> I'm not sure anyone really understands the cognitive processes behind doing math.
As long as we all play by the rules of the symbolic game, I don't really need to understand what's going on inside anyone else's (or even my own) head.
> I rarely write code where I even need to think about complexity bounds! I'd be surprised if that was a dominating concern for even a significant fraction of programmers (systems HPC programmers, for sure, but...UI programmers?).
Invariants still remain, e.g., “the textboxes Red, Green, Blue, Hue, Saturation and Brightness must contain each a number between 0 and 255 inclusive; additionally, these numbers must satisfy the following equations (...)”.
> We don't. But you need to start somewhere. Don't underestimate the value of a few good examples in the problem solving process.
Oh, sure, examples can be a useful tool for finding the general rule, as I mentioned in my previous comment. But they don't replace the general rule.
As long as we all play by the rules of the symbolic game, I don't really need to understand what's going on inside anyone else's (or even my own) head.
> I rarely write code where I even need to think about complexity bounds! I'd be surprised if that was a dominating concern for even a significant fraction of programmers (systems HPC programmers, for sure, but...UI programmers?).
Invariants still remain, e.g., “the textboxes Red, Green, Blue, Hue, Saturation and Brightness must contain each a number between 0 and 255 inclusive; additionally, these numbers must satisfy the following equations (...)”.
> We don't. But you need to start somewhere. Don't underestimate the value of a few good examples in the problem solving process.
Oh, sure, examples can be a useful tool for finding the general rule, as I mentioned in my previous comment. But they don't replace the general rule.