There are a number of implicit concepts I have in my head that seem so obvious that I don’t even bother verbalizing them. At least, until it’s brought to my attention other people don’t share these concepts.
It didn’t feel like a big revelation at the time I learned the concept, just a formalization of something that’s extremely obvious. And yet other people don’t have those intuitions, so perhaps this is pretty non-obvious in reality.
Here’s a short, non-exhaustive list:
Intermediate Value Theorem
Net Present Value
Differentiable functions are locally linear
Theory of mind
Grice’s maxims
If you have not heard any of these ideas before, I highly recommend you look them up! Most *likely*, they will seem obvious to you. You might already know those concepts by a different name, or they’re already integrated enough into your worldview without a definitive name.
However, many people appear to lack some of these concepts, and it’s possible you’re one of them.
As a test: for every idea in the above list, can you think of a nontrivial real example of a dispute where one or both parties in an intellectual disagreement likely failed to model this concept? If not, you might be missing something about each idea!
Sometimes people say that a single vote can’t ever affect the outcome of an election, because “there will be recounts.” I think stuff like that (and near variants) aren’t really things people can say if they fully understand IVT on an intuitive level.
Very similar: ‘Deciding to eat meat or not won’t affect how many animals are farmed, because decisions about how many animals to farm are very coarse-grained.’
Yep! Or donations below a certain amount won’t do anything since planning a shipment of antimalarial nets, or hiring a new AI Safety researcher, is lumpy.
I don’t get how the IVT applies here. Like, the things I would think about here would be there is a chance that my vote can be that one important vote that gives my candidate advantage. Or how we need to coordinate without communication, like if other people thought the same that their vote doesn’t matter, all in all my candidate looses many more votes than one. The number of votes my candidate has is the integral of voter’s preferences, but this is not a smooth function so it shouldn’t apply here as well?
All of them are lovely and extremely useful in my world-models. And all of them have failed me at one time or another. Here are some modes where I’ve thought I understood and it was obvious, but I was missing important assumptions:
Intermediate Value Theorem: Obvious, incontrovertible. A knockout punch in any disagreement. Except, a lot of things aren’t quite as continuous as you think, when you really get formal about them.
Net Present Value: Also clearly the right tool for most comparisons of value. And figuring out the correct discount rate to take into account differing risks is quite nontrivial.
Local linearity: this one I lean on a bit less, but it still bites me when I get too loose with “locally”.
Theory of Mind: I’m getting better, but I’m still a master of Typical Mind Fallacy.
Grice’s Maxims (and Crocker’s Rule): Great when a target I strive for, very misleading when I expect that it’s common.
Extension: Which obvious-in-retrospect-and-to-other-people ideas am I currently missing? Are there conceptual technologies that you’ve noticed that I (Linch) in my conversations or internet comments appear to have missed?
As a test: for every idea in the above list, can you think of a nontrivial real example of a dispute where one or both parties in an intellectual disagreement likely failed to model this concept? If not, you might be missing something about each idea!
I don’t follow how / why this test is supposed to work.
Can you give an example of “a nontrivial real example of a dispute where one or both parties in an intellectual disagreement likely failed to model [one of these concepts]” and how that is indicative of if you’re missing something or not?
It seems like I could understand any of these points, but not be able to think of places where others are missing them?
Decided to write about it for Christmas! I thought about my examples and connections again and decided maybe they’re nonobvious enough (eg LLMs produce very different, and much worse/trivial examples of disputes): https://linch.substack.com/p/unknown-knowns
I’ll think about it! I don’t personally like writing blogposts of well-known concepts unless I have a novel angle or a clear model for why the existing material is inadequate, but maybe!
Other people reading this who have a novel angle are of course free to take these projects on, of course.
There are a number of implicit concepts I have in my head that seem so obvious that I don’t even bother verbalizing them. At least, until it’s brought to my attention other people don’t share these concepts.
It didn’t feel like a big revelation at the time I learned the concept, just a formalization of something that’s extremely obvious. And yet other people don’t have those intuitions, so perhaps this is pretty non-obvious in reality.
Here’s a short, non-exhaustive list:
Intermediate Value Theorem
Net Present Value
Differentiable functions are locally linear
Theory of mind
Grice’s maxims
If you have not heard any of these ideas before, I highly recommend you look them up! Most *likely*, they will seem obvious to you. You might already know those concepts by a different name, or they’re already integrated enough into your worldview without a definitive name.
However, many people appear to lack some of these concepts, and it’s possible you’re one of them.
As a test: for every idea in the above list, can you think of a nontrivial real example of a dispute where one or both parties in an intellectual disagreement likely failed to model this concept? If not, you might be missing something about each idea!
I’m struggling to come up with an example of a real dispute involving the intermediate value theorem. Can you suggest one?
Sometimes people say that a single vote can’t ever affect the outcome of an election, because “there will be recounts.” I think stuff like that (and near variants) aren’t really things people can say if they fully understand IVT on an intuitive level.
Very similar: ‘Deciding to eat meat or not won’t affect how many animals are farmed, because decisions about how many animals to farm are very coarse-grained.’
Yep! Or donations below a certain amount won’t do anything since planning a shipment of antimalarial nets, or hiring a new AI Safety researcher, is lumpy.
I don’t get how the IVT applies here. Like, the things I would think about here would be there is a chance that my vote can be that one important vote that gives my candidate advantage. Or how we need to coordinate without communication, like if other people thought the same that their vote doesn’t matter, all in all my candidate looses many more votes than one. The number of votes my candidate has is the integral of voter’s preferences, but this is not a smooth function so it shouldn’t apply here as well?
Have you heard the argument before that single votes can’t ever matter because there’d be a recount anyway?
no
All of them are lovely and extremely useful in my world-models. And all of them have failed me at one time or another. Here are some modes where I’ve thought I understood and it was obvious, but I was missing important assumptions:
Intermediate Value Theorem: Obvious, incontrovertible. A knockout punch in any disagreement. Except, a lot of things aren’t quite as continuous as you think, when you really get formal about them.
Net Present Value: Also clearly the right tool for most comparisons of value. And figuring out the correct discount rate to take into account differing risks is quite nontrivial.
Local linearity: this one I lean on a bit less, but it still bites me when I get too loose with “locally”.
Theory of Mind: I’m getting better, but I’m still a master of Typical Mind Fallacy.
Grice’s Maxims (and Crocker’s Rule): Great when a target I strive for, very misleading when I expect that it’s common.
Extension: Which obvious-in-retrospect-and-to-other-people ideas am I currently missing? Are there conceptual technologies that you’ve noticed that I (Linch) in my conversations or internet comments appear to have missed?
I don’t follow how / why this test is supposed to work.
Can you give an example of “a nontrivial real example of a dispute where one or both parties in an intellectual disagreement likely failed to model [one of these concepts]” and how that is indicative of if you’re missing something or not?
It seems like I could understand any of these points, but not be able to think of places where others are missing them?
Check out https://linch.substack.com/p/unknown-knowns
Seem like ripe opportunities for posts
Decided to write about it for Christmas! I thought about my examples and connections again and decided maybe they’re nonobvious enough (eg LLMs produce very different, and much worse/trivial examples of disputes): https://linch.substack.com/p/unknown-knowns
I’ll think about it! I don’t personally like writing blogposts of well-known concepts unless I have a novel angle or a clear model for why the existing material is inadequate, but maybe!
Other people reading this who have a novel angle are of course free to take these projects on, of course.