I think how math elasticity is distributed in the general population is an open empirical question. It could be most people will get poor returns on effort wrt math, or it could be we are very bad at teaching math, and making math non-scary to attempt.
Regardless of what the distribution of elasticity is, if you are interested in rationality, you need to be able to push yourself a bit on certain math topics if you want real engagement. I don’t think there is a way around it. So, e.g. I disagree w/ Cyan above where he claims Scott is not being mathy when he’s engaging with rationality. I think Scott absolutely is being mathematic, it just does not look like it because there are no outward signs of “wizarding stuff being done” e.g. scary notation.
[ Random fantasy aside, if you read Scott Bakker, compare to how his Gnostic magic works, there is the audible part, the utteral, and the inaudible part, the inutteral. The inutteral is hard to explain, it is the correct habit of thought to make the magic work. Without the inutteral the spell always fails. My view of math is like this: thinking “in the right way” is the inutteral, the notation/formalization, etc. is the utteral. ]
I worry that all this talk about “top 200 mathematicians” is thinly disguised status talk.
For example, it was taken as given that technique is what’s important (this is common in pure math, and also in theoretical CS). But often conceptual insight is important. Or actually doing the technical proof using a mostly understood approach. There is a lot of heterogeneity in (a) how mathematicians think and (b) what various mathematicians are good at (see e.g. hedgehogs vs foxes). Thinking hard about what sort of contribution is really the most important just feels like status anxiety to me. Let a thousand flowers bloom, I say!
Thinking hard about what sort of contribution is really the most important just feels like status anxiety to me.
I agree that this is mostly status games, and “importance” is not a useful measure relative to, say, marginal value. (That is, I assume most people think of “importance” in terms of, say, “average value,” but the average value of a thing does not tell you whether your current level should increase, decrease, or stay the same.) Find the best niche for you in the market / ecosystem, and make profits/contributions, and only worry about the rest to the extent that it helps you find a better niche.
Re: “value” I am not sure how to think about mathematics in consequentialist terms (and I am not a huge fan of consequentialism in general). The worry is that we should all stop doing math and start working on online ads or something.
I agree with the niche comment as a practical hack given our inability to predict the future.
I think how math elasticity is distributed in the general population is an open empirical question. It could be most people will get poor returns on effort wrt math, or it could be we are very bad at teaching math, and making math non-scary to attempt.
Regardless of what the distribution of elasticity is, if you are interested in rationality, you need to be able to push yourself a bit on certain math topics if you want real engagement. I don’t think there is a way around it. So, e.g. I disagree w/ Cyan above where he claims Scott is not being mathy when he’s engaging with rationality. I think Scott absolutely is being mathematic, it just does not look like it because there are no outward signs of “wizarding stuff being done” e.g. scary notation.
[ Random fantasy aside, if you read Scott Bakker, compare to how his Gnostic magic works, there is the audible part, the utteral, and the inaudible part, the inutteral. The inutteral is hard to explain, it is the correct habit of thought to make the magic work. Without the inutteral the spell always fails. My view of math is like this: thinking “in the right way” is the inutteral, the notation/formalization, etc. is the utteral. ]
I worry that all this talk about “top 200 mathematicians” is thinly disguised status talk.
For example, it was taken as given that technique is what’s important (this is common in pure math, and also in theoretical CS). But often conceptual insight is important. Or actually doing the technical proof using a mostly understood approach. There is a lot of heterogeneity in (a) how mathematicians think and (b) what various mathematicians are good at (see e.g. hedgehogs vs foxes). Thinking hard about what sort of contribution is really the most important just feels like status anxiety to me. Let a thousand flowers bloom, I say!
I agree that this is mostly status games, and “importance” is not a useful measure relative to, say, marginal value. (That is, I assume most people think of “importance” in terms of, say, “average value,” but the average value of a thing does not tell you whether your current level should increase, decrease, or stay the same.) Find the best niche for you in the market / ecosystem, and make profits/contributions, and only worry about the rest to the extent that it helps you find a better niche.
Re: “value” I am not sure how to think about mathematics in consequentialist terms (and I am not a huge fan of consequentialism in general). The worry is that we should all stop doing math and start working on online ads or something.
I agree with the niche comment as a practical hack given our inability to predict the future.