[woopsn]

So for example, do programs 1 and 2 compute the same thing? In general this is quite difficult and unsolvable. But then, if so, is the complexity of 1 less than 2? What is the minimum complexity of any program that computes the thing? These are relevant problems we want to solve. They involve considering isomorphism, orderings, limits, etc. - structuralism - but in many cases the maps are not there to support it, or there is no way to find them. The relationship between two complexity classes, or even two binaries.

At an elementary level what we deal with are representations. In CS this problem is severe, for example almost all boolean functions have exponential circuit complexity - but we cannot offer even a single example up. It's an open question how powerful graph isomorphism even is.

I don't mean to knock the structuralist insight, it is a powerful "imperative" as the article says. There is just incompleteness everywhere, in less mature fields especially, where they work in spaces that can barely be classified as of yet. The knowledge is generated there, and then organized within a higher scheme. Topology sprung partly out of Euler's attack on the Königsberg bridge problem (I suppose structuralism overall does to). It is a revealing perspective, but it seems the insight comes after the large amount of work, not usually before.