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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 str

• avip 4y ago
  I think you’re confusing proving with understanding. The two are almost orthogonal.
  • posix86 4y ago
    Disagree. If you truly understand something, you must have prooven it to yourself, everything is just a mental help ("donkey bridge" in german) that allows you to remember the statement better - weather it's right or not, you can only know once you've prooven it; and before you did that, it can often happen that your intuition on what's right is actually wrong.
    • adlpz 4y ago
      That makes no sense to me. Or maybe your definition of "understand" is completely unrelated to mine. Under your thesis one cannot "understand" anything physical (as in physics, chemistry, etc) as the underlying cannot be "proven", at all, by definition.
    • chongli 4y ago
      I think a lot of people can understand simple statements in math such as Fermat’s Last Theorem or the Collatz Conjecture but proving them is an entirely different matter. While it may be the case that proving some statements is sufficient to understanding them, I would say it’s never necessary.
      • greenpeas 4y ago
        I think you may be confounding different kinds of understanding. There's a big difference between understanding what a statement is saying, versus understanding why a statement must hold true. And understanding why a statement holds doesn't necessarily have to be a formal proof, it just means that you have convinced yourself that some concepts that you are familiar with behave in a way to support the statement. It can actually happen that following a correct formal proof doesn't automatically help you understand why something is true. And vice-versa, it may happen that when you try to formalize your understanding, you discover that you missed some crucial details. But usually true understanding and formal proofs go hand in hand. P.S: Though as a disclaimer, I don't know maths beyond the undergraduate level, and I'm sure there must be very complicated concepts that mathematicians don't understand, but can reason formally about, as well as concepts that mathematicians feel that they intuitively understand but can't quite prove. Additionaly, there's von Neuman saying "Young man, in mathematics you don't understand things. You just get used to them"
  • mxkopy 4y ago
    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.
• osigurdson 4y ago
  I think a lot of people have heard of the Fourier transform and kind of understand how any signal can be represented by a superposition of sine waves. Attempting to improve the intuition of how the algorithm works isn't a bad thing. The casual reader isn't going to invest the time to learn the pre-requisites so the alternative is nothing at all.
• j7ake 4y ago
  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.
• crispyambulance 4y ago
  > 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.
• mafuyu 4y ago
  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.
• jasode 4y ago
  >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.
  • Schiphol 4y ago
    > It's great that it was "never complicated" for you. I don't think they meant "not complicated to learn", but "never complicated to teach, once its time had arrived in the natural progression of the course".
    • Dudeman112 4y ago
      >but "never complicated to teach, once its time had arrived in the natural progression of the course" Which is, of course, true for give or take all subjects out there
      • adamisom 4y ago
        Indeed: the original comment was not at all implying anything special about FTT. Rather that, perhaps whether we like it or not, knowledge is not very flat; you really should honor (as in: recognize and treat appropriately-nothing magical or moral intended) the difficulty of many topics by doing prerequisite study, or, if you can’t, just accepting that you will never have a good understanding. I don’t think it’s at loggerheads with just-in-time learning or the real opportunity cost of more extensive study. I think it’s just true that hard things are hard whether you like it or not.
  • 4y ago
• sidlls 4y ago
  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.
• anthomtb 4y ago
  Did you miss the first sentence in the post? > If, like me, you struggled to understand the Fourier Transformation when you first learned about it No where does the author imply that he is teaching the Fourier Transform to someone who has never heard of it. I agree with your overall point. Blog posts are not going to teach you difficult mathematics unless they are the length of college textbooks. But a blog post like this is great for reinforcement. If, like me, you are an ECE (Electrical and Computer Engineer) who has written software for the last 15 years, an explanation like the one in the post makes a lot of neurons reconnect.
• Snowbird3999 4y ago
  What works for me is learning a single concept in many different ways. A textbook, a youtube video, a friend explaining it to me... Each next source of material (however casual or formal it is) is more likely make the concept "click", or allow me to understand the concept more efficiently. To that extent, this blog post seems valuable to me. The author is using a language and colors to convey an intuition that I have not precisely seen before.
• evanwise 4y ago
  I would tend to agree. The only people I saw really struggle with learning Fourier series and the Fourier transform were people who had struggled with more basic concepts and failed to internalize them. This kind of explanation might be helpful to build someone's intuition up a bit but is not a substitute for a proper education on the subject and definitely not some magic key to understanding.
• fifilura 4y ago
  I wish my university courses had started with the intuition behind and utility of the functions we were about to learn. Be it linear algebra, differential equations or Fourier transforms. This is what all these blog posts excel with. Of course I got it along the way, but I do believe it would have been easier if the background was something like this.
• georgeburdell 4y ago
  I agree. Way back when I learned the FT, I happened to be taking a signals and statistics class in the same semester and rationalizing the Fourier transform as the correlation between a function and a sinusoid was an incredibly natural mental leap and didn’t require me to hold much additional knowledge in my head
• antegamisou 4y ago
  At last someone said it, thanks. It's bothersome how popularized the notion I'm one,two,three,...,n blog posts/YouTube videos away from fully grasping this complex mathematical concept which not only requires fundamental knowledge I may not be familiar with, but also solving problems/writing code where at first I'll have no idea how is it supposed to be of any use but over time it will eventually 'click'. has become. Beautiful animations and witty narrations are nice, but you're in for a (bad) surprise if you think they're adequate. Also nothing beats good old book -> pencil/paper.
• kansface 4y ago
  I have a degree in physics, but have been a working programmer for 15 years. For me, intuition is the only thing that remains and that is slipping, too. This post is like visiting an old friend I haven’t talked to in as much time.
• jchw 4y ago
  I don't get the point. There really isn't anything particularly inherently special about blog posts as a medium versus say, chapters in a textbook, other than the obvious things. You can, of course, learn about complex subject matter through a blog post. If you find someone with a similar mental model of things to your own, I think you can in fact learn from blog posts easier, as they can get from zero to understanding with less detours. On a similar note, I personally believe there are many concepts that have been explained much better by random YouTubers than academic textbooks. Textbooks are more comprehensive almost always, but having an intuitive understanding of something is obviously more important in many cases than simply remembering a long list of bullet points about it. You can always use reference material later. In real life, memorizing facts on their own is rarely useful. The best answer here is that you should use both, or imo, "all three," of blog posts, video content, and academic textbooks/articles/courses. Taking a variety of approaches helps me get to a mental "click" quicker, personally.
• lattalayta 4y ago
  I feel like I've learned some things from high quality interactive blog posts. These posts from Bartosz Ciechanowski come to mind https://ciechanow.ski/archives/ https://ciechanow.ski/archives/
• ivanhoe 4y ago
  There's a lot of math & physics subjects that I formally learned and passed exams at Uni, but frankly never really fully understood them. I've found clarifications on many of these subjects later on web, in exactly these types of blogs or youtube videos. All you need is one or two core concepts better explained and suddenly you can connect all the dots, and that what this type of content is fantastic for.
• jfarmer 4y ago
  I do think "blog post learning" can work, but agree with you that this ain't it. The "explanation" on the blog post would really only work for someone who more-or-less understood Fourier Series already. You're also right that explanations can't be isolated. I'd go further and say they never are. People only come to understand new things in terms of things they already understand. There's no "explaining X" in isolation, there's only "explaining X in terms of Y." A good explanation either supplies a suitable Y or makes it clear to the reader what Y they'll be relying on. So, even if the author tries to isolate, a successful explanation always relies on collateral information. The only question is whether that collateral information is left to chance or intentionally exploited. What's the "Y" here? Well, the author assumes the reader can make sense of phrases like "energy at a frequency", what it means to "spin your frequency around a circle", "average a bunch of points along a path", etc. That's...a lot. I'd go so far as to say that a reader who can make sense of that probably already understands more fundamental concepts like vector spaces, bases, and Taylor Series. And if they understand those things then there are much more straightforward explanations available!
• TeMPOraL 4y ago
  > Does "blog post learning" ever really work? You mean learning by writing a blog post, or learning by reading a blog post? In both cases, the answer is "yes". > In other words, without having the necessary background at your fingertips it is hard to really grasp the core concepts. That is why, IMHO, reading these blog posts may feel good but will rarely make things really stick. The problem these posts solve, at least for me, is that despite having the necessary background, some concepts didn't "click" in my mind when I first learned them. I found that if I then read a couple different posts on a specific concept, each with slightly different perspective or way of presenting it, one of them will eventually hit the "sweet spot" and make it "click" in context of all the background I already have (and often cascade into making me understand a few more things in the topical background).