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Wow... you left me wondering why signal processing teachers in college don't teach Kalman Filters with this simplicity. I know mathematical concepts are best ta

Wow... you left me wondering why signal processing teachers in college don't teach Kalman Filters with this simplicity. I know mathematical concepts are best taught mathematically, but that does led to information loss for those who don't have the background requisites. I used to teach Discrete Cosine Transform and Wavelet Transform through images alone and would always find this teaching method of "intuition before rigor" work better than the other way around.

kccqzy 3y ago
Totally agreed. One of the favorite professors in college would introduce a theorem, and instead of jumping into proving it, would first show us useful applications of the theorem, and then prove it afterwards.
- _a_a_a_ 3y ago
  Aw god, Yes, Yes, Yes! I understand applications not abstractions so show me it's value and I'll understand it immediately, or give me a massive motivation to understand it if I don't. If they'd taken that approach at my schools and university I'd have been so much better off.
- stjohnswarts 3y ago
  This is exactly what I did as a grad student when I taught classes for my prof. She preferred bottom up and I preferred top down. I wanted to give people a reason for learning what they were getting ready to learn rather than "let's start from first principles" that almost all my professors wanted to do.
  - p1necone 3y ago
    I prefer the exact same approach for learning to play board games too. Your 20 minutes of rules explanation will go completely over my head unless you start with "the goal/win condition of the game is to get more points/reach the end faster/collect all the macguffins".
    - djmips 3y ago
      yup. I have the same filter.
- FractalHQ 3y ago
  I can _only_ learn top-down. Facts without context are much less interesting and much more difficult to internalize. The incentive to understand, inspired by said context, is a prerequisite to mustering the motivation needed to to truly learn with sustained focus without losing interest. My ADHD brain will stop cooperating otherwise, and I’ll find myself daydreaming against my will!
deleted 3y ago
[deleted]
anthomtb 3y ago
> why signal processing teachers in college don't teach Kalman Filters with this simplicity > those who don't have the background requisites Any college student studying signal processing should have the background prerequisites. That said, it is easy to forget fundamentals. I have a couple theories for why professors don't use the intuition-before-rigor approach. 1) The professors themselves do not have great intuition but rather deep expertise in manipulating numbers and equations. Unlikely theory, but possible. 2) Professors do not generally get rewarded for their teaching prowess. And breaking mathematical concepts down to an intuitive level requires quite a lot of work and time better spent writing grant proposals or bugging your doctoral students. Cynical theory but probably true in many cases. 3) Once you understand the math, it is so much easier than the intuitive approach that the lazy human brain will not allow you to go back to "the hard way". I like to think this is the primary driver of skipping an intuitive teaching approach. I would say #3 applies much more broadly than mathematical education. It is the difference between expertise and pedagogy. That is to say being an expert in a thing is a completely different skill than teaching others to become competent at the thing. Say you want to improve your golf game with better drives - should you learn from the guy at the range who hits the ball the farthest? Probably not. You should figure out the guy who has improved his drive the most. Eg, the guy who started out driving 100 yards and now consistently hits 300 is better to learn from than the guy who is hitting 350. (Credit Tim Ferriss for driving this concept into my head).
- sn41 3y ago
  Academic here. In my experience, many experts in any given area have massive amounts of intuition about their own area. But keep in mind that we do have to end up teaching outside the area. So it's safer to teach technicalities rather than a (most probably incorrect) intuition. Some other issues: - in many subjects, it is dangerous to work with the wrong intuition - they not only do not give a clear picture, they actually give you the false picture. - even though math gets a bad rep, I think the only reason we are able to work with high-dimensional matrices and vectors is because we let go of geometric imagery at some point. Most people, including myself, have a hard time visualizing even 4 dimensions.
  - 3y ago
dayjaby 3y ago
I remember some online MIT lectures that try to sharpen your intuition without using any formulas.

kccqzy 3y ago

Totally agreed. One of the favorite professors in college would introduce a theorem, and instead of jumping into proving it, would first show us useful applications of the theorem, and then prove it afterwards.

_a_a_a_ 3y ago
Aw god, Yes, Yes, Yes! I understand applications not abstractions so show me it's value and I'll understand it immediately, or give me a massive motivation to understand it if I don't. If they'd taken that approach at my schools and university I'd have been so much better off.
stjohnswarts 3y ago
This is exactly what I did as a grad student when I taught classes for my prof. She preferred bottom up and I preferred top down. I wanted to give people a reason for learning what they were getting ready to learn rather than "let's start from first principles" that almost all my professors wanted to do.
- p1necone 3y ago
  I prefer the exact same approach for learning to play board games too. Your 20 minutes of rules explanation will go completely over my head unless you start with "the goal/win condition of the game is to get more points/reach the end faster/collect all the macguffins".
  - djmips 3y ago
    yup. I have the same filter.
FractalHQ 3y ago
I can _only_ learn top-down. Facts without context are much less interesting and much more difficult to internalize. The incentive to understand, inspired by said context, is a prerequisite to mustering the motivation needed to to truly learn with sustained focus without losing interest. My ADHD brain will stop cooperating otherwise, and I’ll find myself daydreaming against my will!

deleted 3y ago

[deleted]

anthomtb 3y ago

> why signal processing teachers in college don't teach Kalman Filters with this simplicity > those who don't have the background requisites Any college student studying signal processing should have the background prerequisites. That said, it is easy to forget fundamentals. I have a couple theories for why professors don't use the intuition-before-rigor approach. 1) The professors themselves do not have great intuition but rather deep expertise in manipulating numbers and equations. Unlikely theory, but possible. 2) Professors do not generally get rewarded for their teaching prowess. And breaking mathematical concepts down to an intuitive level requires quite a lot of work and time better spent writing grant proposals or bugging your doctoral students. Cynical theory but probably true in many cases. 3) Once you understand the math, it is so much easier than the intuitive approach that the lazy human brain will not allow you to go back to "the hard way". I like to think this is the primary driver of skipping an intuitive teaching approach. I would say #3 applies much more broadly than mathematical education. It is the difference between expertise and pedagogy. That is to say being an expert in a thing is a completely different skill than teaching others to become competent at the thing. Say you want to improve your golf game with better drives - should you learn from the guy at the range who hits the ball the farthest? Probably not. You should figure out the guy who has improved his drive the most. Eg, the guy who started out driving 100 yards and now consistently hits 300 is better to learn from than the guy who is hitting 350. (Credit Tim Ferriss for driving this concept into my head).

sn41 3y ago
Academic here. In my experience, many experts in any given area have massive amounts of intuition about their own area. But keep in mind that we do have to end up teaching outside the area. So it's safer to teach technicalities rather than a (most probably incorrect) intuition. Some other issues: - in many subjects, it is dangerous to work with the wrong intuition - they not only do not give a clear picture, they actually give you the false picture. - even though math gets a bad rep, I think the only reason we are able to work with high-dimensional matrices and vectors is because we let go of geometric imagery at some point. Most people, including myself, have a hard time visualizing even 4 dimensions.
- 3y ago

dayjaby 3y ago

I remember some online MIT lectures that try to sharpen your intuition without using any formulas.