the probability that the child’s questioning will lead to a significant new discovery
The relevant purpose is new discoveries for the child, which is quite plausible. Insufficiently well-understood claims are also not really known, even when they get to be correctly (if not validly) accepted on faith. (And siloing such claims inside appropriate faith-correctness/source-truthfulness hypotheticals is still superior to accepting them unconditionally.) There is also danger of discouraging formation of gears level understanding on the basis of irrefutability of policy level knowledge, rendering ability to make use of that knowledge brittle. The activity of communicating personal discoveries to the world is mostly unrelated.
I get your point, and I totally agree that answering a child’s questions can help the kid connect the dots while maintaining the kid’s curiosity. As a pedagogical tool, questions are great.
Having said that, most people’s knowledge of most everything outside their specialties is shallow and brittle. The plastic in my toothbrush is probably the subject of more than 10 Ph.D. dissertations, and the forming processes of another 20. This computer I’m typing on is probably north of 10,000. I personally know a fair amount about how the silicon crystals are grown and refined, have a basic understanding of how the chips are fabricated (I’ve done some fabrication myself), know very little about the packaging, assembly, or software, and know how to use the end product at a decent level. I suspect that worldwide my overall knowledge of computers might be in the top 1% (of some hypothetical reasonable measure). I know very little about medicine, agriculture, nuclear physics, meteorology, or any of a thousand other fields.
Realistically, a very smart* person can learn anything but not everything (or even 1% of everything). They can learn anything given enough time, but literally nobody is given enough time. In practice, we have to take a lot of things on faith, and any reasonable education system will have to work within this limit. Ideally, it would also teach kids that experts in other fields are often right even when it would take them several years to learn why.
*There are also average people who can learn anything that isn’t too complicated and below-average people who can’t learn all that much. Don’t blame me; I didn’t do it.
My point is not that one should learn more, but about understanding naturally related to any given claim of fact, whose absence makes it brittle and hollow. This sort of curiosity does apply to your examples, not in a remedial way that’s only actually useful for other things. The dots being connected are not other claims of fact, but alternative versions of the claim (including false ones) and ingredients of motivation for looking into the fact and its alternatives, including more general ideas whose shadows influence the claim. These gears of the idea do nothing for policies that depend on the fact, if it happens to be used appropriately, but tend to reassemble into related ideas that you never heard about (which gives an opportunity to learn what is already known about them).
It doesn’t require learning much more, or about toothbrushes, it’s instead emphasis of curiosity on things other than directly visible claims of fact, that shifts attention to those other things when presented with a given claim. This probably results in knowing less, with greater fluency.
To the extent that I understand what you’re saying, you seem to be arguing for curiosity as a means of developing a detailed, mechanistic (“gears-level” in your term) model of reality. I totally support this, especially for the smart kids. I’m just trying to balance it out with some realism and humility. I’ve known too many people who know that their own area of expertise is incredibly complicated but assume that everything they don’t understand is much simpler. In my experience, a lot of projects fail because a problem that was assumed to be simple turned out not to be.
This is useless in practice and detrimental to being a living encyclopedia, distracting from facts deemed salient by civilization. Combinatorial models of more specific and isolated ideas you take an interest in, building blocks for reassembling into related ideas, things that can be played with and not just taken from literature and applied according to a standard methodology. The building blocks are not meant to reconstruct ideas directly useful in practice, it’s more about forming common sense and prototyping. The kind of stuff you learn in the second year of college (the gears, mathematical tools, empirical laws), in the role of how you make use of it in the fourth year of college (the ideas reassembled from them, claims independently known that interact with them, things that can’t be explained without the background), but on the scale of much smaller topics.
Well, that’s the attempt to channel my impression of the gears/policy distinction, which I find personally rewarding, but not necessarily useful in practice, even for research. It’s a theorist’s aesthetic more than anything else.
The relevant purpose is new discoveries for the child, which is quite plausible. Insufficiently well-understood claims are also not really known, even when they get to be correctly (if not validly) accepted on faith. (And siloing such claims inside appropriate faith-correctness/source-truthfulness hypotheticals is still superior to accepting them unconditionally.) There is also danger of discouraging formation of gears level understanding on the basis of irrefutability of policy level knowledge, rendering ability to make use of that knowledge brittle. The activity of communicating personal discoveries to the world is mostly unrelated.
I get your point, and I totally agree that answering a child’s questions can help the kid connect the dots while maintaining the kid’s curiosity. As a pedagogical tool, questions are great.
Having said that, most people’s knowledge of most everything outside their specialties is shallow and brittle. The plastic in my toothbrush is probably the subject of more than 10 Ph.D. dissertations, and the forming processes of another 20. This computer I’m typing on is probably north of 10,000. I personally know a fair amount about how the silicon crystals are grown and refined, have a basic understanding of how the chips are fabricated (I’ve done some fabrication myself), know very little about the packaging, assembly, or software, and know how to use the end product at a decent level. I suspect that worldwide my overall knowledge of computers might be in the top 1% (of some hypothetical reasonable measure). I know very little about medicine, agriculture, nuclear physics, meteorology, or any of a thousand other fields.
Realistically, a very smart* person can learn anything but not everything (or even 1% of everything). They can learn anything given enough time, but literally nobody is given enough time. In practice, we have to take a lot of things on faith, and any reasonable education system will have to work within this limit. Ideally, it would also teach kids that experts in other fields are often right even when it would take them several years to learn why.
*There are also average people who can learn anything that isn’t too complicated and below-average people who can’t learn all that much. Don’t blame me; I didn’t do it.
My point is not that one should learn more, but about understanding naturally related to any given claim of fact, whose absence makes it brittle and hollow. This sort of curiosity does apply to your examples, not in a remedial way that’s only actually useful for other things. The dots being connected are not other claims of fact, but alternative versions of the claim (including false ones) and ingredients of motivation for looking into the fact and its alternatives, including more general ideas whose shadows influence the claim. These gears of the idea do nothing for policies that depend on the fact, if it happens to be used appropriately, but tend to reassemble into related ideas that you never heard about (which gives an opportunity to learn what is already known about them).
It doesn’t require learning much more, or about toothbrushes, it’s instead emphasis of curiosity on things other than directly visible claims of fact, that shifts attention to those other things when presented with a given claim. This probably results in knowing less, with greater fluency.
To the extent that I understand what you’re saying, you seem to be arguing for curiosity as a means of developing a detailed, mechanistic (“gears-level” in your term) model of reality. I totally support this, especially for the smart kids. I’m just trying to balance it out with some realism and humility. I’ve known too many people who know that their own area of expertise is incredibly complicated but assume that everything they don’t understand is much simpler. In my experience, a lot of projects fail because a problem that was assumed to be simple turned out not to be.
This is useless in practice and detrimental to being a living encyclopedia, distracting from facts deemed salient by civilization. Combinatorial models of more specific and isolated ideas you take an interest in, building blocks for reassembling into related ideas, things that can be played with and not just taken from literature and applied according to a standard methodology. The building blocks are not meant to reconstruct ideas directly useful in practice, it’s more about forming common sense and prototyping. The kind of stuff you learn in the second year of college (the gears, mathematical tools, empirical laws), in the role of how you make use of it in the fourth year of college (the ideas reassembled from them, claims independently known that interact with them, things that can’t be explained without the background), but on the scale of much smaller topics.
Well, that’s the attempt to channel my impression of the gears/policy distinction, which I find personally rewarding, but not necessarily useful in practice, even for research. It’s a theorist’s aesthetic more than anything else.