I don’t know how many people, if any, are actually going around in daily life trying to assign or calculate probabilities (conditional or otherwise) or directly apply Bayes’ theorem. However, there are core insights that come from learning to think about probability theory coherently that are extremely non-obvious to almost everyone, and require deliberate practice. This includes seemingly simple things like “Mathematical theorems hold whether or not you understand them,” “Questions of truth and probability have right answers, and if you get the wrong answers you’ll fail to make optimal decisions,” or “It’s valuable, psychologically and for interpersonal communication, to be able to assign numerical estimates of your confidence in various beliefs or hypotheses.” Other more subtle ones like “it is fundamentally impossible to be 100% certain of anything” are also important, and *much* harder to explain to people who aren’t aware of the math that defines the relevant terms.
My day job as a research analyst involves making a lot of estimates about a lot of things based on fairly loose and imprecise evidence. In recent years I’ve been involved in helping train a lot of my coworkers. I find myself paraphrasing ideas from the Sequences constantly (recommending people read them has been less helpful; most won’t, and in any case transfer of learning is hard). I notice that their writing, speaking, and thinking become a lot more precise, with fewer mistakes and impossibilities, when I ask them to try doing simple mental exercises like “In your head, assign a probability estimate to everything you claim will happen or think is true now, and add appropriate “likeliness” quantifiers to your sentences based on that.”
Also, I’ve had multiple people tell me that they won’t, or even literally can’t, make numerical assumptions and estimates without numerical data to back them up, sometimes with very strict ideas about what counts as data. The fact they their colleagues manage to make such assumptions and get useful answers isn’t enough to persuade them otherwise. Math is often more likely to get through to such people.
I don’t know how many people, if any, are actually going around in daily life trying to assign or calculate probabilities (conditional or otherwise) or directly apply Bayes’ theorem. However, there are core insights that come from learning to think about probability theory coherently that are extremely non-obvious to almost everyone, and require deliberate practice. This includes seemingly simple things like “Mathematical theorems hold whether or not you understand them,” “Questions of truth and probability have right answers, and if you get the wrong answers you’ll fail to make optimal decisions,” or “It’s valuable, psychologically and for interpersonal communication, to be able to assign numerical estimates of your confidence in various beliefs or hypotheses.” Other more subtle ones like “it is fundamentally impossible to be 100% certain of anything” are also important, and *much* harder to explain to people who aren’t aware of the math that defines the relevant terms.
My day job as a research analyst involves making a lot of estimates about a lot of things based on fairly loose and imprecise evidence. In recent years I’ve been involved in helping train a lot of my coworkers. I find myself paraphrasing ideas from the Sequences constantly (recommending people read them has been less helpful; most won’t, and in any case transfer of learning is hard). I notice that their writing, speaking, and thinking become a lot more precise, with fewer mistakes and impossibilities, when I ask them to try doing simple mental exercises like “In your head, assign a probability estimate to everything you claim will happen or think is true now, and add appropriate “likeliness” quantifiers to your sentences based on that.”
Also, I’ve had multiple people tell me that they won’t, or even literally can’t, make numerical assumptions and estimates without numerical data to back them up, sometimes with very strict ideas about what counts as data. The fact they their colleagues manage to make such assumptions and get useful answers isn’t enough to persuade them otherwise. Math is often more likely to get through to such people.