Does "blog post learning" ever really work? I have taught these kind of undergraduate subjects and, in the context of a course , the Fourier transform never struck me as something very complicated. First, it feels completely natural to write down a Fourier decomposition for periodic functions; the inverse transform to determine the coefficient is just (real or complex) calculus; and all that is left is to convince th…
I find them excellent if you’ve learned the technical details already in a book or by yourself. Blog posts often are high level and can give alternative perspectives on the same problem.
They’re also excellent to motivate a problem so the reader can find the technical details elsewhere.
This reminds me of an old joke in the Haskell community, where people who struggled to understand Monads would finally get it after a while, and would assume that whatever the last sentence they heard was the only necessary one for the explanation.
This is very much called out in the Monad Burrito Tutorial Fallacy[1]. [1]: https://byorgey.wordpress.com/2009/01/12/abstraction-intuiti...
One of the best explanations of monads I saw was actually using Python.
This reminds me of an old joke in the Haskell community, where people who struggled to understand Monads would finally get it after a while, and would assume that whatever the last sentence they heard was the only necessary one for the explanation.
I’ve understood monads multiple times in my life, but each time that understanding was so fragile that it crumbled when I tried explaining to someone else. I’m currently in a phase where I don’t understand them.
I think it's one of those things you just have to understand through practice.
Does "blog post learning" ever really work? I have taught these kind of undergraduate subjects and, in the context of a course , the Fourier transform never struck me as something very complicated. First, it feels completely natural to write down a Fourier decomposition for periodic functions; the inverse transform to determine the coefficient is just (real or complex) calculus; and all that is left is to convince th…
I think you’re confusing proving with understanding . The two are almost orthogonal.
I think you're confusing understanding with intuition. Which is fair; I'd say understanding builds to intuition as it's accessed more. The line is blurry at points.
Does "blog post learning" ever really work? I have taught these kind of undergraduate subjects and, in the context of a course , the Fourier transform never struck me as something very complicated. First, it feels completely natural to write down a Fourier decomposition for periodic functions; the inverse transform to determine the coefficient is just (real or complex) calculus; and all that is left is to convince th…
> Does "blog post learning" ever really work?
It depends on what the intention is. Is it to promote comprehensive understanding, proof, and the ability to then apply the concept in all situations? Then no.
Is it just to point out something interesting a make a point? Sure. There's nothing wrong with that. It's OK to explore aspects of a subject without a dense canonical treatise. There's a time and place for all sorts of explanations.
Then you have to get into why you are talking about sines and cosines, adding unnecessary complexity to the explanation. The OP is better. It's the frequency that matters for intuiook, the shape of the periodic function is a technical detail.
Sines and cosines are the best choice here because they're the "elementary periodic function" for a given frequency: the sum of two (possibly scaled and shifted) sinusoids at some frequency is also a (scaled and shifted) sinusoid at the same frequency. For other shapes of periodic function it's not true: for example, if you sum two triangle waves of the same frequency but offset from each other, you'll get a shape th…
Minor note: "sinusoids" (as you say yourself in your final sentence) is enough. No need to mention sines & cosines as distinct types.
Does "blog post learning" ever really work? I have taught these kind of undergraduate subjects and, in the context of a course , the Fourier transform never struck me as something very complicated. First, it feels completely natural to write down a Fourier decomposition for periodic functions; the inverse transform to determine the coefficient is just (real or complex) calculus; and all that is left is to convince th…
I mean, it's no replacement for learning something rigorously, but I still find little snippets like this helpful for building intuition. Frankly, I'm not really great at rigor myself, and for areas that aren't my areas of expertise (like signals & systems), intuition is all I really have to go off of. I took undergrad signals & systems years ago and probably could not say anything coherent about the Fourier transform today. Still had enough intuition kicking around somewhere to get the SNR of this ADC signal down via oversampling and an IIR filter, though. I remember churning through blog posts for things like PID loops and Kalman filters as a teen, and eventually got to the point where I kinda understood them. But then when it came time to actually learning them, having that small bit of background helped immensely, since I didn't have to build that basic intuition in the span of a single semester course.
Does "blog post learning" ever really work? I have taught these kind of undergraduate subjects and, in the context of a course , the Fourier transform never struck me as something very complicated. First, it feels completely natural to write down a Fourier decomposition for periodic functions; the inverse transform to determine the coefficient is just (real or complex) calculus; and all that is left is to convince th…
>I have taught these kind of undergraduate subjects and, in the context of a course, the Fourier transform never struck me as something very complicated.
It's great that it was "never complicated" for you. In contrast, the author (David Smith) of this blog post admits that he initially struggled with the Fourier Transform -- and wants to share some insights he gained after he understood it.
He has already graduated with a degree in statistics and computer science and also developed add-on software packages for R so he presumably first got exposed to FT within the _context_ of a college course. So he actually did what you suggested. Nevertheless, he wants to share why some supplementary material he didn't initially have might be helpful to others.
Alternative presentations of topics can sometimes flip the "light bulb" in some brains. I don't think it's a useless blog post.
Does "blog post learning" ever really work? I have taught these kind of undergraduate subjects and, in the context of a course , the Fourier transform never struck me as something very complicated. First, it feels completely natural to write down a Fourier decomposition for periodic functions; the inverse transform to determine the coefficient is just (real or complex) calculus; and all that is left is to convince th…
This is why it’s rare as good Carolina barbecue to find a person self-educated in these topics who also truly understands the material. At least in my experience.
It took me an embarrassingly long time to realize that it was a joke when people said "It's always the last place you look." Like well into my teens. But ever since I figured it out, I always look at least one more place after finding something.
I think that there are many people who don't recognize it as a joke and pass it on as great wisdom. I was also pretty old when I realized the tautology.
If you're disorganized, you'll search in random places until you find it. Joke applies.
But if you are organized, you'll start with the most likely place and progress to increasingly less likely places. When you find it, there's no surprise, and no one gets much of a chuckle over your efforts.
If you don't understand the problem space, then saying "That's the last place I would have looked!" is an expression of exasperation about your lack of knowledge.