One of the more annoying parts of my physics study was getting used to the new matrix multiplication notation they came up with every semester.

bra-ket is the (most?) general form of tensor manipulation.

Raising and lowering operators for summation notation are the beginner tools for covariant derivatives of the metric tensor.

Christoffel symbols are where it's at, if you need to write out the Ricci tensor. The more constrained the space the more concise the notation can be.

Note that MechE tensor notation has an even more compact (eigen) form for principal stresses.

All of this is true, but I don't believe and I want to be wrong about this that there is something in this notation that starts at an ELI 5 level and gently guides you to physicist level expertise. I all but majored in math (deriving back prop was trivial once it was clear it was the chain rule as one example) but I have never been able to keep bra ket notation straight in my head for the more exotic operations. Einsteinian notation on the other hand is a few minutes of furled brows and then all is clear.

It is what has separated me from being able to code just about anything on a GPU and being known for some of that work and coming up with a better way to run ab initio quantum chemistry on them.

It truly has been my Waterloo for many years. So make me wrong.

Yeah, bra-ket is arbitrary tensors (inner and outer multiplication) rather than the nice 4D of space-time (with derivatives).

I will say that seeing transformers written this way gives me a bit more intuition for what is going on (being able to identify correct equations), but there's enough complexity in actual transformer implementations, that it still feels like I'm fooling myself.

Conceivably, I think you could use Feynman diagrams to talk about phonon dispersion in (eg asymetric crystaline) solids, but even though they're a "simplification", they're overkill for the problem.

I don't think there is anything in this article that actually demands bra-ket notation (a state in some Hilbert space), that couldn't be more clearly written with standard notation for a Euclidean inner/outer product, but I suppose everyone has their own preferences for notation.

All real numbers are real, but some real numbers are more real than others.

Yes, as real as they can be.

Or sometimes as real as you can fathom :)

Two of six screenshots show the app. So the rejection fits the rules and is easy to understand. I often agree with complaints that Apple's rejections are unclear or problematic, but this isn't one of those cases.

And I'm kind of confused by these screenshots as well, since there are lines between them, as if they're one screenshot. And the labels over the screenshots are nonsensical and graphically glitched.

It's too bad Apple doesn't require it to be all 6 screenshots must be unedited screenshots.

I think introducing unpredictable new prohibitions is a much bigger problem than the specific bans on cryptocurrency or AI written code. Especially when it leads to existing code becoming unavailable and doesn't just ban new contributions violating the rules.

They weren't exactly unpredictable. People didn't predict it because they're used to dealing with faceless machine platforms instead of human platforms. GitHub bans projects rarely, and when it does, it's without any warning or rule change.

> The best practice is a policy banning PAN over email, instant messaging, SMS, and chat entirely.

Sounds silly to me. A PAN should never even touch an employee's computer.

There are cases for card not present transactions, fraud and complex refunds but generally yes.

> Anyone who cares about security will be using App Attest or the Google store equivalent.

Why? I rarely have security objectives where remote attention would help, and it has a huge impact on user freedom. For B2C attestation is just an evil captcha.

Abusing IP ranges which were assigned to an organization but aren't actually used on the public Internet as private addresses is pretty common. Sure, it's bad practice, but not a big deal.

Of course this looks entirely different when your corporate superstructure has a long and active history of developing military equipment.

When designing a character on a computer, you play around with many options, until you settle on one of them. Since you did exactly the same thing for all those variants, it's difficult to remember which one you ultimately picked. Writing down the final result by hand helps distinguish it from the alternatives in your mind.

That's very different from academic lectures, where you are directly told the facts, and not a multitude of equally valid alternatives.

If you are just copy pasting off of the board then probably. Hard to say since I have not had experience with both methods in this context.

I still think writing by hand makes stuff stick better especially if you are one of those 500 wpm typists where very little thought goes into typing and it is more like a reflex

I definitely got more out of paying full attention to lectures in university compared to wasting effort on hand writing notes. And properly typeset lecture notes written by somebody else are much better for studying than the illegible handwritten notes I produce.

Writing is a distraction from thinking.

I think German non profit organizations are required by law to have a certain level of governance structure.

Ah, interesting! I didn't realize they were German, and didn't realize it's a non-profit as well. I thought it was just an open source project and that was that. That would explain the bureaucracy.

The open source project is Forgejo. You can host is yourself with any policies you want.