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Comment by svat | Hacker News Reader

Indeed. And this applies to mathematics too. Here is Ralph Boas, in Can We Make Mathematics Intelligible? following his own advice:

> Suppose you want to teach the 'cat' concept to a very young child. Do you explain that a cat is a relatively small, primarily carnivorous mammal with retractable claws, a distinctive sonic output, etc.? I'll bet not. You probably show the kid a lot of different cats saying 'kitty' each time until it gets the idea. To put it more generally, generalizations are best made by abstraction from experience.

(See also Tim (Sir Timothy) Gowers on Examples first: https://gowers.wordpress.com/2007/10/19/my-favourite-pedagog... and https://gowers.wordpress.com/2007/10/24/examples-first-ii/)

(I frankly think this applies to the accursed phenomenon of monad tutorials in Haskell too (https://stackoverflow.com/questions/3261729/monad-in-non-pro...), but some disagree.)

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Along the lines of show, don't tell, the best one I've found is http://mightybyte.github.io/monad-challenges/

It helped me grok monads after I had a hazy understanding of them for a while.

Suppose you want to teach the 'cat' concept to a very young child.

Given the context, my mind jumped to the other `cat' and how I would explain it, before I read the rest of the paragraph... and I started imagining the analogy of multiple trains waiting to enter a single track, one after another.

To put it more generally, generalizations are best made by abstraction from experience.

In other words, the value of an abstraction is best understood by seeing the cases it abstracts over. A stark contrast to the "always abstract even if you don't think you need to" attitude that is unfortunately often taught in computer science courses, which leads to overuse of abstraction and the accompanying proliferation of accidental complexity.

The idea of teaching using extensional definitions (an expanding list of examples) is fine, but I came across a weird case of it at a bicycle repair workshop a few years ago.

It's a bizarre example, but it went like this.

Audience: what's a fixed gear bike?

Repair guy: it's uh, it's like a unicycle, for example...

In that scenario an intensional definition is really the way to go. I don't understand how that bicycle repair guys mind worked at all.

Having ridden both fixies and unicycles, the example makes total sense. "It's like a pennyfarthing" works too. The issue is that examples are meant to leverage the recipients intuition. Very few people have intuition for unicycles and pennyfarthings, so the examples fall flat.

That said, "It's like a children's unicycle" would probably count as a valid example too, and refers to something people may have intuition for. But it may also stress the wrong parts of the example. We want to convey the sense of direct drive, not circus prop.

> That said, "It's like a children's unicycle"

Tricycle? Or I’m very interested in a culture where children’s unicycles are a common thing.

Yes, tricycle, of course. If anyone figures out where this children's unicycle culture is I may want to move there.

I don't think the problem is with intuition, though it's probably true that people don't realize that the absence of a freewheel is crucial to the function of a unicycle.

The problem is that a single example which differs on multiple dimensions from the "standard" bike (e.g. number of wheels, stability characteristics, steering, holonomic vs nonholonomic maneuverability) is highly ambiguous.

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