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

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

#61

Earlier quoted context omitted.

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 l…

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-for…

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!

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

#62
post #37

Earlier quoted context omitted.

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…

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 w…

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.

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

#64

Earlier quoted context omitted.

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 w…

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…

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.

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

#65

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. M…

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.

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

#66
post #42

Earlier quoted context omitted.

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 interest…

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…

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.

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

#68

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…

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.

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

#69

Earlier quoted context omitted.

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-for…

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…

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.

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

#70
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.

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