I tried making one just for the math behind rationality/decision theory back in October, but I never got around to finishing it. The main problems I ran into were:
Where should the skill tree start? I’m sure that basic math like algebra, geometry, trig, etc are all really useful, but I’m not sure about the dependencies between them. I ended up lumping them all into “basic mathematics”.
How should the skill tree split subjects? Many subjects are best learned iteratively—for example, it’s probably best to get a rudimentary understanding of probability theory, then learn more probability theory later on once you’ve picked up other related subjects (Linear Algebra, Multivariate Calculus, etc) and then again after more subjects (Measure theory). The complication is that these other subjects are often split into different “levels”. I found that I didn’t have enough familiarity with math to split subjects naturally.
One method that seems promising is taking a bunch of textbooks/courses, and trying to figure out the dependencies between them.
Agreed. I think in light of the fact that a lot of this stuff is learned iteratively you’d want to unpack ‘basic mathematics’. I’m not sure of the best way to graphically represent iterative learning, but maybe you could have arrows going back to certain subjects, or you could have ‘statistics round II’ as one of nodes in the network.
It seems like insights are what you’re really aiming at, so maybe instead of ‘probability theory’ you have a node for ‘distributions’ and ‘variance’ at some early point in the tree then later you have ‘Bayesian v. Frequentist reasoning’.
This would help also help you unpack basic mathematics, though I don’t know much about the dependencies either. I hope too, soon :)
I tried making one just for the math behind rationality/decision theory back in October, but I never got around to finishing it. The main problems I ran into were:
Where should the skill tree start? I’m sure that basic math like algebra, geometry, trig, etc are all really useful, but I’m not sure about the dependencies between them. I ended up lumping them all into “basic mathematics”.
How should the skill tree split subjects? Many subjects are best learned iteratively—for example, it’s probably best to get a rudimentary understanding of probability theory, then learn more probability theory later on once you’ve picked up other related subjects (Linear Algebra, Multivariate Calculus, etc) and then again after more subjects (Measure theory). The complication is that these other subjects are often split into different “levels”. I found that I didn’t have enough familiarity with math to split subjects naturally.
One method that seems promising is taking a bunch of textbooks/courses, and trying to figure out the dependencies between them.
Agreed. I think in light of the fact that a lot of this stuff is learned iteratively you’d want to unpack ‘basic mathematics’. I’m not sure of the best way to graphically represent iterative learning, but maybe you could have arrows going back to certain subjects, or you could have ‘statistics round II’ as one of nodes in the network.
It seems like insights are what you’re really aiming at, so maybe instead of ‘probability theory’ you have a node for ‘distributions’ and ‘variance’ at some early point in the tree then later you have ‘Bayesian v. Frequentist reasoning’.
This would help also help you unpack basic mathematics, though I don’t know much about the dependencies either. I hope too, soon :)