Perhaps one of the most telling examples of the fallacy of one to one correspondence is the experience of opening a fresh packet of gel deodorant. We know that as we turn the dial, the gel will emerge. But we need to turn and turn and turn before the gel is sufficiently activated and motivated to emerge at the application edge. And despite the notion that once things “get going,” there pretty much is one to one relationship between turns and flow, the first perhaps 15-20 turns or so, should make us quite aware that one to one is, for the most part a foolish illusion.
But as we observe the world, hopefully we discover that 1:1 correspondence is, by far the exception and not the rule with causality, change, activation, learning, etc. Consider, for instance the titration experiment in chemistry where we add a reagent to a clear liquid and for 437 drops nothing happens, but on the 438th drop, the liquid suddenly may turn deep purple. Brahms struggled for many years to write his first symphony, but thereafter they seemed to “pour out” of his brain.