Jonathan Gorard (@getjonwithit) / X

Jonathan Gorard

1,755 posts

Jonathan Gorard

@getjonwithit

Applied mathematician, computational physicist @Princeton Previously @Cambridge_Uni Making the universe computable.

Princeton, NJ

Joined November 2012

Following

46K

Followers

Jonathan Gorard
@getjonwithit
May 31, 2025
Calling c the "speed of light" completely misses the point. Rather, c is the "spacetime exchange rate": how many units of space you can exchange for one unit of time. In actuality, everything travels at the "speed of light", just not necessarily through space alone... (1/4)
1.7M
Jonathan Gorard
@getjonwithit
Dec 8, 2024
The apparent "philosophical problems" of quantum mechanics are not unique to QM at all: they are in fact the same problems that arise whenever one attempts to construct an abstract model of reality. We can see these problems already in high school-level mechanics. (1/14)
768K
Jonathan Gorard
@getjonwithit
Nov 4, 2024
Much more work is needed before this is really a robust result (paper forthcoming, hopefully by the end of the year), but the initial findings are clear: Spacetime discreteness may be observationally detectable in things like quasar luminosities. (1/6)
696K
Jonathan Gorard
@getjonwithit
Jul 14, 2024
"Quantum mechanics is just thermodynamics in imaginary time." It sounds like a hand-wavy, quasi-philosophical statement. But with a brief dive into the relationship(s) between hyperbolic and parabolic PDEs, it becomes possible to formalize it mathematically. (1/16)
825K
Jonathan Gorard
@getjonwithit
Jul 28, 2024
Moths are attracted to lights because of the same mathematics that underlies twistor theory and compactification in theoretical physics: projective geometry. It all starts from a simple observation: translations are just rotations whose center is located "at infinity". (1/11)
623K
Jonathan Gorard
@getjonwithit
May 31, 2025
Replying to @getjonwithit
Light is distinctive only insomuch as it (like any massless particle) experiences no time, so all of its velocity vector points in the space directions, and therefore it moves with a purely *spatial* speed of c. c is merely the conversion factor between space and time. (4/4)
115K
Jonathan Gorard
@getjonwithit
May 11, 2024
I distinctly recall a time back in 2022 when various people tried to convince me that this guy was an intellectual heavyweight.
Tsarathustra
@tsarnick
May 11, 2024
Sam Altman says we have stumbled on a new fact of nature: that intelligence is an emergent property of matter
00:00
909K
Jonathan Gorard
@getjonwithit
Nov 4, 2023
The Rabin-Scott theorem is one of the (philosophically) deepest mathematical results I know. When properly understood, I claim that it can't help but alter your view of reality in a fairly foundational way. Yet its typical textbook presentation obscures much of this depth. (1/8)
774K
Jonathan Gorard
@getjonwithit
Aug 10, 2024
Gödel's first incompleteness theorem is commonly proved by means of a diagonal argument. But, in retrospect, we can see that what Gödel was really doing was proving that Peano arithmetic is Turing-complete, and then applying an argument from computational irreducibility... (1/15)
479K
Jonathan Gorard
@getjonwithit
Feb 4, 2025
Energy, momentum, pressure, stress, etc. are all just different ways of quantifying the same basic thing: how our perceptions of space and time get distorted over time. And once you internalize this, it allows you to think about these concepts in a much more general way. (1/12)
308K
Jonathan Gorard
@getjonwithit
Dec 30, 2024
One of the curious things about von Neumann was his ability to do extremely impressive technical work while seemingly missing all the big insights. He did much work on mathematical foundations in the 20s, but completely missed the incompleteness/undefinability theorems... (1/3)
Amjad Masad
@amasad
Dec 28, 2024
As great as Einstein is, he comes no where close to the brilliance of von Neumann. It’s an error of history that he’s not the most eminent scientist.
832K
Jonathan Gorard
@getjonwithit
May 31, 2025
Replying to @getjonwithit
Rather, everything travels through both space *and* time, simultaneously, with a speed of c. If you're standing still, then all of your velocity is focused in the time direction (with none in the space directions), so you move through time with a speed of c. (2/4)
121K
Jonathan Gorard
@getjonwithit
Jul 10, 2024
In physics, one often thinks of space and time as being fundamental, pre-existing concepts, and proceeds to define everything else (energy, momentum, forces, etc.) in terms of them. But it doesn't need to be so - symplectic geometry shows us how to go the other way. (1/16)
485K
Jonathan Gorard
@getjonwithit
Jan 4, 2025
I use computers for mathematics so much that sometimes I opt to do a really nasty piece of tensor calculus by hand just to convince myself I've still got it. Just calculated the covariant divergence of a rank-4 tensor density correctly in one shot. Took 3 pages. I feel *alive*.
204K