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0 pointsjimhefferon6y ago0 comments

For sure there is an effect on Reddit and other places where someone will post a question such as, "I'm having trouble with my Calc class, what is a good book?" and people seriously answer Calculus on Manifolds.

Now, CoM is a classic, a real great book, but it is useful only to people who have reached a certain level of mathematical maturity. That, presumably, is not the questioner.

A version of this is that I also see people who write, "I didn't understand this topic when I took the course but now years later, I see it is all actually very easy."

(I call this Second Book Syndrome because I don't know of a common name for it. I understand this to be what Zen people mean by the "Gateless Gate," that after struggling with something at great length a person can come to see that there is no real difficulty. But I've never heard anyone else apply that name to this phenomenon and I'm not Zen trained so I'm not sure that is right either.)

0 pointsjimhefferon6y ago0 comments

Now, CoM is a classic, a real great book, but it is useful only to people who have reached a certain level of mathematical maturity. That, presumably, is not the questioner.

A version of this is that I also see people who write, "I didn't understand this topic when I took the course but now years later, I see it is all actually very easy."

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6 comments · 1 top-level

Swizec6y ago· 5 in thread

Once you understand monads, you lose the ability to explain monads. Hence the number of monads tutorials grows at an exponential rate as every new understander tries to explain them and fails.

it's a fun problem in teaching

Koshkin6y ago

> Once you understand... you lose the ability to explain

Sorry, this does not make sense to me.

vo2maxer6y ago

Douglas Crockford on Monads:

In addition to its being good and useful, it’s also cursed and the curse of the monad is that once you get the epiphany, once you understand - "oh that's what it is" - you lose the ability to explain it to anybody else.

https://youtu.be/dkZFtimgAcM

jimhefferonOP6y ago

Here is a link that helps me think about it: https://www.alanwatts.org/3-3-10-gateless-gate/ (I teach Math and a common complaint, against all math teachers, is "They obviously know the material but they cannot teach it." When I first heard AW talk about this it was a relevation for me because it so closely linked with my experience. You say to people "A vector space is a place for linear combinations to happen" and they don't get it, of course they don't get it, I wouldn't have gotten it, but that's what a vector space is. So you have to do lots of examples, and work around the edges, and somehow sit with it for a while. Anyway, I find that for me this link conveys the point of that quote about monads.)

jfarmer6y ago

Ironically, I think the original paper that introduced Monads as a useful computational abstraction is the clearest explanation I've seen.

https://homepages.inf.ed.ac.uk/wadler/papers/marktoberdorf/b...

FabHK6y ago

Corollary: a good teacher hasn’t understood anything. Well, that’s wrong, I think.

However, this might be true: A good teacher remembers not having understood it.

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