[OisinMoran]

This was a good read and I really enjoyed it (I'm another person who was turned onto Bongard problems by Hofstadter), but two parts weren't particularly strong.

The first one was the dismissal of intuition in a way that seemed pretty straw man like to me: "Mostly, “intuition” just means “mental activity we don’t have a good explanation for,” or maybe “mental activity we don’t have conscious access to.” It is a useless concept, because we don’t have good explanation for much if any mental activity, nor conscious access to much of it. By these definitions, nearly everything is “intuition,” so it’s not a meaningful category."

I think the author could have spent longer trying to come up with a better definition of what someone would mean by intuition with relation to these problems instead of just setting up a poor one then immediately tearing it down. Intuition here would be contrasted against the deliberate procedural thinking of "let's list out qualities of these shapes" and would be something like seeing the solution straight away, but can also be combined with the procedural thinking too with the intuition originating possible useful avenues and then the deliberate part working through them. The contrast is that you could easily write down one set of the steps to be replicated by others (the deliberate part: "I counted the sides on all shapes") but less so the other (intuition: "I thought x", "x jumped out").

The second is that the example they use for mushiness really isn't. There is a perfectly concrete solution to that that doesn't involve any mushiness and is simply that the convex hull of one set is triangular while the others are circular. The only mushiness involved is that saying "triangles vs circles" feels like enough of answer to us to not need to specify any more. We think that we can continue with just this answer and be able to correctly identify any future instances so it seems mushy but you can probably think of examples that would confound the mushy solution but be fine under the more concrete convex hull one.

[teknopaul]

I thought that one was the most interesting too. The convex hull appears circular but it is not, in one case you have to join the dots between the center point of triangles, none of the points on the triangles are on a circle, or maybe all of them are if we discard the hull abstraction, in which case there are three circles.

Imagine trying to write code that identifies that. However it's one of the most obvious to me.