Jonathan Gorard @getjonwithit Twitter profile

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Jonathan Gorard

@getjonwithit

6 months

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)

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Jonathan Gorard

@getjonwithit

17 days

"The boundary of a boundary is always empty." A huge amount of (classical) physics, including much of general relativity and electromagnetism, can be deduced directly from this simple mathematical fact. Yet, on the surface, it doesn't seem to have much to do with physics. (1/10)

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Jonathan Gorard

@getjonwithit

4 days

I distinctly recall a time back in 2022 when various people tried to convince me that this guy was an intellectual heavyweight.

Tsarathustra

@tsarnick

5 days

Sam Altman says we have stumbled on a new fact of nature: that intelligence is an emergent property of matter

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Jonathan Gorard

@getjonwithit

6 months

What actually *is* curvature? It's a surprisingly hard question, and one which wasn't satisfactorily answered until the early 20th century, thanks to the work of Tullio Levi-Civita, Gregorio Ricci-Curbastro and other (largely Italian) differential geometers. (1/9)

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Jonathan Gorard

@getjonwithit

7 months

Everything we know about fundamental physics may be summarized by the statement: "Nature doesn't care about coordinate systems." Indeed, rather remarkably, all of our most foundational theories of physics appear to have (essentially) no content *apart* from this statement. (1/9)

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Jonathan Gorard

@getjonwithit

19 days

There are many nice ways to think about light, but a fun one is that it's the propagation of a set of coordinate constraints. Suppose that you took each point in spacetime and associated it with a little circle. Each of these little circles is called a "fiber". (1/5)

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Jonathan Gorard

@getjonwithit

6 months

Sometimes it's useful to model these things deterministically, sometimes it's not. But never forget that these notions of determinism and non-determinism are human concepts that *we* have introduced through our choice of models. The universe, fundamentally, doesn't care. (8/8)

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Jonathan Gorard

@getjonwithit

6 months

The conclusion? Determinism and non-determinism are not properties of *systems* but properties of *models*. So it simply doesn't make sense to ask "Is the universe deterministic?" or "Is quantum mechanics non-deterministic?" or even "Do humans have free will?" (7/8)

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Jonathan Gorard

@getjonwithit

18 days

Far from an original observation, but here's a fun "coincidence" (maybe...): There are exactly four known fundamental forces (gravitational, electromagnetic, weak, strong), and exactly four normed division algebras (real numbers, complex numbers, quaternions, octonions). (1/4)

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Jonathan Gorard

@getjonwithit

6 months

Shock waves, solitons and spacetime singularities: what do sonic booms and water ripples have to do with cosmic censorship and the determinism (or otherwise) of general relativity? Brace for a brief adventure in hyperbolic partial differential equations (PDEs). (1/20)

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Jonathan Gorard

@getjonwithit

6 months

[This thread is hopefully(!) the first in a series on tensor calculus, differential geometry and the foundations of general relativity...] This is a blob. This blob has no inputs and no outputs, so we shall refer to it as a "scalar", and we denote it by an "S". (1/10)

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Jonathan Gorard

@getjonwithit

27 days

A few people have asked what "fully covariant computation" means, with regards to my last post. I'm currently writing up a big paper about this, but since that will take a while to finish, let me try explaining the basic idea. Consider, for a moment, general relativity... (1/9)

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Jonathan Gorard

@getjonwithit

6 months

[This is part 2 of my series on tensor calculus, differential geometry, etc.] These blobs are called "tensors", and the "rank" of a tensor represents how many legs it has. Here's a rank-4 tensor with two contravariant indices (inputs) and two covariant indices (outputs). (1/11)

Jonathan Gorard

@getjonwithit

6 months

[This thread is hopefully(!) the first in a series on tensor calculus, differential geometry and the foundations of general relativity...] This is a blob. This blob has no inputs and no outputs, so we shall refer to it as a "scalar", and we denote it by an "S". (1/10)

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Jonathan Gorard

@getjonwithit

6 months

Lots of pop-sci talks about general relativity and quantum mechanics being “incompatible”, but what does that really mean? And how do quantum field theory, curved spacetime and (effective) quantum gravity fit into that picture? It's a surprisingly interesting story... (1/17)

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Jonathan Gorard

@getjonwithit

28 days

It's all coming together: after developing the formalism (and the tools) on-and-off for a couple of years, we now glimpse the beginnings of a fully covariant theory of computation...

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Jonathan Gorard

@getjonwithit

6 months

Namely, if you have a non-deterministic model of something, you can always make an equivalent deterministic model (yielding identical predictions) whose space of states is just the power set of the original. This fact has been (largely) ignored in the philosophy of science. (6/8)

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Jonathan Gorard

@getjonwithit

4 days

@pointed_max That passing off "whoa dude, what if intelligence is an emergent property of matter?" as a profound insight is rather cringe, and illustrative of a broader lack of intellectual curiosity. Spinoza said this stuff back in the 1600s. Some people have bothered to think a bit more.

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Jonathan Gorard

@getjonwithit

6 months

Here's a quick story about comonads, and how they can be used to unify various concepts in functional programming, category theory, rewriting systems and multicomputation. It starts with a practical problem: how to implement better compositional rewriting in Mathematica. (1/11)

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Jonathan Gorard

@getjonwithit

2 months

New paper: unveiling Categorica, my “secret” (read: freely available and fully documented for several years) weapon for doing applied category theory and automated theorem-proving. Including some nice Grothendieck fibrations, if you’re into that sort thing

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Jonathan Gorard

@getjonwithit

6 months

Embarrassing confession: the formal definition of natural transformations always seemed pretty opaque to me (i.e. *why* is that the "natural" definition of a homomorphism between functors?) Until I started thinking about them as universal quantifications over morphisms. (1/7)

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Jonathan Gorard

@getjonwithit

2 months

Fundamental theory of physics has been achieved internally.

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Jonathan Gorard

@getjonwithit

22 days

The real answer was already given excellently by @RBehiel , but let me attempt an "intuitive" answer. The Euclidean norm induces a homomorphism on the complex numbers, such that taking all complex numbers of magnitude 1 forms a Lie group U(1), homeomorphic to the circle S^1. (1/4)

Sam

@SlBrandin

22 days

What’s the cleanest and simplest explanation for why 2D (complex numbers) and 4D (quaternions) numbers exist, but not 3D numbers?

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Jonathan Gorard

@getjonwithit

6 months

Well, no. The Rabin-Scott theorem says that I can still simulate yours by defining each state of my computation to be a *collection* of possible states of yours. So the state space of my computation is simply the power set (i.e. the set of possible subsets) of yours. (3/8)

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Jonathan Gorard

@getjonwithit

10 days

In the process of attempting to formalize and implement higher categories into Categorica, I’ve been thinking a lot about the microcosm principle, which I’ve always found rather fun. I certainly don't claim to understand it in its entirety, but here's the basic idea. (1/6)

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Jonathan Gorard

@getjonwithit

27 days

One of the joys of working at a university is getting to witness all the subtle anthropological dynamics at play as the generation of students whose social skills were destroyed by Covid intermixes with the generation whose cognitive skills are being destroyed by AI.

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Jonathan Gorard

@getjonwithit

6 months

Most people are familiar with the idea that, if you have a deterministic model of something, you can always make it non-deterministic by deleting some information or coarse-graining over certain degrees of freedom. But far fewer people are familiar with the converse. (5/8)

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Jonathan Gorard

@getjonwithit

8 months

Inspirals, mergers, ringdowns, gravitational waves... Discrete spacetime astrophysics is starting to become a reality.

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Jonathan Gorard

@getjonwithit

6 months

My state space is thus exponentially larger (of size 2^n) than yours, but still, the point stands: everything you can compute, I can compute too. Okay, that's cool, but I think there's a much deeper lesson about the nature of (non-)determinism to be extracted here. (4/8)

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Jonathan Gorard

@getjonwithit

9 months

New paper out today: The first in a series, showing how anyone can use the tools I built for @wolframphysics to do practical computational general relativity. (More research coming soon on possible astrophysical probes of spacetime discreteness...)

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Jonathan Gorard

@getjonwithit

6 months

Suppose you have a non-deterministic computer (formally, a non-deterministic finite automaton) which can perform a whole tree of possible actions from a given input state, and I have a deterministic one, which can only follow a single path. Clearly yours is better, right? (2/8)

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Jonathan Gorard

@getjonwithit

7 months

This black hole collision was simulated using the open source Gravitas framework (), used a base resolution of 20,000 vertices and output more than 10GB of total raw data! Once again, @richardassar was the man behind the final rendering.

GitHub - JonathanGorard/Gravitas: Gravitas: Analytical and numerical general relativity in discrete...

Gravitas: Analytical and numerical general relativity in discrete and continuous spacetimes - JonathanGorard/Gravitas

github.com

Stephen Wolfram

@stephen_wolfram

7 months

Two tiny black holes merge in our Wolfram Physics Project...

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Jonathan Gorard

@getjonwithit

1 year

Latest paper: AFAIK, it's the first rigorous construction of an (axiomatic) quantum field theory in the @wolframphysics formalism. And it even gives the right answers! Brief explanation following.

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Jonathan Gorard

@getjonwithit

6 months

So when people talk about spacetime being curved, don't think about rubber sheets (those pictures always confuse me). It just means that you can't define a global set of coordinates over all of space and time, because gravity distorts them. And the connection tells you how. (9/9)

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Jonathan Gorard

@getjonwithit

17 days

Well, the boundary operator, which maps a space to its boundary space, acts formally very much like a derivative (obeys the product rule, etc.). This is no coincidence: the boundary operator on submanifolds is dual to the exterior derivative operator on differential forms. (4/10)

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Jonathan Gorard

@getjonwithit

7 months

The essential distinction between pure and applied mathematics is not rigour vs. sloppiness, exactness vs. approximation, generality vs. specificity, nor theorem-proving vs. calculation, but rather problems posed by mathematicians vs. problems posed by nature.

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Jonathan Gorard

@getjonwithit

10 months

Core @wolframphysics team (JG, SW, Manojna Namuduri, Hatem Elshatlawy and Xerxes Arsiwalla)

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Jonathan Gorard

@getjonwithit

7 months

I’m consistently surprised by how many people in academia seem to be motivated principally by some combination of prestige, vanity, self-image and (imagined) obligation, and how comparatively few by genuine intellectual curiosity or desire to think deeply and figure stuff out.

Maxim Ziatdinov

@MaximZiatdinov

7 months

I frequently come across bios, which are like, “I got my PhD from this fancy place,” “did my postdoc in that very famous lab,” “published many papers and won grants and awards,”… and zero mentions of what that person has really accomplished.

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Jonathan Gorard

@getjonwithit

7 months

The latter three are known as Yang-Mills theories. It is tempting, and consistent with what is currently known, to speculate that our universe may somehow be the most general geometrical structure of a certain class that simply "doesn't care about coordinate choices". (9/9)

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Jonathan Gorard

@getjonwithit

7 months

@pmddomingos In general? The lack of any unitary representation of the Poincaré group, thus prohibiting the construction of a gravitational Yang-Mills theory. (And, more broadly, the linearity of QM vs. the non-linearity of GR.) Personally? My complete lack of scientific competence.

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Jonathan Gorard

@getjonwithit

3 months

New paper: Featuring a tentative(!) astrophysical prediction: rapidly-spinning black holes in discrete spacetimes accrete material slowly and more unstably than in continuous ones. And perhaps we might be able to observe that...

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Jonathan Gorard

@getjonwithit

17 days

Within this formalism, the full system of Einstein equations emerge as rank-2 tensorial analogs of the rank-1 (vector) Maxwell equations. Yet, somehow, it all goes back to boundaries of boundaries, and their emptiness... (10/10)

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Jonathan Gorard

@getjonwithit

6 months

The (deep) answer? Curvature is a measure of how much a space fails to be parameterized by a single coordinate system. The room you're in right now is not (appreciably) curved, meaning that you can describe every point within it uniquely with a set of (x, y, z) coordinates. (2/9)

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Jonathan Gorard

@getjonwithit

1 month

Normalize yelling out “skill issue” in academic talks whenever an open problem is mentioned.

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Jonathan Gorard

@getjonwithit

22 days

What’s the point in being a researcher if you can’t spend a sunny afternoon sitting outside and chasing a crackpot idea once in a while?

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Jonathan Gorard

@getjonwithit

1 month

Hypergraphical Alfvén waves.

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Jonathan Gorard

@getjonwithit

2 years

Happy 98th birthday, Yvonne Choquet-Bruhat! Your proof of existence and uniqueness for local-in-time solutions to the Einstein field equations remains one of my favourite results in all of mathematical physics. Many happy returns.

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Jonathan Gorard

@getjonwithit

17 days

Some spaces (like spheres) don't have boundaries. But, when the boundary exists, it's always one dimension lower (codimension-1). A disc is a 2-dimensional space, but its boundary is a 1-dimensional circle. But what's the boundary of a circle? Well, it doesn't have one. (2/10)

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Jonathan Gorard

@getjonwithit

7 months

Currently developing a multiway/quantum gravity extension of Gravitas, which reduces to classical along any single path of history. Here's a (spacelike slice of a) black hole spacetime, simulated along 1, 2, 3, 4, 5 and 6 branches of history, with branchial edges in pink. (1/2)

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Jonathan Gorard

@getjonwithit

3 years

New paper (with Xerxes) on the homotopic foundations of @wolframphysics , addressing the fundamental question of *how* and *why* geometrical structures in physics (such as spacetime, Hilbert space, etc.) emerge from discrete "pregeometric" data! (1/5)

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Jonathan Gorard

@getjonwithit

1 year

@nntaleb It’s not the paying $8 that I object to (indeed, I’d much rather do that than have Twitter sell my data). It’s the blurring of the boundary between verification and subscription - which are, and IMO ought to be, two entirety orthogonal concepts. I suspect I’m not alone.

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Jonathan Gorard

@getjonwithit

17 days

It turns out that this will always be true, for purely topological reasons: a space may or may not have a boundary, but its boundary never will. Yet physics is about differential equations, not topology, right? So how can this fact have any relevance to physics? (3/10)

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Jonathan Gorard

@getjonwithit

17 days

This allows us to translate topological statements about boundaries into analytic statements about exterior derivatives. So our "boundary of a boundary is empty" statement now becomes a statement about symmetries of the covariant derivative operator on certain tensors. (5/10)

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Jonathan Gorard

@getjonwithit

8 months

Perfect fluid accretion onto black holes of increasing spin (Schwarzschild, Kerr a=0.5, Kerr a=0.9).

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Jonathan Gorard

@getjonwithit

1 month

Several months ago I wrote a lightweight (~10,000 loc) and efficient numerical relativity code in C++ called Cosmos, with fully-unstructured, hypergraph-based AMR and support for relativistic hydrodynamics in arbitrary black hole spacetimes. (1/2)

GitHub - JonathanGorard/Cosmos: The Cosmos numerical relativity code (with unstructured AMR)

The Cosmos numerical relativity code (with unstructured AMR) - JonathanGorard/Cosmos

github.com

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Jonathan Gorard

@getjonwithit

19 days

For the case where your fibers are circles, this wave is what we call light. For the case where your fibers are (double covers of) 3-spheres, this wave is a W or Z boson. For the case where your fibers are weird products of 3-spheres and 5-spheres, this wave is a gluon. (5/5)

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Jonathan Gorard

@getjonwithit

17 days

So the covariant divergence of stress-energy vanishes - in physical terms, this means that energy and momentum are always conserved in relativity! If instead we apply the Bianchi identities to the electromagnetic field tensor, we obtain the (homogeneous) Maxwell equations. (7/10)

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Jonathan Gorard

@getjonwithit

3 months

Ancient China, despite being more intellectually and technologically advanced than the Roman and Egyptian empires in many respects, didn't develop glass-blowing technology until at least the 5th century. Why the lag? Because they knew how to make porcelain. (1/3)

Curt Jaimungal

@TOEwithCurt

3 months

The Lack Of A Paradigm Shift In Physics Since The 1970s

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Jonathan Gorard

@getjonwithit

6 months

What might spinning black holes be telling us about (the futility of) time travel? The metric tensor in general relativity has three positive eigenvalues and one negative eigenvalue; geometrically, this means that three coordinate directions yield positive distances... (1/10)

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Jonathan Gorard

@getjonwithit

18 days

Clearly, the relationship is most direct in the case of the electromagnetic and weak forces, which were unified first (the Weinberg-Salam model). Clearly, the relationship is least direct in the case of gravity, which remains un-unified with the other three. (4/4)

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Jonathan Gorard

@getjonwithit

1 year

A dumb side project to try to learn more about Transformers: attempting to build a GPT+Categorica-based natural language proof assistant. Can now solve many (though not most) exercises in an undergraduate category theory course with fairly minimal prompt engineering.

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Jonathan Gorard

@getjonwithit

3 months

My experience of working almost exclusively with math/physics PhDs is that the “doctor” title is only ever used sarcastically (often to take the piss out of someone for spilling coffee on themselves).

ⓘ Dogs don't have thumbs

@MorlockP

3 months

I saw a study a while back that showed that the harder the degree, the less likely the holder is to insist on use of the title. EVERY education PhD uses "doctor", people who studied astrophysics are "Bob".

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Jonathan Gorard

@getjonwithit

6 months

Got a chance (courtesy of @Dr_CMingarelli ) to visit Yale's @BeineckeLibrary yesterday. But amidst the Copernicus, Galileo, Kepler, du Châtelet and Newton, my favourite was this manuscript from Einstein containing the original (incorrect) version of the field equations! (1/5)

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Jonathan Gorard

@getjonwithit

1 month

The fact that the US sponsors first-rate graduate education + practical training for countless foreign nationals on F visas, at great public expense, and then proceeds *not* to award them green cards more-or-less automatically, still seems hilariously suicidal to me.

Desh Raj

@rdesh26

1 month

H1B lottery ❌ It was less than a 1 in 3 chance, but sucks anyway!

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Jonathan Gorard

@getjonwithit

7 months

Indeed, and it's rather beautiful (and leads to some potentially interesting predictions)! First, imagine a multiway system in which a black hole forms on some branches of history but not on others. Because the BH is a relatively "ordered" state... (1/7)

Michael Cann

@mikeysee

7 months

@getjonwithit @richardassar @getjonwithit have you done anything on figuring out what Hawking radiation is in Wolfram Physics yet?

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Jonathan Gorard

@getjonwithit

18 days

The set of complex numbers of magnitude 1 under complex multiplication forms the gauge group of electromagnetism: U(1). The set of quaternions of magnitude 1 under quaternionic multiplication forms the gauge group of the weak force: SU(2). (2/4)

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Jonathan Gorard

@getjonwithit

7 months

Been thinking recently about the "Hawking question" in metaphysics: "What is it that breathes fire into the equations and makes a universe for them to describe?". I.e. given a set of (syntactic) laws, what guarantees the existence of a (semantic) entity that satisfies them? (1/7)

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Jonathan Gorard

@getjonwithit

17 days

When applied to the Riemann tensor and then contracted, it yields the contracted Bianchi identities: the statement that the covariant divergence of the Einstein tensor vanishes. But, in GR, the Einstein tensor is equal to the stress-energy tensor (times a constant). (6/10)

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Jonathan Gorard

@getjonwithit

18 days

The automorphism subgroup of the octonions preserving a magnitude-1 imaginary element i^2=-1 forms the gauge group of the strong force: SU(3). And the isometry group of a (flat) Lorentzian manifold with real-valued coordinates forms the gauge group of gravity: ISO(1, 3). (3/4)

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Jonathan Gorard

@getjonwithit

4 months

Validating Gravitas' forthcoming general relativistic hydrodynamics capabilities with some good, old-fashioned SRHD problems.

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Jonathan Gorard

@getjonwithit

4 months

New year, new university, new Gravitas paper. (Oh, and new country, I suppose.) Featuring all the details you could possibly want regarding how to set up and run your own numerical relativity simulations with Gravitas.

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Jonathan Gorard

@getjonwithit

1 year

@dmvaldman It’s been so many years, and yet it will never not be painful to see this all being credited to Stephen.

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Jonathan Gorard

@getjonwithit

17 days

This field allows us to decompose the Riemann/Weyl tensors into electrogravitic and magnetogravitic tensors (via the Bel decomposition), formally analogous to electric and magnetic field vectors. And, just as for Maxwell, the Bianchi identities give us the dynamical laws. (9/10)

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Jonathan Gorard

@getjonwithit

26 days

I will forever be thankful to Dan Dennett for proving, by construction, that even in the 21st century it was simultaneously possible to (a) be a philosopher; (b) know what you're talking about; and (c) make contentful and not-entirely-platitudinous statements. RIP.

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Jonathan Gorard

@getjonwithit

1 year

Today I learned that everything I ever thought about the expressive power of nondeterministic computation was invalidated in the 80s by an elementary algebraic construction due to Milner.

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Jonathan Gorard

@getjonwithit

17 days

These encompass both Gauss' law for magnetism and the Maxwell-Faraday law of induction. In fact, under the gravitoelectromagnetic formalism, the entirety of general relativity can be represented in this way. Just start by choosing a unit timelike vector field... (8/10)

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Jonathan Gorard

@getjonwithit

8 days

In a few weeks, I've been invited to speak at “Quantum Gravity and All of That” () to present major new progress - some published, most not-yet-so - in the effort to develop a fully computable foundation for quantum gravity. Come - it'll be livestreamed!

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Jonathan Gorard

@getjonwithit

27 days

Building upon the formalism I developed in , the key to covariant computation is to consider computations not in terms of states and transitions, but in terms of a complete causal structure of discrete tokens, as represented by a weak 2-category. (8/9)

A Functorial Perspective on (Multi)computational Irreducibility

This article aims to provide a novel formalization of the concept of computational irreducibility in terms of the exactness of functorial correspondence between a category of data structures and...

arxiv.org

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Jonathan Gorard

@getjonwithit

1 month

Thanks! My current plan, following G. H. Hardy's doctrine, is to continue doing proper mathematical work for as long as I'm reasonably young, and then pivot to jabbering about philosophy once I'm too old to do anything useful. (This is mostly, though not entirely, sarcastic.)

moissanist

@moissanist

1 month

i swear if he isn't already, @getjonwithit will become the preeminent mathematical philosopher of our time. the way he knits all these disparate parts of math together with such lucidity is beautiful

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Jonathan Gorard

@getjonwithit

7 months

If you start from a smooth, 4-dimensional Lorentzian manifold (spacetime) and want to start "doing physics" on it, it is helpful to define local space and time coordinates at every point. But there is much freedom in how to do this, with many permissible coordinate choices. (2/9)

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Jonathan Gorard

@getjonwithit

7 months

But these coordinates are mere bookkeeping devices, and the laws of physics (presumably) shouldn't care about something so arbitrary. So we can look at the collection of all such (smoothly-invertible) coordinate transformations, namely the spacetime diffeomorphism group. (3/9)

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Jonathan Gorard

@getjonwithit

3 years

Combining @wolframphysics graph rewriting and theorem-proving techniques with @coecke 's ZX-calculus to do blazingly fast automated simplification of quantum circuits (can simplify a ~350 gate circuit in ~0.1 seconds). Here's a proof of correctness of quantum teleportation...

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Jonathan Gorard

@getjonwithit

17 days

I've recently accreted a smattering of new followers. If any of you would like to get a general sense of what I'm about (so that you can assess the scale of the mistake you've made), I heartily (re)recommend @TOEwithCurt 's recent interview:

Jonathan Gorard: Quantum Gravity & Wolfram Physics Project

Jonathan Gorard joins Theories of Everything to delve into the foundational principles of the Wolfram Physics Project. Additionally, we explore its connectio...

www.youtube.com

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Jonathan Gorard

@getjonwithit

1 year

Beginning to classify vortices, monopoles, φ^4 solitons and other stable topological excitations in hypergraph rewriting systems... (With some neat connections to gauge theories, graphons, etc.)

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Jonathan Gorard

@getjonwithit

2 months

There was a point in grad school when I realized reading most math papers didn't scare me anymore. I knew that I could pick up any required notation/terminology/intuitions along the way with the background I already had... ...But algebraic number theory? That's still a big yikes.

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Jonathan Gorard

@getjonwithit

25 days

How to secure the future of computational science? Indoctrinate the young. (Had a great time talking about black holes and computational physics today as part of Princeton's "Spring into Science" event for 4th-10th grade students.)

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Jonathan Gorard

@getjonwithit

28 days

@mayfer No, nothing to do with CAs. A generalization of the Turing model of computation that does not distinguish between global states of data structures (i.e. spacelike hypersurfaces), execution traces of partial data structures (i.e. timelike hypersurfaces), or anything in between.

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Jonathan Gorard

@getjonwithit

2 months

Curt is incredible at what he does, and it's been an honor to follow his output (and, I'm glad to say, to call him a friend) over the years. Inevitably over the course of >3 hours I say a few things that are wrong or don't make sense. But overall this was really fun. @TOEwithCurt

Curt Jaimungal

@TOEwithCurt

2 months

Jonathan Gorard: Quantum Gravity & Wolfram Physics Project Watch here! Jonathan Gorard joins Theories of Everything to delve into the foundational principles of the Wolfram Physics Project. Additionally, we explore its connections to category theory,

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Jonathan Gorard

@getjonwithit

19 days

So, when you choose a coordinate system at one point in spacetime (called "fixing a gauge"), you can imagine a kind of "wave" of constraints on all the neighboring coordinate systems, propagating outwards to all other points in spacetime, in accordance with the connection. (4/5)

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Jonathan Gorard

@getjonwithit

19 days

The collection of all such circles is called a (total space of a) "fiber bundle", and the rule for how they get glued together is called the "connection": the rule for how to "walk" from a point on one fiber to the corresponding point on a neighboring fiber in spacetime. (2/5)

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Jonathan Gorard

@getjonwithit

3 years

Probing the Penrose singularity theorem in discrete spacetime: massive scalar field collapse to a Schwarzschild black hole (simulated using @wolframphysics , with colours designating extrinsic spatial curvature).

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Jonathan Gorard

@getjonwithit

7 days

@dhaaruni If you think that there is a single “objective” definition of the Riemann zeta function, then you have completely failed to understand why it is interesting.

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Jonathan Gorard

@getjonwithit

7 months

Indexing the Library of Babel, empiricism vs rationalism, and why I think the “ruliad” is a little bit silly (a 🧵): When defining a mathematical structure, there are broadly two distinct approaches that one can take: the constructive approach, and the axiomatic approach. (1/10)

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Jonathan Gorard

@getjonwithit

7 months

And, with certain caveats, the most general theory whose dynamics is invariant under this group is general relativity (gravity). What if we now want to introduce a non-gravitational field to spacetime, characterized by a scalar potential in the timelike direction and a... (4/9)

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Jonathan Gorard

@getjonwithit

1 month

Having @MCHammer follow me on X was assuredly not on my 2024 bingo card, but thank you! This totally made my day.

MC HAMMER e/acc

@MCHammer

1 month

Love it ! @getjonwithit is brilliant and a great communicator. @TOEwithCurt

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Jonathan Gorard

@getjonwithit

6 months

All lines of longitude meet at the North Pole, so it has no unique lat-long coordinate value. If you want every point on the surface of the Earth to have a *unique* set of coordinates, you need to use different coordinate systems for the pole(s) as for everywhere else. (4/9)

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Jonathan Gorard

@getjonwithit

25 days

Whenever I’m asked about the emergence of higher cognition in LLMs, I'm reminded of the fictional obituary of Sir Humphrey Appleby: "the advancing years, without in any way impairing his verbal fluency, disengaged the operation of his mind from the content of his speech." (1/2)

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Jonathan Gorard

@getjonwithit

1 year

ICYMI, I've spent the last several months developing "Gravitas": a new computational relativity tool based on @wolframphysics formalism, enabling anyone to perform hypergraph-based numerical relativity simulations on their laptop. (1/4)

Basic Gravitas Demonstration

Demonstration of some of the basic features of the new, hypergraph-based “Gravitas” computational relativity framework (https://github.com/JonathanGorard/Gra...

www.youtube.com

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Jonathan Gorard

@getjonwithit

9 months

We are so back.

Wolfram Physics Project

@wolframphysics

9 months

The Wolfram Institute gets back into action! Announcing a new phase for the Wolfram Institute. Tune in Friday 16:00 UTC to hear from the new Director of Research @getjonwithit , the new Director of Operations Barbara Mack and research fellows.

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Jonathan Gorard

@getjonwithit

7 months

And what is the most general theory whose dynamics doesn't care about *those* coordinate choices? It's quantum electrodynamics, with the field in question being the electromagnetic interaction (and with the aforementioned potential being the electromagnetic 4-potential). (7/9)

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Jonathan Gorard

@getjonwithit

27 days

There is then a (strong, monoidal) functor mapping the "state" perspective of a given computation to its "causal" perspective, and this functor permits a class of deformations that constitute the analog of relativistic gauge transformations. Can't wait to show more soon! (9/9)

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