Oh wow I must be a genius...
Intelligent people take longer to solve hard problems: study
51–60 of 184 posts
Re: Intelligent people take longer to solve hard problems: study
#52I strongly suspect this effect is correlated with a weakness in short-term or working memory. Independent of general intelligence is the necessity for those with a weak short-term or working memory to compensate by relying on long-term, in depth understanding in order to JIT the necessary short-term structures into being on the spot, (often repeatedly as these images decay rapidly) in order to solve a problem. Wherea…
My big stumble in math came when I stopped being able to self-prove everything I saw.
At some point you must memorize in math.
Re: Intelligent people take longer to solve hard problems: study
#53I strongly suspect this effect is correlated with a weakness in short-term or working memory. Independent of general intelligence is the necessity for those with a weak short-term or working memory to compensate by relying on long-term, in depth understanding in order to JIT the necessary short-term structures into being on the spot, (often repeatedly as these images decay rapidly) in order to solve a problem. Wherea…
In my experience short term and long term memory recall speed and accuracy are strongly correlated. It's unlikely someone will be able to swiftly traverse a large long term memory graph, in a manner that would allow you to derive deep insights not just recalling a single piece of information, but have a poor short term memory. However I do believe long term memory is more robust so if you're in a mentally compromised…
Correlated but at what level of the bell curve? I think they are correlated but vary a lot within similar bands, to the point where the broad correlation is actually not interesting and the within-band correlation is much more so.
Adding on, there's a definite weird trade off going on between memory and creativity that I think is very under-appreciated. I think memory acts as a bind on creativity, and it's really easy to make this intuitive with any number of examples whether it be youth or marijuana/psychedelics. When you reduce your ability to access memory you seem to gain an ability to explore new spaces. Likewise the more you learn and build structures in your brain around concepts, the harder it is to accept and process novelties. Feels like there's some similar trade offs going on as with this deep vs fast thinking.
Re: Intelligent people take longer to solve hard problems: study
#54I strongly suspect this effect is correlated with a weakness in short-term or working memory. Independent of general intelligence is the necessity for those with a weak short-term or working memory to compensate by relying on long-term, in depth understanding in order to JIT the necessary short-term structures into being on the spot, (often repeatedly as these images decay rapidly) in order to solve a problem. Wherea…
My big stumble in math came when I stopped being able to self-prove everything I saw. At some point you must memorize in math.
That point is very early. Math finally really took off for me when I realized that, no, it's not enough to understand an equation, or a set of requirements, etc., when I'm introduced to it. I have to actually memorize it. Literally with a flashcard app that I open every day.
By rote memorization, it is available in my head immediately, and I can use it to reason through things, without having to derive anything. It helps tremendously.
Then, at some point, it will become so familiar and understood through working with it, that the rote memorization becomes superfluous. For example, I've worked with the Laplace Transforms and the various Fourier Transforms (FS, FT, DFT, DTFT) so intensely by now, that I can absolutely just recite them by concept and understanding of why they are what they are.
But until then, rote memorization is basically a necessary tool to work with math.
The moment that made me realize that was when I saw a math genius at university, one who clearly understood the topics extremely well, going through his flashcards.
Re: Intelligent people take longer to solve hard problems: study
#55I strongly suspect this effect is correlated with a weakness in short-term or working memory. Independent of general intelligence is the necessity for those with a weak short-term or working memory to compensate by relying on long-term, in depth understanding in order to JIT the necessary short-term structures into being on the spot, (often repeatedly as these images decay rapidly) in order to solve a problem. Wherea…
My pet theory is that this is closely related to the "two cultures" in mathematics with "problem solvers" vs "theory builders": is it easier for you to put more strain on your working memory to solve a problem, or would you rather put in more up-front conceptual effort to reduce that strain?
I'm not a mathematician, but I've seen a similar bifurcation in programming styles and preferences: something like "debuggers" vs "abstraction builders". Would you rather have less to learn up front at the expense of needing to track more details as you're working, or would you rather spend time learning or developing a conceptual foundation to reduce ongoing pressure on your working memory?
I figure this is why discussions about keeping programming "simple" are so unproductive: people end up talking past each other because one camp values reducing up-front complexity, the other reducing ongoing complexity, but everybody talks about it as if there's only one simple–complex dimension.
Re: Intelligent people take longer to solve hard problems: study
#56I strongly suspect this effect is correlated with a weakness in short-term or working memory. Independent of general intelligence is the necessity for those with a weak short-term or working memory to compensate by relying on long-term, in depth understanding in order to JIT the necessary short-term structures into being on the spot, (often repeatedly as these images decay rapidly) in order to solve a problem. Wherea…
I struggled in math in HS for this reason. Every time a concept was presented to me I felt like I needed to deeply understand it at the most universally root level and create a painstaking mental model of it, to a degree that I imposed on myself for some inexplicable reason. To answer "but WHY". Almost like a form of self-sabotage in hindsight because I think there are decreasing returns in "truly, deeply" grokking m…
Yeah, I basically have no choice but to deeply, truly understand something. If I don't "completely get it", I will struggle endlessly to employ the "knowledge" I have. It's been a lifelong challenge (indeed I barely finished high school because I was actually failing classes because it was impossible to keep up -- yet I am a senior software engineer today), while some people forge ahead seemingly effortlessly, I am still solidifying the fundamentals. To be fair though, my deep understanding of stuff results in pretty comprehensive/effective solutions that consider edge-cases/gotchas/etc. and I think that's pretty valuable. Once I have those "fundamentals", I have mastered that shizzle and it's completely solid in my repertoire basically forever. The decay is VERY slow once I learn something, and I can remember deep details about things for years.
The discussions on this post have been the first time I've really hard people describe this phenomenon in such clarity. It's really nice to know there are other people who are similar to me in this way, as I very very often feel like the "odd one out" in this regard...
Re: Intelligent people take longer to solve hard problems: study
#57Related: Thinking, Fast and Slow, by Daniel Kahneman. According to Wikipedia [1]:
"The book's main thesis is a differentiation between two modes of thought: "System 1" is fast, instinctive and emotional; "System 2" is slower, more deliberative, and more logical."
Intelligent people might rely more on System 2 than ordinary people, which pushes latency up.
Re: Intelligent people take longer to solve hard problems: study
#58Earlier quoted context omitted.
I struggled in math in HS for this reason. Every time a concept was presented to me I felt like I needed to deeply understand it at the most universally root level and create a painstaking mental model of it, to a degree that I imposed on myself for some inexplicable reason. To answer "but WHY". Almost like a form of self-sabotage in hindsight because I think there are decreasing returns in "truly, deeply" grokking m…
Just a hunch, but do you find that you perform substantially better if you are an environment where you can talk to yourself out loud as you work through a math or physics problem? If so, this is very much indicative of the phenomenon I'm describing, because what's happening is you're recruiting your audio memory as a compensatory short-term workspace, being able to loop some 2 or 3 additional elements of information…
That's really interesting! Do you know any other techniques to hijack our brains for performance boosts?
I'm reminded of the classic Feynman story about discovering the different mental models that he/his coworkers used, and how those models affected thinking: https://youtu.be/Si6NbKqYEd8?t=105
Re: Intelligent people take longer to solve hard problems: study
#59I strongly suspect this effect is correlated with a weakness in short-term or working memory. Independent of general intelligence is the necessity for those with a weak short-term or working memory to compensate by relying on long-term, in depth understanding in order to JIT the necessary short-term structures into being on the spot, (often repeatedly as these images decay rapidly) in order to solve a problem. Wherea…
I struggled in math in HS for this reason. Every time a concept was presented to me I felt like I needed to deeply understand it at the most universally root level and create a painstaking mental model of it, to a degree that I imposed on myself for some inexplicable reason. To answer "but WHY". Almost like a form of self-sabotage in hindsight because I think there are decreasing returns in "truly, deeply" grokking m…
I elaborated as a reply to a sibling comment, but repeat after me: You need to memorize things in math, especially if you want full understanding. It is a necessary tool.
I realized this when I saw one of the higher math geniuses in university, one who really understood most things better than most of us, learn equations and lemmas from flashcards one day.
That memorization may become superfluous after you worked with something for a while, but until then, it is not just tremendously useful, but downright necessary, to make an equation, or set of axioms, theorem, or whatever, just "pop up" in your head while you're thinking something through.
You say:
> I needed to deeply understand it at the most universally root level and create a painstaking mental model of it
That is my modus operandi in math. I want to fully understand it, down to every little detail. But in my experience, memorization is one step for that model to really build itself up, and actually stick.
Reading through the pages of a math book and going "oh, yeah, I totally understood that, neat" is useless if you later encounter a problem and go "huh, so, what was the exact equation of the Fourier transform again"?
And not just because you now have to look it up to apply it, but also because an equation for example is not just a jumble of symbols that you write down and fill in. It has structure, it has meaning. If you can recite it in your sleep, then you also immediately see properties of it when they are relevant, and are able to make further connections.
As Andrew Wiles said: "Math is not a spectator sport."
It's hard to fully bring across what memorization does for math, but since I started just using a flashcard app (Anki) several years ago, I literally sometimes lie in bed at night, eyes closed and no notepad, and work through math in my head, trying to further understand some aspects. And because I can "look" at what I memorized in my head, it works really well.
Re: Intelligent people take longer to solve hard problems: study
#60So we have to be the smartest because it's been 3 months we are investigating an issue :D