6 ms·

Shameless plug, I write about math on BetterExplained.com For each symbol, I try to make an analogy. For "e", for example, I have the notion of "continuous gro

• catnaroek 9y ago
  > For each symbol, I try to make an analogy. Analogies are utterly unhelpful without a thorough understanding of the actual definitions.
  • kalid 9y ago
    Analogies on their own are limited if you don't continue to the technical definition. They are a raft to cross the river.
    • signa11 9y ago
      > ... They are a raft to cross the river. or rather like net to catch the fish. once you have the fish, you can forget about the net. this is not far removed from words, which are used to convey meaning. once you have meaning you can forget about the words ;) edit-001 : fmt changes.
      • pbhjpbhj 9y ago
        >> ... They are a raft to cross the river. >or rather like net to catch the fish. once you have the fish, you can forget about the net. So you can forget about the net ... like a raft to cross a river?! ;o)
    • catnaroek 9y ago
      When you are a student, rather than a researcher, formal definitions must come first, and intuition can be developed later. Otherwise, you are just allowing yourself to say nonsense.
      • tw1010 9y ago
        I worry about the fact that you're being downvoted, because what you're saying is utterly crucial and important. I fear those who ignore it will waste a lot of time with really misguided ways of doing mathematics. The analogy approach works for programming, but it's not applicable to seriously studying mathematics.
        • jonnybgood 9y ago
          I wouldn’t dismiss analogy so easily. George Polya opened my eyes to the power of analogy in math. I can’t recommend his “Mathematics and Plausible Reasoning” enough.
          • tw1010 9y ago
            Polya's text was targeted towards researchers and people who already understood the basics pretty well. But I don't think the analogy approach is valid (or at least, not recommended) in the context of this thread, where the parent seemed to assume that the audience wasn't even particularly comfortable with limits. It can be a dangerous and seductively-easy path to go down, is all I'm saying. You're not going to understand mathematics without having a firm firm grasp of the rigorous definitions and by doing mountains of exercises (where it will often be quickly apparent that using an analogy is not sufficient).
        • klibertp 9y ago
          > The analogy approach works for programming, but it's not applicable to seriously studying mathematics. Why?
          • catnaroek 9y ago
• shaggyfrog 9y ago
  I like that figure you made! Though shouldn't the whole 1/n fraction be red and not just the numerator?
  • kalid 9y ago
    Thanks! So, the red 1 represents the 100% interest we intend to earn; the pink n in the denominator represents the compounding pieces we divide it into. For example, an approximation of e would be (1 + .01)^100, where the 100% interest had been chopped into 100 separate segments of 1%.
• klibertp 9y ago
  Just wanted to thank you for a great job you do on BetterExplained. I was able to understand and put to use some concepts only thanks to your articles, most recently it was Fourier transform. I'd be much better at math if people writing educational materials realized that there are more effective ways to teach (and to learn) than what they had experienced. Thank you!
  • kalid 9y ago
    I appreciate it, thank you! I have a similar wish, hoping more people would share math in the way that truly helps them.