[Akronymus]

> The way black box composition is done in modern software, your n=100 code (say, a component) gets reused into a another thing somewhere above, and now you're being iterated through m=100 times. Oops, now n=10k

That doesn't seem quite right. as 100 * (100^2) <<<<< 10000^2

[chenglou]

Yeah I was only talking about quantities. Equivalently, assume that it's a linear algorithm in the child and a linear one in the parent. Ultimately it ends up as O(nm) being some big number, but when people do runtime analysis in the real world, they don't tend to consider the composition of these blackboxes since there'd be too many combinations. (Composition of two polynomial runtimes would be even worse, yeah.)

Basically, performance doesn't compose well under current paradigms, and you can see Casey's methods as starting from the assumption of wanting to preserve performance (the cycles count is just an example, although it might not appeal to some crowds), and working backward toward a paradigm.

There was a good quote that programming should be more like physics than math.