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Poisson's Equation

mattferraro.dev

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Re: Poisson's Equation

#81

Post by alisonkisk »

SavantIdiot wrote: post #56

I could have used this 32(!) years ago when I was struggling in college. (This and 3b1b.) 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 k…

Your 30 years of experience is why the article makes so much sense. If you saw this in college you wouldn't have also learned everything else about div and grad.

> these concepts are learned as succinctly

? Succinctness is *why" you didn't learn multiple interpretations of everything.

Re: Poisson's Equation

#82

Post by SavantIdiot »

lordnacho wrote: post #63
SavantIdiot wrote: post #56

I could have used this 32(!) years ago when I was struggling in college. (This and 3b1b.) 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 k…

I feel the same. How can it be that I went to a world famous institution providing 2-to-1 student-teacher ratios, but I still think the best explanations are these modern internet explanations? I guess the best explanations just bubble up in the modern environment. > you're not supposed to learn everything in college, you're supposed to learn how to learn But to learn how to learn, you gotta learn some things to a so…

> Just imagine coding without access to StackOverflow.

That was the beginning of my career in the PC industry!

C compilers for PCs were in their infancy, so all of the code I was writing was x86 assembly using MASM 6 on MS-DOS 5.2 (hello TSRs and config.sys).

I forget the company, but some tech house published a giant 500 page PC encyclopedia every year that listed all of the x86 CPU instructions, IO ports, interrupts, DOS interrupts, etc. The last issue I had was white with pink lines on it and weighed about 3 kilos! Then the internet showed up and that all went away.

Well, except the mentors. Mentors will always be a step-function way to learn new material.

Re: Poisson's Equation

#83

Post by cornel_io »

> This oval (called a separatrix) has the special property that no wind flows through it at all. It acts just like a solid surface. We have already assembled a reasonably accurate simulation of how air flows around an ellipse in some confined space like a wind tunnel!

My understanding of airflow simulation (undergrad-level at best) is that the correct boundary condition is almost without exception the no-slip one: air should be stationary at the surface of each object, not just have zero flow across it.

Am I correct that the calculation mentioned above really only applies to the "dry liquid" scenario where there is no drag and zero viscosity?

Re: Poisson's Equation

#84

Post by SavantIdiot »

alisonkisk wrote: post #81
SavantIdiot wrote: post #56

I could have used this 32(!) years ago when I was struggling in college. (This and 3b1b.) 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 k…

Your 30 years of experience is why the article makes so much sense. If you saw this in college you wouldn't have also learned everything else about div and grad. > these concepts are learned as succinctly ? Succinctness is *why" you didn't learn multiple interpretations of everything.

> ? Succinctness is *why" you didn't learn multiple interpretations of everything.

Good catch. I think that was the wrong word because I was learning s-transforms in three classes sophomore year: differential calculus, linear systems, and thermodynamics. It was the opposite of succinct because the same concept was being thrown at me in three different classes from three different perspectives.

Re: Poisson's Equation

#86

Post by alisonkisk »

infogulch wrote: post #37
burnished wrote: post #21

Earlier quoted context omitted.

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…

Please stop attacking other commenters. instead of attacking (the same person, twice!), try to understand what is being said, or ask questions.

Re: Poisson's Equation

#87

Post by alisonkisk »

infogulch wrote: post #80
enriquto wrote: post #54

Earlier quoted context omitted.

Sorry for the misunderstanding, then. It was not at all my purpose to disparage this article. It is a lovely article and very clearly written and illustrated. 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 ther…

I agree with your point that it may be valuable to the reader to also mention common libraries or built-ins that solve the same problem that was discussed in the article somewhere near the end. More generally, linking to sources, docs, related work, or next steps can be very nice for readers to further their education. Framing your original comments with "the author should also mention... a standard solver like CHOLM…

It's your job to control your snark, not anyone else's job.

Re: Poisson's Equation

#88

Post by sdenton4 »

lordnacho wrote: post #63
SavantIdiot wrote: post #56

I could have used this 32(!) years ago when I was struggling in college. (This and 3b1b.) 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 k…

I feel the same. How can it be that I went to a world famous institution providing 2-to-1 student-teacher ratios, but I still think the best explanations are these modern internet explanations? I guess the best explanations just bubble up in the modern environment. > you're not supposed to learn everything in college, you're supposed to learn how to learn But to learn how to learn, you gotta learn some things to a so…

Interesting to think a bit about student/teacher ratios (STR).

The up-side is that with a low STR (2:1), the teacher can adapt to the particular strengths and weaknesses of the students, to get the best reinforcement. The /downside/ is that the students will typically also have fewer teachers overall, and are maybe stuck with a bad one. (This is the problem of bad grad school advisors in a nutshell...) In this world, teachers are very expensive, though, so we end up with students competing for access to good teachers, by paying super-high tuitions, dedicating their early childhood to olympic-level basketweaving, etc.

In the medium-STR regime (30:1 or 100:1), we get the worst case: There's no teacher adaptation to individual students, but teachers are still the bottleneck.

The internet has something to say about extremely high STR (1MM:1). In this regime, things flip and any teacher can teach every student: Teachers are no longer scarce, and so have to compete on giving the best instruction. Instruction quality increases as a result. And on the flip side, there's no student competition, which /maybe/ causes student quality to drop.

Re: Poisson's Equation

#89

Post by mensetmanusman »

lordnacho wrote: post #63
SavantIdiot wrote: post #56

I could have used this 32(!) years ago when I was struggling in college. (This and 3b1b.) 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 k…

I feel the same. How can it be that I went to a world famous institution providing 2-to-1 student-teacher ratios, but I still think the best explanations are these modern internet explanations? I guess the best explanations just bubble up in the modern environment. > you're not supposed to learn everything in college, you're supposed to learn how to learn But to learn how to learn, you gotta learn some things to a so…

The answer is statistics: what is more likely, that the best explainer of a certain topic is within a group of people you have access to, or that person is somewhere else in the world?

This is very analogous to the problem industrial research groups face trying to answer a certain problem, e.g. ‘how do we ensure that our team is the most likely to solve a particular problem first?’

This is why start up acquisitions are so common even among the best funded tech companies.

Re: Poisson's Equation

#90

Post by sdenton4 »

SavantIdiot wrote: post #84
alisonkisk wrote: post #81

Earlier quoted context omitted.

Your 30 years of experience is why the article makes so much sense. If you saw this in college you wouldn't have also learned everything else about div and grad. > these concepts are learned as succinctly ? Succinctness is *why" you didn't learn multiple interpretations of everything.

> ? Succinctness is *why" you didn't learn multiple interpretations of everything. Good catch. I think that was the wrong word because I was learning s-transforms in three classes sophomore year: differential calculus, linear systems, and thermodynamics. It was the opposite of succinct because the same concept was being thrown at me in three different classes from three different perspectives.

to throw one other, maybe-less-obvious, spin on it:

When you take a class, you see one wrong way to do things. When you teach a class, you see fifty wrong ways to do things.

Puzzling through all the different wrongs ways to think about a problem really helps cement the core ideas... And first-year calc students are masters of creating interesting-but-wrong interpretations.

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