Thresholds

A threshold is a point in a system in which a movement in a certain direction yields unequal returns or is specially significative in some way in comparison with movements in the same direction but ‘previously’. You can add thousands of drops to the glass, until at some point there is one individual drop that causes it to overflow. The world is inherently unequal in this regard. Every single parameter that affects an outcome is affected and modulated profoundly by the notion of threshold.

Every genetic mutation that was unsuccessful and thus ruled out by the mechanism of natural selection must have caused in at least one occasion the non-reproduction (for example because of premature death) of an organism that would have been able to reproduce without the negative mutation. Evolution works because of this. Now, most of mutations (either positive or negative) affect only probabilities, and are not black and white. My remark is that even they affecting probabilities means that there are individual, discrete cases that are affected by thresholds, and this is what actually produces change and evolution in time.

There will always be a first one. There will always be a last one. Every gradual change is, at some point, non-gradual and discrete. Gradual changes are, in fact, made up of huge amount of discrete changes. This is obvious, de Perogrullo, but usually forgotten. And some of those discrete changes will actually make a non-gradual difference, always.

Still, there must be no confusion: most of the value and explanative power of the idea of thresholds comes from situations where numerical value is of paramount importance. Not all situations are thus. To understand whether the situation is numerical or not it is helpful to think about the concrete parameter that varies, and whether that parameter is numerical or not. Verbi gratia, emotion can hardly be measured in a scale, it is therefore a non-numerical parameter. Most real-world social [id est, relating to the environment mediated by interaction between humans or other social species] situations have a very important emotional aspect to them, and therefore attempts to parameterise everything in a numerical fashion are to be viewed with suspicion. While thinking about thresholds might be useful even in this situations, it is useful to make the mental caveat.