Social class amongst the intellectually gifted

Something that I've come to realize is that as a practical matter, intellectually gifted people who haven't developed very strong ability in a quantitative subject tend to be at a major disadvantage relative to those who have. The quantitative subjects that I have in mind as "quantitative subjects" are primarily math, physics, theoretical computer science and statistics, though others such as electrical engineering may qualify. [1]

This point is usually masked over by the fact that people who don't have very strong technical ability are often reasonable functional by the standards of mainstream society, and don't realize how far they're falling short of their genetic potential. They tend to have jobs that don't fully use their strengths, and experience cognitive dissonance around being aware on some level of far they are from utilizing their core competencies. 

Consider the following:

  • The Google co-founders met as computer science graduate students at Stanford. Sergei Brin double majored in math and physics and was an NSF graduate fellow. He comes from a mathematical family: his father was a math professor at University of Maryland. 
  • Bill Gates took Math 55 as a freshman at Harvard, which is the class designed for the most mathematically talented students at Harvard. During his sophomore year he did research which he later published a paper on with well known theoretical computer science professor Christos Papadimitriou.
  • James Simons comes close to being the only elite mathematician to leave academia for the business world. He founded the hedge fund Renaissance Technologies and made ~$12.5 billion.
  • Charles Munger, the Vice-Chairman of Berkshire Hathaway (net worth ~$1.3 billion) often quotes the maxim of the 19th century mathematician Carl Gustav Jacob Jacobi Invert, Always Invert, and characterizes him using that concept to solve difficult business problems 

I can't give a brief justification for this, but I have good reason to believe that the ~10000x+ differential in net worth comes in large part  from the people having had unusually good opportunities to conducive to becoming very technically proficient, that resulted in them developing transferable reasoning abilities and having had an intellectually elite peer group to learn from.

I know a fair number of brilliant people who didn't have such advantages. The situation actually seems to me like one in which amongst intellectually gifted people, there's an "upperclass" of people who had opportunities to develop very strong technical ability and an "underclass" of people who who could have developed them under more favorable environmental circumstances, but haven't. Many intellectually gifted people who didn't have the chance to develop the abilities mistakenly believe that they lack the innate ability to do so. And people who did have the opportunities to develop them often look down on those who didn't, unaware of how much of their own relative success is due to having had environmental advantages earlier in their lives.


[1] James Miller points out that graduates of elite law schools may have analogous advantages – that's a population that I haven't had exposure to. 

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Consider the following

Those are weak examples. The counterpart to Brin is Zuckerberg who's a programmer but haven't shown any flashes of brilliance in math or CS; the counterpart to Gates is Ellison (of Oracle) who certainly understands databases but again, not a genius in math or CS; the counterparts to Simons are a large number of hedge fund founders (e.g. Ray Dalio); and the obvious counterpart to Munger is Warren Buffett himself.

What "major disadvantages" do you have in mind? Brilliant mathematicians are rarely wealthy or enjoy high social status.

Those are weak examples.

You want to take base-rates into account. Of intellectually gifted people outside of academia, what fraction do you think have high technical proficiency in a quantitative subject? How does that compare with the fraction of super-rich people who have such proficiency?

What "major disadvantages" do you have in mind? Brilliant mathematicians are rarely wealthy or enjoy high social status.

No, but to a large degree, that's not what they're motivated by. If you look at revealed preferences, the most intellectually capable people do math disproportionately. Gauss is the one who developed the theory of linear regression and p-values, and he described math as being the queen of science and number theory as the queen of math. Alexander Grothendieck wrote:

I well recall the power of my emotional response ( very subjective naturally); it was as if I'd fled the harsh arid steppes to find myself suddenly transported to a kind of "promised land" of superabundant richness, multiplying out to infinity wherever I placed my hand in it, either to search or to gather... This impression, of overwhelming riches has continued to be confirmed and grow in substance and depth down to the present day.The phrase "superabundant richness" has this nuance: it refers to the situation in which the impressions and sensations raised in us through encounter with something whose splendor, grandeur or beauty are out of the ordinary, are so great as to totally submerge us, to the point that the urge to express whatever we are feeling is obliterated.

All else being equal, wouldn't you want the option to feel that way? :D

Those who do decide that they want to do something outside of math often do very well (again, Simons is virtually the only elite mathematician to have left academia), there just aren't very many of them.

Of intellectually gifted people outside of academia, what fraction do you think have high technical proficiency in a quantitative subject?

I have no idea and I suspect that this strongly depends on the definition of "intellectually gifted".

How does that compare with the fraction of super-rich people who have such proficiency?

Looking here it doesn't strike me that "math, physics, theoretical computer science and statistics" are a path to the riches. I'd bet on business ability instead.

the most intellectually capable people do math disproportionately

Do you have data (as opposed to anecdotes) to show that?

wouldn't you want the option to feel that way?

It depends on the price. Options are expensive :-P

However pick any description of satori, or nirvana, or even a mystical union with Jesus. It will sound very similar, perhaps even better. Wouldn't you want the option to feel that way?

I am not quite sure of your point. It seems to be "if you are intellectually gifted -- study math". However your examples do not support your assertion. Brin, Gates, etc. achieved their station in life not through studying mathematical proofs.

Is there any particular reason to focus on anecdotes and not focus on the percentage of millionaires who have specific degrees?

http://time100.time.com/2013/11/11/these-are-the-most-popular-college-degrees-earned-by-millionaires/ gives for example a list.

Agreed that statistics > anecdotes. That said, the list here leaves me wondering about the direction of causation. I'm less interested in current-net-worth than average annual-change-in-net-worth (both % and $) in the years since graduation.

I don't think this list tells you much.

The most obvious reason why the list might look this way is that there are simply more people getting MBAs or engineering degrees. So of course there would be more of those becoming millionaires than there are math students etc.

I'm also not sure if the study actually measured how many people with a given degree actually got this level of wealth by themselves or if they also asked those who had wealthy parents. I don't have statistics on this but it does sound reasonable (not to say that it necessarily is) that wealthy parents try to direct their children towards those degrees which are 'useful' - in their opinion - in a business environment. Since most of these people have a very poor concept of what math actually is, math probably won't be among that class.

People who study math, theoretical physics or theoretical computer science are also much more likely to stay in academia than do those who studied engineering etc.

For all I know those people who did become millionaires by themselves who got the degrees they got might actually have done much better if they had studied math or theoretical physics.

So a statistic which would really be telling here would be one which measured how many of those getting a certain degree and going into the market are becoming rich.

First, I'd predict that much of the observed correlation between technical proficiency and wealth is just because both of them require some innate smarts. In general, I'm suspicious of claims that some field develops "transferable reasoning abilities", partly because people keep using that to rationalize their fiction-reading or game-playing or useless college degrees. I'm worried that math and physics and theoretical CS are just nerd-snipery / intellectual porn, and we're trying to justify spending time on them by pretending they're in line with our "higher" values (like improving the world), not only with our "lower" values (like intellectual enjoyment).

Second, if technical proficiency does build transferable reasoning ability, I'd expect the overall benefit to be small, much smaller than from, say, spending that time working on whatever contributes most to your goals (which will usually not be building technical proficiency, because the space of all actions is big). You should always be trying to take the optimal action, not a random "beneficial" action, or else you'll spend your time mowing lawns for $10/hour.

Edit: I think this comment is too hostile. Sorry. I do agree that learning technical skills is often worthwhile.

I'm worried that math and physics and theoretical CS are just nerd-snipery

No way, especially not physics. We as a civ need to do more of this stuff, not less, compared to what we are doing now.

I can't think of any category of human activity that did more to improving the world than the hard sciences. Maaaaybe some religions in the "convince people to stop killing each other and cooperate long enough to get science off the ground" sense.

Hehe, it's rare that intellectual satisfaction is called a 'low' value.

Yes, there's also the theory that success in hard math/science fields are strong signals of intellect, and thus smart people flock to them to signal their intelligence.

As someone about to start a CS degree and figuring out what to do with his life, this is a sobering line of thought.

I can't give a brief justification for this, but I have good reason to believe that the ~10000x+ differential in net worth comes in large part from the people having had unusually good opportunities to conducive to becoming very technically proficient, that resulted in them developing transferable reasoning abilities and having had an intellectually elite peer group to learn from.

Either it's a hunch, or you should try to provide the justification.

My counterargument to this claim is summed up by the Dilbert cartoon. For every Gates/Simon/Brin, there are hundreds of technically adept but socially naive Dilberts who are working for dumb pointy-haired bosses.

Graduates of elite law schools are mostly "intellectually gifted people who haven't developed very strong technical ability." How do you think most of them would achieve better life outcomes by developing such an ability? Keep in mind that most of them are relatively much better at verbal and social stuff than math.

Yes, that might be a good nontechnical counterpart. I grew up in San Francisco and live in the Bay Area where the wealthy / privileged people tend to be in tech, and my perceptions are correspondingly skewed. I added a footnote linking your comment.

Well law includes a lot of logic, in the form of verbal reasoning. Bertrand Russell formalised how math can be reduced to logic...kinda. I pray for the haters of a lawyer who can substantiate his reasoning with hard data. Imagine a lawyer who can substantiate an argument for legalising assisted suicide by referring to quality adjusted life years and grounding his/her reasoning in some kind of felsific calculus.

On second thoughts, the poor reception that hedonic calculus (according to that one Charles Dickins book at least) got from the world is evidence against this line of thinking.

:/

edit 1: evidence that lawyers aren't great at quantitative evidence and by extension, some applications of logic.

Bill Gates took Math 55 as a freshman at Harvard, which is the class designed for the most mathematically talented students at Harvard. During his sophomore year he did research which he later published a paper on with well known theoretical computer science professor Christos Papadimitriou.

Bill Gates's father was an antitrust lawyer (focusing on the corporate, rather than government, side), and Gates is proficient at poker--the calculational, strategic, and human elements. Those seem stronger influences on his being able to create a monopolistic software juggernaut and get the better of his counterparties in several critical deals.

As Leo Atreides puts it, "A Mentat Duke would be formidable indeed." But merely being a mentat is not enough! One must also train to be a duke, which is likely the harder part to convince this crowd of.

I think you mean income, not social class. An academic mathematician might have higher social status but lower income than they would as a startup founder, for example.

Social status is relative to a particular subculture. In certain circles startup founders have higher status than math professors.

I can't give a brief justification for this, but I have good reason to believe that the ~10000x+ differential in net worth comes in large part from the people having had unusually good opportunities to conducive to becoming very technically proficient

I would think this would be obvious. Social class and life situations are a big freaking deal.

Do you mean high IQ with "intellectually gifted" or something else?

Certainly this is true for some "theoretically gifted" people. But others do indeed have little to no "technical ability". The "Grothendieck prime" is an extreme example of it, but there are many accounts of the genius theorists told to stay out of the labs, or else.

It is worthwhile for any "intellectually gifted people who haven't developed very strong technical ability in a quantitative subject" to give it an honest try, but not to be too surprised if they find themselves lacking.

there are many accounts of the genius theorists told to stay out of the labs, or else.

http://en.m.wikipedia.org/wiki/Pauli_effect

I just wanted to mention that your last few posts have been very nice. You have clearly worked on exposition, and it has paid off.

I became interested in this sequence after your first post on mathematical ability, and I'm glad to see you factoring your ideas into digestible pieces and writing them up.

My impression significantly differs, though I'm far from confident. I'd be interested in seeing an expanded version of this point because it seems potentially very valuable to me.

If your claim about the difference between having training in a mathematical field and not having it or are you talking about the difference between people with strong achievements in those domains vs. those that don't have them?

Sorry, this was an useless post so now it's gone

I was describing a general trend – one can often find some examples that are in the opposite direction of a general trend.

Furthermore, those that are the most popular are least likely to be representative. There are very strong selection pressures in the popular media.