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I think it has much to do with the abstractness of mathematics (especially category theory). Some just have a hard time anchoring the ideas to something concret

by ch 11y ago

I think it has much to do with the abstractness of mathematics (especially category theory). Some just have a hard time anchoring the ideas to something concrete, and they are in need of that anchoring to make the ideas stick. With engineering and physics equations there is always something physical to relate them to (at least somewhere in the universe(s)) -- not to say there aren't harder equations to grasp in those fields too, but again that is typically trending into the more abstract (less macro) areas of the field. The trouble with math is sometimes you just have to work through equations enough until you form some intuition about how they work. Some folks just want to skip that step and others Oblidge them by assisting their mental model with metaphors which seem to never be universal enough -- if it were it would just be math.

GreaterFool 11y ago
Just thought about something that I think is analogous to explaining monads. I remember reading few articles about "core math" in the States and it had example problems related to addition, subtraction, multiplication. The complaint was that those problems where incomprehensible gibberish and kids and adults alike had really hard time figuring them out. From what I recall the core of the issue was that the question authors had some specific mental model of how addition and multiplication works and the questions were structured in a way that required figuring out what that model was (otherwise it was very hard to understand what was being asked). Why does 2 + 3 = 5? Well, because it does. I don't even know what my mental model of addition is. I just do it. I stared at it long enough as a kid and I developed neural circuits that compute the result. Instead if I asked: I have two stars in a box. How many squares do I have to put in the box to have 5 shapes? | * * | + | ??? | = | * * # # # | Which is how I recall those weird maths questions were structured. Now you a have a (terrible IMHO) model of addition. That's what I think those monad tutorials do for you.
- TuringTest 11y ago
  In order to first learning how to add, examples with apples and bananas are helpful. Learning happens by relating some new concepts to something you already know; that applies also to monads. Those monad metaphors provide the same benefit. Even if some intuitions are wrong and you still need to learn the match to get the whole picture, at least you get a sense of (partial) understanding and purpose during the whole learning process thanks to the metaphor, instead of feeling lost the whole time.

by ch 11y ago

GreaterFool 11y ago

Just thought about something that I think is analogous to explaining monads. I remember reading few articles about "core math" in the States and it had example problems related to addition, subtraction, multiplication. The complaint was that those problems where incomprehensible gibberish and kids and adults alike had really hard time figuring them out. From what I recall the core of the issue was that the question authors had some specific mental model of how addition and multiplication works and the questions were structured in a way that required figuring out what that model was (otherwise it was very hard to understand what was being asked). Why does 2 + 3 = 5? Well, because it does. I don't even know what my mental model of addition is. I just do it. I stared at it long enough as a kid and I developed neural circuits that compute the result. Instead if I asked: I have two stars in a box. How many squares do I have to put in the box to have 5 shapes? | * * | + | ??? | = | * * # # # | Which is how I recall those weird maths questions were structured. Now you a have a (terrible IMHO) model of addition. That's what I think those monad tutorials do for you.

TuringTest 11y ago
In order to first learning how to add, examples with apples and bananas are helpful. Learning happens by relating some new concepts to something you already know; that applies also to monads. Those monad metaphors provide the same benefit. Even if some intuitions are wrong and you still need to learn the match to get the whole picture, at least you get a sense of (partial) understanding and purpose during the whole learning process thanks to the metaphor, instead of feeling lost the whole time.