A couple of interesting points from Fleix Salmon’s piece (Hat tip to Swarup for the pointer):
Horn’s point is that any organized attempt to look deeply at something risks being self-defeating: you can end up disappearing down all manner of silly dead ends, and understanding less than you would with a more-is-more approach.This absolutely rings true to me. For reasons which today elude me, I decided when I was doing my A-levels in England to do what they call “double maths” — essentially taking two mathematics exams (Maths and Further Maths), in the same two years you’d normally spend studying for just one. As a result, we had a highly accelerated mathematics curriculum, and there was no time to circle back and make sure the class had understood something before moving on to the next thing. It was all rather sink-or-swim.
And at any given point in time, I was sinking — along, I think, with most of the rest of my class. I was pretty fuzzy about what we’d been taught in previous weeks, and I was very unlikely to understand what the teacher was trying to say at any given time. Maths class, for me, was a combination of panic and incomprehension, combined with a desperate attempt to bluff my way through as much as I could. (Needless to say, if you’re reduced to trying to bluff, mathematics is not the best subject to choose.)
Yet somehow my classmates and I all did very well, at the end of the two years, when it came time to taking the actual exams. As I recall, nearly everybody taking double maths wound up getting an A in their Maths A-level, and most of us got an A or a B in Further Maths as well. Somehow we had managed to gain a pretty good grasp of the subject by dint of sheer velocity: the mechanism, I think, was that a desperate attempt to understand a new concept had the effect of making earlier ideas drop into place. And that the best way of mastering the Maths curriculum was not so much to study it directly, but rather to try to study the Further Maths curriculum: even getting halfway there would bring you pretty much up to speed on the stuff that went before.
Something similar, I think, happens with blogging. Bloggers tend to be foxes, rather than hedgehogs; it’s pretty clear that Athreya is an archetypal hedgehog and has a deep-seated mistrust of foxes. We skip around a lot of different things, and much of the time we don’t really understand them. But somehow the accumulated effect of all that skipping around is to make connections and develop understandings which hedgehogs often lack. What’s more, we live, as Athreya admits, in a highly complex world — one which there are serious limits to what economics can do on its own.
A good post!