antics

I guess unpopular opinion but (1) I doubt this person is actually an expert and (2) I think the actual problem is that being anonymous is a coddling blanket that absolves you of the social cost of anti-social behaviors (i.e., acting like a dick) or holding an unpopular view. Obviously anonymity has uses, too, but that is now how it is actually used on the Internet most of the time.

The only reason I bring this up is because I think it is counterproductive to view these people as experts when they are likely not.

Written by Walter Murch?? Like, the guy who is considered maybe the best editor and sound designer of all time, who was nominated for 9 Academy Awards, and won 3??? (Editing perhaps second only to Thelma Schoonmaker.)

The point is not that ETH has anything to do with P or NP, but that the bounds theoretical CS chooses for its conjectures tend to be extremely round and convenient. Does reality actually prefer such nice, round bounds in general? Does reality prefer them in the case of P and NP?

In essentially all cases, we have no real reason to believe or disbelieve. We choose these bounds because we can't do better. It's often the case that we later prove them wrong with some extremely strange result. Here, we have weird bounds for 3-SAT, and a few weeks ago we had one for integer multiplication.

But this has also happened repeatedly throughout history. In the 50s Kolmogorov conjectured that n-bit integer multiplication was \Omega(n^2). Karatsuba produced O(n^{1.58}) during Kolmogorov's seminar on the topic. Strassen discovered matrix multiplication is O(n^{2.81}) while trying to prove it is O(n^3). And on and on and on.

Maybe P and NP are well-formulated and they do perfectly capture our intuition of "efficient" and "efficiently verifiable" algorithms. Or maybe they don't. We are probably going to keep finding extremely weird, cheesed-out bounds for famous problems, though. You can choose what you want to believe, but I think it would be more remarkable if the reality of P and NP turned out to be as clean as the bounds indicate.

You can hold that position if you like but you should do so knowing that the vast majority of people (including math people) would say that a formalism that classifies a technically-subexponential solution to an NP-complete problem as “efficient” is in fact improperly formulated, because the goal was specifically to formalize our intuition of efficiency. Our formulation in that case would have failed to do the single thing we laid out for it. Textbook improper formulation. There is not another way of putting this.

It is completely acceptable in math to use "ill-posed" to indicate that something is insufficiently specified, improperly formulated, or ambiguous. Math people do this all the time.

"Ill-posed" here means that the formalisms we've chosen to represent "efficient" and "efficiently verifiable" algorithms could turn out to not correspond to anything humans would consider meaningful ("we posed the problem poorly"). For most people, a solution to an NP-complete problem that's barely-subexponential would be clear evidence of these formalisms being ill-posed.

There are many ways it might turn out to be ill-posed, this is just one of them. Impagliazzo's "5 worlds" survey is in some sense a catalog of some of these ways, and includes some of the ways you seem to be referencing (approxmations, probabilistic techniques, average-case efficiency; depending what you mean this could lie in the "Heuristica" world).

Perhaps this will be the push we need to finally, seriously consider the possibility that our formalisms of “efficient” and “efficiently verifiable” algorithms correspond to nothing resembling reality, and P \in NP is actually ill-posed.

This has been marginally debated since the mid 90s, when Impagliazzo published the “5 worlds” survey. Occasionally it is brought up in talks about average case analysis. There is occasionally a workshop about it. But it has never really got the attention it deserved. How many more of these results do we need to take it seriously? (Assuming we do indeed certify it.)

I'm not sure what you mean. Are you saying you think I'm suggesting they are extremely sophisticated actors on some dimension? I'm saying they're best thought of as a Berkshire Hathaway-style capital allocator, not a tech company.

Tech corporations have always been enormous stores of (1) capital and (2) people. MSFT's flavor of this has always been "tech Berkshire Hathaway": a holding company for a diversified portfolio of a couple-dozen billion-dollar businesses. MSFT in particular is willing to park ~300 people on a seemingly-dead-end product, just waiting for the incumbent to mess up. Sometimes it eventually succeeds commercially (Teams, PowerBI) and sometimes it doesn't (or hasn't, yet, see Bing).

What is happening here is a sign they are changing their view on how this capital allocation works.

To what? We don't know, and I think they might not know yet, either. If you are spending > $4M for a top-end engineer and $8M on their tokens (this refers to a person know personally, it is not hearsay), this will necessarily change the how this allocation works. Maybe it doesn't make sense to park 300 people on tomorrow's PowerBI any more.

What is clear is that we are not in anything approaching an equilibrium state. MSFT (and others like them) clearly do not have enough conviction to fire all the line engineers and only keep the so-called "elite" ones. It's not even clear that they think we're on that trajectory. I think what we are seeing, though, is that they have enough conviction to try to clear the way for more of this kind of spending on these so-called "elite" developers.

That is a very bold claim. Do you really think we have evidence to indicate any of that is true?

No.

Almost everything you'd want to say about it would spoil something interesting about the film. (This is not hearsay. I've seen it and I can't think about how to say anything meaningful about it without spoiling it.)

There are maybe examples where your point stands but that’s probably the worst one. The point of that knowledge is actually to answer questions. That is where social skills in the model come from: training it to answer questions.