[Wyverald]

I think you missed his, though -- which was that any person with a high-school math background can easily grasp the concept of monoids with just a tiny bit of effort.

[igravious]

I see what you mean, but what I meant is that either we get much better at explaining math or we exclude a good portion of our population from being able to program. If you respond with "all you need is high-school math plus more math in college" you're missing my point!

I'm not in any way anti-math.† Imagine that monads were a part of Scratch (the children's programming environment), and I was trying to explain them to my young daughter. If she couldn't get it should I say to her, "this is only high-school math plus a bit more, come on, don't use the fact that you're 11 as an excuse". The other day somebody pointed out that in Tufts they have shown that children as young as five can think computationally. This is the level I'm talking about. I'm talking about being able to teach programming to people who are normally (for whatever reason) math-phobic.

(† I took three years of 3rd-level math.)

[catnaroek]

Could you explain GoF's design patterns to your 11-year-old daughter? Reflection and metaprogramming? Heck, would she be able to understand why the concept of object identity matters for some types (say, any user-defined type in Java) but not others (say, integers)? Are you proposing that we ban those things too?

[catnaroek]

Or even without effort, since all programmers have used monoids all their lives! This situation is very much like knowing about Fido, Spikes and Bones, but lacking a word for “dog”, and thus being unable to talk about a dog without referring to a specific one.