Will Gyory

Announcing presenters in the 2024 Dissertation Showcase! Janusz Kaleta, Sarah Mady, Edwin Grimsley, Kyungjin Jo, Fabiola Fernandez Peer, Hyein Lee, Irit Bloch, Douglas Medina, Will Gyory, Britton Williams & Grace Flores-Robles. RESERVE for the 5/15 event: gc.cuny.edu/events/inside-…

@RealRajanMehta How about “natural” or “canonical”?

I want to talk about the “obvious” isomorphism (A x B) x C —> A x (B x C) but I’m also averse to ever using the word “obvious” in a paper. Any suggestions?

@arm_chirps @gabrielpeyre Hm, is this one of those things that *seems* like it violates locality but really doesn't?

@WillGyory @gabrielpeyre yes!

Nonlinearity matters. Linear diffusion (heat) has non-compactly supported solutions. Non-linear diffusion (porous medium) drives dynamics with compactly supported solutions. The porous medium is the simplest case, studied in details by Otto. mis.mpg.de/preprints/1999…

@SharmaneLane @ProbFact Ah ok. I was treating the ratio as <total> : <full house>, but in fact it is <not full house> : <full house>.

@WillGyory @ProbFact Both assertions are correct. If probability of full house are 1/694 the odds against it are 693:1.

Odds of drawing a full house in a 5-card hand: 693 to 1.

@ProbFact Tried to check who was right from this website: poker.org/poker-hands-ra… Weirdly, they also say 693:1, but their numbers before that are the same as mine: 3,744 / 2,598,960. Someone's just typing the wrong numbers into a calculator.

@ProbFact I'm getting 694.16666... to 1.

@Blair_Young The nuclear bombs dropped by the US in WWII unleashed about 10¹⁴ joules of energy. Our sun’s gravitational potential energy is around 10⁴¹ joules, which is a billion billion billion times greater.

@Blair_Young I think there's a false intuition that “explosions” must be caused by “explosive material.” But explosive material (like TNT) is just matter with lots of potential energy that can be unleashed quickly. Gravitational potential energy is just as powerful if you have enough of it!

@WillGyory When a star goes supernova, isn't the matter left behind compressed into something small but massive by the explosion itself? Similar to how the primary explosion of a nuclear bomb pushes the secondary into a supercritical state? Thanks 👍🏼 #physicsrule

@Blair_Young There's a nice animation of a supernova (and lot's of cool info about neutron stars) in this video. Highly recommended! youtube.com/watch?v=udFxKZ…

@Blair_Young Good question! In short, yes. But I think of it more as a "bounce in, bounce out" process. Gravity pulls the star material to the center, and the intense pressure at the core creates a neutron star. Then most of the star material bounces out, creating a huge explosion.

@waitbutwhy I dunno, there's something instinctual about checking for typos immediately after hitting "send" on anything. Think about texting and the common use of followup "*" texts.

I guess it could work to have the edit feature available for like 30 seconds, but Twitter Blue already has that feature and it's kind of inane. If you're the type to check for typos you'll do it before the deadline, whether that deadline is when you hit Tweet or 30 seconds later.

I don't really understand the argument for a Twitter edit button. It sucks if you retweet something and then the author totally alters its message. But if editing a tweet sets retweets and likes to zero, isn't that the same thing as deleting the old tweet and writing a new one?

@JDHamkins I've been wondering about this ever since I recently asked a related question on Math.SE, math.stackexchange.com/questions/4421….

ZFC proves of each of its finite fragments that this fragment is consistent. And the same for Peano arithmetic PA. Should we regard this as a partial fulfillment of the Hilbert program?

@smartereveryday Spacetime is more fundamental, so let’s say we have already defined that. Then time is (roughly) the spacetime dimension whose sign in the metric signature is opposite to the signs of the other three dimensions.

In your own words, how would you define “time”? Respectfully, I’m not looking for cheeky answers. I’m looking to put words to “time” in a way you’d describe it to a physicist or philosopher.

@MathiasFuchs10 @johncarlosbaez @RogierBrussee Interesting that the precise analysis of this simple idea gets so subtle and complicated.

@johncarlosbaez @RogierBrussee ... and you actually do need the Reed/Simon book to understand the correct version of functional calculus to make sense of the inner product formula. Thanks John for pointing people to all those maths/physics gems (8/8).

@johncarlosbaez I think we also need to omit the non–square integrable solutions, like the basic infinite sine plane waves? Or is there a way to expand the usual L²-style Hilbert spaces to include these?

@johncarlosbaez Cool!

@johncarlosbaez What's the Hamiltonian of this theory, and does it agree with E = ℏω?

@AnalysisFact Or rather, for all x ∈ Dom(T) ⋂ Dom(T*), if T is unbounded.

An operator T on a Hilbert space H is normal iff ||Tx|| = ||T*x|| for all x in H.

@3blue1brown If anyone's still wondering when this email will arrive, check your spam folder. Somehow it wound up there for me :)

Thanks to everyone who participated in the Summer of Math Exposition. Submissions are now closed, with over 1,300(!) total entries. If you took part, you should get an email shortly with next steps. Winners will be announced on Sep 14. Looking forward to seeing what you made :)