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Ask HN: Where did you top out in math classes?

26 points by andrewparker 18y ago

Pretty much everyone (except perhaps tenured professors of mathematics) hits that point in their math training when they realize "I'm just not smart enough to get this." What point in your math career did you hit a brick wall?

LPTS 18y ago
For me the brick wall was social, not related to the math, and I hit it in geometry class in 10th grade. Our teacher was an idiot, and had trouble solving the more difficult proofs at the end of the homework. Day after day I would go up to the board and write down the solution to the problem he couldn't solve. Then, I would get an F for not turning in my homework, which I rightly considered to be a waste of my time, and the people who copied down my answers would get an A's. That was when I decided I had enough formal mathematical education. I taught myself the math to do AP chemistry in high school and tested out of pre calculus in 2000 in college. I am currently teaching myself calculus from Michael Spivak's Calculus. You couldn't get me back in a math class, but I love learning math.
nostrademons 18y ago
Long division. 1st grade. I never really topped out, because I always figure that when I don't understand something, I'm not smart enough to get it yet, but that doesn't mean I'll never get it. This pattern started, as I said, in 1st grade with long division. My dad had been trying to teach me math early, and I whizzed through addition, subtraction, and multiplication, but I just couldn't understand long division. My mom (who always took a dim view of acceleration) said "Just let him learn it in school with the other kids." So that's what we did, and when 3rd grade rolled around and we did long division in class, I got it right away. I did similar things with algebra (dad first tried to teach me it in 2nd grade, didn't get it then, but I started rederiving it on my own in 6th grade and my teachers figured it was time to get me an algebra textbook) and logarithms (which I first tried in 8th grade, but didn't understand for 4 full years...that was my block through all of high school). As for how far my formal mathematical training has gone - I aced up through vector calculus in college, and also took discrete math late in college and aced it. Also took Functions of a Complex Variable and Mathematical Logic, but got lost around halfway through each of them. Passed, but not really competent in them.
- eru 18y ago
  Most of us have forgotten how to do long division on paper - I guess. It is quite a nice exercised (if a bit geekish) to rediscover it on your own.
ctkrohn 18y ago
When taking 2nd level honors linear algebra, we were given a takehome exam. I spent ~40 hrs on it and got just under the median grade. I was able to pull out a decent grade in that class, and I graduated with a degree in math, but now I know I'm not smart enough to hack it as a professor. Not that I'd want to, anyway. Math is a great subject, but it's not what I'd want to do with my life.
cperciva 18y ago
Algebraic number theory, when I was a graduate student in Oxford. Well, sort of -- by that point I was pretty firmly on the CS side of the fence, and was just sitting in on the number theory classes out of interest. I probably could have grokked class field theory and L-functions if I had taken the time, but I was busy and it wasn't my research area...
g00dn3ss 18y ago
Recent evidence tends to indicate that 'not smart enough' is probably a myth. Almost everything can be attributed to exposure and effort at some point rather than some innate smartness. A lot of advanced math takes some serious concentration to understand. For some non-practical aspects, I found that I lacked the motivation rather than ability to understand it . One particular class where I seemed to hit my tolerance was a theoretical linear algebra class. I could understand the practical applications of most of the topics but some of the theory seemed just out of reach. The book was extremely dry and I think the professor may have been taking lessons from Ben Stein. Give me a private tutor, a theoretical linear algebra for dummies book, and a pending disaster for which this is the solution, and I bet the outcome would be a little different.
- aneesh 18y ago
  Very true. I really enjoy math, but after abstract algebra and real analysis, I slowly lost the motivation to go deeper into pure math. Interestingly the most enjoyable areas of math for me are those arguably most applicable to CS: graph theory and number theory.
- flashgordon 18y ago
  Totally agree. Case in point. Up until highschool I was very good at math. Mainly because I would actively seek out books and try to solve problems where ever I could find them. As soon as I started Uni, my interest dwindled (was replaced by love for all things CS). People who I had dominated back in highschool were now getting a good 10-20% higher than me. All in practise I think.
- manvsmachine 18y ago
  Haven't gotten to that point yet, but I can definitely attest to the significance of good materials and enthusiastic teaching. Because I started out as a engineering major, I had taken the entire Calc sequence up through Diff. Eq's, but I ended up having to take Prob/Stats and Discrete when I Switched to CS. I was sick of taking math classes at that time, but my Discrete prof was awesome and motivated me to see how far I could go with it. I went into fall semester never wanting to take another math class again; now I'm taking more so I can get a minor in it. I'll be taking combinatorics in the fall and topology(?) the following spring to close it out.
edw519 18y ago
I'm still asymptotically approaching the "top out limit point".
voidfiles 18y ago
Last class I attempted was trig, and failed completly. I enjoy math, but have given up untill after I finish collage.
rms 18y ago
Calculus III... I think I could have got it, but it's tough material and I had a terrible professor, so I didn't really learn any Calculus III. I passed and did much better in my final math course, a one semester differential equations/linear algebra hybrid course.
- rms 18y ago
  Also, my first semester I took one class of "Honors" calculus which was a proof based differential+integral Calc course. I dropped that really fast in favor of Calc II. So I also hit a wall at proof based calculus. Most of the people who actually took the class didn't get it either and resorted to memorizing all the proofs needed to derive calculus.
tjr 18y ago
I went to Cornell College, which schedules classes on a "block plan", one class at a time for a month each. My first semester, I took four consecutive courses in calculus. By the fourth one, I was extremely burned out on math and barely squeaked by. I ended up taking a couple more math classes before graduating (discrete math and linear algebra), have continued to study math on my own, and have recently been contemplating a master's degree in math, just because I want to learn more. All of that is to say, I'm not sure that the math brick wall is constant, but perhaps sometimes you need to take a break to allow your mind to digest what you've learned so far.
jfarmer 18y ago
I have yet to find it, but Algebraic Topology took me a long, long time to get.
- mnemonicsloth 18y ago
  My first thought on reading this was "dude, you stole my answer." After thinking about it for a while, though, I think General Topology is worse. I still don't get it. Or, what's worse, maybe I do get it, and just don't care enough about the subject to register that fact.
  - davo11 18y ago
    I got it I think and still open up the books every now and then, but it was about topology and model theory that I started to question its applicability. I remember asking my lecturer this (I could have phrased it a little better in hindsight, I sort of burst out during a lecture 'whats the point of this' The lecturer got a little upset :-)). Transfinite numbers are always my favorite example of something way out there, different sorts of infinities and which infinity is bigger than the other, the models are beautiful, but I couldn't spend my life arguing about them. I think for most people maths starts losing its relevance a lot earlier, it justs takes some longer to admit it, because it's prettiness is so seductive :-).
rtf 18y ago
I don't know, how about every subject? Multiplication. Long division. Algebra. Geometry. Trig. Calc. I was never very motivated to study math. The problem was, my older brother was very into it(and now is a math grad student, ever-so-slowly getting his thesis together). This set a model that I could not hope to emulate, but it only meant my mom pushed me more, talked to the school to get me into the advanced/accelerated classes I didn't really want to take. She probably would have done some of that without my brother around, but not as much. This led me down the "please the parents" line of study, which naturally meant some surreptitious, embarrassed attempts at cheating. This only made me feel worse, of course. In college I started into computer science, thinking that I at least liked the programming. But integral calc sunk me for good, and in a particularly bad quarter that was my low point, I tried taking linear algebra as well as a repeat of calculus, thinking that perhaps the extra pressure would do something good. Of course not. I dropped linear algebra and failed calc again. After that, I decided to declare in economics, restarted calculus with the "ez-for-econ-majors" series and sailed through those courses with a solid B average. I struggled through, but passed on the first try, the two intermediate econ courses which started introducing serious mathematical modelling. The remainder of the major was electives, and not difficult ones. I never knew, until after that whole period of my life was over with, exactly what was holding me back. Now I'm pretty sure that it's about motivation and dedication. My brother is fairly normal but can get interested enough in math problems to sacrifice his well-being. The genius researchers of the field sacrifice well-being regularly, without really knowing it, and are typically slightly unhinged socially. As for myself, I tend to run away from a challenging math problem. So, even if I'm forced to tackle it, it will probably take me 10 times as long to solve as it would my brother(not even factoring in his years of experience now). Once I overcome those hurdles particular to a new category of problem I am fine, but I have to take considerable effort to do so. Summing that difference up over a long-term period like that of a college course, the best students can zoom far ahead because of this motivation factor, even if they aren't necessarily the _smartest_. Indeed, many math students reach the upper-division levels on memorization alone and get stuck from there, as proofs take on more and more importance. That's a major failing of current math education in the United States - overdependence on rote techniques. (The former Soviet educational system, OTOH, had probably some of the strongest math education, and much of it has been translated to English - pick up a book from that period and you will probably see a small and dense text that introduces high-level concepts in great, if unforgiving, detail. Very different from the thick drill+practice textbooks I'm used to.) My conclusion: many academic fields can accommodate a half-hearted practice. Math is not one of them. And our society doesn't respect that difference, shoving it under the rug as "I'm just not good at math."
epi0Bauqu 18y ago
Didn't. Just lost interest.
- mattmaroon 18y ago
  Same. Realized I wasn't going to go through life as either a mathematician or a physicist, so didn't pursue beyond Calc 2.
a-priori 18y ago
My most advanced math course is currently Calculus II (integral calculus and so on). However, I don't believe it's my "wall", and I'm planning on taking courses on differential equations and linear algebra whenever I have some time.
streblo 18y ago
Multivariable Calc and Linear Algebra kicked my ass. I didn't really do much beyond that.
vegai 18y ago
I never bothered to invest much to the math classes. The benefit didn't seem so large. Of course, now I see how completely stupid that line of thought is. The time I saved by not attending classes or demonstrations was indeed not well spent.
rw 18y ago
Set theory & mathematical logic. Learning math is all about spending time with the material. I find that upper-level math is easier than lower-level topics. Less grunt work, more pondering.
- mnemonicsloth 18y ago
  Foundations proofs are the worst. I can still remember proving something like "For every left-paren, there is a matching right-paren." Ugh.
mnemonicsloth 18y ago
With one notable exception, math seems very easy to me. I open the book, write down verbatim anything labeled Definition, Theorem, or Lemma, and trace through anything labeled Proof. There's nothing particularly hard about it -- you just have to make sure you actually do every step listed inside your head. It is a little slower than reading for pleasure, but with practice, I'd say only by about half. I think the primary reason I do well, though, is that I take adderall for ADHD. Stimulants make it trivially easy to maintain the necessary level of focus, but whenever I forget to take them before a lecture or study session, I'm gnashing my teeth and tearing my hair out by the end.
- muriithi 18y ago
  Do you take adderal because you suffer from ADHD or you take it get focused?
- jfarmer 18y ago
  As with most subjects there are levels of understanding. One level is the ability to understand what other people are saying or doing. Another is the ability to do it yourself. Once you get to higher level classes, at least where I went to school, the reading is relatively light but the work is relatively hard. I don't think most people had trouble understanding the proofs -- they had trouble applying the lessons in a novel way to exercises and problems they'd never seen before.
loowee 18y ago
Geometry, Logic, Trigonometry
strlen 18y ago
My undergraduate degree is in Computer Science, which at the time I attended the university was (if one was doing their degree in the College of Arts and Sciences vs. School of Engineering) in the math department. In the end I ended up going further than I would have naturally (just by the nature of department requirements). First response to this question would be "what kind of math"? In terms of continuous math, I've topped out at Differential Equations (much like any other CS Major). In terms of discrete mathematics I topped out at abstract algebra (the first class that made me sigh with relief upon seeing actual numbers) and combinatorics. I felt that I could certainly go on further in the discrete field (I particularly regret not taking number theory - other than what I've learned in cryptography courses - and graph theory). I could have received a Math major, but that would have required taking the analysis series (real and complex), which I felt would go beyond my level of abilities (particularly since I was aiming for an early graduation and wanted to take as much of classes that I felt would interest me more).
ekzept 18y ago
there's learning on an academic track timeframe, and there's learning. there are lots of courses i took which i did not do well gradewise, but i learned a lot, enough to go back and re-learn the material at my own pace and better. ultimately, all learning is self-taught.
Tichy 18y ago
Seems to me all or most human understanding of maths is poor. Most things, even if we can prove them, we can not really understand them. I wonder if there is a different way to understand maths out there.
- nazgulnarsil 18y ago
  you're probably a victim of rote learning math classes. learning math for real (getting it) is not a linear process. lots of aha moments where lots of concepts fall into place suddenly and then you move on to more advanced things. that said, I would consider everything below calculus to be merely clever ways of tallying stones. algebra can be tricky at times (abstract algebra sucks) but it is really not that interesting in of itself (yes you can solve a lot of practical problems with it but the questions aren't generally interesting, so the answers aren't that interesting). you do need to have it down pat in order to "get" calculus however. And if you "get" at least the basic concept of calculus down a lot of things fall in to place. OTOH I could be totally biased and/or wrong, but I personally didn't really see how math could describe complex systems in a way that let me get those complex systems until calc. Some really mind blowing aha moments.
  - Tichy 18y ago
    I did understand a lot of maths, I just mean that I think the way we do maths often is not really understanding. If we have proved something with a hundred step proof, I might be able to verify every single step of the proof and conclude that it is correct. But we might not really have a feel for why it is correct. Can't really think of a good example right now :-/ I mean usually we jump through quite a few hoops to prove something - maybe there are other ways of looking at it that would make more sense. One example might be the autistic people who just know if a number is prime or not. Not sure if they are really doing anything special, or just calculating really fast, though.
    - eru 18y ago
      If you search long enough you usually hit upon a prove that does looks more like a really explanation than like pulling a rabbit out of a hat.
deleted 18y ago
[deleted]
akd 18y ago
My first math class at MIT. :-\
jamiequint 18y ago
Vector Calc, because I stopped caring. Somehow Diff. Eq. held my interest but vector didn't. Calculating the area of partial 3D oval objects for the sake of doing it was painful.
- eru 18y ago
  Diff. Eq.: Difference Equation or Differential Equation?
cousin_it 18y ago
Got my masters in math, then kinda lost interest, but I'm pretty sure that everything is understandable with a little effort. When I get genuinely interested, no effort is required at all.
pageman 18y ago
did he mean "tap out"? as in UFC "tap out"? can't get enough of Math (although I barely passed Linear Algebra and Numerical Analysis). Maybe it's the challenge. I shall try more of it when I take up a Masters in CS. :P
maxklein 18y ago
Math is pointless if you are not planning to apply it at some point in your later career. Learning algebraic topology when you are studying digital circuits is like learning literary analysis - it may make you feel smart, but it's a damn waste of time.
thorax 18y ago
I don't know if I topped-out, but I did lose interest. Calc III felt hard with not very much useful information (my comp sci advisers basically gave me grief for taking it). Linear Algebra sparked my interest again, but only because it started out wicked hard and then (just like with Calc years before), it just "clicked" and suddenly it was a lot easier/interesting. I didn't pursue further because after I graduated I preferred diving into new compsci (and engineering) concepts rather than focusing in math areas.
nothingHappens 18y ago
I very nearly hit that point taking Differential Equations my last semester, but thanks to persistence and a very helpful prof, I got over it. Not sure where I'd have ended up if I kept going, but I've always regretted not taking more abstract/"modern" algebra
DaniFong 18y ago
I'm not sure I ever had that reaction. I explored a few topics in different lectures in grad school which were pretty obtuse: ergodic theory, for example. I didn't get it, but I assumed it was because the topic wasn't suited to lectures, and after learning of the basic direction they were headed in and setting out myself, I found I could get pretty far. I've seen others give up on some topic rather than the method they used to try to understand it. It's the equivalent of someone saying "I can't get math" because they're spending all of their time remembering formulae, or someone saying "I'm no good at programming" while spending their time reciting bubble sort line by line in preparation for the exam. Giving up on higher mathematics is like that. Almost always, there's some path to real understanding -- you just have to find it.
geebee 18y ago
In retrospect, I topped out in my upper division coursework for the math major. I still got B's and even some A's in those courses (Real Analysis, Abstract Algebra), but I was reduced to studying solution sets rather than mastering the material creatively. This was when I got more interested in applications (optimization, scientific programming, etc). I figured I'd pick a grad program in Industrial Engineering so that I could get away from math and more into applications. Unfortunately, I picked Berkeley. A graduate intro to optimization was pretty much a series of proofs about convex sets. Same deal for stochastic processes (it might be different with different professors, though). BTW, this isn't meant as a knock on Berkeley - this theory focus is a big part of why it's such a powerhouse program. But it probably wasn't the right choice for me. I've heard Stanford is more flexible (I've also heard the grass is greener, so who really knows). At this point, I topped out in grades as well as understanding, because I didn't have the motivation to continue. I tanked, and squeaked by with a MS. I actually missed problems that I would have gotten right as an undergraduate. I was thinking "I've had enough of proofs, I just don't want to do this anymore." In a way, I got a lot out of the experience. My interest in academics waned, and I pretty much just started hacking with like-minded students. In other words, I finally, belatedly arrived at the process of becoming self-educated, which is really the only kind that sticks, right?
eru 18y ago
Perhaps differential equations for me. But that's more a question of motivation. I like optimization more and look forwand to having more lectures.
jimbokun 18y ago
I was required to take two semesters of Statistics as an undergrad. I didn't think it was especially difficult, but I didn't see applications for the things I was interested in (mainly Computational Linguistics at the time). A few years later, pretty much all Computation Linguistics/Natural Language Processing research revolved around Machine Learning approaches, which is largely Probability and Statistics applied in various ways. I really kicked myself for not taking Statistics more seriously at the time, and not learning more. I was away from this field for about a decade, but have been working with researchers in this field again in my current job and have been taking classes to catch up. In addition to Probability and Statistics, I've been learning Linear Algebra as fast as I can and want to take a course on Optimization. So, I suppose the moral of the story is: you never know when that particular branch of Mathematics that doesn't seem at all relevant to you might suddenly turn out to be very relevant.

doubleplus 18y ago

Would you happen to have any links or book references to this "recent evidence"? While most of success comes from effort and discipline, I've always been under the impression that only the naturally gifted (who also have discipline and drive) can/have achieve/achieved certain things. The dwarf down the street from me will never be a professional football player, and someone with a 100 IQ will never be an astronaut. I've always felt the you-can-always-achieve-whatever-you-want-no-matter-what-if-you-want-it-bad-enough approach to be more than a little cliched and misguided. If recent scientific evidence has disproved this stance of mine, I'm open to changing it.

elai 18y ago
To be honest, I believe that all intelligence comes from innate motivations and practice. You suddenly become 10x more "intelligent" when you actually give a shit or get some innate joy or obsession relieved when you do it. If that is something that is constant within you, you become more and more practiced and a virtuious cycle results. Nothing is too hard to explain, it's just mathematicians are really horrible at communicating.
- byrneseyeview 18y ago
  For whom, though? Brains are complicated, but if yours is severely damaged (through a stroke or head injury) motivation is not necessarily going to fix that. And as far as I know, there aren't any permanent ways to raise IQ. Some environmental factors lead to higher childhood IQ, but these vanish by adulthood. And there are tricks people can use to bump up their scores on IQ tests, but I haven't seen a situation in which practicing for test A raises your score, years later, on test B. This stuff is just more static than that. The danger with what you're saying now is that someone with an IQ of 90 -- someone who could be a fine contributor to society in lots of practical, necessary fields that don't require lots of abstract thinking -- could be inspired to throw away lots of time and risk lots of frustration trying to be a mathematician. We should deal with the fact that wasting education on someone who can't use it is as much a tragedy as failing to educate someone who can use it. By pretending that 'smart' just means 'trying hard', you're doing more harm than good.
  - DaniFong 18y ago
    The problem may be that our predictors are terrible. There are a lot of Nobel prize winners who later discover their 'dismal' performance on IQ tests. I know grad students at Princeton who've confided sub-100 IQ scores, bad SAT's, horrible performance on one math test or another -- it's like this big, shameful secret for otherwise brilliant people. Everyone carries around the absurd burdens of judgments and measurements, but they don't always mean what people think they mean.
    - byrneseyeview 18y ago
      Are there any other quantifiable variables with such high predictive power? I'd be really interested if there were some other test that could better estimate the odds that someone would get a degree, earn lots of money, stay out of jail, vote often, delay having kids, etc. It would be interesting to know more details, which I'm sure you can't divulge without violating someone's privacy. But it would be neat to find out if those people had other skills that correlate strongly with IQ, like the various digit-memorization/recitation tests, or reaction time. Were these people autistic? Were they taking a test in a language they didn't know too well?
      - DaniFong 18y ago
        They weren't autistic, and there didn't seem to be any strange behaviors socially, and they were quite inquisitive and swift on the uptake. I once heard IQ defined as "ability to navigate bureaucracy, getting the answers others think correct in a manner testwriters imagined, and color in the lines" (paraphrased). This may have something to do with the phenomenon here. The odds that someone would 'get a degree, earn lots of money, stay out of jail, vote often, delay having kids, etc.' seem to have more to do with successfully conforming to certain values of society's upper-middle class. I think I'm capable of inventive thought, but I don't particularly want to get another degree, or earn much money, or delay having kids, or vote often, and the sort of things that one has to do to stay out of jail, are, honestly, quite often absurd, and I often rail against them. And if you start to observe, closely, just how these things are tested, you'll start to get the impression that maybe bright people will find their ways through the cracks more than anticipated. There's an enormous weight given to quick answers -- time directly influences scoring. Linear answers are expected, and alternative interpretations are docked. There's often insufficient information in the questions, or it's based on a model of the world that's wrong. Domain knowledge like mathematics or vocabulary is brought into it. Analogies are made to hone in on one relationship from the many that could exist. Scorers of essays give insufficent weight to substance and too much to form -- despite their lipservice, they are indeed swayed by big words. Even tests like GRE physics are bad. They claim to be testing rapid physical intuition, but in practice what divides good from poor scores is prior experience with 100 simple systems and the ability to get the factors of 2 and pi right with three minutes per question.
  - aswanson 18y ago
    someone who could be a fine contributor to society in lots of practical, necessary fields that don't require lots of abstract thinking -- could be inspired to throw away lots of time and risk lots of frustration But the bottom line though, is that it's none of your business to determine how one should spend ones effort and life. Nobody asked for your take on parameterizing their lifes limits. Thats what living is for. I could tell you what you should do with your life after a test or battery of tests and send you on your way. Like that idea? Even if you do, let it apply to you and you alone.
    - byrneseyeview 18y ago
      How do you go from "Nobody should prevent someone from aspiring to do what they want to do" to "It is wrong to point out that people with low IQs are very unlikely to succeed at tasks which require high IQs, and telling them that these real constraints are not real at all is cruel and insensible, since it's factually incorrect advice that will lead them to make poorer decisions."? I mean, I could tell you that if you are really super-passionate and very very outraged, you can convince me to abandon my factual beliefs for some kind of feel-good claptrap. But that might lead you to make another comment of similar tone and content to the one to which I responded, leaving us both worse off. Do you see where I'm coming from? I am in a business that most batteries of tests would predict I'd fail at, so I clearly don't follow your parody of my thought processes.
      - aswanson 18y ago
        since it's factually incorrect advice that will lead them to make poorer decisions The problem with this assertion is the assumption that you have all the facts, facts meaning absolute certainty what a person is capable of given a scalar score from a test. But that might lead you to make another comment of similar tone and content to the one to which I responded, leaving us both worse off. Do you see where I'm coming from? I'm guessing not from a vantage point of omniscience. I am in a business that most batteries of tests would predict I'd fail at, so I clearly don't follow your parody of my thought processes. Not a parody, just an observation that your aggregates mean nothing to a given instantiation. And congratulations on defying what the stats say you would fail at. Hard worker, indeed.
g00dn3ss 18y ago
Here is a pop-sci version of some recent research: http://www.sciam.com/article.cfm?id=the-secret-to-raising-smart-kids http://www.sciam.com/article.cfm?id=the-secret-to-raising-sm... However, this isn't particularly surprising. Research on "grandmasters" in many activities, like chess or pilots, usually shows they've put in 25K hours of practice in their field. I'm certainly not in favor of saying anyone can do anything. Especially in physical activity. There are definitely physiological advantages. The same is also true in mental activities to some extent. A kid with down syndrome probably isn't going to become a math professor. However, I think the point is that most normally developed folks probably haven't hit a ceiling in their math aptitude. They just stopped caring or putting in the effort.

byrneseyeview 18y ago
I think your quote comes from Cosma Shalizi. Thomas Sowell addressed that complaint years before by noting that most of the countries where you find that modern complexity are pretty nice places to live, whereas other places are hellholes. The correlation between IQ and income holds true for places outside of the US, too, so one might be tempted to think that a bureaucratic, find-objective-answers, fill-out-these-forms-in-triplicate society is better than most of the brutal alternatives. "...seem to have more to do with successfully conforming to certain values of society's upper-middle class. I don't particularly want to get another degree, or earn much money, or delay having kids, or vote often, and the sort of things that one has to do to stay out of jail, are, honestly, quite often absurd, and I often rail against them." My point is that, all else being equal, you could get a great job if you chose to, and that if you do illegal things, you apparently do them in such a way that you won't get caught. IQ seems to correlate with the ability to delay gratification, which itself seems to be a better predictor of success than IQ (sadly, it hasn't been tested in a rigorous, long-term way -- so it can't match the hundred or so years worth of data people have compiled on IQs). One of the reasons that these tests emphasize time is that 'quickness' is a component of IQ. Francis Galton, the first guy to really study the subject, liked to think of things in that way -- and given that physical reaction time correlates so well with IQ, he had a point. I agree that the essay part of standardized tests is messed up. Lots of the recent changes to tests seem to arise from political correctness. Test-makers found out that you can't design a test that has predictive value without getting politically incorrect results, like lots of men on the extremes, or lots of high-IQ Jews and Asians and low-IQ Mexicans and blacks. So they periodically adjust the scoring mechanism or the test to get bell curves closer to the same median and standard deviation (more focus on the median than the SD, since most of the people who complain about such things don't know what 'standard deviation' means). So keep that in mind when complaining about the essay, or the rebalanced scores, or the analogies (which were dropped from the SAT -- analogies happen to be more IQ-weighted than other categories of questions).
- DaniFong 18y ago
  For the most part, life in latin america seems a lot happier than in more bureaucratically encumbered states. So I don't really buy that argument. My main point is that truly excellent thought doesn't depend on the same skills that would allow scoring highly in an IQ test. In many cases such skills would inhibit it. In an IQ test it helps to rapidly adapt to the assumed constraints of the problem and come quickly to the closest, most linear answer. If you have a mind compelled to bring questions back to reality, to challenge assumptions or think of things from many different angles, you'll do, on the whole, more poorly than if you had not. But these behaviors are sometimes precisely what you'd want!
  - byrneseyeview 18y ago
    For the most part, life in latin america seems a lot happier than in more bureaucratically encumbered states. So I don't really buy that argument. The millions of immigrants from there to here don't seem to buy your argument. Which Latin American countries do you mean? "... truly excellent thought doesn't depend on the same skills that would allow scoring highly in an IQ test." I happen to agree with you! One thing that's bugged me for years is that you can't design a test that distinguishes, in advance, between cleverness and original stupidity. So that means that whole lot of time-consuming activities can only be measured after the fact if at all. The difference in our views, I think, is that I would argue that IQ tests measure the kind of raw data-processing skills that are useful in any situation (the military tests people heavily, and for all tasks they've found that IQ correlates positively with results -- I think for some technician jobs, it explains about 60% of the variance in individual performance). There just aren't any studies I know of showing that people with low scores on IQ tests go on to succeed in any measurable way. It would be convenient, to say the least, if you argued that the success-deficit among low IQ people is more than compensated for by a success-surplus that happens to be impossible to measure. So I'd like to know if you can find some way to quantify your argument. It would change my thinking on a lot of subjects if I found that doing poorly on an IQ test predicted doing well at some other task.
    - DaniFong 18y ago
      In happiness surveys, Latin America does pretty well -- I think as a region it comes out on top. This is contentious, but for most of the immigrants, they didn't move because the culture was more enjoyable here. Most of the Latin American immigrants had ther livelihood strip from them in two stages: one, from general industrialization pressures that have affected practically every country, forcing specialization into cash crops to compete, two, increasing competition from the USA and other countries, coupled with crop failures endemic to semi-arid areas. The few areas in which modestly educated Latin Americans could reliably compete were in illegal cash crops (for which they had less competition in the USA), which continues to cause economic distruption and criminal activity, and manual labor. Those forced into either business might have better chances in the USA, but on the whole they're happy countries. When you're there, you can feel it. As for success and low IQs, if I recall correctly, someone got the bright idea of testing Caltech professors while Feynman was there -- this may have been prompted after he won the nobel prize, and found out his score from highschool was 125. When they tested the professors, the scores were surprisingly low. I forget who it was, but someone got to make a big deal of his 105 score, since it was three points higher than Feynman's. My point is that these measures can be stunningly irrelevant, and, if so, while they might have some utility for, say, selecting an undergraduate class, they are often best ignored by an individual when it comes time to decide what one is capable of.
sethg 18y ago
I will never forget one of the questions from the IQ tests that I took in fifth grade. The tester asked me, "Who discovered America?" Ah, I thought, a trick question. "The Indians!" I said. Pause. "Who is generally credited with discovering America?"