Are we in a recession? I don't think so. There was (still is) a possibility of a recession, due to elevated interest rates, but the way fiscal policy works, through Congress's appropriations, it is hopelessly lagging behind monetary policy (the Fed).
It's a chapter from here: Rumelhart, D. E., McClelland, J. L., & the PDP research group. (1986). Parallel distributed processing: Explorations in the microstructure of cognition. Volume I. Cambridge, MA: MIT Press.
We are talking about different kinds of "probabilistic" proofs. Igor Pak's blog post and the root message in this thread refer to statements that are validated only probabilistically. The probabilistic method, by Erdos and others, is a proof as rigorous as any. "Probabilities" in the this method are just a convenient apparatus for counting objects.
(As an aside, there's important distinction with statements that are believed to be true based on empirical evidence, such as hardness of factoring or the Riemann conjecture. If the bunkbed conjecture was refuted based on Monte Carlo simulations, it'd be possible to reduce the level of uncertainty arbitrarily low by throwing more resources at running more simulations.)
Right - I admit I stopped reading the blog post at the point they linked to the paper and started reading that instead (which contains a rigorous proof). Having read the rest of the blog now I can see where the OP is coming from.
That's correct! The text is presented on the source web page as a story, and it does not claim to be factual.
Alexander Grothendieck was indeed awarded the Crafoord Prize, which he rejected. (It was never worth 40 mil francs as the translation above claims. The original French put it at "40 briques" = 400,000, currency not specified, which is much closer to the more accurate 800K SEK ~ 800K FFr that he would have received. The fact that the full amount, 1,6M SEK, would be split between him and Pierre Deligne, whom Grothendieck had denounced, might have contributed to his decision.) Grothendieck's rejection letter was remarkably lucid and articulate: https://www.fermentmagazine.org/quest88.
> But the “riddle” requires P to be exactly true or false.
Your choice of P (whether the continuum hypothesis holds) is still ill-defined! This is because the answer depends on the system of axioms one subscribes to. Or, if you feel like playing God, you may pick an answer (CH holds / does not hold) and find axioms that support it. (Which can be as simple as ZF + CH holds/does not hold.)
> A Turing machine with finite states must eventually either halt or loop. Those are the only options, because there are only finitely many configurations it can be in, and each configuration completely determines the next.
The Turing machine writes and reads from an infinite tape, and as such, the number of configurations (the machine's state + tape) is countably infinite.
> the other 99.99% of academics should reconsider their presentation style; the reason their papers don't spark such arguments is that they've given up on educating the ignorant the way scott does
I don't see how the second part of the sentence implies the first. The primary role of academics is generating new knowledge. Educating the ignorant is a public service that few are willing or able to do. Scott Aaronson deserves a lot of credit for dedicating so much energy to his blog, it does not mean that 99.99% of his peers are wrong in focusing on advancing the frontier of knowledge.
it's a public service that nobody else is able to do, and if nobody does it, the result is catastrophe: legislating the value of pi, creationism in schools, prohibitions on glassware and borax and teflon, lynchings for witchcraft, acid attacks on girls for attending school, the ransomware pandemic, boko haram, the cambodian mass executions for wearing glasses or speaking french
i won't go so far as to claim that this imposes an individual moral obligation on every academic—that would be a variety of consquentialism with many consequences i shrink from—but at least it would be good to figure out how to demarginalize what scott is doing
