Math is training for the mind, but not like you think
Just a hypothesis:
People have long thought that math is training for clear thinking. Just one version of this meme that I scooped out of the water:
“Mathematics is food for the brain,” says math professor Dr. Arthur Benjamin. “It helps you think precisely, decisively, and creatively and helps you look at the world from multiple perspectives . . . . [It’s] a new way to experience beauty—in the form of a surprising pattern or an elegant logical argument.”
But math doesn't obviously seem to be the only way to practice precision, decision, creativity, beauty, or broad perspective-taking. What about logic, programming, rhetoric, poetry, anthropology? This sounds like marketing.
As I've studied calculus, coming from a humanities background, I'd argue it differently.
Mathematics shares with a small fraction of other related disciplines and games the quality of unambiguous objectivity. It also has the ~unique quality that you cannot bullshit your way through it. Miss any link in the chain and the whole thing falls apart.
It can therefore serve as a more reliable signal, to self and others, of one's own learning capacity.
Experiencing a subject like that can be training for the mind, because becoming successful at it requires cultivating good habits of study and expectations for coherence.
The thing I like about math is that it gives the feeling that the answers are in the territory. (Kinda ironic, when you think about what the "territory" of math is.) Like, either you are right or you are wrong, it doesn't matter how many people disagree with you and what status they have. But it also doesn't reward the wrong kind of contrarianism.
Math allows you to make abstractions without losing precision. "A sum of two integers is always an integer." Always; literally. Now with abstractions like this, you can build long cha... (read more)
Feedback, yes. Clarity... well, sometimes it's "yes, it works" today, and "actually, it doesn't if the parameter is zero and you called the procedure on the last day of the month" when you put it in production.
2DirectedEvolution
Sometimes programming is like that, but then I get all anxious that I just haven’t checked everything thoroughly!
My guess is this has more to do with whether or not you’re doing something basic or advanced, in any discipline. It’s just that you run into ambiguity a lot sooner in the humanities