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    I actually enjoyed the comments more than the article. Not that I disagreed with everything the author had to say, I just think he spends too much time rhetorically splitting hairs.

    "It isn't exactly wrong to say that Terry Tao and other former prodigies like him are geniuses. But it is more accurate to say that what they accomplished was genius." and "Most child prodigies are highly successful—but most highly successful people weren't child prodigies."

    I'm uncertain as to whether he harbors some strange guilt about his lot in life, but with pronouncements like the above, he sure is trying to minimize the value and/or role of the genius.

    I've seen that quote by Twain on occasion, and it always irritates me. There's another line from that source, rarely included, that seems to belittle the person ultimately credited with a given accomplishment: "He added his little mite--that is all he did." Ugh.

    But I do agree with the bit about needing more mathy doctors, CEOs, teachers, etc.


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    Maybe about 0.0001% of kids get the kind of attention he describes.

    But the vast majority of kids in America are not being offered an education that teaches to their level.

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    So, eye opening to see how consistently, no matter what, over decades (my biological father is almost 80 years old and my biological paternal grandfather was about 55 years older than me and his father got close to 100 years)human behavior has not changed and then I remember well evolution takes time and if the human spark occurred 50,000? years ago, we have a long way to go and are there any 'geniuses' who think that this current Earth environment is going to hold out for us to get there? I actually worry about people because every once in a while I see an article about really poor air quality and it is no wonder some people are wearing masks to cover mouths, noses and even eyes.

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    Originally Posted by Dandy
    I just think he spends too much time rhetorically splitting hairs. . . . "Most child prodigies are highly successful—but most highly successful people weren't child prodigies."

    This is absolutely not splitting hairs. This is an important point about statistics that people generally have poor intuitions about. Put very generally, the probability of A given B can be very different from the probability of B given A, yet people treat them as equivalent.

    Here is a cartoon that may help. In the cartoon the "frequentist statistician" is calculating the probability that the machine says the sun exploded (A), if in fact the sun didn't (B); but he is using this as a proxy for the probability that the sun didn't explode (B) if the machine says it did (A). Which does not follow at all, leading the Bayesian statistician to bet money that the sun hasn't exploded.

    Returning to the case in the article: What are the chances that a child prodigy (B) will go on to do great things (A)? Pretty high. What are the chances that the next Great Thing Doer (A) was a child prodigy (B)? Not the same thing.

    Let's run some numbers. Just for the sake of argument, let's say a child prodigy who goes into the field of physics has a 1 in 100 chance of winning a Nobel prize (we'll use that as our stand-in for greatness). And let's say that the chances for a non-prodigy physicist are a paltry 1 in 10,000.* Now, when this year's Nobel prize for physics is announced, will you bet on that person having been a child prodigy, or not having been a child prodigy? If you choose "prodigy," you are going to be wrong 99% of the time. This type of error is called "ignoring base rates."


    *These numbers are completely made up for the sake of argument. The point is about the intuitions that follow from them.


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    MegMeg's Nobel prize example is relevant to the board, but I can't resist pointing out that the example of this phenomenon that everybody needs to be aware of - because sadly, we have good research evidence* that most doctors completely fail to understand it, or at least to apply it correctly!! - is:

    the probability that the test will be positive, given that you have the disease

    is completely different from

    the probability that you have the disease, given that the test is positive.

    Doctors - i.e. even trained people who should know better - often treat these two as though they were the same, and hence overestimate the chance of disease by a lot (e.g., by a factor of 10).

    * Gigerenzer, and Kahnemann and Tversky, have written about this extensively.


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    From the article:

    Quote
    Those of us who managed sky-high SAT scores at 13 were 20 times as likely as the average American to get a doctorate; let's say, being charitable, that we're 100 times as likely to make a significant scientific advance. Since we're only 1 in 10,000 of the U.S. population, that still leaves 99% of scientific advances to be made by all those other kids who didn't get an early ticket to the genius club. We geniuses aren't going to solve all the riddles. Most child prodigies are highly successful—but most highly successful people weren't child prodigies.
    Suppose a Study of Exceptional Talent qualifier who goes to graduate school is twice as likely to have a very successful academic career (getting tenure at a research university) than someone with a similar undergraduate GPA but who was not in SET. Depending on the interests and values of the non-SET person, it may well be rational to "quit" -- to not aim for a PhD but to look for work or go to professional school (law, business, medicine) instead. It is so difficult to get the academic jobs that PhDs want that I would encourage only the true superstars to go to graduate school. That is the advice I will give my children.

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    I enjoyed the article. He makes some good points. I ran across his book at a friends house recently and it looked really interesting. We were at a labor day bbq and of course was hiding from conversation and found this cool book.

    This article reminded me that I wanted to get the book from the library to read.

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    I must need more coffee because I've read the article a few times and can't figure out what he's really trying to say.

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    I agree with others-- especially MegMeg and Colinsmum, who point out the logical fallacy related to the statistics here.

    Quote
    Returning to the case in the article: What are the chances that a child prodigy (B) will go on to do great things (A)? Pretty high. What are the chances that the next Great Thing Doer (A) was a child prodigy (B)? Not the same thing.

    Worth repeating. smile YES.

    I also found it puzzling that the real problem highlighted by the author (well, in my own estimation, anyway) seems to have been quite clearly identified by many of those high-ability persons commenting on it-- that is, that it's all the more important to give such children truly appropriate educational and socio-emotional supports as children.

    That's not the same thing as media feting, or parental fawning. The author seems to be stating that it's unfair to children such as he was to place unrealistic notions in their heads, and unfair to make them arrogant or 'too sure of their greatness.' (maybe it was just me?) Because, naturally, most of them (just like everyone else) are destined to be just one of a great herd of "pretty awesome" people, not "Very Superior and Awesome" ones, in the double-secret inner sanctum. Or something.

    That false dichotomy really struck me as an out-of-touch kind of outlook, to be honest. For every HG+ person with this kind of upbringing, there are ten others who are berated, ignored, or just plain ground into dust by their circumstances.

    I do agree that we should encourage non-prodigies to explore "hard" topics that prodigies shine at... and that we should NOT anticipate that there is "something wrong" with a prodigy that hasn't won a Fields or Nobel at at 25. Was Bach a less impressive composer than Mozart because he was a "late bloomer?" I hardly think so.


    I'd also like to point out-- both to this author and also to Bostonian, above, that there is life outside of the Ivory Tower. Even if you happen to have a PhD. wink



    Schrödinger's cat walks into a bar. And doesn't.
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