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.
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.
I have no idea and I suspect that this strongly depends on the definition of “intellectually gifted”.
But this is highly relevant :D. As I say elsewhere:
“There are so few people who do publishable TCS research as college sophomores that it’s very unlikely that the wealthiest person in the world is one of them by chance. I acknowledge that the correlation may be entirely spurious, but it still warrants a Bayesian update.”
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.
See my response to D_Malik and to shminux. I’m not making an argument, I’m just presenting a perspective, and some evidence, intended as food for thought.
There are so few people who do publishable TCS research as college sophomores that it’s very unlikely that the wealthiest person in the world is one of them by chance.
Of course not by chance: there is a common cause—high IQ. This tells you that high IQ is very useful and can be used both for CS and for business success. However this tells you nothing about the relationship between publishing CS papers and becoming a billionaire.
Bill Gates also famously dropped out of college. Does that warrant a Bayesian update, too? (Peter Thiel probably thinks so :-D)
I’m not making an argument,
You mean you are not offering a proof. But you are still asserting things. For example, this
...as a practical matter, intellectually gifted people who haven’t developed very strong technical ability in a quantitative subject tend to be at a major disadvantage relative to those who have.
looks very much like a point you’re trying to make.
Of course not by chance: there is a common cause—high IQ.
Supposing his IQ to be at the 1 in 10k level (at the level of standard deviations, it’s very unlikely that he’s much higher than this, on priors). There are 400 such Americans of each age. What fraction do you think do publishable math or TCS research as college sophomores?
Bill Gates also famously dropped out of college. Does that warrant a Bayesian update, too? (Peter Thiel probably thinks so :-D)
Yeah, it’s an update in the direction of it being a good idea for people of his demonstrated ability by that age and with his ambitions to drop out.
Yeah, it’s an update in the direction of it being a good idea for people of his demonstrated ability by that age
Well, let’s look at Mark Zuckerberg… and we’re updating right back to where we started. And there is Sergey Brin...oh! we’re now updating in a different direction?
Every example (Brin, Gates, Zuckerberg) should inform the implicit statistical model that we create: every time we learn about about one of them, we should update our model. If you don’t do that, you’re not fully utilizing the evidence available to you! ;-). Also, the model isn’t just of “is this a good idea or isn’t it?”, what we’re doing implicitly is determining probability distributions… And factors specific to individuals matter, the update is just of the type “all else being equal, this now looks to be a better idea.”
Every example … should inform the implicit statistical model that we create: every time we learn about about one of them, we should update our model. If you don’t do that, you’re not fully utilizing the evidence available to you!
This is a popular banner to fly at LW. I don’t agree with it.
The problem is that “evidence available to us” is vast. We are incapable of using all of it to update our models of the world. We necessarily select evidence to be used for updating—and herein lies the problem.
Unless your process of selecting evidence for updating is explicit, transparent, and understood, you run a very high risk of falling prey to some variety of selection bias. And if the evidence you picked is biased, so would be your model.
There is a well-known result of an experiment which asks people to name some random numbers. To the surprise of no one at LW, the numbers people name are not very random. In exactly the same way you may think that you’re updating on a randomly selected pieces of evidence and that the randomness should protect your from bias. I am afraid that doesn’t work.
I would update on evidence which I have reason to believe is representative. Updating on cherry-picked (even unconsciously) examples is worse than useless.
Ok, so I have to put more work in to externalizing my intuitions, which will probably take dozens of blog posts. It’s not as though I haven’t considered your points: again, I’ve thought about these things for 10,000+ hours :-). Thanks for helping me to understand where you’re coming from.
I’m a bit confused about the point that you are trying to make here. As far as I can see there is nothing in this about social class in the traditional meaning of the phrase. It’s about your view that people who study quantitative subjects (rather than poor benighted arts students like me) do better in “business”, make more money, and become more successful.
You’ve cited some examples of people who, it is undeniable, are successful, but who also happen to fit your argument. But equally there are many successful businesspeople who did not study maths/CS/physics (John Paulson, hedge fund manager, started NYU doing film studies) and there are many examples of people with qualifications that you would probably argue show them to be intellectually gifted, who have completely failed in business (the example par excellence here is Long Term Capital Management, stuffed full of PhDs from top schools).
A key in this whole discussion is to define success. If you are just using money to keep score, then consider Tom Cruise, who didn’t attend any university and is worth around half a bill.
You’ve cited some examples of people who, it is undeniable, are successful, but who also happen to fit your argument. But equally there are many successful businesspeople who did not study maths/CS/physics
You mean you are not offering a proof. But you are still asserting things.
What I wrote is vague. (What do I mean by “tend” and major” and “disadvantage”?) It’s very hard to convey quantitative effect sizes in words. I’m pointing at a phenomenon – the particulars of how I’m pointing to it are not of the essence. Bruce Lee said:
It is like a finger pointing a way to the moon. Don’t concentrate on the finger or you will miss all that heavenly glory.
If you doubt that there’s anything to what I’m saying then we can talk about that.
It’s very hard to convey quantitative effect sizes in words.
Huh? No, it’s not hard at all. Besides it’s not like something prohibits you from using, y’know, numbers on LW.
What I wrote is vague … there’s anything to what I’m saying
Hold on. You’re a smart guy and there are a bunch of smart people on LW. You wrote a top-level post which implies that you want to communicate something and, moreover, you think it’s important. What’s all this backsliding into vagueness and the very very low bar of “anything”?
As far as I can read you, you are saying that studying math, in particular among the peer group of mathematicians, is desirable for high-IQ people. You implied two reasons for that: it might lead to riches (and so you mentioned Brin, Gates, Munger, etc.), and it might lead to awesome internal experience and, to use a Maslowian term, self-actualization (and so in the follow-up comments you quoted e.g. Grothendieck).
Whether math is a good way to achieve wealth or internal rapture is debatable, but your position seemed to be fairly defined. Why are you backing away from it now?
Huh? No, it’s not hard at all. Besides it’s not like something prohibits you from using, y’know, numbers on LW.
It’s hard to convey the quantitative effect sizes as encoded in our intuitions: they’re not stored in our brains as numbers.
What’s all this backsliding into vagueness and the very very low bar of “anything”?
:D. The threshold that I’m trying to clear is “get readers to think seriously about whether or not developing strong proficiency with a quantitative subject would be good for those intellectually gifted people who they know (possibly including themselves), based on the considerations that I raise.
I have no idea whether you should try to develop strong proficiency in a quantitative subject: there’s so much that I don’t know about you and your situation, so I’m not going to try to make an argument on that front. What I have to say is actionable only with a lot of individual-specific context that I don’t have. I’m trying to present information that individuals can use to help them make decisions.
quantitative effect sizes as encoded in our intuitions
I don’t understand what that means.
get readers to think seriously about whether or not developing strong proficiency with a quantitative subject would be good for those intellectually gifted people who they know (possibly including themselves), based on the considerations that I raise.
Cool. That’s an entirely reasonable position which can be discussed. Now these “considerations” that you raise, can you make them more coherent and explicit as well? Then the discussion can proceed about whether they are valid, whether there are more considerations which support them or, maybe, counterbalance them, etc.
I mean, e.g. that your brain doesn’t have a numerical answer to the question “What’s the probability that I’ll get into a car crash if I drive to work tomorrow morning?”—it has information that can be used to derive a numerical answer, but the number itself isn’t there.
Yes, I need to make the considerations more coherent and explicit. Thanks for the feedback.
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.
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?
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:
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.
I have no idea and I suspect that this strongly depends on the definition of “intellectually gifted”.
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.
Do you have data (as opposed to anecdotes) to show that?
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.
But this is highly relevant :D. As I say elsewhere:
“There are so few people who do publishable TCS research as college sophomores that it’s very unlikely that the wealthiest person in the world is one of them by chance. I acknowledge that the correlation may be entirely spurious, but it still warrants a Bayesian update.”
See my response to D_Malik and to shminux. I’m not making an argument, I’m just presenting a perspective, and some evidence, intended as food for thought.
Of course not by chance: there is a common cause—high IQ. This tells you that high IQ is very useful and can be used both for CS and for business success. However this tells you nothing about the relationship between publishing CS papers and becoming a billionaire.
Bill Gates also famously dropped out of college. Does that warrant a Bayesian update, too? (Peter Thiel probably thinks so :-D)
You mean you are not offering a proof. But you are still asserting things. For example, this
looks very much like a point you’re trying to make.
Supposing his IQ to be at the 1 in 10k level (at the level of standard deviations, it’s very unlikely that he’s much higher than this, on priors). There are 400 such Americans of each age. What fraction do you think do publishable math or TCS research as college sophomores?
Yeah, it’s an update in the direction of it being a good idea for people of his demonstrated ability by that age and with his ambitions to drop out.
Well, let’s look at Mark Zuckerberg… and we’re updating right back to where we started. And there is Sergey Brin...oh! we’re now updating in a different direction?
Cherry-picking examples is not a good way to go.
Every example (Brin, Gates, Zuckerberg) should inform the implicit statistical model that we create: every time we learn about about one of them, we should update our model. If you don’t do that, you’re not fully utilizing the evidence available to you! ;-). Also, the model isn’t just of “is this a good idea or isn’t it?”, what we’re doing implicitly is determining probability distributions… And factors specific to individuals matter, the update is just of the type “all else being equal, this now looks to be a better idea.”
This is a popular banner to fly at LW. I don’t agree with it.
The problem is that “evidence available to us” is vast. We are incapable of using all of it to update our models of the world. We necessarily select evidence to be used for updating—and herein lies the problem.
Unless your process of selecting evidence for updating is explicit, transparent, and understood, you run a very high risk of falling prey to some variety of selection bias. And if the evidence you picked is biased, so would be your model.
There is a well-known result of an experiment which asks people to name some random numbers. To the surprise of no one at LW, the numbers people name are not very random. In exactly the same way you may think that you’re updating on a randomly selected pieces of evidence and that the randomness should protect your from bias. I am afraid that doesn’t work.
I would update on evidence which I have reason to believe is representative. Updating on cherry-picked (even unconsciously) examples is worse than useless.
Ok, so I have to put more work in to externalizing my intuitions, which will probably take dozens of blog posts. It’s not as though I haven’t considered your points: again, I’ve thought about these things for 10,000+ hours :-). Thanks for helping me to understand where you’re coming from.
I’m a bit confused about the point that you are trying to make here. As far as I can see there is nothing in this about social class in the traditional meaning of the phrase. It’s about your view that people who study quantitative subjects (rather than poor benighted arts students like me) do better in “business”, make more money, and become more successful.
You’ve cited some examples of people who, it is undeniable, are successful, but who also happen to fit your argument. But equally there are many successful businesspeople who did not study maths/CS/physics (John Paulson, hedge fund manager, started NYU doing film studies) and there are many examples of people with qualifications that you would probably argue show them to be intellectually gifted, who have completely failed in business (the example par excellence here is Long Term Capital Management, stuffed full of PhDs from top schools).
A key in this whole discussion is to define success. If you are just using money to keep score, then consider Tom Cruise, who didn’t attend any university and is worth around half a bill.
If only there were some way of quantifying this.
nice link
I’m not making a point. I do have responses to some of what you say, which I’ll be writing about later.
What I wrote is vague. (What do I mean by “tend” and major” and “disadvantage”?) It’s very hard to convey quantitative effect sizes in words. I’m pointing at a phenomenon – the particulars of how I’m pointing to it are not of the essence. Bruce Lee said:
If you doubt that there’s anything to what I’m saying then we can talk about that.
Huh? No, it’s not hard at all. Besides it’s not like something prohibits you from using, y’know, numbers on LW.
Hold on. You’re a smart guy and there are a bunch of smart people on LW. You wrote a top-level post which implies that you want to communicate something and, moreover, you think it’s important. What’s all this backsliding into vagueness and the very very low bar of “anything”?
As far as I can read you, you are saying that studying math, in particular among the peer group of mathematicians, is desirable for high-IQ people. You implied two reasons for that: it might lead to riches (and so you mentioned Brin, Gates, Munger, etc.), and it might lead to awesome internal experience and, to use a Maslowian term, self-actualization (and so in the follow-up comments you quoted e.g. Grothendieck).
Whether math is a good way to achieve wealth or internal rapture is debatable, but your position seemed to be fairly defined. Why are you backing away from it now?
It’s hard to convey the quantitative effect sizes as encoded in our intuitions: they’re not stored in our brains as numbers.
:D. The threshold that I’m trying to clear is “get readers to think seriously about whether or not developing strong proficiency with a quantitative subject would be good for those intellectually gifted people who they know (possibly including themselves), based on the considerations that I raise.
I have no idea whether you should try to develop strong proficiency in a quantitative subject: there’s so much that I don’t know about you and your situation, so I’m not going to try to make an argument on that front. What I have to say is actionable only with a lot of individual-specific context that I don’t have. I’m trying to present information that individuals can use to help them make decisions.
I don’t understand what that means.
Cool. That’s an entirely reasonable position which can be discussed. Now these “considerations” that you raise, can you make them more coherent and explicit as well? Then the discussion can proceed about whether they are valid, whether there are more considerations which support them or, maybe, counterbalance them, etc.
I mean, e.g. that your brain doesn’t have a numerical answer to the question “What’s the probability that I’ll get into a car crash if I drive to work tomorrow morning?”—it has information that can be used to derive a numerical answer, but the number itself isn’t there.
Yes, I need to make the considerations more coherent and explicit. Thanks for the feedback.