Like water through a sieve.
391 karma · joined May 6, 2023
Like water through a sieve.
Emacs folks may also like the Maxima mode, a very capable interface to a full-blown CAS: https://www.emacswiki.org/emacs/MaximaMode
Anecdotally, my personal attempts at incorporating only slightly exotic CASes (Maxima or Sagemath) into calculus courses were met with tepid response at best. Part of the issue was, I believe, that freshmen are rarely interested in setting up software for a non-CS course.
That being said, for slightly higher-level classes it can work quite well as an optional component — I've had really good results with Python projects in an ODE course. Python not being a niche language certainly helped, too.
This description seems to fit Julia really well. What other languages are like this?
Your guess is (largely) correct. For most users, the workflow is exactly as you described:
> They make the notebook, use the build-in R functions and then their work is done.
https://www.dmg.tuwien.ac.at/gruber/gruber_arbeiten/johnelli...
— one elegant trick I remember from there was that the value of a quadratic form with matrix A on vectors u and v (^T for transpose):
u^T A v
is interpreted as the dot product between the matrix A and the tensor product u v^T,
A • (u v^T)
— and dot product • on matrices is just from them being n×n vectors.
With that a lot of things are really nice now, e.g. interiors of ellipsoids correspond to intersections of halfspaces of matrices with the positive semidefinite cone. And halfspaces are simple to reason about and intersect!
This trick is also implicitly in the parent post, of course.
A philosopher interested in the real world: something that became quite a rarity in later times...
Edit: looking further than the abstract, this is rather an exploration of scale necessary for a strong engine. Could go without "without search" in the title I guess.
[1]: IIRC, it also uses a Leela-inspired NN for evaluation.
The anecdote goes that with his eyesight already severely deteriorated, he would dictate papers with a grandkid or two in his lap and a cat on his shoulder.
Clearly, Leibniz notation does not intrinsically contain any deep insights since at one point Leibniz himself was erroneously induced by it to think that d(xy)= d(x)d(y), which is false. Newton on the other hand thought in terms of simple geometric concepts (areas), which make it crystal clear that d(xy) = x d(y) + y d(x).
On the topic of history of early analysis I cannot recommend enough this collection of anecdotes from Arnold:
Such a beautiful hermetic formula. It could totally describe a god in Lovecraftian universe. That, and also the fact that a minor deity was so easily transplanted from an Egyptian myth into a Japanese video game to me illustrates the amazing unity of human culture.
I mean, I get that a lot of biblical material was lifted from e.g. the myth of Osiris, but this is on another level.
It should be understood though that there are cases when math(-like) language is abused, leading to overcomplication and obscurantism [1]. In mathematics, there is always the temptation of formalizing for formalization's sake. Indeed, 99% of pure math is non-constructive ("there exists a group such that", "the algorithm converges in O(N) steps"), as opposed to the practical CS and applied math ("here are the runtimes on real world data") which are likely the primary concerns of the HN crowd.
None of this can diminish the sheer impractical appeal of pure math and pure CS, not unlike that of poetry, but I would rather not oversell either of the two.
[1] A good illustration is a rant by Cosma Shalizi at http://bactra.org/notebooks/nn-attention-and-transformers.ht..., recently posted on HN.
For metric spaces, sequential and usual compactness coincide:
https://archive.org/details/sovietbusstops0000herw
Edit: I see that the book about Spomeniks and the one linked above were actually both released by the same publisher — Fuel.
> there were many in Yugoslavia who refused to fully integrate into this communist-led multi-cultural society [...] During the hey-day of Yugoslavia, this resentment and anger was very much kept in check by the Yugoslavian government's intense efforts in stamping out inter-ethnic retaliations, nationalism or religious hatred in any form, accompanied by the intense promotion of the ideals of 'Brotherhood and Unity'.
— to me read like they celebrate the Yugoslav communists. Would be curious to know if it's just me, or others also share the impression.
Borland really had a series of these fantastic products, it's a shame they are no more. The only modern company in this space is JetBrains, it seems, so the niche is small.
I swear I had to read that twice to stop seeing "alternatives to Emacs". I'll see myself out now.
(Doom Emacs is really nice though, and modal editing does help with key bindings, just as a sibling comment points out.)
As to the rest of it — authors routinely revise their works. The very notion that readers (or critics) get any say in this strikes me as bizarre. They get to observe the process and decide which version they like better, but nothing more. Ne supra crepidam.
https://www.bbc.co.uk/programmes/m0016ptt
If I recall correctly, the panelists express the idea that it might have been the feature that impressed the Romans most and served as a powerful ad for this new religion.
Philosophy is science in the circumstances of insufficient knowledge. That is, given insufficient data it may still be beneficial to ponder possible future directions of research, contemplate lines of attack on long-standing questions, or even determine beforehand how these big questions should be posed. All of these circumscientific activities and thinking together constitute philosophy.
There's sci-fi of course, but also crime fiction, "realistic" fiction, philosophy essays. Further, something not easily gleaned from the table is that his sci-fi can be humorous, horror-y, thriller-y, book-for-kids-y, etc.