Somewhere along the line, years after I was in college, I “internalized” the point that local realism (for instance, a box either has X in it or does not have X in it, be it a marble or a cat or a spin state) works at human scales and is deemed to be part of our “rationality.” But it manifestly DOES NOT WORK at smaller scales (nor at any scales, actually, but at large scales or long times, decoherence dominates).

And when one realizes that it is this QM-type of non local realism that makes for stable atoms, to name but one of a hundred such example, one realizes that QM is really more “rational” than the classical world is.

(Another way to put this is that really are only two choices for the “norm” of reality. The L1 “Manhattan geometry” norm or the L2 (“shortcut through the diagonal”) norm. (There are reason s why other norms can’t work. Scott’s book alludes to them, and real mathematicians no doubt can elaborate.) Both Lucien Hardy and Scott have made this point poignantly (and pointedly), and maybe it’s buried somewhere in John von Neumann’s papers, but this seems to be key. So, L1 is classical physics, L2 is quantum physics. There are no other “physical realities.” A really, really bright mathematician/physicist could have (perhaps) “predicted” a lot of quantum physics 200 years ago. Especially with just the results of Young’s light diffraction results. But the best we had, Newton, Lagrange, Laplace, Maxwell, Einstein, etc. did not.

The revolution of QM made this much clearer.

(And, in my own opinion, the “second revolution” of Bell, quantum computing, entanglement, which was largely a realization of the implications already laid-out by around 1930, has led to all this cool new stuff. Some say it was already known by way back then in the 1930s, but I think it too a while for people to think about the implications. And even probably wrong ideas like the AMPS “firewall” theory have served to trigger this huge flurry of papers and theories. Oftentimes a “wrong” theory stimulates fresh analysis. Einsteing, a critic of QM, was a major contributor just through is ER and EPR, separate analysis.

Lenny Susskind had a hilarious line at his Stanford lecture several weeks ago. About ER and EPR, “they didn’t call him Einstein for nothing.” The whole lecture hall erupted with laughter.

]]>Great point. A world based on Rationality alone might be a scary place.

Aren’t emotions like sentimentality, attachment etc. at odds with pure rational decision making?

]]>– Assume that the Fermat Theorem’s is consistent

– Assume that integers a, b, c, violate the Fermat Theorem

– Then, the Fermat Theorem is inconsistent.

Therefore, proving that the Fermat Theorem is consistent would immediately prove the Fermat Theorem.

In the same way, many mathematical statements are proven immediately as soon as a consistency proof is given. I.e., an independence proof is impossible for these statements and that’s why there aren’t independence proofs. Perhaps many of the unproven statements are actually independent but we can’t prove that.

Also, I personally find it striking that the Continuum Hypothesis is independent. If that is not disconcerting, I don’t know what would be.

]]>Actually it just means we need irrationality to make the world work.

]]>I mean sure lots of turning down happens in the routing process of scientific publishing but this sort of work seems very high impact just so long as it is legit.

I mean it doesn’t even have to be right but just has to meet the bars of legitimate scientific discourse to get published when the potential impact is so revolutionary.

]]>Exciting indeed! You lucky man. It pains me to think that I will never properly understand this stuff (I am 62 and not a physicist) but even the simplified versions convey a strong feeling of something both beautiful and fundamental. I’ll keep watching those guys on YouTube…..

]]>About hoping that Scott turns his guns towards physics over complexity theory, Lenny Susskind said at his recent Stanford lecture that his main focus in the big program is more complexity theory than some of the other areas.

(I was able to catch lectures by Polchinski, Preskill, Van Raamsdonk, and Susskind at Stanford in the last couple of years. What a great place and time I find myself in.)

A lot of the stuff about tensor networks and “cuts” in sketches of Escher-like diagrams is beyond me, but there seems to be something potentially there that is not just woo-woo.

Exciting times. Complexity theory seems unrelated, except as Scott has hinted at in his book, and utterly impractical (10^89 years, come on!), but then entropy looked similarly difficult to actually consider a century or so ago.

]]>Interesting suggestion. Scott perhaps knows as much about TCS + Complexity as anyone, and is not not likely to be looking for a new field to take up. Nevertheless, I can guess how the unnamed physicist was thinking, perhaps something like the following:

TCS+C is a fascinating extrapolation of basic concepts, following the path of discovering “What’s out there”. The intellectual excitement is palpable.

You can say the same thing about TLC (Topology of Large Cardinals), ST (String Theory), MWI, etc. TLC and TSC+C have in common starting with key useful facts (basic functional analysis; analysis of algorithms) and going off into the ozone. There is absolutely a chance that something useful will be found in the ozone. In contrast, ST has a remote chance of ever being worthwhile; MWI has no chance.

Current students might wonder; can a really smart person find happiness in boring old practical science, full of real world complications? Or is all the excitement in speculative stuff, where anything you can dream up goes?

It is possible. A great example is Subrahmanyan Chandrasekhar. Many times he studied up on a major topic of the day, figured out much of what everyone was trying to do, organized and summarized the material in a book, and moved on the something new. Each time the entire field took a big jump forward; now grad students could read his book, and be prepared for the next generation of problems. See the obituary in “Physics Today”, or https://en.wikipedia.org/wiki/Subrahmanyan_Chandrasekhar

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