Comment by addicted | Hacker News Reader

Comment by addicted | Hacker News Reader

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How much of this explainer however seems better to us precisely because of the more comprehensive knowledge and understanding we already have?

For example the author uses the word function liberally in the explanation. However, when studying functions in school in math it was super complicated for me. It was only after I started programming, learning the programming language meaning of function, and then when I was reintroduced to mathematical functions through functional programming that I truly grasped mathematical functions and all the stuff I was taught in school.

I’m not arguing that school level math does not need to be improved. I just think we should be cautious that because an explanation that seems intuitive to us now after having gained a complete introduction to all math concepts as well as programming (esp on HN) may not necessarily be as intuitive when students who are only exposed to a very small subset of mathematical concepts encounter them.

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.)

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

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...

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

Sorry, this does not make sense to me.

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

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.)

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.

Actually a rather famous example of your point are the Feynman lectures. They are often hailed as a great, "easy" and intuitive explanation of physics. However, supposedly at the time, the undergrad students Feyman was teaching did not think their were all the rage. It was actually the grad students who retook the material and really enjoyed them. To support your point I think sometimes it is really necessary to have been exposed to the material and been able to grasp some part of it, then you are open to these type of explanations which really lift you over the hurdle of the things that you didn't quite get before.

As someone who learned to program before taking any interesting math I was always so confused by the amount of early math classes spent explaining function notation.

It wasn't until I tried teaching people that I realized how odd the notation can seem.

you should be happy someone explained it to you- I feel that notation was overlooked tremendously in my math education- I actually just brought this up in a thread yesterday. It was like "oh, we have this dx now... k."

I agree with your post. I had the same problem where match was harder for me to comprehend. It wasn't until I started programming that I started to understand the concept you cite (Functions.).

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