My understanding of the "quantity to quality conversion" phrase is that in many situations the relation between some inputs and outputs is not linear. More specifically, there are many situations where at the beginning the relation seems linear, but later at some point the increase of outputs becomes incredibly huge (incredibly = for people who based their models on extrapolating the linear relationship at the beginning). Even more specifically, you can have one input "A" that has obvious effect on "X", but almost zero effect on "Y" and "Z". Then at some moment with additional increases of "A" also "Y" and "Z" start growing (which was totally unexpected by the old model).
Specific example: You start playing piano. At the beginning, it feels like it has a simple linear impact on your life. You spend 1 hour playing piano, you get an ability to play a simple song quite well. You spend 2 hours playing piano, you get an ability to play another simple song quite well. Extrapolate this, and you get a model. According to this model, after spending 80000 hours playing piano, you would expect to be able to play 80000 simple songs quite well. -- What happens in reality is that you get an ability to play any simple song well just by looking at the music sheets, an ability to play very complex music, an ability to make money by playing the music, you become famous, get a lot of social capital, lot of friends, lot of sex, lot of drugs, etc. (Both non-linear outputs, and the outputs not predicted by the original model.)
A similar pattern appears in many different situations, so some people invented a mysteriously sounding phrase to describe it. Now it seems like some law of nature. But maybe it is just a selection effect (some situations develop like this, and we notice "oh, the law of quantity to quality conversion", other situations don't, and we ignore them).
In other words, "quantity" seems to mean "linear model", "quality" means "model", and the whole phrase decoded means "if you change variables enough, you may notice that the linear model does not reflect reality well (especially in situations where the curve starts growing slowly, and then it grows very fast)".
I was more after some discontinuity than a simple nonlinearity, like a quadratic or even an exponential dependence. And you are right, the selection effect is at work, but it's not a negative in this case. We want to select similar phenomena and find a common model for them, in order to be able to classify new phenomena as potentially leading to the same effects.
For example, if you look at some new hypothetical government policy which legislates indexing the minimum savings account rate to, say, inflation, you should be able to tell whether after a sizabl...
Related to: What Do We Mean By "Rationality?"
Rationality has many facets, both relatively simple and quite complex. As a result, it can often be hard to determine what aspects of rationality you should or shouldn't stress.
An extremely basic and abstract model of how rationality works might look a little something like this: