[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] ___________________________________________________________________ (page generated 2023-06-22 23:01 UTC)