>Personally, I'm looking forward to a world where the very best explanations / analogies can bubble to the top.
Please do keep in mind that there isn't one best explanation per subject, just a "local maximum" explanation that is best to a class of people sharing a similar way of thinking. Personally, the normal explanation of "representing (approximating) a complex cyclic function as a linear combination of complex trigonometric functions" made the most sense, while your explanation reads like a convoluted mess of analogies. Therefore, try to have a few completely different explanations per topic, rather than just the one which makes most intuitive sense to you.
Definitely, appreciate the feedback here. It's easiest to share the explanations that come to me, but I love finding a few different ways to look at things, and as they emerge I like to include them.
As a simple example, here's the formula for adding the numbers 1...n:
The explanation I was originally given (pair the first and last items, and count the pairs) seems gnarly because you have even/odd issues, off-by-one errors, etc. There are others which click better.
I agree here. The solution for me on not quite getting concepts in calculus and engineering was to delve into greater abstraction. When you get linear algebra, you understand the inverse function theorem in analysis. When you understand Hilbert spaces, the Fourier series makes a lot more sense.
A lot of the simple analogies and explanations I can use to talk about determinants or Fourier transforms now I can only conjure because of the complex study taking years to soak through.
Please do keep in mind that there isn't one best explanation per subject, just a "local maximum" explanation that is best to a class of people sharing a similar way of thinking. Personally, the normal explanation of "representing (approximating) a complex cyclic function as a linear combination of complex trigonometric functions" made the most sense, while your explanation reads like a convoluted mess of analogies. Therefore, try to have a few completely different explanations per topic, rather than just the one which makes most intuitive sense to you.