> It's unclear to me how you could separate knowledge and reasoning
yeah, me too. There are a few cases I'd point your attention to.
1, preschool toys, kids somehow manage to put the square peg in the square hole. I mean, they may chew on them or push them around, but there's a "moment of magic" when they make it all click together.
Maybe there's some implicit knowledge there, I know I played games like that, but I don't remember.
2, sudoku. you don't really need to know anything, just make each line row and box different. no memorization, just look.
but what about the rules? does that count as knowledge?
I've been reading some math books lately, and I think we're not alone. Coping with sets of sets is a hard question that people have been wondering about for, as far as I can tell, a long time.
For now, it's probably safe to say, knowledge about knowledge is different that just knowledge, and having one layer work on k1 and another layer work on k2 is ok. maybe someday add k3...kn. Other fields do that. Worth checking out.
I think, we could both get very fussy about what exactly that _means_. But for now, I'm happy to be charitable in my reading. I'd also expect them to run into some really thorny problems when they try to pin down exactly what's going on, just like everybody else does. For today, good for them. Seems like a nice win.
Different people might think diffrent, but when solving complex problems I do think I have seperate "think about / gather the facts" and "formulate the solution" phases.
I don't think about the totality of facts in the world - I think my brain is mentally extracting the facts that are relevant to the problem and then reason about those facts.
There is certinaly back/forth though, but I think I go "here is a bit of information, how does that apply? ok but what about this fact? ok here is how that would apply considering something else..." but I think this is still a gather -> solve -> gather -> solve
yeah, me too. There are a few cases I'd point your attention to.
1, preschool toys, kids somehow manage to put the square peg in the square hole. I mean, they may chew on them or push them around, but there's a "moment of magic" when they make it all click together. Maybe there's some implicit knowledge there, I know I played games like that, but I don't remember.
2, sudoku. you don't really need to know anything, just make each line row and box different. no memorization, just look. but what about the rules? does that count as knowledge?
I've been reading some math books lately, and I think we're not alone. Coping with sets of sets is a hard question that people have been wondering about for, as far as I can tell, a long time.
For now, it's probably safe to say, knowledge about knowledge is different that just knowledge, and having one layer work on k1 and another layer work on k2 is ok. maybe someday add k3...kn. Other fields do that. Worth checking out.
I think, we could both get very fussy about what exactly that _means_. But for now, I'm happy to be charitable in my reading. I'd also expect them to run into some really thorny problems when they try to pin down exactly what's going on, just like everybody else does. For today, good for them. Seems like a nice win.