I chose Ramanujan as my example because mathematics is extremely meritocratic, as proven by how he went from poor/middle-class Indian on the verge of starving to England on the strength of his correspondence & papers. If there really were countless such people, we would see many many examples of starving farmers banging out some impressive proofs and achieving levels of fame somewhat comparable to Einstein; hence the reference class of peasant-Einsteins must be very small since we see so few people using sheer brainpower to become famous like Ramanujan.
(Or we could simply point out that with average IQs in the 70s and 80s, average mathematician IQs closer to 140s—or 4 standard deviations away, even in a population of billions we still would only expect a small handful of Ramanujans—consistent with the evidence. Gould, of course, being a Marxist who denies any intelligence, would not agree.)
And not just that, but he had more education than the poorest Indians, and probably more than the second poorest. And got his hands on a math textbook, which was probably pretty low probability.
My bet is that there aren’t a lot of geniuses doing stoop labor, especially in traditional peasant situations, but there are some who would have been geniuses if they’d had enough food when young and some education.
And not just that, but he had more education than the poorest Indians, and probably more than the second poorest.
Even the poorest Indians (or Chinese, for that matter) will sacrifice to put their children through school. Ramanujan’s initial education does not seem to have been too extraordinary, before his gifts became manifest (he scored first in exams, and that was how he was able to go to a well-regarded high school; pg25).
And got his hands on a math textbook, which was probably pretty low probability.
Actually, we know how he got his initial textbooks, which was in a way which emphasizes his poverty; pg26-27:
Ramanujan’s family, always strapped for cash, often took in boarders. Around the time he was eleven, there were two of them, Brahmin boys, one from the neighboring district of Trichinopoly, one from Tirunelveli far to the south, studying at the nearby Government College. Noticing Ramanujan’s interest in mathematics, they fed it with whatever they knew. Within months he had exhausted their knowledge and was pestering them for math texts from the college library. Among those they brought to him was an 1893 English textbook popular in South Indian colleges and English preparatory schools, S. L. Loney’s Trigonometry, which actually ranged into more advanced realms. By the time Ramanujan was thirteen, he had mastered it.
...He became something of a minor celebrity. All through his school years, he walked off with merit certificates and volumes of English poetry as scholastic prizes. Finally, at a ceremony in 1904, when Ramanujan was being awarded the K. Ranganatha Rao prize for mathematics, head- master Krishnaswami Iyer introduced him to the audience as a student who, were it possible, deserved higher than the maximum possible marks. An A-plus, or 100 percent, wouldn’t do to rate him. Ramanujan, he was saying, was off-scale.
So just as well he was being lent and awarded all his books, because certainly at age 11 as a poor Indian it’s hard to see how he could afford expensive rare math or English books...
but there are some who would have been geniuses if they’d had enough food when young and some education.
A rather tautological comment: yes, if we removed all the factors preventing people from being X, then presumably more people would be X...
Is the distribution for mathematicians in general stochastic with respect to IQ and a wealthy upbringing / proximity to cultural centres that reward such learning? That might give you signs of whether wealth / culture is a third correlate.
Otherwise, one way or the other, I’m not sure one person shifts the prob any appreciable distance.
Otherwise, one way or the other, I’m not sure one person shifts the prob any appreciable distance.
It really depends on what ‘prob’ you’re talking about. For example, the mean of some variable can be shifted an arbitrary amount by a single person if they are arbitrarily large, which is why “robust statistics” shuns the mean in favor of things like the median, and of course a single counter-example disproves a universal claim. When you are talking about lists of geniuses where the relevant group of geniuses might be 10 or 20 people, 1 person may be fairly meaningful because the group is so small.
Being a Brahmin does not put rice on the table. Again, he was on the brink of starving, he says; this screens off any group considerations—we know he was very poor.
Being a Brahmin does not put rice on the table. Again, he was on the brink of starving, he says; this screens off any group considerations—we know he was very poor.
It screens off any wealth considerations, with the exception of his education (which is midlly relevant). It has a big impact on the question of average IQ and ancestry, though. Brahmin average IQ is probably north of 100,* and so a first-rank mathematician coming from a Brahmin family of any wealth level is not as surprising as a first-rank mathematician coming from a Dalit family.
So we still need to explain the absence (as far as I know) of first rate Dalit mathematicians. Gould argues that they’re there, and we’re missing them; the hereditarian argues that they’re not there. One way to distinguish between the two is to evaluate the counterfactual statement “if they were there, they wouldn’t be missed,” and while Ramanujan is evidence for that statement it’s weakened because of the potential impact of caste prejudice / barriers.
(It seems like the example of China might be better; it seems that young clever people have had the opportunity to escape sweatshops and cotton fields and enter the imperial service / university system for quite some time. Again, though, this is confounded by Han IQ being probably slightly north of 100, and so may not generalize beyond Northeast Asia and Europe.)
*Unfortunately, there is very little solid research on Indian IQ by caste.
It has a big impact on the question of average IQ and ancestry, though. Brahmin average IQ is probably north of 100,* and so a first-rank mathematician coming from a Brahmin family of any wealth level is not as surprising as a first-rank mathematician coming from a Dalit family.
You’d need to examine the IQ of the poorer Brahmins, though, before you could say it’s not surprising; otherwise if the poor Brahmins have the same IQs as equally poor Dalits, then it ought to be equally surprising.
One way to distinguish between the two is to evaluate the counterfactual statement “if they were there, they wouldn’t be missed,” and while Ramanujan is evidence for that statement it’s weakened because of the potential impact of caste prejudice / barriers.
But Ramanujan is evidence against the Great Filters of nationality and poverty, which ought to be much bigger filters against possible Einsteins than caste.
It seems like the example of China might be better; it seems that young clever people have had the opportunity to escape sweatshops and cotton fields and enter the imperial service / university system for quite some time.
Yes, but I’m not very familiar with the background of major Chinese figures (eg. I just looked him up now and while I had assumed Confucius was a minor aristocrat, apparently he was actually the son of an army officer and “is said to have worked as a shepherd, cowherd, clerk, and a book-keeper.”); plus, you’d want to look at the post-Tang major Chinese figures, but that will exclude most major Chinese figures period like all the major philosophers—looking up the Chinese philosophy table in Murray’s Human Accomplishment, like the first 10 are all pre-examination (and Murray comments of one of them, ” it was Zhu Xi who was responsible for making Mencius as well known as he is today, by including Mencius’s work as part of “The Four Books” that became the central texts for both primary education and the civil service examinations”).
I think it can be illustrative, as a counter to the spotlight effect, to look at the personalities of math/science outliers who come from privileged backgrounds, and imagine them being born into poverty. Oppenheimer’s conjugate was jailed or executed for attempted murder, instead of being threatened with academic probation. Gödel’s conjugate added a postscript to his proof warning that the British Royal Family were possible Nazi collaborators, which got it binned, which convinced him that all British mathematicians were in on the conspiracy. Newton and Turing’s conjugates were murdered as teenagers on suspicion of homosexuality. I have to make these stories up because if you’re poor and at all weird, flawed, or unlucky your story is rarely recorded.
Oppenheimer’s conjugate was jailed or executed for attempted murder, instead of being threatened with academic probation.
A gross exaggeration; execution was never in the cards for a poisoned apple which was never eaten.
Gödel’s conjugate added a postscript to his proof warning that the British Royal Family were possible Nazi collaborators, which got it binned, which convinced him that all British mathematicians were in on the conspiracy.
Likewise. Goedel didn’t go crazy until long after he was famous, and so your conjugate is in no way showing ‘privilege’.
Newton and Turing’s conjugates were murdered as teenagers on suspicion of homosexuality.
Likewise. You have some strange Whiggish conception of history where all periods were ones where gays would be lynched; Turing would not have been lynched anymore than President Buchanan would have, because so many upper-class Englishmen were notorious practicing gays and their boarding schools Sodoms and Gomorrahs. To remember the context of Turing’s homosexuality conviction, this was in the same period where highly-placed gay Englishman after gay Englishman was turning out to be Soviet moles (see the Cambridge Five and how the bisexual Kim Philby nearly became head of MI6!) EDIT: pg137-144 of the Ramanujan book I’ve been quoting discusses the extensive homosexuality at Cambridge and its elite, and how tolerance of homosexuality ebbed and flowed, with the close of the Victorian age being particularly intolerant.
The right conjugate for Newton, by the way, reads ‘and his heretical Christian views were discovered, he was fired from Cambridge—like his successor as Lucasian Professor—and died a martyr’.
I have to make these stories up because if you’re poor and at all weird, flawed, or unlucky your story is rarely recorded.
The problem is, we have these stories. We have Ramanujan who by his own testimony was on the verge of starvation—and if that is not poor, then you are not using the word as I understand it—and we have William Shakespeare (no aristocrat he), and we have Epicurus who was a slave. There is no censorship of poor and middle-class Einsteins. And this is exactly what we would expect when we consider what it takes to be a genius like Einstein, to be gifted in multiple ways, to be far out on multiple distributions (giving us a highly skewed distribution of accomplishment, see the Lotka curve): we would expect a handful of outliers who come from populations with low means, and otherwise our lists to be dominated by outliers from populations with higher means, without any appeal to Marxian oppression or discrimination necessary.
Do you really think the existence of oppression is a figment of Marxist ideology? If being poor didn’t make it harder to become a famous mathematician given innate ability, I’m not sure “poverty” would be a coherent concept. If you’re poor, you don’t just have to be far out on multiple distributions, you also have to be at the mean or above in several more (health, willpower, various kinds of luck). Ramanujan barely made it over the finish line before dying of malnutrition.
Even if the mean mathematical ability in Indians were innately low (I’m quite skeptical there), that would itself imply a context containing more censoring factors for any potential Einsteins...to become a mathematician, you have to, at minimum, be aware that higher math exists, that you’re unusually good at it by world standards, and being a mathematician at that level is a viable way to support your family.
On your specific objections to my conjugates...I’m fairly confident that confessing to poisoning someone else’s food usually gets you incarcerated, and occasionally gets you killed (think feudal society or mob-ridden areas), and is at least a career-limiting move if you don’t start from a privileged position. Hardly a gross exaggeration. Goedel didn’t become clinically paranoid until later, but he was always the sort of person who would thoughtlessly insult an important gatekeeper’s government, which is part of what I was getting at; Ramanujan was more politic than your average mathematician. I actually was thinking of making Newton’s conjugate be into Hindu mysticism instead of Christian but that seemed too elaborate.
Do you really think the existence of oppression is a figment of Marxist ideology?
I’m perfectly happy to accept the existence of oppression, but I see no need to make up ways in which the oppression might be even more awful than one had previously thought. Isn’t it enough that peasants live shorter lives, are deprived of stuff, can be abused by the wealthy, etc? Why do we need to make up additional ways in which they might be opppressed? Gould comes off here as engaging in a horns effect: not only is oppression bad in the obvious concrete well-verified ways, it’s the Worst Thing In The World and so it’s also oppressing Einsteins!
If being poor didn’t make it harder to become a famous mathematician given innate ability, I’m not sure “poverty” would be a coherent concept.
Not what Gould hyperbolically claimed. He didn’t say that ‘at the margin, there may be someone who was slightly better than your average mathematician but who failed to get tenure thanks to some lingering disadvantages from his childhood’. He claimed that there were outright historic geniuses laboring in the fields. I regard this as completely ludicrous due both to the effects of poverty & oppression on means & tails and due to the pretty effective meritocratic mechanisms in even a backwater like India.
Even if the mean mathematical ability in Indians were innately low (I’m quite skeptical there)
It absolutely is. Don’t confuse the fact that there are quite a few brilliant Indians in absolute numbers with a statement about the mean—with a population of ~1.3 billion people, that’s just proving the point.
to become a mathematician, you have to, at minimum, be aware that higher math exists, that you’re unusually good at it by world standards, and being a mathematician at that level is a viable way to support your family.
The talent can manifest as early as arithmetic, which is taught to a great many poor people, I am given to understand.
I’m fairly confident that confessing to poisoning someone else’s food usually gets you incarcerated, and occasionally gets you killed (think feudal society or mob-ridden areas), and is at least a career-limiting move if you don’t start from a privileged position.
Really? Then I’m sure you could name three examples.
Goedel didn’t become clinically paranoid until later, but he was always the sort of person who would thoughtlessly insult an important gatekeeper’s government, which is part of what I was getting at
Sorry, I can only read what you wrote. If you meant he lacked tact, you shouldn’t have brought up insanity.
Ramanujan was more politic than your average mathematician.
Really? Because his mathematician peers were completely exasperated at him. What, exactly, was he politic about?
the effects of poverty & oppression on means & tails
Wait, what are you saying here? That there aren’t any Einsteins in sweatshops in part because their innate mathematical ability got stunted by malnutrition and lack of education? That seems like basically conceding the point, unless we’re arguing about whether there should be a program to give a battery of genius tests to every poor adult in India.
The talent can manifest as early as arithmetic, which is taught to a great many poor people, I am given to understand.
Not all of them, I don’t think. And then you have to have a talent that manifests early, have someone in your community who knows that a kid with a talent for arithmetic might have a talent for higher math, knows that a talent for higher math can lead to a way to support your family, expects that you’ll be given a chance to prove yourself, gives a shit, has a way of getting you tested...
I’m fairly confident that confessing to poisoning someone else’s food usually gets you incarcerated, and occasionally gets you killed (think feudal society or mob-ridden areas), and is at least a career-limiting move if you don’t start from a privileged position.
Really? Then I’m sure you could name three examples.
Sorry, I can only read what you wrote. If you meant he lacked tact, you shouldn’t have brought up insanity.
I was trying to elegantly combine the Incident with the Debilitating Paranoia and the Incident with the Telling The Citizenship Judge That Nazis Could Easily Take Over The United States. Clearly didn’t completely come across.
Really? Because his mathematician peers were completely exasperated at him. What, exactly, was he politic about?
He was politic enough to overcome Vast Cultural Differences enough to get somewhat integrated into an insular community. I hang out with mathematicians a lot; my stereotype of them is that they tend not to be good at that.
He claimed that there were outright historic geniuses laboring in the fields.
And this part seems entirely plausible. American slaves had no opportunity to become famous mathematicians unless they escaped, or chanced to have an implausibly benevolent Dumbledore of an owner.
Gould makes a much stronger claim, and I attach little probability to the part about the present day. But even there, you’re ignoring one or two good points about the actions of famous mathematicians. Demanding citations for ‘trying to kill people can ruin your life’ seems frankly bizarre.
Do you really think the existence of oppression is a figment of Marxist ideology?
The specific oppressions you led off with: yes.
I’m fairly confident that confessing to poisoning someone else’s food usually gets you incarcerated, and occasionally gets you killed (think feudal society or mob-ridden areas)
I thought we were talking about Oppenheimer and Cambridge? It looks like if Oppenheimer hadn’t had rich parents who lobbied on his behalf, he might have gotten probation instead of not. Given his instability, that might have pushed him into a self-destructive spiral, or maybe he just would have progressed a little slower through the system. So, yes, jumping from “the university is unhappy” to “the state hangs you” is a gross exaggeration. (Universities are used to graduate students being under a ton of stress, and so do cut them slack; the response to Oppenheimer of “we think you need to go on vacation, for everyone’s safety” was ‘normal’.)
“Oppenheimer wasn’t privileged, he was only treated slightly better than the average Cambridge student.”
I’m sorry, I never really rigorously defined the counter-factuals we were playing with, but the fact that Oppenheimer was in a context where attempted murder didn’t sink his career is surely relevant to the overall question of whether there are Einsteins in sweatshops.
the fact that Oppenheimer was in a context where attempted murder didn’t sink his career is surely relevant to the overall question of whether there are Einsteins in sweatshops.
I don’t see the relevance, because to me “Einsteins in sweatshops” means “Einsteins that don’t make it to ”, for some Cambridge equivalent. If Ramanujan had died three years earlier, and thus not completed his PhD, he would still be in the history books. I mean, take Galois as an example: repeatedly imprisoned for political radicalism under a monarchy, and dies in a duel at age 20. Certainly someone ruined by circumstances—and yet we still know about him and his mathematical work.
In general, these counterfactuals are useful for exhibiting your theory but not proving your theory. Either we have the same background assumptions- and so the counterfactuals look reasonable to both of us- or we disagree on background assumptions, and the counterfactual is only weakly useful at identifying where the disagreement is.
I don’t think Epicurus was a slave. He did admit slaves to his school though, which is not something that was typical for his time. Perhaps you are referring to the Stoic, Epictetus, who definitely was a slave (although, white-collar).
Whups, you’re right. Some of the Greek philosophers’ names are so easy to confuse (I still confuse Xenophanes and Xenophon). Well, Epictetus was still important, if not as important as Epicurus.
Well, it is also democratic in the sense that what convinces the mathematical community is what matters, and there’s no ‘President of Mathematics’ or ‘Academie de la Mathematique’ laying down the rules, but yes, ‘meritocratic’ is closer to what I meant.
pg169-171, Kanigel’s 1991 The Man Who Knew Infinity:
It wasn’t the first time a letter had launched the career of a famous mathematician. Indeed, as the mathematician Louis J. Mordell would later insist, “It is really an easy matter for anyone who has done brilliant mathematical work to bring himself to the attention of the mathematical world, no matter how obscure or unknown he is or how insignificant a position he occupies. All he need do is to send an account of his results to a leading authority,” as Jacobi had in writing Legendre on elliptic functions, or as Hermite had in writing Jacobi on number theory.
And yet, if Mordell was right-if “it is really an easy matter”—why had Gauss spurned Abel? Carl Friedrich Gauss was the premier mathematician of his time, and, perhaps, of all time. The Norwegian Niels Henrik Abel, just twenty-two at the time he wrote Gauss, had proved that some equations of the fifth degree (like x^5 + 3x^4 + … = 0) could never be solved algebraically. That was a real coup, especially since leading mathematicians had for years sought a general solution that, Abel now showed, didn’t exist. Yet when he sent his proof to Gauss, the man history records as “the Prince of Mathematics” tossed it aside without reading it. “Here,” one account has him saying, dismissing Abel’s paper as the work of a crank, “is another of those monstrosities.”
. Then, too, if “it is really an easy matter,” why had Ramanujan’s brilliance failed to cast an equal spell on Baker and Hobson, the other two Cambridge mathematicians to whom he had written?...The other Cambridge mathematician, a Senior Wrangler, was E. W. Hobson, who was in his late fifties when he heard from Ramanujan and more eminent even than Baker. His high forehead, prominent mustache, and striking eyes helped make him, in Hardy’s words, “a distinguished and conspicuous figure” around Cambridge. But he was remembered, too, as a dull lecturer, and after he died his most important book was described in words like “systematic,” “exhaustive,” and “comprehensive,” never in language suggesting great imagination or flair. “An old stick-in-the-mud,” someone once called him.
...Of course, Ramanujan’s fate had always hung on a knife edge, and it had never taken more than the slightest want of imagination, the briefest hesitancy, to tip the balance against him. Only the most stubborn persistence on the part of his friend Rajagopalachari had gained him the sympathy of Ramachandra Rao. And Hardy himself was put off by Ramanujan’s letter before he was won over by it. The cards are stacked, against any original mind, and perhaps properly so. After all, many who claim the mantle of “new and original” are indeed new, and original—but not better. So, in a sense, it should be neither surprising nor reason for any but the mildest rebuke that Hobson and Baker said no. Nor should it be surprising that no one: in India had made much of Ramanujan’s work. Hardy was perhaps England’s premier mathematician, the beneficiary of the finest education, in touch with the latest mathematical thought and, to boot, an expert in several fields Ramanujan plowed …. And yet a day with Ramanujan’s theorems had left him bewildered. I had never seen anything in the least like them before. Like the Indians, Hardy did not know what to make of Ramanujan’s work. Like them, he doubted his own judgment of it. Indeed, it is not just that he discerned genius in Ramanujan that redounds to his credit today; it is that he battered down his own wall of skepticism to do so. That Ramanujan was Indian probably didn’t taint him in Hardy’s eyes.
Personally, having finished reading the book, I think Kanigel is wrong to think there is so much contingency here. He paints a vivid picture of why Ramanujan had failed out of school, lost his scholarships, and had difficulties publishing, and why two Cambridge mathematicians might mostly ignore his letter: Ramanujan’s stubborn refusal to study non-mathematical topics and refusal to provide reasonably rigorous proofs. His life could have been much easier if he had been less eccentric and prideful. That despite all his self-inflicted problems he was brought to Cambridge anyway is a testimony to how talent will out.
I am already a half starving man. To preserve my brains I want food and this is my first consideration. Any sympathetic letter from you will be helpful to me here to get a scholarship either from the university or from the government.
Googling the text finds it quoted a bunch of places.
Besides his letter to Hardy, Wikipedia cites The Man Who Knew Infinity (on Libgen; it also quotes the ‘half starving’ passage), where the cited section reads:
Describing the obsession with college degrees among ambitious young Indians around this time, an English writer, Herbert Compton, noted how “the loaves and fishes fall far short of the multitude, and the result is the creation of armies of hungry ‘hopefuls’-the name is a literal trans- lation of the vernacular generic term omedwar used in describing them- who pass their lives in absolute idleness, waiting on the skirts of chance, or gravitate to courses entirely opposed to those which education in- tended.” Ramanujan, it might have seemed in 1908, was just such an omedwar. Out of school, without a job, he hung around the house in Kumbakonam.
Times were hard. One day back at Pachaiyappa’s, the wind had blown off Ramanujan’s cap as he boarded the electric train for school, and Ramanujan’s Sanskrit teacher, who insisted that boys wear their traditional tufts covered, asked him to step back out to the market and buy one. Ramanujan apologized that he lacked even the few annas it cost. (His classmates, who’d observed his often-threadbare dress, chipped in to buy it for him.)
Ramanujan’s father never made more than about twenty rupees a month; a rupee bought about twenty-five pounds of rice. Agricultural workers in surrounding villages earned four or five annas, or about a quarter rupee, per day; so many families were far worse off than Ramanujan’s. But by the standards of the Brahmin professional community in which Ramanujan moved, it was close to penury.
The family took in boarders; that brought in another ten rupees per month. And Komalatammal sang at the temple, bringing in a few more. Still, Ramanujan occasionally went hungry. Sometimes, an old woman in the neighborhood would invite him in for a midday meal. Another family, that of Ramanujan’s friend S. M. Subramanian, would also take him in, feeding him dosai, the lentil pancakes that are a staple of South Indian cooking. One time in 1908, Ramanujan’s mother stopped by the Subramanian house lamenting that she had no rice. The boy’s mother fed her and sent her younger son, Anantharaman, to find Ramanujan. Anantharaman led him to the house of his aunt, who filled him up on rice and butter.
To bring in money, Ramanujan approached friends of the family; perhaps they had accounts to post, or books to reconcile? Or a son to tutor? One student, for seven rupees a month, was Viswanatha Sastri, son ofa Government College philosophy professor. Early each morning, Ramanujan would walk to the boy’s house on Solaiappa Mudali Street, at the other end of town, to coach him in algebra, geometry, and trigonometry. The only trouble was, he couldn’t stick to the course material. He’d teach the standard method today and then, if Viswanatha forgot it, would improvise a wholly new one tomorrow. Soon he’d be lost in areas the boy’s regular teacher never touched.
Sometimes he would fly off onto philosophical tangents. They’d be discussing the height of a wall, perhaps for a trigonometry problem, and Ramanujan would insist that its height was, of course, only relative: who could say how high it seemed to an ant or a buffalo? One time he asked how the world would look when first created, before there was anyone to view it. He took delight, too, in posing sly little problems: If you take a belt, he asked Viswanatha and his father, and cinch it tight around the earth’s twenty-five-thousand-mile-Iong equator, then let it out just 271″ feet-about two yards-how far off the earth’s surface would it stand? Some tiny fraction of an inch? Nope, one foot.
Viswanatha Sastri found Ramanujan inspiring; other students, however, did not. One classmate from high school, N. Govindaraja Iyengar, asked Ramanujan to help him with differential calculus for his B.A. exam. The arrangement lasted all of two weeks. You can think of calculus as a set of powerful mathematical tools; that’s how most students learn it and what most exams require. Or else you can appreciate it for the subtle questions it poses about the nature of the infinitesimally small and the infinitely large. Ramanujan, either unmindful of his students’ practical needs or unwilling to cater to them, stressed the latter. “He would talk only of infinity and infinitesimals,” wrote Govindara,ja, who was no slouch intellectually and wound up as chairman oflndia’s public service commission. “I felt that his tuition [teaching] might not be of real use to me in the examination, and so I gave it up.”
Ramanujan had lost all his scholarships. He had failed in school. Even as a tutor of the subject he loved most, he’d been found wanting. He had nothing.
And yet, viewed a little differently, he had everything. For now there was nothing to distract him from his notebooks-notebooks, crammed with theorems, that each day, each week, bulged wider.
If you take a belt, he asked Viswanatha and his father, and cinch it tight around the earth’s twenty-five-thousand-mile-Iong equator, then let it out just 271″ feet-about two yards-how far off the earth’s surface would it stand? Some tiny fraction of an inch? Nope, one foot.
I can’t parse ’271″ feet’, is this an OCR issue? If you loosen the belt by two yards, it can obviously reach at least a yard above the surface, because you can just go from ____ to __|__. And I recall that the actual answer is considerably more than that.
Given that the symbol ” is the symbol for inches, and ′ is the symbol for feet, I would suspect that there has been a mistyping in the quote.
I think that what was meant to be there was 72“ or 72.1” (inches), which is exactly/one-tenth of an inch over two yards (one yard = three feet). That would produce the desired result of a nearly one-foot increase in the radius of the belt; adding 72 inches to the circumference of the belt would produce an increase of 11.46 inches (72 inches / (2 * pi)) in the radius of the belt, which in this case is the height above the ground.
“The Collapse of the Soviet Union and the Productivity of American Mathematicians” comes to mind as an interesting recent natural experiment where the floodgate of Russian mathematical talent was unleashed after the collapse of the USSR and many of them successfully rose in America despite academic math being a zero-sum game; consistent with meritocracy.
Okay, maybe there aren’t other examples quite as good as him, but a few of these people surely come close.
Or we could simply point out that with average IQs in the 70s and 80s, average mathematician IQs closer to 140s—or 4 standard deviations away, even in a population of billions we still would only expect a small handful of Ramanujans—consistent with the evidence.
Yes, but I’m not sure all of the populations working in cotton fields and sweatshops had such a low average IQ. (And Gould just said “people”, not “innumerable people” or something like that.)
Doesn’t your observation that most successful autodidacts come from financially stable backgrounds SUPPORT the hypothesis that intelligent individuals from low-income backgrounds are prevented from becoming successful?
With the facts you’ve highlighted, two conclusions may be drawn: either most poor people are stupid, or the aforementioned “starving farmers” don’t have the time or the resources to educate themselves or “[bang] out some impressive proofs,” on account of the whole “I’m starving and need to grow some food” thing. I don’t see how such people would be able to afford books to learn from or time to spend reading them.
Doesn’t your observation that most successful autodidacts come from financially stable backgrounds SUPPORT the hypothesis that intelligent individuals from low-income backgrounds are prevented from becoming successful?
No, it doesn’t; see my other comment. I was criticizing the list as a bizarre selection which did not include anyone remotely like Einstein.
I don’t see how such people would be able to afford books to learn from
How did Ramanujan afford books?
The answer to the autodidact point is to point out that once one has proven one’s Einstein-level talent, one is integrated into the meritocratic system and no longer considered an autodidact.
Presumably the people who write the IQ test, based on whatever population sample they use to calibrate it. Is the point that the average IQ in India is 70-80, as opposed to the average in the US? (This could be technically true on an IQ test written in the US, without being meaningful, or it could be actually true because of nutrition or whatever). What data does the number 70-80 actually come from?
Or we could simply point out that with average IQs in the 70s and 80s, average mathematician IQs closer to 140s—or 4 standard deviations away, even in a population of billions we still would only expect a small handful of Ramanujans—consistent with the evidence.
It would naively seem that an IQ of 160 or more is 5 SDs from 85 , but 4SDs from the 100 , so the rarity would be 1⁄3,483,046 vs 1⁄31,560 , for a huge ratio of 110 times prevalence of extreme genius between the populations.
Except that this is not how it works when the IQ of 100 population has been selected from the other and subsequently has lower variance. Nor is it how Flynn effect worked. Because, of course, the standard deviation is not going to remain constant.
There was only one Ramanujan; and we are all well-aware of Gould’s views on intelligence here, I presume.
they are not well known to me
http://lesswrong.com/lw/65b/scientific_misconduct_misdiagnosed_because_of/
http://lesswrong.com/lw/kv/beware_of_stephen_j_gould/
http://www.debunker.com/texts/jensen.html
Thanks
In what reference class?
I chose Ramanujan as my example because mathematics is extremely meritocratic, as proven by how he went from poor/middle-class Indian on the verge of starving to England on the strength of his correspondence & papers. If there really were countless such people, we would see many many examples of starving farmers banging out some impressive proofs and achieving levels of fame somewhat comparable to Einstein; hence the reference class of peasant-Einsteins must be very small since we see so few people using sheer brainpower to become famous like Ramanujan.
(Or we could simply point out that with average IQs in the 70s and 80s, average mathematician IQs closer to 140s—or 4 standard deviations away, even in a population of billions we still would only expect a small handful of Ramanujans—consistent with the evidence. Gould, of course, being a Marxist who denies any intelligence, would not agree.)
It is worth pointing out that Ramanujan, while poor, was still a Brahmin.
And not just that, but he had more education than the poorest Indians, and probably more than the second poorest. And got his hands on a math textbook, which was probably pretty low probability.
My bet is that there aren’t a lot of geniuses doing stoop labor, especially in traditional peasant situations, but there are some who would have been geniuses if they’d had enough food when young and some education.
Even the poorest Indians (or Chinese, for that matter) will sacrifice to put their children through school. Ramanujan’s initial education does not seem to have been too extraordinary, before his gifts became manifest (he scored first in exams, and that was how he was able to go to a well-regarded high school; pg25).
Actually, we know how he got his initial textbooks, which was in a way which emphasizes his poverty; pg26-27:
So just as well he was being lent and awarded all his books, because certainly at age 11 as a poor Indian it’s hard to see how he could afford expensive rare math or English books...
A rather tautological comment: yes, if we removed all the factors preventing people from being X, then presumably more people would be X...
Is the distribution for mathematicians in general stochastic with respect to IQ and a wealthy upbringing / proximity to cultural centres that reward such learning? That might give you signs of whether wealth / culture is a third correlate.
Otherwise, one way or the other, I’m not sure one person shifts the prob any appreciable distance.
It really depends on what ‘prob’ you’re talking about. For example, the mean of some variable can be shifted an arbitrary amount by a single person if they are arbitrarily large, which is why “robust statistics” shuns the mean in favor of things like the median, and of course a single counter-example disproves a universal claim. When you are talking about lists of geniuses where the relevant group of geniuses might be 10 or 20 people, 1 person may be fairly meaningful because the group is so small.
Being a Brahmin does not put rice on the table. Again, he was on the brink of starving, he says; this screens off any group considerations—we know he was very poor.
It screens off any wealth considerations, with the exception of his education (which is midlly relevant). It has a big impact on the question of average IQ and ancestry, though. Brahmin average IQ is probably north of 100,* and so a first-rank mathematician coming from a Brahmin family of any wealth level is not as surprising as a first-rank mathematician coming from a Dalit family.
So we still need to explain the absence (as far as I know) of first rate Dalit mathematicians. Gould argues that they’re there, and we’re missing them; the hereditarian argues that they’re not there. One way to distinguish between the two is to evaluate the counterfactual statement “if they were there, they wouldn’t be missed,” and while Ramanujan is evidence for that statement it’s weakened because of the potential impact of caste prejudice / barriers.
(It seems like the example of China might be better; it seems that young clever people have had the opportunity to escape sweatshops and cotton fields and enter the imperial service / university system for quite some time. Again, though, this is confounded by Han IQ being probably slightly north of 100, and so may not generalize beyond Northeast Asia and Europe.)
*Unfortunately, there is very little solid research on Indian IQ by caste.
You’d need to examine the IQ of the poorer Brahmins, though, before you could say it’s not surprising; otherwise if the poor Brahmins have the same IQs as equally poor Dalits, then it ought to be equally surprising.
But Ramanujan is evidence against the Great Filters of nationality and poverty, which ought to be much bigger filters against possible Einsteins than caste.
Yes, but I’m not very familiar with the background of major Chinese figures (eg. I just looked him up now and while I had assumed Confucius was a minor aristocrat, apparently he was actually the son of an army officer and “is said to have worked as a shepherd, cowherd, clerk, and a book-keeper.”); plus, you’d want to look at the post-Tang major Chinese figures, but that will exclude most major Chinese figures period like all the major philosophers—looking up the Chinese philosophy table in Murray’s Human Accomplishment, like the first 10 are all pre-examination (and Murray comments of one of them, ” it was Zhu Xi who was responsible for making Mencius as well known as he is today, by including Mencius’s work as part of “The Four Books” that became the central texts for both primary education and the civil service examinations”).
He’s literally as much evidence against those filters as he is evidence against hypothetical very low prevalence of poor innate geniuses.
I think it can be illustrative, as a counter to the spotlight effect, to look at the personalities of math/science outliers who come from privileged backgrounds, and imagine them being born into poverty. Oppenheimer’s conjugate was jailed or executed for attempted murder, instead of being threatened with academic probation. Gödel’s conjugate added a postscript to his proof warning that the British Royal Family were possible Nazi collaborators, which got it binned, which convinced him that all British mathematicians were in on the conspiracy. Newton and Turing’s conjugates were murdered as teenagers on suspicion of homosexuality. I have to make these stories up because if you’re poor and at all weird, flawed, or unlucky your story is rarely recorded.
A gross exaggeration; execution was never in the cards for a poisoned apple which was never eaten.
Likewise. Goedel didn’t go crazy until long after he was famous, and so your conjugate is in no way showing ‘privilege’.
Likewise. You have some strange Whiggish conception of history where all periods were ones where gays would be lynched; Turing would not have been lynched anymore than President Buchanan would have, because so many upper-class Englishmen were notorious practicing gays and their boarding schools Sodoms and Gomorrahs. To remember the context of Turing’s homosexuality conviction, this was in the same period where highly-placed gay Englishman after gay Englishman was turning out to be Soviet moles (see the Cambridge Five and how the bisexual Kim Philby nearly became head of MI6!) EDIT: pg137-144 of the Ramanujan book I’ve been quoting discusses the extensive homosexuality at Cambridge and its elite, and how tolerance of homosexuality ebbed and flowed, with the close of the Victorian age being particularly intolerant.
The right conjugate for Newton, by the way, reads ‘and his heretical Christian views were discovered, he was fired from Cambridge—like his successor as Lucasian Professor—and died a martyr’.
The problem is, we have these stories. We have Ramanujan who by his own testimony was on the verge of starvation—and if that is not poor, then you are not using the word as I understand it—and we have William Shakespeare (no aristocrat he), and we have Epicurus who was a slave. There is no censorship of poor and middle-class Einsteins. And this is exactly what we would expect when we consider what it takes to be a genius like Einstein, to be gifted in multiple ways, to be far out on multiple distributions (giving us a highly skewed distribution of accomplishment, see the Lotka curve): we would expect a handful of outliers who come from populations with low means, and otherwise our lists to be dominated by outliers from populations with higher means, without any appeal to Marxian oppression or discrimination necessary.
Do you really think the existence of oppression is a figment of Marxist ideology? If being poor didn’t make it harder to become a famous mathematician given innate ability, I’m not sure “poverty” would be a coherent concept. If you’re poor, you don’t just have to be far out on multiple distributions, you also have to be at the mean or above in several more (health, willpower, various kinds of luck). Ramanujan barely made it over the finish line before dying of malnutrition.
Even if the mean mathematical ability in Indians were innately low (I’m quite skeptical there), that would itself imply a context containing more censoring factors for any potential Einsteins...to become a mathematician, you have to, at minimum, be aware that higher math exists, that you’re unusually good at it by world standards, and being a mathematician at that level is a viable way to support your family.
On your specific objections to my conjugates...I’m fairly confident that confessing to poisoning someone else’s food usually gets you incarcerated, and occasionally gets you killed (think feudal society or mob-ridden areas), and is at least a career-limiting move if you don’t start from a privileged position. Hardly a gross exaggeration. Goedel didn’t become clinically paranoid until later, but he was always the sort of person who would thoughtlessly insult an important gatekeeper’s government, which is part of what I was getting at; Ramanujan was more politic than your average mathematician. I actually was thinking of making Newton’s conjugate be into Hindu mysticism instead of Christian but that seemed too elaborate.
I’m perfectly happy to accept the existence of oppression, but I see no need to make up ways in which the oppression might be even more awful than one had previously thought. Isn’t it enough that peasants live shorter lives, are deprived of stuff, can be abused by the wealthy, etc? Why do we need to make up additional ways in which they might be opppressed? Gould comes off here as engaging in a horns effect: not only is oppression bad in the obvious concrete well-verified ways, it’s the Worst Thing In The World and so it’s also oppressing Einsteins!
Not what Gould hyperbolically claimed. He didn’t say that ‘at the margin, there may be someone who was slightly better than your average mathematician but who failed to get tenure thanks to some lingering disadvantages from his childhood’. He claimed that there were outright historic geniuses laboring in the fields. I regard this as completely ludicrous due both to the effects of poverty & oppression on means & tails and due to the pretty effective meritocratic mechanisms in even a backwater like India.
It absolutely is. Don’t confuse the fact that there are quite a few brilliant Indians in absolute numbers with a statement about the mean—with a population of ~1.3 billion people, that’s just proving the point.
The talent can manifest as early as arithmetic, which is taught to a great many poor people, I am given to understand.
Really? Then I’m sure you could name three examples.
Sorry, I can only read what you wrote. If you meant he lacked tact, you shouldn’t have brought up insanity.
Really? Because his mathematician peers were completely exasperated at him. What, exactly, was he politic about?
Wait, what are you saying here? That there aren’t any Einsteins in sweatshops in part because their innate mathematical ability got stunted by malnutrition and lack of education? That seems like basically conceding the point, unless we’re arguing about whether there should be a program to give a battery of genius tests to every poor adult in India.
Not all of them, I don’t think. And then you have to have a talent that manifests early, have someone in your community who knows that a kid with a talent for arithmetic might have a talent for higher math, knows that a talent for higher math can lead to a way to support your family, expects that you’ll be given a chance to prove yourself, gives a shit, has a way of getting you tested...
Just going off Google, here: People being incarcerated for unsuccessful attempts to poison someone: http://digitaljournal.com/article/346684 http://charlotte.news14.com/content/headlines/628564/teen-arrested-for-trying-to-poison-mother-s-coffee/ http://www.ksl.com/?nid=148&sid=85968
Person being killed for suspected unsuccessful attempt to poison someone: http://zeenews.india.com/news/bihar/man-lynched-for-trying-to-poison-hand-pump_869197.html
I was trying to elegantly combine the Incident with the Debilitating Paranoia and the Incident with the Telling The Citizenship Judge That Nazis Could Easily Take Over The United States. Clearly didn’t completely come across.
He was politic enough to overcome Vast Cultural Differences enough to get somewhat integrated into an insular community. I hang out with mathematicians a lot; my stereotype of them is that they tend not to be good at that.
And this part seems entirely plausible. American slaves had no opportunity to become famous mathematicians unless they escaped, or chanced to have an implausibly benevolent Dumbledore of an owner.
Gould makes a much stronger claim, and I attach little probability to the part about the present day. But even there, you’re ignoring one or two good points about the actions of famous mathematicians. Demanding citations for ‘trying to kill people can ruin your life’ seems frankly bizarre.
The specific oppressions you led off with: yes.
I thought we were talking about Oppenheimer and Cambridge? It looks like if Oppenheimer hadn’t had rich parents who lobbied on his behalf, he might have gotten probation instead of not. Given his instability, that might have pushed him into a self-destructive spiral, or maybe he just would have progressed a little slower through the system. So, yes, jumping from “the university is unhappy” to “the state hangs you” is a gross exaggeration. (Universities are used to graduate students being under a ton of stress, and so do cut them slack; the response to Oppenheimer of “we think you need to go on vacation, for everyone’s safety” was ‘normal’.)
I’m sorry, I never really rigorously defined the counter-factuals we were playing with, but the fact that Oppenheimer was in a context where attempted murder didn’t sink his career is surely relevant to the overall question of whether there are Einsteins in sweatshops.
I don’t see the relevance, because to me “Einsteins in sweatshops” means “Einsteins that don’t make it to ”, for some Cambridge equivalent. If Ramanujan had died three years earlier, and thus not completed his PhD, he would still be in the history books. I mean, take Galois as an example: repeatedly imprisoned for political radicalism under a monarchy, and dies in a duel at age 20. Certainly someone ruined by circumstances—and yet we still know about him and his mathematical work.
In general, these counterfactuals are useful for exhibiting your theory but not proving your theory. Either we have the same background assumptions- and so the counterfactuals look reasonable to both of us- or we disagree on background assumptions, and the counterfactual is only weakly useful at identifying where the disagreement is.
I don’t think Epicurus was a slave. He did admit slaves to his school though, which is not something that was typical for his time. Perhaps you are referring to the Stoic, Epictetus, who definitely was a slave (although, white-collar).
Whups, you’re right. Some of the Greek philosophers’ names are so easy to confuse (I still confuse Xenophanes and Xenophon). Well, Epictetus was still important, if not as important as Epicurus.
I think a better term might be ‘meritocratic’, and not ‘democratic’. Unless mathematicians vote on mathematics?
Well, it is also democratic in the sense that what convinces the mathematical community is what matters, and there’s no ‘President of Mathematics’ or ‘Academie de la Mathematique’ laying down the rules, but yes, ‘meritocratic’ is closer to what I meant.
Well, “democratic” strongly suggests a majority vote, and it’s not like something that convinces 54% of the mathematicians who read it ‘wins’.
pg169-171, Kanigel’s 1991 The Man Who Knew Infinity:
Personally, having finished reading the book, I think Kanigel is wrong to think there is so much contingency here. He paints a vivid picture of why Ramanujan had failed out of school, lost his scholarships, and had difficulties publishing, and why two Cambridge mathematicians might mostly ignore his letter: Ramanujan’s stubborn refusal to study non-mathematical topics and refusal to provide reasonably rigorous proofs. His life could have been much easier if he had been less eccentric and prideful. That despite all his self-inflicted problems he was brought to Cambridge anyway is a testimony to how talent will out.
I haven’t heard that before. Do you have a source?
From his letter to G.H. Hardy:
Googling the text finds it quoted a bunch of places.
Wow, thanks!
Besides his letter to Hardy, Wikipedia cites The Man Who Knew Infinity (on Libgen; it also quotes the ‘half starving’ passage), where the cited section reads:
I can’t parse ’271″ feet’, is this an OCR issue? If you loosen the belt by two yards, it can obviously reach at least a yard above the surface, because you can just go from ____ to __|__. And I recall that the actual answer is considerably more than that.
Given that the symbol ” is the symbol for inches, and ′ is the symbol for feet, I would suspect that there has been a mistyping in the quote.
I think that what was meant to be there was 72“ or 72.1” (inches), which is exactly/one-tenth of an inch over two yards (one yard = three feet). That would produce the desired result of a nearly one-foot increase in the radius of the belt; adding 72 inches to the circumference of the belt would produce an increase of 11.46 inches (72 inches / (2 * pi)) in the radius of the belt, which in this case is the height above the ground.
Was extremely democratic. Do we know this is still true?
“The Collapse of the Soviet Union and the Productivity of American Mathematicians” comes to mind as an interesting recent natural experiment where the floodgate of Russian mathematical talent was unleashed after the collapse of the USSR and many of them successfully rose in America despite academic math being a zero-sum game; consistent with meritocracy.
At the outlier level, I think so—see e.g. Perelman. At the normal professor-of-mathematics level, probably not.
Okay, maybe there aren’t other examples quite as good as him, but a few of these people surely come close.
Yes, but I’m not sure all of the populations working in cotton fields and sweatshops had such a low average IQ. (And Gould just said “people”, not “innumerable people” or something like that.)
Most of those people either seem to come from middle-class or better backgrounds, fall well below Einstein, or both (I mean, Eliezer Yudkowsky?)
Doesn’t your observation that most successful autodidacts come from financially stable backgrounds SUPPORT the hypothesis that intelligent individuals from low-income backgrounds are prevented from becoming successful?
With the facts you’ve highlighted, two conclusions may be drawn: either most poor people are stupid, or the aforementioned “starving farmers” don’t have the time or the resources to educate themselves or “[bang] out some impressive proofs,” on account of the whole “I’m starving and need to grow some food” thing. I don’t see how such people would be able to afford books to learn from or time to spend reading them.
No, it doesn’t; see my other comment. I was criticizing the list as a bizarre selection which did not include anyone remotely like Einstein.
How did Ramanujan afford books?
The answer to the autodidact point is to point out that once one has proven one’s Einstein-level talent, one is integrated into the meritocratic system and no longer considered an autodidact.
Did you mean innumerate people?
I meant ‘lots of people’, not ‘people who cannot do arithmetic’. looks word up EDIT: Huh, looks like that was the right word after all.
Sorry, then. Your phrasing sounded wrong to me, but I was wrong.
Will you update your post after looking the word up confirms that it means what you thought it did?
I was going to but I forgot to. Thank you.
Isn’t the average IQ 100 by definition?
Yes—but whose average?
Presumably the people who write the IQ test, based on whatever population sample they use to calibrate it. Is the point that the average IQ in India is 70-80, as opposed to the average in the US? (This could be technically true on an IQ test written in the US, without being meaningful, or it could be actually true because of nutrition or whatever). What data does the number 70-80 actually come from?
Presumably from this list.
It would naively seem that an IQ of 160 or more is 5 SDs from 85 , but 4SDs from the 100 , so the rarity would be 1⁄3,483,046 vs 1⁄31,560 , for a huge ratio of 110 times prevalence of extreme genius between the populations.
Except that this is not how it works when the IQ of 100 population has been selected from the other and subsequently has lower variance. Nor is it how Flynn effect worked. Because, of course, the standard deviation is not going to remain constant.
You presume too much, the only thing I remember about Gould’s views is that they are controversial.