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But a good teacher can be judged on how they explain monads, so I'd like this lesson to be exemplary. If anyone has any suggestions for improvements, I'd love to know!
The typical explanation by analogy obfuscates ‚why’. Your explanation targets the why, which is much more useful than topological comparisons.
It always struck me that most of the explanations that say "a monad is like an X" would be more correct to say "X has a monad", in which case you might as well use List or Try as examples. And I think that if there were a perfect analogy in the real world, we'd know it by now...
I love seeing first principal thinking vs thinking by analogy applied to education, thank you @propensive for your hard work on this!
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