Given the energy scales involved, it's more likely that the issue lies with the approximations DFT makes to quantum mechanics, rather than the approximations quantum mechanics makes to quantum field theory.
I'm a professor of physics; my research area is computational quantum field theory. I was beginning a new approach for a certain kind of model. I know the model has not been simulated before (a collaborator has just constructed it for the first time using in-field knowledge developed in the last year).
I've been steadily more impressed, but the real startling moment was earlier this week, I could show that in a particular operation I had a bug (some identity wasn't satisfied) but I couldn't understand why. In one try Claude Code grokked my code, explained the problem to me (there were some dimension-dependent minus signs that needed to be computed), and fixed it.
By the Standard Model of Physics Software you can edit Quarkdown in Atom to get Quarkup and change your Neutron Mail to Proton Mail, but it only works if you type with your left hand and create an Electron app and an anti-Neutrinos AI blogpost.
In case the author is reading this, if you're going to introduce the complex-valued harmonics you should be careful to put the complex conjugate in the inner product
<f, g> = ∫ f(ω)^* g(ω) dω
which does match the corresponding linear-algebra inner product if the vectors are over the complex numbers
p . q = Σ_i p^*_i q_i
which guarantees that p.p ≥ 0 even for complex p (and does not change the only-real case).
Hmm. As a physicist my intuition is that information-preserving transformations are unitary (unitary transformations are 1-to-1). If a compression algorithm is going to yield a bit string (the zip file, for example) shorter than the original it can't be 1-to-1. So it must yield the zip file and some other stuff to make up for the space saved by the compression.
You could package all your data into a zip using this language but you would also have a worthless stretch of memory seemingly filled with noise / things you’re not interested in.
I have always anthropomorphized my computer as me to some extent. "I sent an email." "I browsed the web." Did I? Or did my computer do those things at my behest?
As a term-rewriting system the rule x-x=0 presumably won’t be in Simplify, it’ll be inside - (or Plus, actually). Instead I’d expect there to be strategies. Pick a strategy using a heuristic, push evaluation as far as it’ll go, pick a strategy, etc. But a lot of the work will be normal evaluation, not Simplify-specific.
Mathematica has Infix [0], which expresses the adjacency with a ~ (because Mathematica reserves pure blankspace for multiplication). But it works fine to do eg. `"hello"~StringJoin~" world"`; I was always surprised we could only have the predefined operators in many other languages and we couldn't define our own.
This seems like a great attempt. I would be worried about how much parsing and backtracking might be required to infer the infix precedence in a totally general system (like garden-path sentences[1]) or actually ambiguous parse trees (which is cured by adopting some rule like right precedence and parens, but what rule you pick makes some 'natural language' constructions work over others).
They did consider it, got a contract that affirmed that the military would be bound by the same pre-existing terms of service as every other user, and want to resist the military's pressure to renegotiate.
Surely that might be naive but the entire issue is that they want to stick to the original contract, which is of course the purpose of a contract in the first place.