My point isn’t just that they are really weird, but that people think about mathematics in an extremely heterogeneous way, and reducing human brains to one number as some sort of “math hit points” is silly for that reason. You are just ignoring most relevant information.
What made Erdos good and what made Ramanujan good were weird complicated facts about their brains (I expect Ramanujan’s IQ wouldn’t be very different from his cohort in India, e.g. likely not super high, but for some reason he just “saw” natural numbers). This does not make Ramanujan or his cohort stupid. I just don’t think “smart” and “stupid” is what IQ measures in any interesting way.
Telling people to go take an IQ test as a way to selecting themselves out from trying math is an especially toxic practice (especially if this advice is not coming from a mathematician).
I prove theorems for a living, and I say: ignore the haters, just read about math that interests you, try your hand at following and constructing arguments, etc. Math is hard (for everyone), don’t worry about it. It’s fun, too.
people think about mathematics in an extremely heterogeneous way
Sure, that’s true.
reducing human brains to one number as some sort of “math hit points” is silly
And I agree. But consider the setup: we have a person who doesn’t quite know what he wants to do and who has shown no signs of possessing any “supernatural” math abilities. Could he turn out to be another Groethendieck? Well, sure, it’s possible, but we are talking about the base population rate here, the chances are, let’s say, not very high.
Now, it so happens that most math professionals have high IQ. That’s not a coincidence, of course—if your brain is insufficiently weird to see math “directly”, you have to rely on the same dimensions of performance (working memory, etc.) which are reflected in the IQ score.
Trying out a profession has costs, sometimes considerable. You can’t try everything on the off chance that it might work out—you want to focus on the areas where you expect to do well. And someone with an IQ of 130 has much, MUCH better chances of becoming a mathematician than someone with the IQ of 80.
Aaaanyway I haven’t had a crude IQ test done but I’ve had a tailored subset of psychometric tests including subscales from the WAIS from which IQ is derived which indicate my maths skills are above average. The same tests indicated my concentration skills are below average....
Aaaanyway I haven’t had a crude IQ test done but I’ve had a tailored subset of psychometric tests including subscales from the WAIS from which IQ is derived which indicate my maths skills are above average. The same tests indicated my concentration skills are below average....
Hmm. I haven’t put much thought into what professions are a good fit for someone with concentration as a comparative disadvantage.
I would suspect that research, and mathematics research in particular, is a bad bet. Much of a day will be spent just thinking about ideas, and being able to think about the same idea all day long is necessary to reach the end of long and complicated chains of reasoning. The difference between Newton and his contemporaries, for example, seems to have mostly been superior concentration ability on Newton’s part, not considerably higher intelligence.
But people use machine learning many other places; you might be able to work as an industrial data scientist or analyst. It’s not clear to me whether low concentration ability would be a smaller or larger handicap there.
Ooh my main strengths are vocabulary and verbal abstract reasoning which are apparently greater than 3 standard deviations away from several populations means. Could you reassess possible career paths that might suit those strengths?
Other weaknesses include social cognition and memory. The neuropsychologists reckons the memory thing may be due to lapses in concentration though.
I’m highly skeptical of my verbal abstract reasoning results aince whenever I’ve done job psychometric tests or related tests when I was in school my verbal abstract reasoning can range very broadly including into the below average group albeit in sometimes competitive populations.
I am very confident in my vocabulary though. It’s probably the strongest in anyone I’ve ever seen except spelling b competition kids on TV, assuming they actually know what the words they’re familiar with denote and connote in practice. I’m not so sure it’s useful since among regular people people don’t get what I’m saying when I slip in technical words often. I reckon it would be good in cross disciplinary technical communication. Don’t know an example of that other than systems engineering but I’m no engineer and engineering isn’t the broadest category. Politicians span multiple portfolios but I get totally stressed dealing with multiple issues or assignments at once. :S thanks for your assistance everyone once again
I thought becoming an intelligence analyst would be a good choice. Military intelligence analysts in Australia may do shift work which isn’t good for one’s health.
Sales is standard advice for people with high verbal ability, and there’s plenty of sales jobs for technical subjects that do not require direct technical ability. (Someone sells MRI machines to hospitals, and they aren’t an engineer.) There’s a fairly large industry in machine learning enterprise solutions, where all you would need is the ability to tell apart Spark and Impala and R and Hive and Hadoop, not necessarily the ability to use any of them competently.
Two issues: ‘social cognition’ is rather important, and there will be multiple issues or assignments at once.
I think most other verbal fields are in a bad way and have declining prospects. Verbal + abstract reasoning has historically screamed law, but going to law school now is a terrible mistake. Similarly, journalism has very poor options that I suspect will continue to get worse.
Yes—sales at the corporate level is mostly about gladhanding and networking. People who can’t seamlessly insinuate themselves into the local old-boy network will do poorly.
going to law school now is a terrible mistake
Well… going to some law school has been a terrible mistake for years by now. On the other hand, if you can get into a top-tier law school (and there about half a dozen of those in the US), I would hesitate to call it a mistake.
On the other hand, if you can get into a top-tier law school (and there about half a dozen of those in the US), I would hesitate to call it a mistake.
Yes, there are still top tier law firms, and you have a chance of getting hired by one if you go to a top tier law school.
My point is more that even conditioned on knowing that you would survive law school and make it into a top tier law firm, it’s not obvious to me that law is the best path to take: options in other industries may be far more valuable. (Consider claims about how doctors only get rich in real estate, or compare physics PhDs in academia and quantitative trading, or Peter Thiel narrowly missing out on a Supreme Court clerkship and founding a company instead.)
it’s not obvious to me that law is the best path to take: options in other industries may be far more valuable
It all depends, of course. Each path has its risks and its rewards. However, if—and that’s a huge if—you can get admitted to a top-tier law school, get hired by Biglaw, and spend a few years in, say, a white-shoe NYC law firm, that doesn’t sound like horrible fate to me (subject to the sensitivities of your soul, naturally).
My point isn’t just that they are really weird, but that people think about mathematics in an extremely heterogeneous way, and reducing human brains to one number as some sort of “math hit points” is silly for that reason. You are just ignoring most relevant information.
What made Erdos good and what made Ramanujan good were weird complicated facts about their brains (I expect Ramanujan’s IQ wouldn’t be very different from his cohort in India, e.g. likely not super high, but for some reason he just “saw” natural numbers). This does not make Ramanujan or his cohort stupid. I just don’t think “smart” and “stupid” is what IQ measures in any interesting way.
Telling people to go take an IQ test as a way to selecting themselves out from trying math is an especially toxic practice (especially if this advice is not coming from a mathematician).
I prove theorems for a living, and I say: ignore the haters, just read about math that interests you, try your hand at following and constructing arguments, etc. Math is hard (for everyone), don’t worry about it. It’s fun, too.
Sure, that’s true.
And I agree. But consider the setup: we have a person who doesn’t quite know what he wants to do and who has shown no signs of possessing any “supernatural” math abilities. Could he turn out to be another Groethendieck? Well, sure, it’s possible, but we are talking about the base population rate here, the chances are, let’s say, not very high.
Now, it so happens that most math professionals have high IQ. That’s not a coincidence, of course—if your brain is insufficiently weird to see math “directly”, you have to rely on the same dimensions of performance (working memory, etc.) which are reflected in the IQ score.
Trying out a profession has costs, sometimes considerable. You can’t try everything on the off chance that it might work out—you want to focus on the areas where you expect to do well. And someone with an IQ of 130 has much, MUCH better chances of becoming a mathematician than someone with the IQ of 80.
Aaaanyway I haven’t had a crude IQ test done but I’ve had a tailored subset of psychometric tests including subscales from the WAIS from which IQ is derived which indicate my maths skills are above average. The same tests indicated my concentration skills are below average....
Hmm. I haven’t put much thought into what professions are a good fit for someone with concentration as a comparative disadvantage.
I would suspect that research, and mathematics research in particular, is a bad bet. Much of a day will be spent just thinking about ideas, and being able to think about the same idea all day long is necessary to reach the end of long and complicated chains of reasoning. The difference between Newton and his contemporaries, for example, seems to have mostly been superior concentration ability on Newton’s part, not considerably higher intelligence.
But people use machine learning many other places; you might be able to work as an industrial data scientist or analyst. It’s not clear to me whether low concentration ability would be a smaller or larger handicap there.
Sports commentator :-D
Ooh my main strengths are vocabulary and verbal abstract reasoning which are apparently greater than 3 standard deviations away from several populations means. Could you reassess possible career paths that might suit those strengths?
Other weaknesses include social cognition and memory. The neuropsychologists reckons the memory thing may be due to lapses in concentration though.
I’m highly skeptical of my verbal abstract reasoning results aince whenever I’ve done job psychometric tests or related tests when I was in school my verbal abstract reasoning can range very broadly including into the below average group albeit in sometimes competitive populations.
I am very confident in my vocabulary though. It’s probably the strongest in anyone I’ve ever seen except spelling b competition kids on TV, assuming they actually know what the words they’re familiar with denote and connote in practice. I’m not so sure it’s useful since among regular people people don’t get what I’m saying when I slip in technical words often. I reckon it would be good in cross disciplinary technical communication. Don’t know an example of that other than systems engineering but I’m no engineer and engineering isn’t the broadest category. Politicians span multiple portfolios but I get totally stressed dealing with multiple issues or assignments at once. :S thanks for your assistance everyone once again
I thought becoming an intelligence analyst would be a good choice. Military intelligence analysts in Australia may do shift work which isn’t good for one’s health.
Sales is standard advice for people with high verbal ability, and there’s plenty of sales jobs for technical subjects that do not require direct technical ability. (Someone sells MRI machines to hospitals, and they aren’t an engineer.) There’s a fairly large industry in machine learning enterprise solutions, where all you would need is the ability to tell apart Spark and Impala and R and Hive and Hadoop, not necessarily the ability to use any of them competently.
Two issues: ‘social cognition’ is rather important, and there will be multiple issues or assignments at once.
I think most other verbal fields are in a bad way and have declining prospects. Verbal + abstract reasoning has historically screamed law, but going to law school now is a terrible mistake. Similarly, journalism has very poor options that I suspect will continue to get worse.
Yes—sales at the corporate level is mostly about gladhanding and networking. People who can’t seamlessly insinuate themselves into the local old-boy network will do poorly.
Well… going to some law school has been a terrible mistake for years by now. On the other hand, if you can get into a top-tier law school (and there about half a dozen of those in the US), I would hesitate to call it a mistake.
Yes, there are still top tier law firms, and you have a chance of getting hired by one if you go to a top tier law school.
My point is more that even conditioned on knowing that you would survive law school and make it into a top tier law firm, it’s not obvious to me that law is the best path to take: options in other industries may be far more valuable. (Consider claims about how doctors only get rich in real estate, or compare physics PhDs in academia and quantitative trading, or Peter Thiel narrowly missing out on a Supreme Court clerkship and founding a company instead.)
It all depends, of course. Each path has its risks and its rewards. However, if—and that’s a huge if—you can get admitted to a top-tier law school, get hired by Biglaw, and spend a few years in, say, a white-shoe NYC law firm, that doesn’t sound like horrible fate to me (subject to the sensitivities of your soul, naturally).
Philosophy? Journalism?
Philosophy grad students tend to get very high combined analytic/verbal scores on tests.
Heterogeneous compared to what? It’s a lot more homogeneous then how people think about nearly any other subject.
I suppose I will defer to your expertise on how people think about everything, Eugene.