To be honest, the alternative for a good chunk of these users is no interaction at all, and that sort of isolation doesn't prepare you for human interaction either.
2,956 karma · joined September 19, 2020
To be honest, the alternative for a good chunk of these users is no interaction at all, and that sort of isolation doesn't prepare you for human interaction either.
Tangentially, is there a good alternative to Qt or SDL in Rust yet?
I think many of the people fantasizing about revolution are aware.
What exactly is wrong ("moaning and groaning", something that you "grew up" from), in your estimation, about that perspective?
> realized family is extremely meaningful
I believe that many people with the aforementioned perspective would agree with you, but would add that reducing further suffering is an overriding priority.
Adobe, at least, makes money by selling software. Google makes money by capturing eyeballs; only incidentally does anything they do benefit the user.
What historical evidence supports that Jesus helped the poor?
What does this mean? There doesn't seem to be a popular alternative to C++ yet, unfortunately.
It's possible that something similar might be the right path for metaprogramming. Rust's generics are simple and weaker than Zig's comptime, while proc macros are complicated and stronger than Zig's comptime.
So I think the jury's still out on whether Rust's metaprogramming is "better" than Zig's.
What does this mean?
For example (you can pick another example if you want), how is C++'s std::vector less abstract than Java's ArrayList?
I'm not even sure I'd call this type inference (other people definitely do call it type inference) given that it's only working in one direction. Even Java (var) and C23 (auto), the two languages the author calls out, have that. It's much less convenient than something like Hindley-Milner.
(Rust has refcounting, but it's slow, and needing to handle cycles manually limits its usefulness.)
That's like complaining that unsafe{} breaks Rust's safety guarantees. It's true in some sense, but the breakage is in a smaller and more easily tested place.
What applications are written in OCaml? All I can think of (which says more about me than it does about OCaml) is the original Rust compiler.
Even Haskell has Pandoc and Xmonad.
Yes, it's an argument from authority.
> The typical push-pull on a message board is between Strang and Axler
We're not playing Pokemon with linear algebra textbooks here...
> the centrality of the angular interpretation
It's not central. It's one of the ways to think of it. I think 3B1B actually did a good job emphasizing this in his video series: there are many ways to look at vectors, and all of them are sometimes useful. They can be arrows in space, or sequences of numbers, or black boxes that obey the vector space axioms, or polynomials, and so on.
> if your primary purpose for learning linear algebra is to program video games.
What an odd guess. Seriously, I would be surprised if most math teachers didn't mention angles and norms, scalar projections, etc. An important part of math is being able to see things from multiple angles (no pun intended), and this is a useful angle to view the dot product from.
> Linear algebra isn't "about" geometry
Sort of. Linear algebra proper, the study of vector spaces and linear maps between them, is not about geometry, but geometry comes in almost precisely once you equip the vector space with an inner product, such as the dot product. A bare vector space has almost no geometric content, but the inner product gives you lengths, angles, isometries, orthogonality, and all that jazz.
> Strang's teaching goal centers vector spaces and the relationship between spaces.
That's a good goal.
> You need inner products to apply linear transformations with matrices.
I think you have a fundamental misunderstanding of linear algebra here. You do not need an inner product to "apply linear transformations with matrices".
> You basically don't need the angular interpretation... at all? if your goal is to teach linear algebra as a tool for data manipulation
Off the top of my head, cosine similarity? It's not uncommonly used.
But if you're teaching linear algebra for data manipulation, you rarely need the dot product, either. Most "dot products" in data manipulation, like the ones in this article, would be better expressed as row-vector-column-vector matrix products.
> (You need orthogonality, but you didn't say `a⟂b=0`, you said `|a||b|cosθ`).
I said "||a||·||b||·cos(θ) or at least talks about how the dot product relates to parallel and orthogonal vectors". Anyway, it's hard for a person not to interpret orthogonality as a statement about angles, so I'm not sure what distinction you're trying to draw here.
> I'm not rating this blog post "higher" than 3B1B
I guess I misinterpreted "its sauce is stronger", then.
Sorry for any mistakes; this took way too long to type.
I haven't read Strang's book, so I can't comment on that. But yeah, if it never mentions the formula ||a||·||b||·cos(θ) or at least talks about how the dot product relates to parallel and orthogonal vectors, I would consider that a big hole in an introduction to the dot product.
> How would that have fit with the goals of this post?
Because the post is titled "an introduction to linear algebra... the dot product", and this is something that I believe should be in anything that considers itself an introduction to the dot product.
You seem to disagree, and I'd like to ask: why? I think this a fundamental aspect of the dot product, again, just as fundamental as the relationship between complex multiplication and rotation. I think my view is common.
> calling out a blog post
I didn't intend to do anything as strong as "call out" the blog post. I just wanted to express surprise at someone so strongly praising ("its sauce is stronger [than 3B1B's video series]") an alright post.
I agree. I don't think "Linear Algebra Done Right" is a good fit for most people. It's way too dry, and I don't think his crusade against determinants helps the book. I don't know what a good book suggestion would be, though. Maybe just nab the course notes/slides/exercises off some university's website?
> this is a blog post
Blog posts can be and often are amazing.
> My feeling is that a lot of the critique here is really signaling.
Weird accusation, so just to be clear, I haven't done anything serious with anything, ever.