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Sorry but can there be more context to why it is a powerful tool?
Of course, the author here isn't really selling anything, at least not to the lay man. He's writing niche articles for a niche audience. That is to say, not me.
https://www.ted.com/talks/simon_sinek_how_great_leaders_insp...
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This is a typical issue with HN posts. Some poor soul wrote a somewhat competent and maybe even lengthy blog post / article about something they really care about and are knowledgeable about. It may be directed at a specific audience, or maybe just screaming into the void to record down some insight they had for themselves to read again later, or similar. And they use a more-than-necessary general title like "the bes…
I'd rather have more submissions like this on the HN frontpage than the slew of entrepreneurship advice (good or bad), programming-languages-du-jour and disguised content marketing. Anyway, the premise that "everything I see has to appeal to me" would best stay on YouTube where it originated.
Parent's concern was for the misleading titles that appear on HN, due to HN's fear of submitters.
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Everything being referenced is stuff you'd learn in a typical technical education as part of either calculus or statistics. Your reply comes off as of defensive in a way that implies that you're shocked some one would know any of this stuff.
My reply stems from enriquto's misunderstanding of the purpose of the article, which is the "typical technical education" itself . It's like they are wondering why the article even exists, and isn't just a one line reference to the julia docs. Clearly there's nothing wrong with already having specific knowledge of a subject, but questioning the purpose of technical education because you already have it is bizarre. Ma…
I'll state my point following your json parser example. If you write an article about the implementation of several json parsers, you may still want to call JSON.parse at the end, as a sanity check that your implementation is working. The function is right there and you may as well say that!
In the present case, since the author has already set-up explicitly Poisson equation as a linear system of equations, it would make sense to call julia's built-in solver. (If only to marvel that it is much, much faster than the simple methods shown before, thus it must make some really fancy stuff inside!)
A friend of mine broke a badminton racket during a match, and I was struck by how the sharply bent and twisted metal rim was transformed into a smooth, continuously double-curved surface by the racket weave. I looked closely at the balance of tension in the woven cord, thought of how it resembles Poisson's equation, and suddenly it all made sense. Edit - it looked something like this: https://thumbs.dreamstime.com/b/…
Some links for people who've never heard of minimal surfaces:
https://en.wikipedia.org/wiki/Minimal_surface
https://minimalsurfaces.blog/ (lots of illustrations)
https://makmanx.github.io/math3435s18/talks/MSE.pdf (brief intro with historical remarks and illustrations)
[0]: More specifically, it's a solution to Plateau's problem: https://en.wikipedia.org/wiki/Plateau%27s_problem
It amazes me just how many key topics were so inaccessible to the majority of the class at engineering school. I base this on observations from group study sessions and the hyper-aggressive test curves.
I knew lots of people who never got the hang of div/grad/curl, or a Jacobians, or eignenvectors, or Z-transforms... These are key engineering concepts, you'd think colleges would bend over backwards to make sure these concepts are learned as succinctly as possible rather than add a curve to a test that makes a 23 out of 100 an "A" grade.
I'm digressing, and complaining, but the counter argument has always been: you're not supposed to learn everything in college, you're supposed to learn how to learn. Sure, right, but who has time to keep learning advanced calculus after college? (Well, I still study math & physics for fun, but over the course of decades, not years.) Not being able to see the world through these lenses I think means missing key engineering perspectives and relationships.
Anyway, very well written article.
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Just to point out, it seems like the author themselves submitted the story to HN. Still I agree with your reasoning, but I think slight clickbaity titles do get clicks which is why we keep seeing them.
Yup. This wouldn’t get nearly the same amount of attention if the title were “Poisson’s equation is the most powerful tool in your toolbox for finding steady-state solutions to the heat equation with arbitrarily placed sources ”
I tried to skim the article, I started to read comments, and it's only now that I've gotten to yours that I have the slightest idea of what this article is even about.
If it wouldn't get as much attention with that title, then perhaps it isn't appropriate for HN in the first place.
My (unorthodox and somewhat rickety) note-taking gizmo uses Poisson's equation to classify (continuously) entries. Basically the note-taking gizmo is a graph. Nodes are given conceptual masses either through pagerank or betweenness centrality (i.e. either through how many random walks or how many shortest paths cross a node). Then we calculate a potential energy (gravity potential) if we by inverting the graph laplac…
Since you have written it as a symmetric, positive definite, sparse linear system, why don't use a standard solver like CHOLMOD which is available in Julia? (and behind octave's anti-slash operator). It should be faster than the ad-hoc single-scale Gauss-Seidel.