using a false distribution. The asymmetry comes from the fact that one of them is the true one (and therefore the one that you take the expected value with respect to).

I enjoyed reading this post quite a bit, but the exact reason why eludes me. I think I've had or almost had a lot of these thoughts before, and this post clarified them for me.

I have a tendency to be constantly asking something like "but what is the real thing going on?". This is obviously very useful overall, but as in the post, it is sometimes also to useful to say "within this context, let's only reason as if this is all that's going on" and then try to improve my understanding of something that way. I think this would have significantly improved my experience of learning thermo and stat mech.

For anyone who's interested in going deeper on a formalism of thermo with no stat mech, I once found this niche book that seems to do exactly that: A First Course in the Mathematical Foundations of Thermodynamics. (It's published by Springer so it's probably legit, but I didn't actually get that far into it, so this isn't a recommendation per se.)

Oops, I said two things.

Er, bug report, the right-click menu is where my spell-check's suggestions were. So now I get a red underline telling me a word is not in the dictionary, but to correct it I have to just, try to type the correct spelling. Or google it I guess.

Turing completeness, let alone error correction, has not been shown for leptonic matter on its own.

Curious if you have a citation for this!

There are, as far as I can tell, no book-length biographies of Kolmogorov's life. The world is worse for it! His life was long, and his accomplishments innumerable and broad-reaching. An aspiring biographer could establish a career with such a book.

(There are a few different compilations of essays about Kolmogorov, but they're by fellow academics, and largely focus on his work rather than him.)

"Inkhaven" is already modifying the name of the campus "Lighthaven" (which is already a modification of "Lightcone"). Since you're still doing the "ink" part by writing, but not doing the haven part (by not being at Lighthaven) I'd recommend a different name.

May I suggest "Inkhalven"/"Inkhalfen"? Maybe the verb "Inkhalfing"?

Now that I think about it, it could be useful to have a timed sequence of posts that are just for discussing the book chapters, sort of like a read-along.