&gt; I&#x27;m not sure anyone really understands the cognitive processes behind doing math.<p>As long as we all play by the rules of the symbolic game, I don&#x27;t really need to understand what&#x27;s going on inside anyone else&#x27;s (or even my own) head.<p>&gt; I rarely write code where I even need to think about complexity bounds! I&#x27;d be surprised if that was a dominating concern for even a significant fraction of programmers (systems HPC programmers, for sure, but...UI programmers?).<p>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 (...)”.<p>&gt; We don&#x27;t. But you need to start somewhere. Don&#x27;t underestimate the value of a few good examples in the problem solving process.<p>Oh, sure, examples can be a useful tool for finding the general rule, as I mentioned in my previous comment. But they don&#x27;t replace the general rule.