Hahaha, I want to get that on a t-shirt

It was definitely one of the things that got me hooked on bias-variance decompositions, and more generally on information geometry... Even if I'm not especially active in either any more

I guess you never know what's going to resonate with people!

I had always wondered why you hadn't done more with it. FWIW, we didn't find Buja et al's result until long after yours, so having it there was a huge boon to us

I'm really glad to see this on arXiv after all these years!

As David points out, he wasn't the first to discover this result, though he certainly deserves a great deal of credit both for its rediscovery and for (apparently somewhat accidentally) popularising it with a punchy paper/note containing clear and succinct proofs

You could say that having chosen a reference distribution, the KL divergence tells you how far away another distribution is in the particular way that you care most about

It's vaguely distance flavoured, but in a way that we don't (as far as I know) have a general word to describe

I disagree slightly that it's not just semantics: when deciding how to generalise the notion of distance, we get to decide which attributes have to be retained in order to retain the "distance" label

Requiring symmetry is perhaps the most reasonable choice but it's not the only possible choice

I think there's a divide between those who use "distance" synonymously with "metric" and those who use it for any function with a more general sense of dissimilarity-ness.

I wonder if the former group want to say KL isn't a distance whenever possible to make their definition the more prevalent one

The video is a fun watch but if you don't check it out, the counterexample I'm referring to is the Alexander horned sphere

en.wikipedia.org/wiki/Alexand...

It's interesting that its blend of coherence and unexpected nonsense capture a dreamy quality that most things described as "dreamlike" don't quite match for me

How best to define "open problem" depends largely on whether you start off with a problem metric or just a problem topology

For me, it's roughly:

Monday: Odd
Tuesday: Odd
Wednesday: Even if you were just thinking about Tue/Thu, Odd if you were just thinking about Monday
Thursday: Odd
Friday: Same as Wednesday
Saturday: Even
Sunday: Weakly even

Answering my own question, the example from the "Infinite-dimensional vector function" Wikipedia page makes it feel clear that a curve with these properties will exist

Even so, without more thought, this feels more like it side-steps the issue in my intuition than directly tackles it

Wait... what?!

Even though continuity means that the arcs have to exist in a countable-basis subspace, it feels so unintuitive that this gives room for a curve with uncountably many orthogonal chord pairs set up like this

Do you have any intuition on how you reconcile these two things?

It seems chronological for me too with the caveat that reposts are shown according to when they were reposted but display the time elapsed since original posting