Apropos of nothing, some of my first programming lessons were FORTRAN programs from my dads old engineering textbooks. The book’s graphics showed them being handwritten on graph paper and even showed the punch cards they would ultimately be put on.
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.
It is easier to study from a theoretical point of view (easier that the heat or the wave equation: [1], Ch. 2), and it's easier to implement a solving method. When you are learning the finite element method, this is one of the first examples that people use to test if they got the right implementation.
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.
If you take the divergence of the incompressible Navier-Stokes equations you get a Poisson equation for the pressure, with a function of velocity on the RHS. So it’s important in fluid dynamics.
The opening of this article had me recalling an old TED talk: "People don't buy what you do, they buy why you do it."
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.
It's a simple and general method that works in many domains, which is an usual combination.
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.
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.
I didn't intend to demand "everything I see has to appeal to me". I was merely pointing out that the meaning and impact of a headline are relative to the target audience and this was an example that illustrated the difference. With the effect that somebody somewhat rightfully asked "eh what is this about again"?
The HN crowd has a different average toolbox than the article's author, so the apparent mismatch between headline and article content was confusing.
It IS a good article, but the audience of the article is fairly specific yet left unspecified.
As a general principal in technical writing it is advisable to start with a "why you should care" statement because this naturally informs the reader about the context.
Is the second section “when would I use this” sufficient to provide a “why you should care statement”? Or is there a more common way to call this out in technical writing? Perhaps an “intended audience” or “necessary prerequisites”?
I mean there is nothing "wrong" with starting at the 2nd paragraph (and that was was just for the more limited Laplace version of Poisson's), its just not generally the most effective writing style. Yes, there is some subjectivity here, but writing is hard, and it is only through criticism that we learn to be better technical writers.
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.
There should exist a subreddit for exactly these type of articles which are in depth. Who know article like this may want someone to learn something entirely different than their domain and then they end up applying it in their domain in a whole new way.
From the poster sharer username here in HN it seems "the poor author" is also the one sharing it here, so it seems this blog post is at least partly directed to the general HN audience, not like the hypothetical situation you are placing here. So the whole "It's just not for the overall HN crowd" is probably not a valid point?
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.
What's getting confusing with this discussion is that the title has changed. Now it's just "Poisson's Equation". But before it was "Most Powerful Tool not yet in your Toolbox" which was really off topic for a mainly sw dev crowd.
That the author himself submitted it (under that original title?) would then be his own "fault". But my general original point remains.
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.
The examples are about heat transfer, because it is an intuitive concept for most people, but as the article explains Poisson's Equation and these methods can be applied to a broad range of problems.
Yes, I would love it if HN had optional descriptive titles as subtitles to the main story titles (which would then always be the title given by the author at the time of submission).
Well said. There is also the other extreme, where articles of the kind you described don't "use a more-than-necessary general title" but one that is so specific and narrow that it will never fly on HN, even if the content is otherwise a good fit for a valuable HN discussion.
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.
> For an aerospace engineer this all makes a lot of sense and is a super great tool, I'm sure.
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.
Except prionassembly's post here shows it's WAY more useful than the original "model physical things" of the original article. Also glad this is here, if only to surface such interesting things!
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.