λ-calculus
Documenting my journey to the sewer
- Oct 24, 2023
- 1,357
I know that intelligence is a very wide thing, but I'll only talk about the type of intelligence related to math/logic puzzle solving stuff. So what is intelligence? Certainly when a person can solve a lot of tricky math problems faster than others, we think they are intelligent, but what is the difference between a person who can solve these puzzles and someone who can't (or maybe they can but it takes them a really long time)? I used to think it was mostly luck. Sometimes solving a puzzles does end up requiring a bit of luck, think of it this way: There are multiple approaches you can take to solving a puzzle, not all of them will pan out, but you can't know if they will pan out or not until you try them, so you pick an approach and check where it leads, in the end it leads nowhere and you have to pick something else. Someone else might have picked a different approach and this approach did work out for them, even though the only difference between you and them is that they were lucky enough to pick an approach that would pan out. So there's definitely luck involved, but that's not all, after all some people can consistently pick the right approach faster than others and with less trial and error. I witnessed this multiple times back when I used to solve sudoku variants, I follow this YouTube channel with two veteran sudoku solvers and watching them solve a puzzle is like watching someone perform magic. Somehow they always know what is the right approach to solving a problem, even when solving them blind, they can always discern what thoughts processes will lead to a solution and they solve the puzzle fairly quickly. By comparison, I would take much longer because I would waste time on approaches that led nowhere. So for you to solve a puzzle quick you need both the luck and the experience but also some intuition, some sort of subconscious bias that leads you down the right path and I think this intuition is something that you're born with, of course you can improve it with experience, but very little.
But I think there's more to intelligence than the ability to discern the right approach to a problem faster than others: There is also the ability to come up with approaches to solving a problem that nobody else could have come up with. Thoughts processes that are so convoluted and complex, there's no way the average person could have come up with that, even if you gave them infinite time. I think this second thing is what truly makes the difference between an average mathematician and a world class famous mathematician who will be remembered for ages to come.
Personally, I don't feel like I have this ability to come up with super mind blowing ideas. In all of my years of living, I have never had an idea that made me go "woah I really knocked it out of the park with this one", I feel like all of my thoughts processes are so linear and just what anyone would do if they had the same information I have. I mean maybe not anyone, after all the average person really does truly suck at math, but like I feel like any competent mathematician could have come up with that same idea no problem.
Ultimately I think that's ok, after all, I don't need to be a super famous genius mathematician to be happy, or to advance the field of math. Truth is people like me that are smart enough to understand complex math, but not smart enough to come up with the next big idea that will revolutionize entire fields of math, are still needed to make progress. There are millions of people with the same level of math ability or better than me, and even though we will no be coming up with any brilliant ideas, we can chip away at math problems so that perhaps a truly smart person can one day fully solve it.
Thanks for listening to me ramble.
But I think there's more to intelligence than the ability to discern the right approach to a problem faster than others: There is also the ability to come up with approaches to solving a problem that nobody else could have come up with. Thoughts processes that are so convoluted and complex, there's no way the average person could have come up with that, even if you gave them infinite time. I think this second thing is what truly makes the difference between an average mathematician and a world class famous mathematician who will be remembered for ages to come.
Personally, I don't feel like I have this ability to come up with super mind blowing ideas. In all of my years of living, I have never had an idea that made me go "woah I really knocked it out of the park with this one", I feel like all of my thoughts processes are so linear and just what anyone would do if they had the same information I have. I mean maybe not anyone, after all the average person really does truly suck at math, but like I feel like any competent mathematician could have come up with that same idea no problem.
Ultimately I think that's ok, after all, I don't need to be a super famous genius mathematician to be happy, or to advance the field of math. Truth is people like me that are smart enough to understand complex math, but not smart enough to come up with the next big idea that will revolutionize entire fields of math, are still needed to make progress. There are millions of people with the same level of math ability or better than me, and even though we will no be coming up with any brilliant ideas, we can chip away at math problems so that perhaps a truly smart person can one day fully solve it.
Thanks for listening to me ramble.