i don’t ever use bottle caps or cars. but in the case of screws (and bottle caps), the choice to make them tighten clockwise and loosen counter clockwise is entirely arbitrary.

my main point is that i think it’s confusing that clockwise is negatively oriented and counterclockwise is positively oriented (in the mathematical sense). and the mathematical definition of orientation is ultimately dependent on trigonometry. and it just feels wrong that clocks are negatively oriented.

You’re the person people have to say “no, your other left” a lot to, aren’t ya?

no.

this would also be society if counterclockwise and clockwise were swapped. it’s the universal way to talk about 2d rotations but pretty much nothing (except a clock) ends up turning clockwise. it didn’t have to be this way

language!

damn i wish my eyes did that

i think it’s mainly people being cranky and set in their ways. they got used to working around all the footguns/bad design decisions of the C/C++ specifications and really don’t want to feel like it was all for nothing. they’re comfortable with C/C++, and rust is new and uncomfortable. i think for some people, being a C/C++ developer is also a big part of their identity, and it might be uncomfortable to let that go.

i also think there’s a historical precedent for this kind of thing: when a new way of doing things emerges, many of the people who grew up doing it the old way get upset about it and refuse to accept that the new way might be an improvement.

it’s rough when the math gets so complicated that you have to break your finger in order to be able to visualize things

i wish they would do this in math instead of the boring system where it’s always alphabetical

that’s an extremely rare sighting but it’s so satisfying to read

what are your thoughts on “whence”?

that would be a lot clearer. i’ve just been burned in the past by notation in analysis.

my two most painful memories are:

• in the (baby) rudin textbook, he uses f(x+) to denote the limit of _f _from the right, and f(x-) to denote the limit of f from the left.
• in friedman analysis textbook, he writes the direct sum of vector spaces as M + N instead of using the standard notation M ⊕ N. to make matters worse, he uses M ⊕ N to mean M is orthogonal to N.

there’s the usual “null spaces” instead of “kernel” nonsense. ive also seen lots of analysis books use the → symbol to define functions when they really should have been using the ↦ symbol.

at this point, i wouldn’t put anything past them.

unless f(x₀ ± δ) is some kind of funky shorthand for the set f(x) : x ∈ ℝ, x - x₀ | < δ . in that case, the definition would be “correct”.

it’s much more likely that it’s a typo, but analysts have been known to cook up some pretty bizarre notation from time to time, so it’s not totally out of the question.

i think the ε-δ approach leads to way more cumbersome and long proofs, and it leads to a good amount of separation between the “idea being proved” and the proof itself.

it’s especially rough when you’re chasing around multiple “limit variables” that depend on different things. i still have flashbacks to my second measure theory course where we would spend an entire two hour lecture on one theorem, chasing around ε and η throughout different parts of the proof.

best to nip it in the bud id say

i still feel like this whole ε-δ thing could have been avoided if we had just put more effort into the “infinitesimals” approach, which is a bit more intuitive anyways.

but on the other hand, you need a lot of heavy tools to make infinitesimals work in a rigorous setting, and shortcuts can be nice sometimes

🤐

they chose to hide it in plain sight

the “categorical” way of defining tensor products is essentially “that thing that lets you turn multi-linear maps into linear maps”, and linear maps (of finite dimensional vector spaces) are basically matrices anyways. so i don’t see it as much of a stretch to say tensors are matrices.

(can you tell that i never took a physics class?)

a tensor is a multi-linear map V × … × V × V^* × … × V^* → F, and a multi-linear map V × … × V × V^* × … × V^* → F is the same as a linear map V ⊗ … ⊗ V ⊗ V^* ⊗ … ⊗ V^* → F. and a linear map is ““the same thing as”” a matrix. so in this way, you can associate matrices to tensors. (but the matrices are formed in the tensor space V ⊗ … ⊗ V ⊗ V^* ⊗ … ⊗ V^*, not in the vector space V.)

scary to think of how big the horses themselves must have been

they must have been wild

but imagine you’ve just gotten use to living on a moss planet over the past 40 million years, and now all of a sudden you walk outside and all the moss is gone