I’m confused and alarmed that there is apparently some very large group of people who consider themselves rationalists but do not understand bayes theorem. (Bayesian statistics as a whole is a lot more complicated, of course, but Bayes theorem is not the hard part.) it’s not a particularly complicated piece of math! the core idea can definitely trip you up if you’ve never ever heard of it, but it’s also not that deep and shouldn’t be hard to explain. and even if you don’t remember the exact formula, it should be very easy to rederive within a few minutes from first principles once you understand the core idea.
how did we end up in a world where a community that attracts people of above-average intelligence and education, that places a large emphasis on math and STEM, that worships a particular theorem for some reason and has produced dozen(s?) of explainers for that theorem, still end up having the median member not understand the theorem? I think the missing thing here is not the one true intuitive bayes guide that will once and for all explain things the right way.
I am if not alarmed then at least consider it a problem, but haven’t felt confusion here for at least a year. I have a pretty good model of how it happens. Someone’s doing some searching on the internet, and gets recommended a LessWrong article on an Boston rents, or an AI paper, or hikers going missing. Maybe a friend recommended them a fun essay on miracles or a goofy Harry Potter fanfic. They hang around, read a few more things, comment a bit. Then they see a meetup announcement, and show up, and enjoy conversation. (Very very roughly a third of LessWrong/ACX meetups are socials, with no or minimal readings or workshops.) They go to more meetups, they make more comments on the internet, maybe they make some posts of their own and their posts get upvoted. Maybe they step up and run the meetup when the previous organizer is sick or busy or moves.
At no point did someone give them a math test. I’m basically describing my arc above, and nobody asked me to solve a mammogram problem in that process.
That’s how we end up in this world.
As for what the missing thing is: my theory is to change this state of affairs, we’d need two things. We’d need to start actually regularly asking folks questions where they’d need to use it, and we’d need an explanation fast and simple enough that it can survive being taught by non-specialists who are also juggling having snacks out and getting the door for people. I love this not for its intuitiveness, but for rearranging the numbers to a shape people can do easier.
I’d give much higher odds on members of the community being able to gesture at the key ideas of base rates and priors in English sentences! (Not as high as I’d like, but higher, anyway.) But that’s not the same as being able to do the calculations. And there’s something slippery about describing a piece of math in intuitive sentences then trying to use it as a heuristic without quite being able to actually run the numbers, which is why I’d like to change that.
Again, I suck too! I’m running around doing a dozen things in my day to day life, none of which is remedial math practice. This kind of thing happens a lot actually. Once upon a time I did some basic interviews for some software developers, and watched comp sci grads fail to fizzbuzz correctly.
My hope is that if somehow I can get a tweet or two worth of text that teaches the numbers in a way that can fit in math people already do in their daily life (multiplication between two to four numbers) and add a small battery of exercises that use it, I might be able to package that in a way local organizers not only could use but would spread. Like you say, maybe hoping for just one more Bayes explanation is not the path. To me, this one was a meaningful step simpler and easier.
I guess I’ll note as well that I want to raise the sanity waterline. To do that, I can’t work with a version that wants above average intelligence. I do genuinely want to figure out how to teach Bayes to fourth graders and then go out and teach some fourth graders. C’mon, don’t you want to see what people turn out like if they have access to a better mental toolkit from a young age?
Also,
it’s not a particularly complicated piece of math … even if you don’t remember the exact formula, it should be very easy to rederive within a few minutes from first principles once you understand the core idea.
I’m confused and alarmed that there is apparently some very large group of people who consider themselves rationalists but do not understand bayes theorem. (Bayesian statistics as a whole is a lot more complicated, of course, but Bayes theorem is not the hard part.) it’s not a particularly complicated piece of math! the core idea can definitely trip you up if you’ve never ever heard of it, but it’s also not that deep and shouldn’t be hard to explain. and even if you don’t remember the exact formula, it should be very easy to rederive within a few minutes from first principles once you understand the core idea.
how did we end up in a world where a community that attracts people of above-average intelligence and education, that places a large emphasis on math and STEM, that worships a particular theorem for some reason and has produced dozen(s?) of explainers for that theorem, still end up having the median member not understand the theorem? I think the missing thing here is not the one true intuitive bayes guide that will once and for all explain things the right way.
I am if not alarmed then at least consider it a problem, but haven’t felt confusion here for at least a year. I have a pretty good model of how it happens. Someone’s doing some searching on the internet, and gets recommended a LessWrong article on an Boston rents, or an AI paper, or hikers going missing. Maybe a friend recommended them a fun essay on miracles or a goofy Harry Potter fanfic. They hang around, read a few more things, comment a bit. Then they see a meetup announcement, and show up, and enjoy conversation. (Very very roughly a third of LessWrong/ACX meetups are socials, with no or minimal readings or workshops.) They go to more meetups, they make more comments on the internet, maybe they make some posts of their own and their posts get upvoted. Maybe they step up and run the meetup when the previous organizer is sick or busy or moves.
At no point did someone give them a math test. I’m basically describing my arc above, and nobody asked me to solve a mammogram problem in that process.
That’s how we end up in this world.
As for what the missing thing is: my theory is to change this state of affairs, we’d need two things. We’d need to start actually regularly asking folks questions where they’d need to use it, and we’d need an explanation fast and simple enough that it can survive being taught by non-specialists who are also juggling having snacks out and getting the door for people. I love this not for its intuitiveness, but for rearranging the numbers to a shape people can do easier.
I’d give much higher odds on members of the community being able to gesture at the key ideas of base rates and priors in English sentences! (Not as high as I’d like, but higher, anyway.) But that’s not the same as being able to do the calculations. And there’s something slippery about describing a piece of math in intuitive sentences then trying to use it as a heuristic without quite being able to actually run the numbers, which is why I’d like to change that.
Again, I suck too! I’m running around doing a dozen things in my day to day life, none of which is remedial math practice. This kind of thing happens a lot actually. Once upon a time I did some basic interviews for some software developers, and watched comp sci grads fail to fizzbuzz correctly.
My hope is that if somehow I can get a tweet or two worth of text that teaches the numbers in a way that can fit in math people already do in their daily life (multiplication between two to four numbers) and add a small battery of exercises that use it, I might be able to package that in a way local organizers not only could use but would spread. Like you say, maybe hoping for just one more Bayes explanation is not the path. To me, this one was a meaningful step simpler and easier.
I guess I’ll note as well that I want to raise the sanity waterline. To do that, I can’t work with a version that wants above average intelligence. I do genuinely want to figure out how to teach Bayes to fourth graders and then go out and teach some fourth graders. C’mon, don’t you want to see what people turn out like if they have access to a better mental toolkit from a young age?
Also,
I think you might be having an xkcd feldspar moment.