Keepin' it real with UFC fighter Kevin Lee (JRE podcast)

A great ~20 minutes starting at ~1:01 with UFC 155 contender Kevin Lee. Lee talks about self-confidence, growing up in an all-black part of Detroit, not knowing any white people his age until attending college, getting started in wrestling and MMA. If you don't believe early environment affects life outcomes you are crazy...

They also discuss Ability vs Practice: 10,000 hour rule is BS, in wrestling and MMA as with anything else. Lee was a world class fighter by his early twenties, having had no martial arts training until starting wrestling at age 16. He has surpassed other athletes who have had intensive training in boxing, kickboxing, wrestling, jiujitsu since childhood. It will be interesting to see him face Khabib Nurmagomedov, who has been trained, almost since birth, in wrestling, judo, and combat sambo. (His father is a famous coach and former competitor in Dagestan.)

Here are some highlights from Lee's recent domination of Edson Barboza.

The cult of genius?

In one of his early blog posts, Terence Tao (shown above with Paul Erdos in 1985) wrote

Does one have to be a genius to do maths? The answer is an emphatic NO. In order to make good and useful contributions to mathematics, one does need to work hard, learn one’s field well, learn other fields and tools, ask questions, talk to other mathematicians, and think about the “big picture”. And yes, a reasonable amount of intelligence, patience, and maturity is also required. But one does not need some sort of magic “genius gene” that spontaneously generates ex nihilo deep insights, unexpected solutions to problems, or other supernatural abilities.

The popular image of the lone (and possibly slightly mad) genius – who ignores the literature and other conventional wisdom and manages by some inexplicable inspiration (enhanced, perhaps, with a liberal dash of suffering) to come up with a breathtakingly original solution to a problem that confounded all the experts – is a charming and romantic image, but also a wildly inaccurate one, at least in the world of modern mathematics. We do have spectacular, deep and remarkable results and insights in this subject, of course, but they are the hard-won and cumulative achievement of years, decades, or even centuries of steady work and progress of many good and great mathematicians; the advance from one stage of understanding to the next can be highly non-trivial, and sometimes rather unexpected, but still builds upon the foundation of earlier work rather than starting totally anew. (This is for instance the case with Wiles‘ work on Fermat’s last theorem, or Perelman‘s work on the Poincaré conjecture.)

Actually, I find the reality of mathematical research today – in which progress is obtained naturally and cumulatively as a consequence of hard work, directed by intuition, literature, and a bit of luck – to be far more satisfying than the romantic image that I had as a student of mathematics being advanced primarily by the mystic inspirations of some rare breed of “geniuses”. This “cult of genius” in fact causes a number of problems, since nobody is able to produce these (very rare) inspirations on anything approaching a regular basis, and with reliably consistent correctness. (If someone affects to do so, I advise you to be very sceptical of their claims.) The pressure to try to behave in this impossible manner can cause some to become overly obsessed with “big problems” or “big theories”, others to lose any healthy scepticism in their own work or in their tools, and yet others still to become too discouraged to continue working in mathematics. Also, attributing success to innate talent (which is beyond one’s control) rather than effort, planning, and education (which are within one’s control) can lead to some other problems as well.

These are insightful comments, and deserve to be taken very seriously, coming as they do from the one of the youngest Fields Medalists in history and a legendary child prodigy.

But many readers misinterpreted Tao's remarks as minimizing the impact of native ability on success in research. Recently, Tao corrected this impression in the comment thread to his original post.

4 December, 2015 at 12:40 pm Terence Tao

It appears my previous comment may have have been interpreted in a manner differently from what I intended, which was as a statement of (lack of) empirical correlation rather than (lack of) causation. More precisely, the point I was trying to make with the above quote is this: if one considers a population of promising young mathematicians (e.g. an incoming PhD class at an elite mathematics department), they will almost all certainly have some reasonable level of intelligence, and some subset will have particularly exceptional levels of intelligence. A significant fraction of both groups will go on to become professional mathematicians of some decent level of accomplishment, with the fraction likely to (but not necessarily) be a bit higher when restricted to the group with exceptional intelligence. But if one were to try to use “exceptional levels of intelligence” as a predictor as to which members of the population will go on to become exceptionally successful and productive mathematicians, I believe this to be an extremely poor predictor, with the empirical correlation being low or even negative (cf. Berkson’s paradox).

Now, at the level of theoretical causation rather than empirical correlation, I would concede that if one were to take a given mathematician and somehow increase his or her level of intelligence to extraordinary levels, while keeping all other traits (e.g. maturity, work ethic, study habits, persistence, level of rigor and organisation, breadth and retention of knowledge, social skills, etc.) unchanged, then this would likely have a positive effect on his or her ability to be an extraordinarily productive mathematician. However, empirically one finds that mathematicians who did not exhibit precocious levels of intelligence in their youth are likely to be stronger in other areas which will often turn out to be more decisive in the long-term, at least when one restricts to populations that have already reached some level of mathematical achievement (e.g. admission to a top maths PhD program).

For instance, many difficult problems in mathematics require a slow, patient approach in which one methodically digests all the existing techniques in the literature and applies various combinations of them in turn to the problem, until one gets a deep enough understanding of the situation that one can isolate the key obstruction that needs to be overcome and the key new insight which, in conjunction with an appropriate combination of existing methods, will resolve the problem. A mathematician who is used to using his or her high levels of intelligence to quickly find original solutions to problems may not have the patience and stamina for such a systematic approach, and may instead inefficiently expend a lot of energy on coming up with creative but inappropriate approaches to the problem, without the benefit of being guided by the accumulated conventional wisdom gained from fully understanding prior approaches to the problem. Of course, the converse situation can also occur, in which an unusually intelligent mathematician comes up with a viable approach missed by all the more methodical people working on the problem, but in my experience this scenario is rarer than is sometimes assumed by outside observers, though it certainly can make for a more interesting story to tell.

Some comments on Tao's comment:

1. Individuals accepted into elite PhD programs in mathematics are already highly selected. I would guess, based on my familiarity with test scores of applicants to similar programs in theoretical physics, that a typical person in this population is well beyond +3 SD in overall cognitive (or at least mathematical) ability, which means fewer than one in a thousand in the general population. Tao doesn't say what he thinks the chances are for someone who has significantly less ability than this; I would say their chances at a research career in math are poor. Individuals with what Tao refers to as “exceptional levels of intelligence” would be at least +4 SD or more, making them fewer than one in ten thousand in the general population, or even much more rare. (To be totally frank I think a large fraction of good mathematicians are +4 SD and Tao is really talking about people who are exceptional even relative to them.)

2. Tao describes a schematic model with several quasi-independent input factors (raw cognitive ability, work ethic, maturity, breadth of knowledge, etc.) contributing to success. This is my working model as well. The claim that within the population of PhD students at top departments there might be only small or even negative correlation between factors such as raw ability and work ethic also seems plausible to me given a minimum threshold of undergraduate achievement (which can be obtained using various combinations of the individual factors) necessary for admission.

3. Tao's comments seem entirely consistent with results from SMPY (Study of Mathematically Precocious Youth), a longitudinal study of gifted children that finds increasing probability of success (e.g., STEM tenure at top research university) as ability increases from 99th to 99.99th percentile.

4. Should young people be made aware of the brute facts presented above? It seems terrible to limit one's ambitions based on some crudely measured construct like general cognitive ability or math ability. On the other hand, we do this all the time. When was the right time in my life to wise up about the fact that I would probably never make it to the NFL? After playing linebacker at 200 lbs for Division III Caltech (which doesn't even have a football team now), I was considering walking on at UC Berkeley as a 19 year old grad student. Should I have clung to my dream, or wised up about my dim future in Division I sports? :-)

5. Related to Tao's last remark the converse situation can also occur, in which an unusually intelligent mathematician comes up with a viable approach missed by all the more methodical people, see Sidney Coleman on Feynman:

"I think if he had not been so quick people would have treated him as a brilliant quasi crank, because he did spend a substantial amount of time going down what later turned out to be dead ends," said Sidney Coleman, a theorist who first knew Feynman at Caltech in the 50's.

"There are lots of people who are too original for their own good, and had Feynman not been as smart as he was, I think he would have been too original for his own good," Coleman continued. "There was always an element of showboating in his character. He was like the guy that climbs Mont Blanc barefoot just to show that it can be done."

Feynman continued to refuse to read the current literature, and he chided graduate students who would begin their work on a problem in the normal way, by checking what had already been done. That way, he told them, they would give up chances to find something original.

"I suspect that Einstein had some of the same character," Coleman said. "I'm sure Dick thought of that as a virtue, as noble. I don't think it's so. I think it's kidding yourself. Those other guys are not all a collection of yo-yos. Sometimes it would be better to take the recent machinery they have built and not try to rebuild it, like reinventing the wheel. Dick could get away with a lot because he was so goddamn smart. He really could climb Mont Blanc barefoot."

Related posts:

Success, Ability and All That

One hundred thousand brains

Bezos on the Big Brains

Annals of psychometry: IQs of eminent scientists

What is the difference?

Colleges ranked by Nobel, Fields, Turing and National Academies output

Out on the tail

Success, Ability, and all that

I came across this nice discussion at LessWrong which is similar to my old post Success vs Ability. The illustration below shows why even a strong predictor of outcome is seldom able to pick out the very top performer: e.g., taller people are on average better at basketball, but the best player in the world is not the tallest; smarter people are on average better at making money, but the richest person in the world is not the smartest, etc.

This seems like a trivial point (as are most things, when explained clearly), however, it still eludes the vast majority. For example, in the Atlantic article I linked to in the earlier post Creative Minds, the neuroscientist professor who studies creative genius misunderstands the implications of the Terman study. She repeats the common claim that Terman's study fails to support the importance of high cognitive ability to "genius"-level achievement: none of the Termites won a Nobel prize, whereas Shockley and Alvarez, who narrowly missed the (verbally loaded) Stanford-Binet cut for the study, each won for work in experimental physics. But luck, drive, creativity, and other factors, all at least somewhat independent of intelligence, influence success in science. Combine this with the fact that there are exponentially more people a bit below the Terman cut than above it, and Terman's results do little more than confirm that cognitive ability is positively but not perfectly correlated with creative output.

In the SMPY study probability of having published a literary work or earned a patent was increasing with ability even within the top 1%. The "IQ over 120 doesn't matter" meme falls apart if one measures individual likelihood of success, as opposed to the total number of individuals at, e.g., IQ 120 vs IQ 145, who have achieved some milestone.

It is plausible that, e.g., among top execs or scientists or engineers there are roughly equal numbers of IQ 120 and IQ 145 individuals (the actual numbers could vary depending on how the groups are defined). But the base population of the former group is 100 times that of the latter! (IQ 120 is about top 10% and IQ 145 is roughly top 0.1% in the population.) This means, e.g., that the probability that an IQ 145 person becomes a top scientist could be ~100x higher than for an IQ 120 person.

This topic came up last night in Hong Kong, at dinner with two hedge funders (Caltech/MIT guys with PhDs) who have had long careers in finance. Both observed that 20 years ago it was nearly impossible to predict which of their colleagues and peers would go on to make vast fortunes, as opposed to becoming merely rich.

Better to be lucky than good

Shorter Taleb (much of this was discussed in his first book, Fooled by Randomness):

Fat tails + nonlinear feedback means that the majority of successful traders were successful due to luck, not skill. It's painful to live in the shadow of such competitors.

What other fields are dominated by noisy feedback loops? See Success vs Ability , Nonlinearity and noisy outcomes , The illusion of skill and Fake alpha.

Why It is No Longer a Good Idea to Be in The Investment Industry 

Nassim N. Taleb 

Abstract: A spurious tail is the performance of a certain number of operators that is entirely caused by luck, what is called the “lucky fool” in Taleb (2001). Because of winner-take-all-effects (from globalization), spurious performance increases with time and explodes under fat tails in alarming proportions. An operator starting today, no matter his skill level, and ability to predict prices, will be outcompeted by the spurious tail. This paper shows the effect of powerlaw distributions on such spurious tail. The paradox is that increase in sample size magnifies the role of luck. 

... The “spurious tail” is therefore the number of persons who rise to the top for no reasons other than mere luck, with subsequent rationalizations, analyses, explanations, and attributions. The performance in the “spurious tail” is only a matter of number of participants, the base population of those who tried. Assuming a symmetric market, if one has for base population 1 million persons with zero skills and ability to predict starting Year 1, there should be 500K spurious winners Year 2, 250K Year 3, 125K Year 4, etc. One can easily see that the size of the winning population in, say, Year 10 depends on the size of the base population Year 1; doubling the initial population would double the straight winners. Injecting skills in the form of better-than-random abilities to predict does not change the story by much. 

Because of scalability, the top, say 300, managers get the bulk of the allocations, with the lion’s share going to the top 30. So it is obvious that the winner-take-all effect causes distortions ...

Conclusions: The “fooled by randomness” effect grows under connectivity where everything on the planet flows to the “top x”, where x is becoming a smaller and smaller share of the top participants. Today, it is vastly more acute than in 2001, at the time of publication of (Taleb 2001). But what makes the problem more severe than anticipated, and causes it to grow even faster, is the effect of fat tails. For a population composed of 1 million track records, fat tails multiply the threshold of spurious returns by between 15 and 30 times. 

Generalization: This condition affects any business in which prevail (1) some degree of fat-tailed randomness, and (2) winner-take-all effects in allocation. 

To conclude, if you are starting a career, move away from investment management and performance related lotteries as you will be competing with a swelling future spurious tail. Pick a less commoditized business or a niche where there is a small number of direct competitors. Or, if you stay in trading, become a market-maker.

Bonus question: what are the ramifications for tax and economic policies (i.e., meant to ensure efficiency and just outcomes) of the observation that a particular industry is noise dominated?

Personnel Selection: horsepower matters

[ Unfortunately some of the links below are broken. See updated 2014 version of this post: Talent Selection. ]

Personnel Selection, whether by sports teams, militaries, universities or corporations, is all about identifying statistical predictors of future performance. How good are these predictors?



Let's take college football as an example. Talent evaluation is difficult, but scouts definitely know something. A five star high school football prospect is almost four times more likely to become an NCAA All-American than a four star prospect. (Graphs from this article; NFL draft order related to HS ranking here.)



Oregon, which finished last season ranked #4 in the country (Rose Bowl and PAC-12 champs), and played in BCS bowls each of the last three seasons, landed only one five star recruit this year. Schools like Alabama (3), Texas (3), USC (3) and Michigan (2) landed significantly more.

What about other kinds of talent? Below is an example from psychometrics applied to 13 year olds.

Horsepower matters: Can psychometrics separate the top .1 percent from the top 1 percent in ability? Yes: SAT-M quartile within top 1 percent predicts future scientific success, even when the testing is done at age 13. The top quartile clearly outperforms the lower quartiles. These results strongly refute the "IQ above 120 doesn't matter" claim, at least in fields like science and engineering; everyone in this sample is above 120 and the top quartile are at the 1 in 10,000 level. The data comes from the Study of Mathematically Precocious Youth (SMPY), a planned 50-year longitudinal study of intellectual talent. ...

Another example: this graph displays upper bounds on probability of graduating with a physics GPA greater than 3.5 (about .5 SD above the average) at Oregon as a function of SAT-M. Note the blue markers are conservative (95 percent confidence level) upper bounds; the central value for the probability at SAT-M > 750 is around 50 percent. The upper bounds were computed to show that the probability for SAT-M below about 600 is close to zero. The red line is the probability of earning an A in calculus-based introductory physics.

High investment parenting 2: quality vs quantity

The WSJ recently hosted a discussion about Bryan Caplan's book Selfish Reasons To Have More Kids.

In his arguments Caplan relies heavily on the behavior genetics findings I have discussed previously here and here. These findings show that it is very difficult for parents to shape their kids, and that genes have a larger impact than "shared environment" (i.e., effects from being raised in the same family). One can study these effects by varying genetic relatedness (e.g., identical twins vs fraternal twins) and environment (adoption into different families, variation of family characteristics such as SES, parental education, etc.).

This is from some correspondence (slightly edited) I had with a new father about Caplan's book.

The question is whether you accept the behavior genetics conclusions at the Tiger Mom/Dad extremes. That is, the twin/adoption data covers mostly normal people and probably cannot be extrapolated with confidence to exceptional cases like high IQ families with a strong focus on education and achievement.

I am very committed to helping my kids, although not in the Amy Chua way, and I wonder how well I could succeed if I had, say, 4 instead of 2 kids. As it is I can think of stuff almost every day that I could have done with them if I wasn't so busy with other things.

I take my kids out and play with them as much as I can. But not just random play. For example, I run races with them and I notice that at this age they can improve their running ability a lot by practicing. They have probably run hundreds (or maybe thousands!) more flat out sprints (say 40 yards) than a typical Taiwanese kid of the same age. (Cities there are very crowded, so it's not easy even to find a place to do something like this.) I can imagine that their self-esteem and ability to do well in school sports might be improved by my willingness to not only spend time with them but to insist that we do something modestly constructive while we are having fun.

I see lots of US dads already teaching their kids how to hit a baseball or do other sports specific things. I've spent a lot of time in sports and athletics, and while genes matter, training also matters, especially at the K-12 level where the threshold for making the team is much lower than in college. Even in football, basic skills like accelerating out of a 3 point stance are things you learn through early repetition and are hard to pick up later in life.

My dad was a professor but not a natural teacher. We had a neighbor who was a math professor and very extroverted and passionate about his subject. His kids really didn't like to discuss math with him but I loved it and it was one of the best experiences of my life. I could offer that kind of thing to my kids (in many subjects), assuming the dynamics are right. But I certainly couldn't if I were too busy or had too many kids.

Early success in anything (sports, math, etc.) can be self-reinforcing and have non-linear effects down the line. I realize the behavior genetics data suggests that *averaged over large groups* such effects are small, but the studies are still crude and could easily miss some relatively significant strategies that you or I might take advantage of. Are you willing to take the risk of forgoing such positive impacts you might have on your kids?

I like Caplan in general but I think he's a little too hardcore libertarian and also a bit robotic (autistic economist) and simple-minded in his thinking.

Jon Jones, phenom

Watch this great profile of 23 year old MMA phenom Jon Jones, who will fight Shogun Rua for the LHW (205) title later today.

Anyone who has watched Jones fight knows he is incredibly talented. His background is wrestling -- he gave up a scholarship to Iowa State when he started his pro career. I notice he hits a lot of Judo throws in his fights. Most fans think those are greco throws but they aren't -- he's using his legs, which is illegal in greco. When I investigated this, expecting to find that he had trained in Judo as many wrestlers have, I was amazed to discover that he taught himself using internet videos!

Las Vegas Sun: ... Widely regarded as an unorthodox and unpredictable fighter, Jones has built his style based on what he's learned in the gym from instructors and what he's taught himself using methods like YouTube.

While it's known that Jones comes from a Greco-Roman wrestling background, he's evolved that style into his own by combining it with moves he's picked up from studying judo on the Internet.

"A lot of the moves I'm performing aren't actually Greco-Roman, they're judo," Jones said. "You can't use a trip in Greco-Roman. I don't have an official judo coach but I've been, it sounds weird, getting on the Internet and watching a lot of Judo moves. I take it seriously."

This highlight video shows some nice throws, including by Jones.




Is Jones ready for Rua? The biggest question in my mind is whether Rua is fully recovered from knee surgery. If he is, he could give Jones a tough fight, maybe even a beatdown. Rua is a legend, but are his best days behind him? This is one of the most exciting match ups in some time.

BJ Penn forever

Last night BJ Penn, whose natural weight class is 155 (or even 145 if he were any good at cutting weight), took the #2 ranked welterweight (John Fitch, whose natural weight is probably around 190-200) to a draw. In his career Penn has held the championship belt at 155 and 170, and faced world champions at 155, 170 and even 205 (LHW - Lyoto Machida). He was the first non-Brazilian to win a world championship in BJJ, after only a few years of training. Penn lacks a lot of things you might want from a top level fighter -- he's not that strong, his endurance is suspect, he's usually undersized, etc., etc. But in terms of raw fighting ability he is one of the all time greats. The most exceptional quality Penn has is gameness -- he'll fight anyone, anytime.





Here's the Gracie technique analysis. Flow with the go ;-)





Here is a better shot of BJ and Fitch. Does it look like they should be in the same weight class?

Frauds!

Callow postdocs are often the most caustic, but deadly accurate, observers of the scientific world. A postdoc has to be careful about what he or she says to a senior colleague, but get a few together and pretty soon the real scoop will emerge.

One of my buddies from those days, who is now a well known professor in high energy theory, liked (and likes) to use the term "fraud" to describe other physicists who didn't deserve their positions. So and so is a fraud! Did you see his last paper? Have you ever talked physics with the guy?

Of course, the presence of frauds is inevitable given a random component (sheer luck!) or additional factors (e.g., personal charisma, hype) influencing career success. Below is a figure from an old post on success vs ability. Let the vertical axis be career success and the horizontal axis the ability of the individual. Even if the correlation between the two is as high as .85, we'd still expect to see relatively incompetent individuals in high positions. (Or, equivalently, two individuals of vastly different abilities at the same level of success.) In fact, the correlation between ability and success in academic science is probably anomalously high compared to other fields, with the possible exception of competitive sports.



If you are still unconvinced about the existence of frauds among us, see this research article, as summarized below in the Times magazine.

“The Doctor Fox Lecture: A Paradigm of Educational Seduction,” a 1973 article still widely cited by critics of student evaluations, Donald Naftulin, a psychiatrist, and his co-authors asked an actor to give a lecture titled “Mathematical Game Theory as Applied to Physician Education.” The actor was a splendid speaker, his talk filled with witticisms and charming asides — but also with “irrelevant, conflicting and meaningless content.” Taking questions afterward, the silver-haired actor playing “Dr. Myron L. Fox” affably answered questions using “double talk, non sequiturs, neologisms and contradictory statements.” The talk was given three times: twice to audiences of psychiatrists, psychologists and social workers, the last time to graduate students in educational philosophy. In each case, the evaluations by the audience were highly laudatory. To these audiences, Dr. Fox was apparently articulate and intellectual, not a fraud.

Note: the figure is only meant to illustrate the amount of residual scatter present when two variables have a high but not perfect correlation. It does NOT represent any specific data set.

Success vs ability

The figure above illustrates the correlation between two variables, let us say success and ability. Each point represents an individual whose level of success and ability are shown on the vertical and horizontal axes, respectively. In the figure, the correlation is high, but not 100%.

For example, in American football the ability axis might represent the quantities obsessively tracked by NFL scouts: sprinting speed (40 yard dash time), natural strength (bench press), etc., while the vertical axis represents actual output, like passes caught or rushing yards gained. In real life, output is never purely determined by a single, or even several, input ability or abilities. If nothing else, luck ensures that the correlation is imperfect. Sports fans know that the fastest wide receiver isn't necessarily the best, nor the tallest basketball center the most productive, even if being fast or tall confer specific advantages. In the figure, the most able individual is not the most successful. They are seldom the same individual unless the correlation is 100%

In science or academia, we might take the horizontal axis to represent raw intellectual ability. The graph tells us to expect that the smartest person is not necessarily the most successful. It also suggests a population of successful but insecure people (the upper right dots above the fit line -- they are dumber than peers of similar accomplishment) and a population of smart people who are bitter about their unrecognized genius (dots on far right below the fit line -- they are smarter than peers of similar accomplishment).