You’re definitely right that there’s some areas where it’s easier to make beliefs pay rent than others! I think there’s two replies to your concern:
1) First, many theories from math DO pay rent (the ones I’m most aware of are statistics and computer-science related ones). For example, better algorithms in theory (say Strassen’s algorithm for multiplying matrices) often correspond to better results in practice. Even more abstract stuff like number theory or recursion theory do yield testable predictions.
2) Even things that can’t pay rent directly can be logical implications of other things that pay rent. Eliezer wrote about this kind of reasoning here.
You’re definitely right that there’s some areas where it’s easier to make beliefs pay rent than others! I think there’s two replies to your concern:
1) First, many theories from math DO pay rent (the ones I’m most aware of are statistics and computer-science related ones). For example, better algorithms in theory (say Strassen’s algorithm for multiplying matrices) often correspond to better results in practice. Even more abstract stuff like number theory or recursion theory do yield testable predictions.
2) Even things that can’t pay rent directly can be logical implications of other things that pay rent. Eliezer wrote about this kind of reasoning here.