This process of formalization is one of the skills that studying mathematics can help build.
Huh, really? My experience of studying math is that you are given the formalizations and must derive conclusions from them, which doesn’t seem like it would help much for the skill of coming up with good formalizations.
That is definitely part of studying math. The thing I was trying to point to is the process of going from an idea or intuition to something that you can write in math. For example, in linear algebra you might have a feeling about some property of a matrix but then you actually have to show it with math. Or more relevantly, in Optimal Policies Tend to Seek Power it seems like the definition of ‘power’ came from formalizing what properties we would want this thing called ‘power’ to have.
But I’m curious to hear your thoughts on this, and if you think there are other useful ways to develop this ‘formalization’ skill.
For example, in linear algebra you might have a feeling about some property of a matrix but then you actually have to show it with math.
I would distinguish between “I have an informal proof sketch, or idea for why a theorem should be true, and now I must convert it to a formal proof” and “I am looking at some piece of reality, and have to create mathematical definitions that capture that aspect of reality”. These might be sufficiently similar that practicing the former helps the latter, but I suspect they aren’t.
Or more relevantly, in Optimal Policies Tend to Seek Power it seems like the definition of ‘power’ came from formalizing what properties we would want this thing called ‘power’ to have.
I agree this is a good example of formalization, but it’s not an example of “studying math”?
if you think there are other useful ways to develop this ‘formalization’ skill.
I don’t really know. Maybe some kinds of economic modeling? Though I haven’t done this myself.
Huh, really? My experience of studying math is that you are given the formalizations and must derive conclusions from them, which doesn’t seem like it would help much for the skill of coming up with good formalizations.
That is definitely part of studying math. The thing I was trying to point to is the process of going from an idea or intuition to something that you can write in math. For example, in linear algebra you might have a feeling about some property of a matrix but then you actually have to show it with math. Or more relevantly, in Optimal Policies Tend to Seek Power it seems like the definition of ‘power’ came from formalizing what properties we would want this thing called ‘power’ to have.
But I’m curious to hear your thoughts on this, and if you think there are other useful ways to develop this ‘formalization’ skill.
I would distinguish between “I have an informal proof sketch, or idea for why a theorem should be true, and now I must convert it to a formal proof” and “I am looking at some piece of reality, and have to create mathematical definitions that capture that aspect of reality”. These might be sufficiently similar that practicing the former helps the latter, but I suspect they aren’t.
I agree this is a good example of formalization, but it’s not an example of “studying math”?
I don’t really know. Maybe some kinds of economic modeling? Though I haven’t done this myself.
Maybe someone should compile a bunch of exercises that train the muscle of formalizing intuitions
Strongly second this^