blakestacey

What's the best way for Effective Altruists to allocate grant money? Purchasing malaria nets? Direct giving? No, of course not. It's buying $28k worth of copies of HPMOR (archive)

If I had to guess, I'd say it's One True Nerd Opinion-ism.

Numberwang racism

"Conspiratorial" implies intent, and I didn't get the sense that 2007--2013 Scott Aaronson was saying that. The tone is more that orthodox physicists are incompetent at explaining things, or indifferent to the need to explain things, or unenlightened to the glorious simplifying power of computerological thinking.

Yeah, doing full-blown quantum physics with the usual mathematical formalism really does require complex numbers, but I don't know of any derivations of that which appeal to computation, for reasons along the lines you indicate.

(It actually all started with Fourier series. Back in 1919 or so, Bohr started speculating that transition rates between atomic energy levels depend on the coefficients in a Fourier expansion. This led, through confusing intermediate steps, to Born's "square the absolute value of a complex number to get a probability" rule in 1927.)

Math competitions need to start assigning problems that require counting the letters in fruit names.

https://tmbw.net/wiki/Lyrics:Your_Racist_Friend

(sees YouTube video)

I ain't [watchin] all that

I'm happy for u tho

Or sorry that happened

This is outside my own department, but I think there's a problem with Aaronson's treatment of Gödel's incompleteness theorems. He says that Gödel's first incompleteness theorem follows directly from Turing's proof that the halting problem is undecidable. This doesn't quite work, as I understand it. The result conventionally known as Gödel's theorem is stronger than what you can get from the undecidability of the halting problem. In other words, the result that the Turing machines get you depends upon a more demanding precondition than "consistency", and so it is somewhat less impressive than what was desired. My best stab at a semi-intuitive explanation would be in the vein of, "When you're discussing the consistency of mathematics itself, you have to be double-special-careful that ideas like the number of steps a Turing machine takes really do make sense."

The historical problem is that Turing himself did not prove the undecidability of the halting problem. He wasn't even focused on halting. His main concern was computing real numbers, where naturally a successful description of a number could be a machine that doesn't stop. The "halting state" as we know and love it today was due to Emil Post.

Moreover, this is one of the passages where Aaronson seems to be offering the one and only true Nerd Opinion. He is dismissive of any way to understand Gödel's theorems apart from the story he offers, to the extent that a person who had only read Aaronson would be befuddled by anyone who used Gödel numbering after 1936.

I happened to learn recently that that's probably not from Keynes:

https://quoteinvestigator.com/2011/08/09/remain-solvent/

Aaronson goes on:

Look, obviously the physicists had their reasons for teaching quantum mechanics that way, and it works great for a certain kind of student. But the “historical” approach also has disadvantages, which in the quantum information age are becoming increasingly apparent. For example, I’ve had experts in quantum field theory – people who’ve spent years calculating path integrals of mind-boggling complexity – ask me to explain the Bell inequality to them, or other simple conceptual things like Grover’s algorithm. I felt as if Andrew Wiles had asked me to explain the Pythagorean Theorem.

And then, did anyone clap?

This is a false analogy. I don't think it's a surprise, I am not convinced that it's an actual problem, and if it is, I don't think Aaronson makes any progress to a solution.

The Pythagorean theorem is part of the common heritage of all mathematics education. Moreover, it's the direct ancestor to the problem that Wiles famously solved. It's going to be within his wheelhouse. But a quantum field theorist who's been deep into that corner of physics might well not have had to think about Bell inequalities since they were in school. It's like asking an expert on the voyages of Zheng He about how Charlemagne became Holy Roman Emperor. There are multiple aspects of Bell inequalities that someone from a different specialization could want "explained", even if they remember the gist. First, there are plenty of questions about how to get a clean Bell test in the laboratory. How does one handle noise, how do we avoid subtly flawed statistics, what are these "loopholes" that experimentalists keep trying to close by doing better and better tests, etc. Aaronson has nothing to say about this, because he's not an experiment guy. And again, that's entirely fair; some of us are best as theorists. Second, there are more conceptual (dare I say "philosophical"?) questions about what exactly are the assumptions that go into deriving Bell-type inequalities, how to divide those assumptions up, and what the violation of those inequalities in nature says about the physical world. Relatedly, there are questions about who proved what and when, what specifically Bell said in each of his papers, who built on his work and why, etc. Aaronson says very little about all of this. Nothing leaps out at me as wrong, but it's rather "101". The third broad category of questions are about mathematical specifics. What particular combination of variables appears in which inequality, what are the bounds that combination is supposed to satisfy, etc. The expressions that appear in these formulae tend to look like rabbits pulled out of a hat. Sometimes there are minus signs and factors of root-2 and such floating around, and it's hard to remember where exactly they go. Even people who know the import of Bell's theorem could well ask to have it "explained", i.e., to have some account given of where all those arbitrary-looking bits came from. I don't think Aaronson does particularly well on this front. He pulls a rabbit out of his hat (a two-player game with Alice and Bob trying to take the XOR of two bits), he quotes a number with a root-2 in it, and he refers to some other lecture notes for the details, which include lots of fractional multiples of pi and which themselves leave some of the details to the interested reader.

Aaronson leads into this rather unsatisfying discussion thusly:

So what is Bell’s Inequality? Well, if you look for an answer in almost any popular book or website, you’ll find page after page about entangled photon sources, Stern–Gerlach apparatuses, etc., all of it helpfully illustrated with detailed experimental diagrams. This is necessary, of course, since if you took all the complications away, people might actually grasp the conceptual point!

However, since I’m not a member of the Physics Popularizers’ Guild, I’m now going to break that profession’s time-honored bylaws, and just tell you the conceptual point directly.

The tone strikes me, personally, as smarmy. But there's also an organizational issue. After saying he'll "just tell you the conceptual point directly", he then goes through the XOR rigmarole, which takes more than a page, before he gets to "the conceptual point" (that quantum mechanics is inconsistent with local hidden variables). It's less direct than advertised, for sure. I have not systematically surveyed pop-science explanations of Bell's theorem prior to 2013, but the "page after page of entangled photon sources..." rings false to me.