Sorry but can there be more context to why it is a powerful tool?
One of the most impressive programs solved Laplaces equation for heat flow in a pipe. They used some mysterious plotting library that put ASCII art to draw contour lines and output directly to a line printer. I thought it was the coolest thing ever, but it was hard for a high school kid to understand.
Over the years I’ve thought of writing that program in a modern language, but it was never worth the time and effort to go over that FORTRAN program in detail. Numerical methods are too often explained from the point of view of mathematicians and engineers, and not computer programmers.
The blog post here is 1000x more readable and much higher quality and does a lot to demystify the subject. I especially like his progression from simple brute force methods to more efficient solutions…which is the natural way to learn. His comment about “Laplace’s equation just means every point is the average of its neighbours” is perfect.
Believe or it not I was in need of just such a tutorial … for something I’ve been thinking about at work. His article really hit the spot and I’m grateful for it.
Now, I wonder if the author regards it important in his particular area (aerospace engineering), I'm new to the field so I don't see how. Right now I'm reading a book [0] on models to solve problems concerning aerospace applications and they mostly use a simplified form of the Navier-Stokes equations together with some elasticity assumptions.
[0] Fluid Structure Interacion, Morand-Ohayon.
[1] Partial Differential Equations, Evans.
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...
The other ways of solving the example of arbitrary heat sources and sinks on a plate range from hacky combinations of simpler methods, to tedious math, to complicated general methods. If you switch from heat to pressure distribution, you'd have the same types of options, but the specific methods would be different.
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 best tool you'll ever see" with "you" meaning either just themselves or a narrow target audience or so.
And then somebody comes along who finds it interesting, submits it to HN, it makes front page, and now it looks like the poor author with their more-general-than-needed title is making a general statement about sth for the changed audience which is the HN crowd, but which is distinctly different from the original target audience.
Case in point: The articles author self describes as: "I'm an aerospace engineer that writes software. I love math and science, and I have two cats."
For an aerospace engineer this all makes a lot of sense and is a super great tool, I'm sure. It's just not for the overall HN crowd. And it's not the authors fault.
Anyway, the premise that "everything I see has to appeal to me" would best stay on YouTube where it originated.
The HN crowd has a different average toolbox than the article's author, so the apparent mismatch between headline and article content was confusing.
The first paragraph of the conclusion would have better served as the Introductory remark: "Poisson's equation comes up in many domains. Once you know how to recognize it and solve it, you will be capable of simulating a very wide range of physical phenomena." That is a great sentence. I'm interested now, and I know its context.
Hence the line of questioning. Thanks for the response!
Parent's concern was for the misleading titles that appear on HN, due to HN's fear of submitters.
I found it a throwback to my university years, but I did study Industrial Engineering with thermodynamics, fluid mechanics and whatnot so I did find it interesting. I'm pretty sure it's usable by a bunch of people in HN as well in many fields where software intends to emulate the real world, like designing a smart appliance, games, VR, etc.
That the author himself submitted it (under that original title?) would then be his own "fault". But my general original point remains.
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.
The dilemma with titles is that most of them fall into one of two categories:
- titles where the author didn't put much effort into
- titles where the author tried too hard
The first category is often confusing because the article doesn't fit the title well. The second category often ends up as clickbait.
The article seems like a decent introduction to the Poisson-equation. But the original title was very misleading.
Because the Poisson-equation isn't some super-useful tool so much as a Day-1 topic discussed in intro-level classes. It's a really simple equation compared to others used in Engineering, Math, and Physics, so it's often introduced as a starting point.