[HN Gopher] Intelligent people take longer to solve hard problem...
___________________________________________________________________
Intelligent people take longer to solve hard problems: study
Author : Brajeshwar
Score : 175 points
Date : 2023-06-22 16:25 UTC (6 hours ago)
(HTM) web link (bigthink.com)
(TXT) w3m dump (bigthink.com)
| wizeman wrote:
| > needed more time to solve challenging tasks but made fewer
| errors [1]
|
| As someone else said, I can solve problems very quickly if the
| solutions don't have to be correct...
|
| But more seriously, it seems like different people might have
| different thresholds for when they consider a problem solved?
|
| If you decide to go back and review the problem and solution
| (even just mentally) to make sure you didn't make mistakes, of
| course that would take longer and give you more correct answers
| than the person who doesn't do that?
|
| [1] https://www.bihealth.org/en/notices/intelligent-brains-
| take-...
| pcurve wrote:
| I don't claim to be intelligent, but I do dread doing group
| brainstorming sessions using Post-it notes because it takes me
| time to think about the problem.
|
| I'm usually the the guy in the group with the fewest notes. I've
| rarely see anything useful come out of these sessions, even
| though I've participated in hundreds of these with different
| people, companies, and settings.
| jamesdelaneyie wrote:
| Your goal during the ideation phase of those workshops should
| be to output as many post its as possible in the given time.
| Output the bad ideas quickly and you'll move along to better
| ideas much faster when you're not humming and hawing over one
| post it. You have to be ok with looking slightly crazy however
| and not mind being linked to your poor ideas.
| lanstin wrote:
| Yeah, I'll have no answer the first day of mulling over a
| complex problem, but often I'll have an excellent answer the
| next day.
|
| It's worked well for my own work, but sometimes people are
| surprised that the slow seeming person, me, has useful ideas.
| feiszli wrote:
| Oh wow I must be a genius...
| dimal wrote:
| This must be why I can't do well in any coding interviews. I'm
| just too damn smart.
| pschuegr wrote:
| Yep. Going to mention that next time. "I'm too smart to solve
| this quickly, can I get back to you next week?"
| jawns wrote:
| A while back, I created an online experiment, based on a 2020
| study, that identifies dogmatic thinking.
|
| https://shaungallagher.pressbin.com/blog/dogmatism.html
|
| Without giving too much away, this tracks with the 2023 study's
| results, in that people with higher intelligence scores are less
| likely to trust their System 1 gut reaction and more likely to
| involve their System 2 deliberate, logical processes.
| abathur wrote:
| > people with higher intelligence scores are less likely to
| trust their System 1 gut reaction and more likely to involve
| their System 2 deliberate, logical processes
|
| Amusingly, I mistrust my attention and visual ~memory so much
| that I reasoned I would find the "easier" task just as hard
| unless it was literally like 1 vs 3 dots, or unless it stayed
| up so long that I could count (maybe harder, since I'd likely
| get more annoyed at myself for missing questions I believed to
| be easier). I ignored this option because I was fairly sure
| it'd just mostly waste 200 points.
|
| I went back after completing to check out this option and don't
| feel like it made the task noticeably easier (to me).
| carabiner wrote:
| Have you read Superforecasting? One conclusion they had was
| that very partisan thinkers, basically dogmatic, were the worst
| at predicting future events, and it didn't matter _what_ that
| dogma was. Liberal or conservative or anti big business or
| whatever. All of the really good forecasters were relentlessly
| fact based and spent a huge amount of time diving deeply into
| facts, and microfacts that supported facts. It sounded
| exhausting and one of the author 's takeaways was "the world is
| enormously complex" and that most of us don't know anything
| about anything (hello gelman amnesia).
| vorpalhex wrote:
| This is funny because I've heard this from the opposite
| approach: using forecast accuracy to determine personal model
| accuracy.
|
| If you can accurately predict the future above random chance,
| that lends evidence that your internal state aligns with
| reality.
|
| (There are obviously traps here, eg the conspiracy theorist
| who sees every outcome as proof of the conspiracy)
| Verdex wrote:
| Neat experiment. Although, I was able to guess a higher than
| average number of dots correctly, I wonder if I would feel
| differently had I been under the average.
|
| The explanation given at the end is interestingly to me.
| However, consider the following alternate: People more likely
| to answer honestly that they view others opinions as wrong or
| immoral (ie they would appear to have dogmatic thinking) are
| also people who consider the easy dot guesses as cheating and
| desire to avoid cheating. Whereas people who are more likely to
| want to win the dot guessing by any means are also more likely
| to lie about their negative views about the opinions of others.
| bobsoap wrote:
| I don't think you can infer that a person answers a 10-minute
| anonymous online quiz more honestly because they refuse to
| take a hint out of principle.
|
| It would be a stretch to consider the hints cheating; they
| are an integral part of the game, they are clearly explained
| and carry a penalty if used.
| SamPatt wrote:
| That was fun, I scored lower (2.1) dogmatism and higher on the
| test (840), which they claim supports their hypothesis.
|
| In day to day life the major difference I notice in terms of
| speed and intelligence personally is that I'm often slow to
| respond to questions.
|
| It didn't even occur to me to be self-conscious about this
| until eventually a friend pointed it out, but he kindly framed
| it as "you think before you speak" and this seems to have
| served me well.
| mordae wrote:
| I had 3.4 and similar number of points as you. The questions
| don't really work that well.
|
| E.g. the healthcare one doesn't work for my country where
| universal healthcare is a law and thus State truly has duty
| to provide it and anyone who believes otherwise is
| objectively wrong.
|
| I have also received more points for being "dogmatic" in that
| having strong opinion (that is different than mine of
| "neutral") on migration is a bad person.
| bobsoap wrote:
| Just because something is the current status quo in your
| country doesn't mean you can't have a different opinion. I
| think the question is perfectly valid no matter where you
| live.
|
| The irony is, faulting the question because "that's just
| the way it is here" beautifully illustrates the exact
| premise of the experiment. I'd say that explains a 3.4
| score (at least in this game).
| antisthenes wrote:
| No offense, but the experiment is nonsense.
|
| What makes you think there's any relationship between visual
| recognition and dogmatism?
|
| Even your own results only show a 2.5% difference between the
| most dogmatic and least dogmatic participants, assuming they
| even answered the dogmatic portion of the test truthfully and
| thoughtfully. I can't see how that amounts to anything more
| than a statistical error.
|
| Just in case, my score was 940/3.0, although again, I don't see
| anything to show there should be any relation.
| kaechle wrote:
| The test states at the end that dogmatism is measured based
| on the answers to a subset of the questions--the game is
| simply a correlate.
| KennyBlanken wrote:
| A 2% difference in scores between the most and least dogmatic
| users means your test complete hogwash.
|
| Your refusal to provide any data beyond averages is very
| telling. My guess is that there's a very wide distribution of
| scores, little trend, and very little correlation.
| MSFT_Edging wrote:
| I definitely got more dogmatic, but I also find it interesting
| because I scan visual stuff really fast, and typically notice
| things a while before people, ie while driving I'll spot a
| slick-top cop far ahead. So I have a lot of trust in my visual
| acuity. I got a score of 900 without trying the easy one.
|
| The latter part of the test was 100% incriminating and I think
| I am quite dogmatic.
| alwaysbeconsing wrote:
| I will come back to try this later, but I skimmed it and just
| wanted to say that the third button gave me a good laugh.
| wodenokoto wrote:
| > This might be because the least dogmatic participants were
| more willing to view the easier version of the challenge when
| they were initially uncertain.
|
| Can't you test that hypothesis, or do you not have the data?
|
| I also find it super annoying that one of the buttons to choose
| left is on the right and vice versa.
| mcint wrote:
| This link would better serve you and the community as a top-
| level post. I guess you did share it 2 years ago, though it
| looks like commenting is now closed.
| https://news.ycombinator.com/item?id=26620690
|
| Share it again! The iron is hot!
|
| I find the initial paragraphs of analysis rather insistent, one
| might say _dogmatic_ , in their praise of _non-dogmatism_. Some
| later paragraphs express my immediate response: perhaps this
| dogmatism varies based on your relationship to your current
| information environment.
|
| I'll suggest that consideration of these numbers might be
| better supported by _tables_ to show participant and average
| numbers, and invite comparisons.
| kstrauser wrote:
| Problem: I need to typeset a book.
|
| Normal person: _typesets the book_
|
| Knuth: _takes a decade to solve book typesetting once and for
| all_
|
| I wonder if the intelligent people tend to solve more general
| problem classes and then apply that to the specific problem at
| hand.
| entropicgravity wrote:
| Ah, that's my problem with the 2nd Law of Thermodynamics.
| fxtentacle wrote:
| Extremely misleading title, in my opinion.
|
| Let me quote the actual research at
| https://www.nature.com/articles/s41467-023-38626-y :
|
| "subjects with higher PMAT24_A_CR (fluid intelligence) made fewer
| mistakes, but were slower"
|
| Yes, intelligent people took longer to solve hard problems. But
| they made fewer mistakes. Getting things right on the 1st try
| might be much faster than needing a 2nd attempt, even if the 1st
| try takes 20% longer.
| NotYourLawyer wrote:
| Social science is ridiculous. What a non-result.
| alach11 wrote:
| Alternate title: "Less intelligent people give up on hard tests
| and begin guessing answers."
| proc0 wrote:
| Slow is smooth, smooth is fast.
|
| Forgot where that's from but I think it's a Navy or Marine
| saying.
| jandrewrogers wrote:
| It is a common aphorism in military training, related to the
| latency of effective fast-twitch reaction. The jerkiness of
| trying to point your weapon at a target as quickly as
| possible and then yanking on the trigger means you usually
| miss it.
|
| The most important motion is bring your weapon to bear on
| target in a mechanically efficient way and pulling the
| trigger as it comes on target in a single motion. That single
| integrated motion can only be learned by doing it slowly but
| it is very accurate and smooth. If you practice the motion
| enough it becomes very fast. It is fine muscle memory. This
| is virtually always faster in terms of putting a bullet on
| target than relying on raw muscle speed. Also why military
| firearm skills are perishable, it has to be constantly
| practiced to keep the latency down.
| mordae wrote:
| Actually, solving problem quick and dirty, putting the solution
| to a test and iterating will probably result in better outcomes
| than simply thinking super hard and making less attempts for a
| whole bunch of tasks.
|
| It sure helps to be able to iterate quickly in software
| development for one.
|
| It has reminded me of an exchange from Shirobako (best anime
| ever, 100/100, watch it even if you prefer other forms); older
| animator is telling their younger colleague to learn to draw
| faster, because while they can work on the quality for the rest
| of their life, but they won't be able to draw fast when they
| are older. Drawing faster means more iterations, means more
| experience gained overall.
| thorncorona wrote:
| If what you're doing is getting a math problem correct than I
| would imagine doing it once correctly is the fastest
| approach...
| galaxyLogic wrote:
| Right they take longer but they actually solve the problem
| correctly. And if you don't solve it correctly you are not
| really solving it at all.
|
| The title could have been "Intelligent people take time to make
| sure their answer is more likely to be correct than not"
| commandlinefan wrote:
| > if you don't solve it correctly you are not really solving
| it at all.
|
| Try telling that to the time-tracking gestapo. As Dilbert
| says: "our boss can't judge the quality of our work, but he
| knows when it's late".
| hirvi74 wrote:
| In regards to the study you linked:
|
| > _Intelligence is here defined as the performance in
| psychometric tests in cognitive domains like verbal
| comprehension, perceptual reasoning or working memory. A
| consistent finding is that individuals who perform well in one
| domain tend to perform well in the others, which led to the
| derivation of a general factor of intelligence called g-factor_
|
| Whelp, I guess I broke the mold on this one. I have more than
| 1.5 standard deviations between some of my scores lol.
|
| I do not put much faith in IQ tests to begin with. I do not
| think the tests are completely useless, but I do think their
| utility is vastly overstated and the meaning of one's results
| are highly misused.
| tetha wrote:
| I'm thinking about too many things like chess. But in chess
| played with slower time controls, a critical skill is t
| recognize important positions and take time on them. And for
| many people, another important skill is to take more time in
| general.
|
| Like, a lot of lower Elo game at 10-minute time controls end
| with the losing person having 8 minutes left. That's not good.
| jollyllama wrote:
| Is this innately biological, or have intelligent people just been
| trained not to jump to conclusions/trust their gut, while this
| training was not as successful in other population segments?
| nerdo wrote:
| People who don't attempt the answer just guess, which takes less
| time than solving. News at 11.
| biomcgary wrote:
| Although your response is a bit clever, I think you capture the
| actual dynamic, which the paper
| (https://www.nature.com/articles/s41467-023-38626-y) tries to
| obscure by avoiding the comparisons (time taken for each
| correctly answered question vs incorrect) needed to make it
| obvious.
| pazimzadeh wrote:
| On the other hand, "more intelligent" people's brains work less
| hard during reasoning.
|
| https://www.nature.com/articles/s41467-018-04268-8
| Solvency wrote:
| Something tells me trying to bluntly define "more" and "less
| intelligent" and then compare the two groups with blanket
| studies like this is utterly ridiculous.
| Frameshift wrote:
| The "less likely to jump to conclusions" is the important part.
| This doesn't necessarily mean they are slower at processing
| information.
| no_butterscotch wrote:
| Yup.
|
| I also wonder if they could see another part of the brain to
| see if intelligent people are more concerned of judgement from
| other intelligent people, or perhaps even from everyone in
| general for some intelligent people that intelligence is their
| identity.
| sobriquet9 wrote:
| People with higher intelligence scores, not intelligent people.
| devnull255 wrote:
| If I try giving this as an explanation for churn on any issue I'm
| investigating, they'll probably take longer paying me ...
| adverbly wrote:
| Related: https://www.youtube.com/watch?v=vKA4w2O61Xo
|
| TL;DW:
|
| I have a rule and you need to figure it out. The rule relates to
| a sequence of three numbers. You can propose a sequence and I'll
| tell you yes/no if it meets the rule.
|
| I'll give you the first sequence to get you started:
| sequence: 2,4,8 passes: Yes
| paulpauper wrote:
| I think people are overreading into this, assuming the results
| even mean much anyway. people who score higher on timed tests
| which corelate well with IQ, such as the Wonderlic or the SATs,
| are smarter.
| ChainOfFools wrote:
| There's a confounding factor here, which is that people who
| score poorly could do so either because they could not solve
| the problem at all, or because they took too long to solve it
| (due to having to create mental tooling on the spot that others
| could buy off the shelf through memorization) and had reached
| only a partial result.
|
| In timed standardized exams where work is not shown or graded,
| both results are equally assigned zero points. As AI, even the
| ersatz AI available currently, becomes more sophisticated and
| widespread the value of a human who can mimic the capabilities
| of a machine will diminish rapidly.
|
| Creative and explorative thinkers will, provided they are not
| merely skilled at the derivative "craft" of performative
| creativity but are truly creating value without precedent, will
| accordingly become increasingly sought after.
| dorianmariefr wrote:
| So we have to be the smartest because it's been 3 months we are
| investigating an issue :D
| poomer wrote:
| These shape matching questions are the problems asked in the
| study:
|
| https://www.researchgate.net/profile/Jordan-Barbone-2/public...
|
| I would bet that quite a few people just guess when they find
| this type of question too difficult.
| chankstein38 wrote:
| Honestly this makes the most sense to me. I guessed first
| before thinking it through and if I were doing the test and it
| were timed I might've just guessed.
| elcritch wrote:
| > The findings challenge the assumption that higher intelligence
| is the result of a faster brain. They suggest that faster is not
| necessarily better, and that under certain circumstances there is
| a tradeoff between speed and accuracy which results in better
| decisions.
|
| Talk about conflating different aspects of something to arrive at
| faulty logic.
|
| There clearly is a relationship between higher intelligence and a
| faster brain, to some degree. However faster thinking enables
| more sophisticated searching of complex problem spaces.
| s1artibartfast wrote:
| >There clearly is a relationship between higher intelligence
| and a faster brain, to some degree. However faster thinking
| enables more sophisticated searching of complex problem spaces.
|
| I don't think that's clear at all. The confusion is around
| different definitions of speed and different definitions of the
| task.
|
| You have the speed to process data points or variables, and the
| speed to come to a result. You also have the number of
| variables used to calculate a result and the number of
| variables _needed_ to come to a result.
|
| It is reasonable to believe that some brains can process the
| same data faster than others. It is also reasonable to believe
| that some brains consider more variables than others.
|
| However, more variables is not always better. You can process
| faster, and include more variables, but still perform worse
| overall if you are using too many unecessary variables.
|
| In terms of computing, an example would be multiplying 2x2. A
| slower computer can give you a result faster if it is
| representing 2 as a 2-bit number than a faster computer
| representing it as a 64-bit number
| david38 wrote:
| I think of it as a computer with moderately fast registers
| but horribly slow main memory. In this case, more registers
| would clearly show a win. BUT a more organized person would
| eventually win as the number of variables grow.
|
| Hence why systems and habits beat out raw intelligence on
| general life success, but why an intelligent person lives a
| simple life on easy mode and why those at the (uninherited)
| top are often scary smart AND hard core driven and organized.
| s1artibartfast wrote:
| I basically agree.
|
| I would only add that some computers are simply incapable
| of performing a sufficiently complicated computation given
| their hardware and programing.
|
| Similarly, some computers with more limited hardware and
| programming can be more efficient at certian classes of
| computations.
| pazimzadeh wrote:
| Faster thinking allows to you brute force problems, which means
| you may not look for a more elegant solution because you don't
| need to.
|
| Like how Von Neumann was able to solve the fly and trains
| problem the hard way instead of finding the simple solution:
| https://www.pleacher.com/mp/mlessons/calculus/mobinfin.html
| [deleted]
| MisterPea wrote:
| While I agree I think Von Nuemann is the worst example to use
| in any topic about intelligence. He's not really like the
| rest of us
| robertakarobin wrote:
| Ooh, that's a much better explanation for my zillion half-
| finished projects. I'm not an undisciplined perfectionist, I'm
| just too intelligent. :)
| acchow wrote:
| Maybe subclinical ADHD?
| robertakarobin wrote:
| Why not both?
| hateful wrote:
| I know I am Twice Exceptional[1] in that regard.
|
| [1] https://en.wikipedia.org/wiki/Twice_exceptional
| Madmallard wrote:
| It's very likely just not enough incentive to go through the
| difficult and lengthy unfun parts. That's most people. It's
| not abnormal.
| carabiner wrote:
| Damn straight.
| robertakarobin wrote:
| In the words of Calvin and Hobbes, "You know how Einstein got
| bad grades as a kid? Well, MINE are even WORSE!""
| booleandilemma wrote:
| Can we also rephrase this as: if you want to be more intelligent,
| slow down and take the time to think through a problem?
| lanstin wrote:
| A thirst to deeply understand the systems around one is
| irreplaceable. Curiosity and an openness to seeing what is
| there instead of loading some fast model on top of the problem.
| hax0ron3 wrote:
| The title of the article should be "People with higher
| intelligence scores take longer to solve complex problems".
|
| Let's say that I define being very intelligent as being able to
| rapidly solve hard problems. I think this is a reasonable
| definition of the word "intelligent". Indeed, I think that it is
| in many ways a more meaningful definition of "intelligence" than
| defining it as scoring well on intelligence tests.
|
| Well, then the article title becomes self-contradictory.
| commandlinefan wrote:
| Yeah, the title (and the article) doesn't say "than what". If
| intelligent people take longer to solve complex problems than
| stupid people, then stupid people are smart and smart people
| are stupid. But the article doesn't really explain that either.
| PartiallyTyped wrote:
| Dupe: https://news.ycombinator.com/item?id=36172461
| lapcat wrote:
| Also https://news.ycombinator.com/item?id=36160582 and
| https://news.ycombinator.com/item?id=36211454
| beepbooptheory wrote:
| I always find it so strange and a little creepy to treat
| "intelligent" as a category like "brown haired" or "diabetic."
|
| You take a test and receive a score (an "intelligence score"
| apparently) and if you are past X points you are intelligent. Now
| you are among the set of intelligent people in the world.
|
| I know this is an agreed upon reality (especially among us nerdy
| types), but it always rubbed me the wrong way. Even bracketing
| off all the very real issues around measurement tools here, it
| always felt in general like neurotic pursuit to quantify the
| qualitative, or even an egoistic pursuit to claim superiority out
| of thin air.
|
| And I read articles like these, and I can't help but feel
| slightly validated despite their presuppositions: maybe there
| isnt a spectrum of intelligences, but just heterogenous minds. We
| have come up with these tests, but they just show how well a
| person is at that test that we happen to call "an intelligence
| test." But you start digging deeply with the numbers... and of
| course you going to get counter intuitive results! You have
| investigated categories that are themselves sustained out of
| thinnest of scientific consensus and dubious ideological origins,
| delegating your measurement to fraught tools laden with cultural
| specificity. It just feels crazy to me, it feels like never
| leaving grade school.
|
| But maybe they'll find "intelligence" one day, and then I'll have
| to eat my shoe while waiting in line to be recycled because I
| didn't pass muster as an intelligent human.
| foxbyte wrote:
| This complements the idea that problem-solving is the essence of
| intelligence. It's not always about speed, but the quality of
| decisions made, especially in complex situations
| alexfromapex wrote:
| Intelligence is related to increased perception throughput
| abilities, i.e. neural volume and density, so more intelligent
| people are processing more information which takes slightly
| longer (probably logarithmic). It all ties back to the same sort
| of results in neural networks. Not sure why I got
| downvoted...seems studies support my conclusion.
| boredumb wrote:
| In my experience when you're younger you can make a decision
| quickly without thinking through a lot of the edge cases and it
| works most of the time so it's much faster and just as good. Most
| of the time.
| [deleted]
| giovannibonetti wrote:
| Related: 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.
|
| [1] https://en.wikipedia.org/wiki/Thinking,_Fast_and_Slow
| thorncorona wrote:
| A large portion of the effects and studies mentioned in that
| book have been retracted or refuted, just fyi.
| giovannibonetti wrote:
| Wow, good to know!
| ChainOfFools wrote:
| I 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. Whereas those with a short-
| term memory advantage can simply rely on memorized sets of
| arbitrary relationships to address the problem.
|
| In other words if you have a weak short-term or working memory
| you have to, by necessity, deeply think through everything -
| whether simple or complex. This may allow spotting the rare
| inconsistency or opportunity others may not, but as it comes at a
| performance and time penalty which, under circumstances commonly
| encountered in one's educational career (timed examinations) it
| more typically results in filtering such people out of fields
| where excursive, highly lateral modes of thinking would be
| beneficial.
|
| To survive this filter one must either acquire (or be gifted
| with) the talent of exceptionally swift traversal of a large and
| heterogeneous general knowledge graph, as one cannot rely on a
| handful of tightly knit but relatively isolated silos of
| memorized specialization.
| coldblues wrote:
| A lot of replies here talk about short term memory, needing to
| truly understand information on a deep level and have the
| "why?" question answered, using software to externalize
| information and a lot more that I can't really mention right
| now on a phone in the middle of the night browsing HN and
| coming across this gem.
|
| A lot of this stuff seems highly related to ADHD. I exhibit
| them, and have done quite some amateur research myself on these
| behaviors and others seem to relate as well.
|
| P.S: I am also an i3wm user btw ;)
| bowenjin wrote:
| 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 state, such as having a
| headache, it will be less affected. So if you have to work
| through a hard problem on a deadline but have a headache, you
| can rely on heuristics stored in long term memory rather than
| deriving everything in short term memory.
| nwienert wrote:
| 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.
| ldehaan wrote:
| [dead]
| visarga wrote:
| This explanation fits me to a T.
| ajkjk wrote:
| Agree with this; also, it feels like you are reading out the
| same theories I have somewhere in my brain and that's a weird
| sensation.
|
| A related theory: being good at math, especially mental math,
| correlates with aphantasia (not being able to see pictures in
| your head). People who can see images in their head learn to do
| arithmetic early on with visual algorithms, which are
| fundamentally not good for understanding as well as rather
| error-prone (because the brain remembers gestalts, not finicky
| details like where a decimal is).
|
| Aphantasiacs are forced to learn to do math differently, and
| use some different part of the brain as 'scratch space'. In my
| case it's the language brain: calculations which are set aside
| live in the same part of your brain that can repeat what was
| said a moment to you without understanding it. Turns out,
| though, that this verbal part is quite _accurate_ at
| remembering things, and this makes it easier to juggle multi-
| step calculations without paper.
| ChainOfFools wrote:
| We are definitely aware of the same phenomenon! Check out a
| reply I made elsewhere in this thread which addresses
| compensatory recruiting of ones verbal/ audio immediate
| recall as an extension of working memory store.
| xigency wrote:
| > A related theory: being good at math, especially mental
| math, correlates with aphantasia (not being able to see
| pictures in your head)
|
| This is the kind of condition I wonder if I have. Because on
| one hand, if I do a visualization exercise I would describe
| it as foggy at best. Then again, I struggle to understand how
| our brains could be wired that differently from person to
| person, that we could have or lack certain mental senses. I
| would suggest that everyone has some latent capability,
| whether they recognize it or not. After all the visual cortex
| is quite important.
|
| In the context of your example, those good at mental math
| might see a chalkboard like image of the problem with all the
| detail. Those who struggle might be distracted visualizing
| the items that are being counted themselves, and all their
| detail.
|
| For another riddle, consider the question of whether one
| recognizes their thoughts as an internal monologue or not,
| and how that relates to communication and action.
| thorncorona wrote:
| > being good at math, especially mental math, correlates with
| aphantasia
|
| as someone who used to do math competitions as a kid,
| everyone I knew who was "good" at mental math had a good
| number sense, a big bag of tricks for doing different things
| with numbers, and practiced with their bag of tricks.
| fwungy wrote:
| 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.
| chongli wrote:
| You have to remember things in math. You don't have to
| memorize by rote. I'm very close to finishing a degree in
| pure and computational math and I've never sat down to
| consciously memorize anything. I don't really study much for
| exams either. I just work on the assignments and then show up
| and do my best for the exams. My grades are pretty much
| average but they're not a priority for me.
|
| For me, memorizing math means just working on problems until
| the theorems and definitions are like muscle memory. I know
| other people get by on flash cards but I can't stand them.
|
| Heck, I just wrote a midterm in network flow theory today and
| they gave us a sheet with all the theorems and definitions in
| the course up to this point. Needless to say, memorizing that
| sheet wouldn't help you at all on the proofs. You have to
| actually practice writing proofs to get good at it.
| anyfoo wrote:
| 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.
| dvwobuq wrote:
| I can entirely relate to this.
|
| About three weeks into my first undergraduate class on
| abstract algebra, it dawned on me that the instructor
| wasn't giving me math tests. He was giving me vocabulary
| tests. In that class, most of the answers to questions flow
| straight from the definitions. Once I broke out the
| flashcards and started memorizing definitions, that class
| became almost trivial.
|
| I used flashcards in all my classes after that to memorize
| terms, definitions, and concepts. Math and engineering are,
| for me anyway, like a foreign language. To converse in that
| language fluently, one must be very comfortable with the
| vocabulary. It just makes sense.
| anyfoo wrote:
| Well put, and I like that analogy. You have to learn the
| vocabulary, and only then are you well equipped to
| discuss grammar and finer subtleties of the language. It
| goes hand in hand.
| beepbopboopp wrote:
| This is a really interesting idea. I throw some money toward
| seeing this hypothesis tested or further explored.
|
| Ben Stiller _do it_ meme
| MSFT_Edging wrote:
| I've always felt like I have awful short term memory. I use
| tiling WMs so I can see information side-by-side. If I need to
| type something exactly, I forget the exact details almost
| immediately.
|
| I need to derive things to understand them, ie music theory.
| I'm jealous of people who can memorize and take at face value
| but if I'm looking at a chord, I need to know the components
| that create that chord, which gets frustrating because music
| has a lot of rules that seem to be based on vibe and closeness.
| Two things can be identical but distinct based on their
| context.
|
| It used to take me 2-3x as long to do homeworks or labs
| compared to other classmates. Same with work assignments. It
| often triggers an imposter syndrome type feeling.
|
| Yet I have proof that I'm capable of solving complex problems,
| I understand certain things almost immediately compared to
| others, other things I need to study for a long time.
|
| I tend to rarely know an answer on the spot, but I know how to
| determine many things, by knowing how to find the information
| needed.
|
| I don't pretend to be a genius, but I have proof via a degree,
| others opinions of me, and material results that basically say
| I'm intelligent to a point.
|
| Once I get into a flow I can retain a fairly complex system in
| my head but before or after that state, it's a terrible blur
| where I can barely focus my eyes.
| ilc wrote:
| Source: Principal Software Engineer, 25+ YOE.
|
| You are far smarter than you think.
|
| Learn to get into flow, and also figure out how to get your
| state back faster... Once you do, it is a super power.
|
| Simple things like leaving your editor/IDE open, create the
| same situation you left. I personally use music + IEMs to
| help me block sound and focus. -30-35 DB off the IEMs, and
| +70DB off my music... yeah, I don't hear anything.
|
| I learned the editor trick recently, though I'd probably done
| it un-intentionally for years. I stopped, and I was wondering
| what the inertia I was facing was. It is only 2-3m to get
| setup... that's 2-3m to lose my thoughts, etc.
|
| Good luck.
| cookiengineer wrote:
| The reason I love vim and i3/kitty so much as a combination
| is exactly this. I have 4 monitors in the exact state I
| left them when I get back, with the last TODO comments I
| added and what the problem was (that I thought about deeply
| overnight).
|
| For me the best way to get into the flow is by directly
| getting back to where I left. If I take time to wake up,
| make breakfast or anything else I usually lost my ideas
| already and it takes me hours to get back to them.
| coldblues wrote:
| I have ADHD and I relate a lot. Do you as well?
| pschuegr wrote:
| Not OP but identify strongly and yes.
| ChatGTP wrote:
| Hey, do you drink alcohol ?
|
| A few years back I accepted a challenge to take a year off
| drinking from a family member.
|
| I cannot tell you how much it improved my memory.
|
| Before that I was always losing things, frustrated I couldn't
| remember the names of things etc.
|
| After about 3 months I felt like I had doubled my memory.
|
| I wasn't really a heavy drinker, but I would go for a few
| months having 1-2 beers a day.
|
| Anyway just curious if you drink and have tried taking a
| break?
| screye wrote:
| I've always told friends that I have a massive knowledge
| graph on disk, and very low RAM. Reaching every leaf takes
| traversing the hierarchy, but it allows me to make
| connections and remember better over the long term.
|
| People are always blown away by my ability to recall a story
| perfectly or create 2 page white boarded proofs, but
| inability to remember my SSN or why I entered a room.
| Solvency wrote:
| 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 math if you're
| not going to be pursuing math as a career.
|
| But I also abhor rote memorization. Not because I don't think
| it's valuable, I just hate extremely repetitive tasks. Close
| friends of mine with zero interest in the subject just took
| everything at face level and preferred to rote memorize
| everything and slap it down as needed. And they tested much
| better than I did. Neither I or they are more intelligent than
| one another and these days we all excel at our own areas we
| enjoy. But for that subject in particular, in a rushed
| classroom standardized testing situation, I think their
| approach was "better".
| anyfoo wrote:
| 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.
| ChainOfFools wrote:
| I agree with this, and the rationalization that I
| eventually worked out and learned to live with is that as
| you get into more advanced areas of math, much of what you
| are learning are building blocks for assembling more
| complex tools - but those are tools you have no use for
| yet, and therefore can't hook constituent elements into any
| existing framework of understanding.
|
| There is no way to pass through these obstacles (without
| spending the multiple lifetimes it took to forge them from
| first principles) except to memorize them and gradually
| extend understanding backwards from that memorization into
| the broader context of dependencies that converge into its
| formalization.
|
| But having this predicament explained to me up front,
| ideally somewhere around the age one learns about something
| as basic as fractions, would have been enormously helpful.
| anyfoo wrote:
| > except to memorize them and gradually extend
| understanding backwards
|
| That is not the only reason, but also a big part of it,
| yes. Some of the things (but not all) that I memorize I
| admittedly don't fully understand. I try to avoid that,
| but it happens. Usually though, the sudden realization
| comes at a later point, when I understood more of
| something else.
|
| Literally happened last week to me. I had been memorizing
| a "stupid" theorem for a while[1], not realizing why it's
| useful, until something I read was about discontinuities
| in the n-th derivation of a function, and what that means
| for the terms of the function's Taylor series, and it all
| lit up in me, tying it all together.
|
| It's a good feeling!
|
| [1] https://www.dsprelated.com/freebooks/sasp/Spectral_Ro
| ll_Off....
| eYrKEC2 wrote:
| I took your approach to math and it was vital to my
| scholastic success.
|
| Once my engineering school load got too big for me to
| continue to use that approach in my math classes, I took an
| alternative strategy of just accepting theories without
| deeply understanding them and I had a much harder time
| applying those particular math concepts outside of those
| classes.
| volkk wrote:
| i imagine this is probably the healthier/much better approach
| to learning anything. unfortunately society mostly
| prioritizes extreme speed and shallow understanding of
| anything due to the upside of moving quickly and making
| numbers go up at the end of a quarter.
| LTL_FTC wrote:
| I discovered the difference in these two types of students
| much later than I would have liked: last year of college. I
| like you, felt like I really needed to understand the
| material to do well, and I did, but there were so many
| students at discussion sections and office hours with much
| shallower understandings who would perform better on exams
| and assignments. These students often ask questions like, "is
| it always the case..." looking for a hammer they can apply to
| all similar problems rather than trying to understand
| nuances. Learning how to get an A in the course is very
| different than learning the course material.
| amatecha wrote:
| 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...
| painted-now wrote:
| I pretty much have the same experience as you! (See my
| other comment in this thread)
|
| I really agree: this discussion is great!
| painted-now wrote:
| I had a very similar experience studying physics and I still
| have some form of that in my current job as software engineer
| working on a quite large code base:
|
| I really can't operate on things for which I don't have a
| deep intuition. If I really have to treat something as a
| blackbox, I need to explicitly spell out the assumptions and
| "compress them enough" (which is actually probably also just
| about building an intuition on those assumptions).
|
| I envy people a lot that can just "copy & paste" some
| knowledge in their thinking.
|
| I think I now got to the point where I accepted that to be a
| part of me and made it "my brand" and I see that I can add
| value with being different in this aspect.
|
| I often wonder how it must feel like to be able to "copy
| paste" knowledge. If you painstakingly have to sweat through
| all kinds of things that others can just "copy&paste", it can
| feel like others are "cheating" - but in the end it's just me
| being jealous.
| ChainOfFools wrote:
| 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 in this extra area essentially acts as an
| extension of your working store. And guess what behavior
| students are typically prohibited or highly discouraged from
| doing during an exam?
|
| I further suspect that this is also the mechanism responsible
| for some people's apparent tendency to do all the talking in
| a conversation, rather than allow a balanced share of time
| between conversants. The quick decay of short-term
| information requires constant refreshing, and talking is one
| means of augmenting this.
| Solvency wrote:
| Actually for me I perform best when I can hear my inner
| monologue. If I'm in a social setting learning math it's
| not ideal at all, because I can't "listen" to myself think:
| I think through things entirely in my head when I can
| reason through and almost dictate to myself. But not
| verbally! It's almost like the moment I try to verbalize
| anything it gets muddied by whatever weird
| social/colloquial construct I've made to communicate with
| others.
| a_wild_dandan wrote:
| 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
| pchangr wrote:
| I write. It's like having an internal monologue slowly
| repeating you whatever you're thinking so it let's the
| brain re-structure knowledge. It's super helpful to force
| myself to pay attention. I rarely read what I wrote but
| because I did, there's a higher chance I remembered.
| sigg3 wrote:
| > I also abhor rote memorization. Not because I don't think
| it's valuable, I just hate extremely repetitive tasks.
|
| Memorization leads to a different kind of knowledge, I think.
| You don't know the thing, you know the steps to reproduce.
|
| It's like my grandmother who knows several songs by heart,
| but if you ask about the second line in the third verse
| she'll sing it from the start until she reaches the line in
| question. For a song this is sufficient, because it is
| analogous to the primary use cases.
| growingkittens wrote:
| I have a childhood brain injury that affects my working memory
| and sequencing ability, among other things. I think in pictures
| with a verbal commentary, although words disappear soon after I
| think them. My brain stores information everywhere it can fit:
| in emotions, music, patterns, movement, etc. Interpreting
| reality is fraught with error. You describe the effect very
| well.
|
| I am working on a personal knowledge system to compensate. What
| are your ideas on this subject?
|
| Popular PKS systems expect the user to adapt to "the system,"
| rather than adapting to the user's particular set of needs. I
| consider each user to be a unique combination of common
| components.
| tikhonj wrote:
| 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.
| growingkittens wrote:
| A distinction you might find interesting:
|
| Systemic thinking - considering the system as a whole.
| Systematic thinking - considering the components of a system
| step-by-step.
| hawski wrote:
| I think I am almost grasping what you are saying, but am not
| sure.
|
| Those short memory people (who I think I may be among) that
| GP said about relate to which group of mathematicians and
| programmers?
|
| I am one of those that prefer to reduce complexity and prefer
| lower level programming. I think that such a type of person
| likes C for example.
| brazzledazzle wrote:
| Am I projecting or does this sound like an compensating
| strategies for an intelligent person with an executive
| dysfunction disorder?
| robbywashere_ wrote:
| Shame that whiteboard problem took you 1hr (and 5 minutes) to
| solve. NEXT!
| ldehaan wrote:
| [dead]
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