prof-g

@parmita reminds me of the biologists' explanation of gravity: rocks that did not express gravitational attraction all floated away long ago...

There's an old joke in systems biology called "How Biologists Fix a Radio." A biologist, tasked with figuring out why a radio doesn't work, removes components one by one and catalogs the result. Remove this transistor: the radio makes a horrible screeching sound. Conclusion: this is the "horrible screeching transistor." Remove another component: the radio goes silent. Conclusion: this is the "silence transistor." This is essentially what we do with genomics. We see which genes are mutated in cancer and assume they must be "cancer genes." We see which genes are differentially expressed and assume they must be "important." But correlation is not causation, and a parts list is not a circuit diagram. You can have a complete inventory of every resistor, capacitor, and transistor in a radio and still have no idea how it plays music.

@elonmusk It's not as good at hard mathematics as earlier versions, alas. But I like the configurable agents a lot and give them the personalities of different mathematicians.

What are your initial impressions of Grok 4.20? Major upgrades are still landing every week.

More wins for Diamond Open Access: a new issue of JAMR @AMathRes is out! Enjoy: jamathr.org/index.php/jamr…

@lu_sichu more incoming...

@prof_g this looks amazing

people aren't uniformly stubborn... new paper with Vicente Bosca models this precisely using cellular sheaves. the payoff: the equilibrium is no longer harmonic, but satisfies a sheaf poisson equation, with the fixed opinions acting as sources...

am about to teach my students the F-bomb : so useful!

@politicalmath 1) is the loneliest # that you'll ever do

OK, here's the PT Anderson ranking: 1) Magnolia 2) There Will Be Blood 3) One Battle After Another 4) Boogie Nights 5) Licorice Pizza 6) Phantom Thread 7) Punch Drunk Love 8) Sydney (Hard Eight) 9) Inherent Vice 10) The Master This is a terrible list because I've watched Inherent Vice 3 times and it is a wonderful entertaining film that is also very flawed

I agree that One Battle After Another was PT Anderson's 3rd best film

happy frolicking

@StrawHatGustav Glory! To mathkind!

NieR: Automata meets Poisson geometry.

we are burning the gpus...

Picked an open problem and used Grok Heavy to solve it. After a few prompts (try this, compute that, tweak this etc) it discovered a counterexample that settles the question. The problem (first appeared on MathOverflow back in 2017 #287030" target="_blank" rel="nofollow noopener">mathoverflow.net/questions/1842…) asks to find the smallest C>0 such that for every d ≥ 1 and every polynomial f of degree ≤ d on the Hamming cube {-1,1}^n, ‖f‖₂ ≤ C^d ‖f‖₁ ? The author suggests that C = √2 might work, a plausible guess because for d=1 it coincides with the sharp Khinchin inequality (Szarek's constant √2). For d=2 it would imply an old conjecture of Pelczyński that the best constant for 2-homogeneous polynomials on the cube is 2. But Grok Heavy found a counterexample showing that the best constant is at least √3. The full chat conversation grok.com/share/c2hhcmQt…

Gordon Fremen, via @grok imagine

great news about @axiommathai i have been telling math phd students to bail/grad asap and head straight to the math \cap ai startup world... this is where things in math are headed

Just got some more great news: JXM (Journal of Experimental Math) will now be indexed in zbMATH, and reviewed in MathSciNet. More wins for open science!

Synthetic text extrusion. Virtual teaching assistants. Illusions of mastery. Silicon Socrates. Robert Ghrist, Bhuvnesh Jain, and Chris Callison-Burch comment on how higher education is starting to look different four years after the debut of ChatGPT. thepenngazette.com/hyper-text/

@politicalmath finally, someone who gets that THS was CSL trying (poorly) to imitate CW's style; good job. (CW would have written a much better/weirder THS)

Tolkien didn't dislike Charles Williams, but they weren't close. Lewis was a much closer friend with Williams, whose mystical predisposition influenced Lewis in later life. Tolkien didn't much care much for that.

Tolkien never called it "That hideous book". That is an urban legend. Tolkien wrote "That Hideous Strength, the end of the trilogy, which (good though it is in itself) I think spoiled it."

@prof_g Why is that?

the most amazing view of Penn/Philly, but you never ever want to be here to enjoy it 😔