Yep, the counterpoint to the unreasonable effectiveness of maths in the natural sciences is accompanied by the unreasonable ineffectiveness of maths in the social sciences, humanities, etc. Although at least to some extent statistics is the one branch of mathematics that does seem to be applicable (but the way this influences results, as opposed to methods, seems to be mathematically not that interesting).
There have been a lot of efforts of modelling social phenomena, the arts, etc. mathematically and while there are some interesting partial results (e.g. that languages can to some reasonable extent be analysed by parse trees or some aspects of music), most "grander" theories I have seen do not really stand up to much scrutiny.
I'm not an expert, but I could assume that part of this is due to a lot of nonlinearity in the phenomena studies, which means that many classical methods don't work well; maybe chaos theory etc. could shed more light on these things, but I don't know enough about it.
> Yep, the counterpoint to the unreasonable effectiveness of maths in the natural sciences is accompanied by the unreasonable ineffectiveness of maths in the social sciences, humanities, etc.
Except it's not ineffective at all in these subjects. Social science experiments have so many variables that the small experiments that can be conducted given the financial resources are insufficient to infer a good model. This is not a math problem, it's a money problem.
If it's ineffective in practice, I consider it to be ineffective.
But even if you could design an experiment perfectly and come up with some strong statistical evidence and then had other means to tease out what is actually causal and what is only correlational, you'd only know what influences what and not necessarily why. But yes, I did say that statistics/probability is some rare exception.
You can study group theory and understand the way physical forces work better, or hilbert spaces to understand quantum mechanics, but I haven't yet heard of anyone who has studied topology or galois theory and found that incredibly useful for understanding social phenomena better.
> If it's ineffective in practice, I consider it to be ineffective.
Except you have no way to conclude that it's ineffective. Analytical solutions require data to study. Without data, or with little data, what analysis are you going to perform? At best, broad statistical correlations, which is exactly what we find.
You're effectively claiming that spoons are ineffective at a restaurant that provides only forks. Well no, if a spoon were available, then it would probably work just fine.
> but I haven't yet heard of anyone who has studied topology or galois theory and found that incredibly useful for understanding social phenomena better.
The main stumbling block is that mathematicians are interested in mathematical problems, and so they make a common but mistaken assumption that social sciences either don't have such problems, or they are too messy for elegant math. Take it from a mathematician, this is incorrect: https://www.mathtube.org/sites/default/files/lecture-notes/S...
You may have a point. And I did forget about things like social choice theory or game theory (although I'd assume that partially this is also due to e.g. social choice procedures or "games" often being very limited and artificial settings where by their very nature the relevant space of options/outcomes can be explored in some systematic way, which is generally less the case in more organic, complex settings, such as e.g. gradual societal changes).
When it comes to economics, I know that a lot of people don't agree with the basis of many mathematical models that are used, but I'm not an economist, so I can't speak to that.
So maybe I was overzealous in discounting mathematics for the social sciences altogether. Still, I would contend (albeit with much less evidence):
- There's some measure of people trying to construe "nice models" of things in those subjects instead of trying to make sure they agree with reality. I have a degree in linguistics and I've seen this over and over. Most of these models haven't convinced me at all.
- The amount of maths that you either need or at least benefit from in order to do good research in such areas is still substantially lower than in, say, physics. I think it's still to be noted how we can describe much of physics just with a small number of economic and elegant models. I haven't seen anything comparable in any of the social sciences.
There have been a lot of efforts of modelling social phenomena, the arts, etc. mathematically and while there are some interesting partial results (e.g. that languages can to some reasonable extent be analysed by parse trees or some aspects of music), most "grander" theories I have seen do not really stand up to much scrutiny.
I'm not an expert, but I could assume that part of this is due to a lot of nonlinearity in the phenomena studies, which means that many classical methods don't work well; maybe chaos theory etc. could shed more light on these things, but I don't know enough about it.