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by dkarl
2508 days ago
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John von Neumann famously said that in mathematics you don't understand things, you just get used to them. I think monads are an example of this, and all the attempts to make them intuitive before you use them are a huge waste of time. Many mathematical concepts are like this. Take compactness. At first, the definition of compactness seems a little random, but it's useful for proving things, so you keep using it, and after you do enough proofs you develop an intuition for it. It feels very clear and fundamental instead of random. Once you have this feeling of obviousness, how do you transmit it to the next person? Many things can be explained, but in math it was figured out long ago that at any given time there are many things we don't know how to explain, and aren't sure we ever will be able to explain in a way that transmits understanding faster than experience can instill it. The best thing you can do for someone is give them the definitions and some problems to work on. We can't rule out that someone may eventually come up with a brilliant explanation that provides a shortcut to understanding, but we know from experience that some things persistently defy our efforts to explain them. If hundreds of people's earnest attempts to explain something have failed, then perhaps teachers should keep trying, but learners should not waste their time with these experiments; they should skip the explanations and seek active engagement with the idea through problem solving. That's how I feel about monads. I can't absolutely rule out the possibility that someday an effective way to explain them will be found, but I think we can agree at this point that there is ample evidence that people who want to understand monads should not waste their time waiting for the right analogy to be blogged and posted on HN. They should just start programming, and soon enough they too will feel like a great explanation is on the tip of their tongue. |
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I have had this experience, that I've moved much faster learning to use math tools when a friend much more advanced than me suggested that I can use a tool even if I don't know how it works. It's like if I stopped building a house because I want to see if I can build a hammer myself !
(Well, this is also my experience programming, implementing the low level stuff myself is a much more attractive exercise than actually assembling off-the-shelf parts into something people would actually use!)