Oh yeah, I didn’t link that back. Basically what I mean is that it might be the case that most people actually have trouble thinking in the way math really requires. It’s like they think you are doing magic. It’s a specific case where it really feels like you can see the difference in the way the wheel turn in people’s heads. Now that could be cultural just as easily as genetic (perhaps more easily). Just when you are sitting there in class and that guy just can’t get “All A are B does not imply all B are A” - there’s no way we could say that understanding that kind of concept requires much intelligence. There is some kind of difference there in the whole architecture of thinking.
I have no particular expertise in teaching or neurology, but I think it may have to do with analogies.
Pretty much everything else that humans do can be learned by analogy. When you learn pretty much any physical skill, “It’s like doing X, but with Y change.” As you learn more about doing the skill, it eventually gets its own brain patterns (and you can use it in its own analogies) but until then, it piggy-backs off of something else similar.
There’s really nothing similar to math other than more math, so if your brain is good at math, learning harder math will be easy (trigonometry is like algebra, but with triangles), but if you have nothing for math to piggyback on after the initial learn learn learn learn learn spurt in early childhood, you’re going to have a rough time picking it up.
Well, I think that is kind of the difference I’m describing. It’s not that you only get math analogies if you already get math, it’s that math is a constructed system where analogies don’t work.
I took calculus in highschool and it was taught very functionally: this is how you figure out a limit, these are the rules to calculate a derivative, etc. I could do it just fine, but I wouldn’t say I understood it. Then I went to my first university calculus lecture and the professor defined a limit:
And what did I think? I thought, “Aha, that’s what a limit is.” I actually didn’t really get it in highschool when I heard the analogies, but that made perfect sense of it to me. If he had given me the first assignment to do having said only that I would have been able to do it just fine. Also, I had never been exposed for formal math proofs, so until I saw him write that, and say it aloud as he did, I had never seen most of those symbols before (iff, ∀, ε, ∃, δ, s.t., ⇒).
I didn’t have to go look that up to type it out now, I still remember that more than a decade later. And when my little sister needed help on her highschool calculus homework I couldn’t remember the product rule for derivatives, so I wrote out the limit definition of a derivative and derived the product rule myself rather than thinking, “I have a calculus textbook in front of me, I could look this up.”
Obviously underlying this thought process needs to be the same kind of stuff as everyone else’s brain is made of, but that’s what makes me think that I think through a different architecture.
[Sorry. Stumbled on the old topic, and I realized I hadn’t read a bunch of replies and I just had to revive it.]
[ETA: Not a reply to @daneel… I think I must’ve hit “Reply” on a pseudothread.]
…and the world makes a little more sense.
This is very important and while there’s all kinds of trauma associated with it, I’m glad I flunked out of university and became estranged from family that would have been there for me financially. I shed excess pride the way some people shed excess pounds in infomercials. I have huge pride pants I keep in the closet now.
I took up a bunch of crap jobs with no sense that they were in any way a temporary phase in my life and in the process I’ve met people who have been indisputably damaged by lack of opportunity. I mean, I don’t know what it’s like to grow up in a house without books. I could ask my mom questions about language or literature, and my dad questions about math or science whenever I felt like it and could expect an answer. I don’t know what it’s like to have people tell me that I should be careful not to learn too much in college, or to drop out of high school because of a drug or alcohol problem. I learned very quickly that there wasn’t anything special about me, just that I was lucky. A new acquaintance has brought this home in uncomfortable ways. Ever meet someone who is basically you at a younger age, and kind of dislike them? It’s very disconcerting. The guy isn’t terrible, and he’s smart, but there’s a special kind of naivete there that comes with being “smart” that I wonder if he’ll ever be able to shake without losing some of his privilege.
It’s hard, too- because I’ve struggled with self-loathing in the relatively recent course of my life as a consequence of PTSD. So it’s hard to tell myself that I’ve been merely lucky and then take enough pride in myself that I stay sane. I have yet to figure out that balance. I do wish American culture took a little from the British when it comes to opportunity. While I think the British obsession with where you went to school is annoying and hilarious in equal measure, they do have an overt class consciousness that I think is more honest than the prevailing American myth that every has a real shot at [insert criteria for success here].
I think you’ve inadvertently hit on something critical here: Smart is culturally defined, and most often culturally defined in ways that have to do with economic activity or societal needs. The merchant’s son with a head for arithmetic in ancient Greece was a smarter kid than the same kid as a hunter-gatherer who was outclassed by the kids who seemed to innately understand how to track animals. “Smart” is incredibly relative. Throw in highly plastic populations like children, and I think it muddies the issue even more.
I firmly believe that what most people refer to as “intelligence” is a matter of learned information and methods of attacking problems.
There definitely are people who have been “wired” (either through nature or nurture) to attack certain classes of problems in an optimal manner, but in general most of the things people think of as indicators of someone being “smart” are just a matter of the person having had enough interest in something to integrate it more than most other people.
Of course, there’s also the completely different issue of people thinking that certain looks indicate intelligence (or that that “intelligence” translates to extra knowledge of completely mundane things). I once overheard someone say “oh, they’ve got glasses, they look smart. Let’s ask them” followed by a pair walking up to me and asking me the time. I think I responded by giving them the wrong time, and then when they asked if I had a light I handed them a shocking lighter. Almost earned me a fist to the face, but it served them right…
Of course, there are always going to be some of us who have specific, narrow traits that start dramatically below average and just because of how our mind works are likely never to improve beyond ‘way below average’…but we humans have huge brains and almost all of us has a few things we’re above-average to amazing at.
I think the mission (and one we’re not doing too well at) in society should party be to bring those things into sync so as many of us as is possible are maximizing our potential and not having to leverage our worst traits. We don’t have blind people driving trucks, but we’re not far enough off.
