One confusion I wrote down in advance was “I still don’t quite know how to predict that there will not be a simple mathematical apparatus that explains something. Why the motion of the planets, why the game of chance, why not the color of houses in England or the number of hairs on a man’s head?”
It seems very hard to say a priori that there won’t be any interesting new abstract structure discovered by looking at some new domain, especially when Science is young and you don’t know the base rate of ‘how often do we discover useful new formalisms?’. E.g., Fibonacci numbers and Lucas numbers show up in the distribution of petals for many flowers; hair could have turned out to reveal something similar.
I think the correct process for zeroing in on relatively promising domains is something like:
First, try to come up with the simplest accounts for everything, unifying as many different phenomena as possible. (Reasoning: these are easier to generate and think about, and there are a lot fewer simple stories to evaluate than complex ones, and simple stories can often serve as useful approximations for more complex ones.)
Go look at really weird / really different domains. (Because if you can’t find a simple account to explain ‘normal’ stuff, there might still be simple accounts that explain the weird stuff, because weird stuff is weird so Many Things Are Possible. And if you do have simple accounts to explain the normal stuff, you should check whether weird stuff violates those generalizations.)
Planets are a weird domain — there aren’t a bunch of things we knew about in the 17th century that were similar to planets, or that formed a continuum between planets and ordinary objects like lanterns and pigeons. In contrast, hairs are a lot like whiskers, feathers, etc.; and house colors are a lot like cave colors, tent colors, etc. So if there are surprising new generalizations to find, they’re more likely to crop up by studying planets than by studying hair or house colors.
Similarly, gambling is weird relative to non-probabilistic inference. If you’re really into Aristotle and you’re trying to model all human reasoning and decision-making using deductive syllogisms, you should be really curious about the domains where people do weird things like ‘bet things based on guesswork, with no certainty they’re right’. (You might similarly take an interest in dreams, emotions, divine inspiration, self-deception, bullshit, etc.; they won’t all be winners, but an occasional winner is sufficient.)
It seems very hard to say a priori that there won’t be any interesting new abstract structure discovered by looking at some new domain, especially when Science is young and you don’t know the base rate of ‘how often do we discover useful new formalisms?’. E.g., Fibonacci numbers and Lucas numbers show up in the distribution of petals for many flowers; hair could have turned out to reveal something similar.
I think the correct process for zeroing in on relatively promising domains is something like:
First, try to come up with the simplest accounts for everything, unifying as many different phenomena as possible. (Reasoning: these are easier to generate and think about, and there are a lot fewer simple stories to evaluate than complex ones, and simple stories can often serve as useful approximations for more complex ones.)
Go look at really weird / really different domains. (Because if you can’t find a simple account to explain ‘normal’ stuff, there might still be simple accounts that explain the weird stuff, because weird stuff is weird so Many Things Are Possible. And if you do have simple accounts to explain the normal stuff, you should check whether weird stuff violates those generalizations.)
Planets are a weird domain — there aren’t a bunch of things we knew about in the 17th century that were similar to planets, or that formed a continuum between planets and ordinary objects like lanterns and pigeons. In contrast, hairs are a lot like whiskers, feathers, etc.; and house colors are a lot like cave colors, tent colors, etc. So if there are surprising new generalizations to find, they’re more likely to crop up by studying planets than by studying hair or house colors.
Similarly, gambling is weird relative to non-probabilistic inference. If you’re really into Aristotle and you’re trying to model all human reasoning and decision-making using deductive syllogisms, you should be really curious about the domains where people do weird things like ‘bet things based on guesswork, with no certainty they’re right’. (You might similarly take an interest in dreams, emotions, divine inspiration, self-deception, bullshit, etc.; they won’t all be winners, but an occasional winner is sufficient.)