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Here's the video: http://www.youtube.com/watch?v=hBW4S9xcTOk

He starts solving the problem at the 9:50 mark.

He's supposed to prove that a certain infinite series converges, and he applies the integral test for convergence. It is of course extremely impressive that a 12-year-old would even think of doing this, but the test is clearly not applicable in this case. The summand function is neither non-negative nor monotone decreasing, both of which are requirements for the applicability of the integral test.

To be fair to him, though, they (unintentionally?) gave him a trick question. He was asked to prove that the series converges, but it actually doesn't. Also, I'm sure if I was put on the spot in front of a TV camera there's a high probability I'd make silly mistakes.

It is quite possible that he's improved markedly since then, and if he's a university student and published in Phys. Rev. A then I would guess he has.

Dmytry13y00

Well my instinctive feeling would've been - this won't converge. The problem with people educated by tests. The tests imply there is an answer. In real world when you do something new you don't have clues like 'it converges'. When i was studying stuff, we just had fairly hint-less questions.

1RobertLumley13y

Beck said "show us what you showed me in my office" implying that he'd been shown the problem before. But it should be fairly obvious to any calculus student that that series doesn't converge since the limit as it goes to infinity isn't 0... It doesn't even exist. Sine and cosine functions are an immediate red flag to this, all you need to do to look at it is a simple order of magnitude analysis. Nevertheless, I'm sure he's very smart. But I'm not sure he has much common sense if he didn't see that right away. I'll also echo Alex's sentiments below...

12Alex_Altair13y

I am extremely worried to see him in the context of Glenn Beck pushing Christianity. As far as I know, his ideas to disprove the Big Bang have nothing to do with religion, and I sure hope he hasn't written the bottom line. And you're right about the integral test.

See in context

18 Does anyone know any kid geniuses?

by Solvent

28th Mar 2012

1 min read

18

I'm friends with an incredibly smart kid. He's 14, but has been put up three grades in school at one point. He does all the obvious enrichment things which are available in the relatively small Australian city he lives in.

His life experience has been pretty unusual. He doesn't really know what it's like to be challenged in school. All his friends are way older than he is. (Once, I asked him how being constantly around people older than him made him feel. He replied, "Concerned for my future.")

He doesn't know anyone like him, which I think is a shame: he'd probably get along very well with them.

Does anyone know any similar kid geniuses? If so, can I give them my friend's details?

Thanks.

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[-]Dr_Manhattan13y270

Phew, I was really worried this was for some kind of SIAI kid-cloning experiment.

[-]beoShaffer13y400

Dang, I was really hoping this was for some kind of SIAI kid-cloning experiment.

[-]Kaj_Sotala13y70

Only the cover story for one.

[-]Viliam_Bur13y30

It could be much worse -- a brain transplantation, or more precisely a whole-body transplantation.

If someone wanted to prolong their life by transplanting their brain to a new young body, they would need to be very careful about not appearing too wise for their age. Younger than full age, and even their freedom to conduct mad science would be seriously limited. But when you get the body of a known child genius... suddenly everything has a natural explanation and all kinds of people are trying to help you!

[-]DanArmak13y260

His life experience has been pretty unusual. He doesn't really know what it's like to be challenged in school.

If that's really unusual in Australian schools, they are vastly better than Israeli ones or, from what I hear, most others in the Western world. (Possibly excepting some expensive, private ones.) (I realize this isn't the reason you call him a genius.)

I was certainly never challenged in school, and neither were my friends. This was not because I was a genius, however, but because the teachers and textbook authors were of the grade better used as landfill. Sadly I had no encouragement from adults and couldn't switch schools or drop out, and I didn't have the will or resourcefulness to do anything useful in my free time.

This kid is very fortunate in having you as a friend. With the resources available on the Internet today, having "official" approval and encouragement in his intellectual development is half the hard work done.

Thank you for helping raise the next generation well.

[-]Multiheaded13y80

I was no genius either, but I was always recognized as a gifted kid. I had a private tutor when I was very young, then I studied in a pretty decent downtown Russian school and fell prey to the same old trap (which few children who are the smartest in their class and know it can avoid): zero challenge, zero socialization, zero work ethic. In my case, I had one outstanding skill, English language (well, aptitude for languages in general, but I started learning English at a very young age), so my parents naturally decided to guide me along that track and I didn't resist... but I did nothing to prepare for real life, either. I loved learning English through video games, books and, later on, Internet, and thought it would be like that in college too. During the last year of high school, after intense training, I got third prize at the regional "Olympiad" in English, and secured a free admission to a fairly prestigious university.
A year later, drained and demotivated, aghast at all the difficult and obscure subjects and skills (like advanced phonetics and medieval European literature) I was required to learn, I dropped out. Things went downhill from there on, until I got finally diagnosed with my brain condition and started getting treatment. And I still occasionally feel like a useless burnout. That lesson wasn't all that terribly painful to me, but it was a colossal waste of time. I've since read up on the perspectives of many kids who found themselves in similar situations during high school; I pity them. So many burn out or just end up underachieving. It seems that no country's educational system can currently help young people who have high IQ but not the willpower or social skills to capitalize on it.

[-]Viliam_Bur13y80

Many of us heard many times about the typical problems of gifted children, but is there a reproducible working solution?

Contacting intelligent people with each other can be useful to remove the feeling of "I am alone with this problem". But then what? You essentially get Mensa -- a group of people who are happy to belong, but at the same time they are all used to be special, and they all want to be special in the same criterium they now officially recognize: intelligence. And the signalling war starts. Everyone talks about "what is intelligence", "how should intelligence be measured", "why the most intelligent people should rule the world, but unfortunately the majority is too stupid to accept this simple logical fact", random redefinitions of intelligence, quack intelligence tests, pseudoscience of every kind, and also the theory of relativity and quantum physics because you are supposed to talk about it and prove Einstein wrong even if you never learned the basic theory... and I guess behind this all is one big unspoken fear that if you do not prove to be the smartest among the smartest, then you don't really belong anywhere: too weird for the everyday life, but not exceptional enough for the elite.

Schools for gifted children? I have only one data point (and would like to hear other reports), but it was mostly signalling. So you put all the gifted kids in the same building, and you get a building with many entitled children with mostly zero work ethic, and now what? Some of the children win olympiads and you present this as the result your school has achieved. Then they are out of school, ready for the typical life failures of the gifted children.

Socialization is not the complete answer. Guidance is needed, too. In addition to study what separates gifted children from average children (there is already a lot of literature on this) we need to study that separates successful gifted people from unsuccessful gifted people, and how to teach the latter to become the former. Who knows, some things we do for the gifted children may be even harmful in long term. I think it is good to let gifted children work on their own projects, but we should be extra careful not to reward them for sloppy work. Also the proverbial lack of attention should not be an excuse for a bad behavior.

I think if I was a child again in today's world, I would probably prefer some long-term support outside of the school system (so I don't lose the support system when I change school). It should be some organization with more people (so I don't lose the support system when one person quits). Something available both online and personally, where I could ask questions, where people would give me study resources, guide me through my projects, and also look at my finished projects and review them seriously (not "wow this is great for your age", but "you did this part correctly and that part incorrectly, see me again when you fix it, and here is something related to study"). And while supporting me on my desired way, they should also sometimes challenge me to try something new. I wouldn't need anyone to tell me that I am special (that just creates anxiety: what if I stop being so special?), but I would like to have as much help as possible to become stronger. Unfortunately, I feel our treatment of gifted children is mostly "you are so cool, and we actually have no idea about what to do next, so just enjoy your coolness as long as you have it".

[-]Kaj_Sotala13y70

Schools for gifted children? I have only one data point (and would like to hear other reports), but it was mostly signalling. So you put all the gifted kids in the same building, and you get a building with many entitled children with mostly zero work ethic, and now what?

Shouldn't schools for gifted children work so that you present them with a challenging enough workload that they'll end up developing a work ethic? I thought that was the whole point of gifted-kid schools - to create an environment where you don't need to worry about the ordinary kids not being able to keep up with the unnaturally difficult curriculum that you're teaching.

[-]Viliam_Bur13y40

It seems that being gifted visibly correlates with some kinds of psychological problems. If the school would only increase the workload, some children could not pay attention, and some might commit suicide.

In my opinion it would be better to separate psychologically healthy gifted children from giften children with psychological problems. Unfortunately, the idea of "elite education" is so politically incorrect that it is already a great success that there is one such school in Slovakia. So this school contains both kinds of giften children, and officially decides to err on the side of caution. Which means that children can choose the increased workload voluntarily, per subject (during some subjects, the class is split into "standard" and "advanced" parts, there are also additional elective subjects). Some children choose these advanced lessons, many don't. And you can't even press the volunteers too hard, otherwise you lose them.

In addition, the whole school system in Slovakia is failing, there is a grade inflation and a political pressure to give everyone university education regadless of their skills (result of intra-EU signalling competition: which nation will have higher % of population university-educated; it also helps to hide some unemployment), so there is like no external motivation to study hard. And the intrinsic motivation only work for some children, and even there only for selected subjects.

Failures of the school systems could be a whole separate topic. I already gave up hope, so I'm trying to think about solutions that work outside of the system. For people who don't have teaching experience, here is a great no-nonsense blog by a British teacher, some parts are relevant for other countries too.

[-]sketerpot13y50

If the school would only increase the workload, some children could not pay attention, and some might commit suicide.

Increased difficulty is not the same thing as increased workload. I always found that I learned best in classes which had difficult material but did not necessarily place huge demands on your time. That way I could always pick one or two things that really interested me and put a lot of extra effort into them, because I would have time and energy to spare.

For example, in a computer architecture class in college, we were supposed to design and simulate a miniature MIPS-like processor. We were given considerable head-starts and hints, and diagrams, and so on. I found that class particularly interesting, and I had some spare time, so I ignored the hints, invented my own instruction set, a stack-based CPU architecture, made an assembler and simulator for it, and designed the hardware. It worked, and I got a nice grade -- but more importantly, I learned a lot from this, and had a good time doing it. If my classes had been loading me down with large amounts of work, I never would have had the chance, and my education would have suffered.

Later, when I did teaching, I always offered my students alternate options that were harder, but potentially less work. The ones who voluntarily took me up on the offer learned more than they would have otherwise, and generally had more fun. A lot of them ended up doing quite a bit more work than they had to, apparently just because it was interesting.

[-]TheOtherDave13y10

Agreed that access to learning resources, guidance through and serious review of projects, and occasional challenge are the way to go when educating exceptionally gifted kids. Also, I would argue, when educating non-exceptionally gifted kids. Also adults.

[-]thomblake13y00

In my experience, unschooling is a great option. My wife and I plan to not do anything like school with our kids.

[-]Viliam_Bur13y20

What learning resources will you use?

I suppose that you want your children to have knowledge at least comparable with a decent high-school student. And then, as adults they can decide whether they want to study at university, but they should be ready if they choose so. (This is what I would want for my children.) I have no experience with unschooling, because it's illegal in my country, so maybe I'm missing something obvious, but here is what I imagine:

For simple things, like grades 1-4 of elementary school, teaching your children should be trivial, except that it takes a lot of time, and depending on their temper, perhaps a lot of patience. Probably not possible if both parents work full-time, but should be possible if one of them stays at home or works half-time.

For the rest of elementary school, and for high school, teaching your children is possible and not very dificult, but also not trivial. You would need some preparation; maybe there is a subject that you didn't understand well at high school; maybe your children will want to learn a foreign language you don't speak or something else outside of your competence (for many parents, computer science would be a good example). Good part is, your children can already read, so you just have to give them good materials and make sure they use it.

Still there is a problem of choosing the right studying materials. (In my opinion, this is a very important task of school system. Teaching per se is often done badly, some students would be better with a book and/or internet. Problem is, there is a lot of nonsense published, and as a total beginner you have problems to separate good resources from bad resources. Selecting the good resources and providing you with a top-level view is an important thing school does. Another good thing is contacting you with people who study the same thing at the same time.) How do you want to solve this part, especially in subjects which are not an area of expertise of neither you nor your wife? Though even for an expert it may be difficult to recommend a study material accessible for a newbie. First idea is Khan Academy, what else?

[-]thomblake13y00

What learning resources will you use?

That sounds like homeschooling. The difference for unschooling is, you don't use "learning resources".

Kids who aren't exposed to the soul-crushing institution that is school, will learn things on their own. Having someone around to help them learn how to use reference materials and teach them to read is a good idea, but that's about all they need. Unschooled children tend to do better and be brighter than schooled children (though most of that might just be selection effects). I know several siblings who were unschooled, and they're all very interesting, intelligent people who are very well-adjusted.

It's particularly helpful if you bring them around and do whatever activities they're interested in together.

[-]Viliam_Bur13y60

Kids who aren't exposed to the soul-crushing institution that is school, will learn things on their own.

This seems too good to be true.

Please note that I don't overestimate the quality of school system (I was a teacher and then I quit, because I felt the system is hopeless), and I also do not underestimate natural curiosity, especially of a child that has intelligent parents, so is naturally exposed to talk about interesting topics. Here are my two pieces of evidence:

Montessori education is based on giving children great freedom, and only providing them interesting learning tools. Are you saying that removing those tools would make education even more efficient?

Internet is full of distractions. Many people on LW suffer from procrastination (see, we even have a special word for "spending all your time on internet, accomplishing nothing"). I thank Bayes for not having internet access when I was of school age. Today many children play online games all day long. What makes you think that a child will be able to resist all that?

[-]DanArmak13y00

Unfortunately this is illegal, here in Israel and in many other countries.

[-]thomblake13y00

Yeah, that's the kind of thing we'd oppose with violence if necessary (though more likely by moving).

The legality of unschooling in the US varies mostly on a state-by-state basis. When compulsory schooling was first introduced in Massachusetts, there was armed resistance and the children ended up being marched off to school by soldiers. Fortunately, there are still some bastions of sanity - at least, in most places you can just fill out some "homeschooling" paperwork and they won't bother you.

[-]DanArmak13y00

Good for you. Unfortunately, there's no other state that would admit me, probably ever (unless I become very rich somehow). I have to live under laws I can't really influence and just hope they don't change too much for the worse. This is the situation for the great majority of world people.

Opposition with violence to your state sounds completely unrealistic, in any state, including the US. You yourself say that in MA the state sent in soldiers and won. Moving is plausible, of course.

[-]thomblake13y00

Opposition with violence to your state sounds completely unrealistic, in any state, including the US.

It's not unrealistic at all. It's what the US was founded on. It's why there exists the second amendment to the constitution. Yes, most revolutions will fail. But as far as we're concerned, the proper response to a stranger trying to steal your children is "Over my dead body."

[-]wedrifid13y20

Yes, most revolutions will fail. But as far as we're concerned, the proper response to a stranger trying to steal your children is "Over my dead body."

It's a little ironic that the 'defection' here is the act of not having the "Over my dead body" reaction when successful defiance is not realistic. If other people go about doing suicidal defiance you get most of the deterrence benefits and at least get to live on and have more childeren!

[-]DanArmak13y00

It's not unrealistic at all. It's what the US was founded on.

And yet some states have passed mandatory education laws, which makes me assign a nontrivial probability to a future where more states will do so, until they all do or you find that you don't wish to live in any of the rest.

Yes, most revolutions will fail

Given that, and given that resistance to this particular governmental intrusion has already failed in MA, and that there doesn't seem to be very widespread popular support for such a resistance unless on principle (percentage of people who homeschool or unschool where legal today is low) - why do you still proclaim defiance?

Signalling defiance for deterrence is expected, but will you personally really risk your life and be jailed or otherwise punished, merely to make a public statement of protest - the most likely outcome?

[-]thomblake13y10

Signalling defiance for deterrence is expected, but will you personally really risk your life and be jailed or otherwise punished, merely to make a public statement of protest - the most likely outcome?

Yes. It might be irrational - I might change my mind later. But in my opinion, if your children are being tortured, abused, raped, etc., then you do whatever you can to try to stop it, even risking your life. And knowing that parents really do say "Over my dead body" (with an implied "Over your dead body first") when it comes to their children's safety, really does make their children safer.

[-]VincentYu13y00

I think if I was a child again in today's world, I would probably prefer some long-term support outside of the school system (so I don't lose the support system when I change school). It should be some organization with more people (so I don't lose the support system when one person quits). Something available both online and personally, where I could ask questions, where people would give me study resources, guide me through my projects, and also look at my finished projects and review them seriously (not "wow this is great for your age", but "you did this part correctly and that part incorrectly, see me again when you fix it, and here is something related to study"). And while supporting me on my desired way, they should also sometimes challenge me to try something new. I wouldn't need anyone to tell me that I am special (that just creates anxiety: what if I stop being so special?), but I would like to have as much help as possible to become stronger. Unfortunately, I feel our treatment of gifted children is mostly "you are so cool, and we actually have no idea about what to do next, so just enjoy your coolness as long as you have it".

Perhaps something like REU programs for high school students that run throughout the year (which would be possible because of the low workload in high school). There are some REU-like summer research opportunities for high school students, and I mention some in my other comment. But it may be infeasible to expand these programs simply because there aren't enough faculty members who are both willing and capable of mentoring high school students. And, of course, there isn't always a university nearby.

[-]Solvent13y00

He and I both went to a fairly good school. He's doing the IB at the moment, which was certainly difficult for me, and very challenging to most of the people who did it.

I was certainly never challenged in school, and neither were my friends. This was not because I was a genius, however, but because the teachers and textbook authors were of the grade better used as landfill. Sadly I had no encouragement from adults and couldn't switch schools or drop out, and I didn't have the will or resourcefulness to do anything useful in my free time.

Yeah, my school was better than that, even if nowhere as good as university.

[-]dbaupp13y160

Another solution may be for him to get involved in "smart kid" camps/teams where he can meet people like him (and be challenged intellectually!). These include the various Olympiads (Physics, Biology, Chemistry, Informatics, Mathematics), and others like the National Computer Science School, the National Mathematics Summer School (NMSS) and National Youth Science Forum.

I went to NMSS (twice in fact!) and I can't say enough good things about it; both intellectually and socially (I met most of my closest friends there).

However, 14 is probably a little young for those specific camps, but I know that people can be involved in the Olympiads from quite young, and I'm sure there are other camps around. (This is assuming an interest in science/maths.)

[-]Solvent13y20

Yeah, he does that stuff. Incidentally, I went to the NYSF and loved it as much as you loved the NMSS. NMSS is nowhere near as cool.

[-]dbaupp13y10

You keep telling yourself that: I have it on good authority that NMSS is far superior. (A friend went to both, and obviously she wouldn't just tell me what I wanted to hear. ;P )

Also, are there activities and programs run by any universities near you that are designed for high school students? Because those are probably good places for him to meet similar people.

[-]Solvent13y00

My city has a really crappy university, but that's it. I don't think there are any more people like him in high school currently in my city, because I would have probably met them.

[-]James_Miller13y90

See:

http://www.davidsongifted.org/

For children with IQs in the top .1% Members get access to a listing of other members.

[-]Viliam_Bur13y70

Contacting people with high IQs is generally a good thing, but without additional structure it can easily become a signalling fest. Intelligence is just a capacity of the brain, not a strategy to use it well. It would be like Mensa -- a lot of smart people, most of them doing nothing important.

And -- although I am not completely sure about this -- I suspect that speaking about top 0.1% IQ is methodologically nonsense. It literally means "one in a thousand", so the proper test would require calibrating on tens of thousands or maybe hundreds of thousands of randomly selected children of the same age, repeating every few years. In my estimate, a probability that someone paid the costs of such calibration is much lower than a probability that someone used a standard IQ test mixed with a customized hocus-pocus, especially because most people don't understand the difference. (If this is true, then the whole thing was a signalling fest since the very beginning. But it still can be mined for useful contacts.)

[-]James_Miller13y30

so the proper test would require calibrating on tens of thousands or maybe hundreds of thousands of randomly selected children of the same age, repeating every few years.

I think this effectively happens with the tests that Davidson relies on because so many children take them.

See also.

[-]Viliam_Bur13y20

Thanks for the links. Now I would tell they are doing it very seriously.

It still leaves some space for metodological doubts, for example being in "top 0.1% at least in one of three or four subcategories" is not the same as being in "top 0.1%" generally. But I respect them for using only the existing serious tests and not developing their own (as e.g. many self-proclaimed high-IQ societies do).

[-]Logos0113y-20

Wonder what I'd be like now if I'd had something like this when I was that age...

At the very least, I probably would've graduated college.

[-]Dmytry13y80

Actually, to expand on challenging yourself - when I see someone smart - I don't think much of them. Majority of smart people never achieve anything noteworthy; they're nothing like geniuses we see when we look into the past and grade by accomplishment. You only call them geniuses because they do well on a test on which geniuses do well. If I see a smart person who challenges himself - there is always a lot of things this person tried, some successfully, some stalled (if you always succeed you aren't choosing tasks hard enough!) - those people can go very far.

The notion that school must challenge people like him, that's rather new. If you look at all the accomplished scientists - none of them were challenged by the school system; they had their own labs in the basements, doing stuff; they were studying mathematics at university level when they were 12 (and actually doing exercises, not 'i've read a book, okay'); that sort of stuff. Nobody was baby-fed baby challenges. To do all enrichment things is to study all the advanced math (linear algebra, calculus, statistics, etc) at age 12; you can do that even in a fairly backwards place. In advanced place - there will be adults baby feeding you baby challenges of no importance, wasting your time doing what they think is accomplishments appropriate for your age, but what doesn't train you anything. Science fairs for example. There's no use doing baby science; the genius needs to study important stuff (math mostly), and perhaps mess with idk electronics in the basement, and then he'll be more than well equipped to do actual science better than adults with degrees (because more intelligent).

Does he have some sort of lab in basement doing interesting stuff out of curiosity? Or alternatively, making computer programs because he wants to see if he could? Or something similar?

[-]Douglas_Reay13y00

Majority of smart people never achieve anything noteworthy; they're nothing like geniuses we see when we look into the past and grade by accomplishment.

Yep, IQ is only one of the components of genius, as that word is commonly used.

There's a good explanation on the genius knol

[-]Dmytry13y20

Yea. The IQ test is pretty much designed with attempt to ignore ability to learn; it does not test person's ability to e.g. build searchable databases of huge volumes of information, through the life.

Ultimately: the geniuses are within top 1% or better on many categories, not just IQ test, and while someone with high IQ is much more likely to be a genius than average, the odds of high IQ person being a genius in the pre-IQ-test sense of the word are still very low, in the one in thousands level.

Furthermore, all tests like that suffer from a sort of over-fitting at the extreme high range. When it is pretty close to 100, you have people who are more intelligent solve the test better; when it is past 150 or so, the extra ability is gained via factors not so related to intelligence. E.g. with the progressive matrices and other means of testing where the correct answer is highly subjective, at the normal range, the gains are realisable by seeing fairly obvious patterns but at high range gains may be only realisable by mental similarity to the test maker. Intelligence can not predict which one of the alternatives the test maker favoured, but similar intelligence with similar cultural exposure can. It may well be that past the intelligence level of test makers (considering the time factor), the IQ test stops working. After all, for all the questions on IQ test, someone with not very extraordinary abilities must know an answer. And the answers are not computer-generated so far.

Imagine people with IQ of 80 having to make IQ test, as an intuition pump. It is kind of obvious that the test wouldn't work terribly well past 100 or so. You can't test for genius level intelligence; all you can do is let genius convince you with some real accomplishments, but even this can fail.

[-]David_Gerard13y70

My first thought, if he's not being challenged at school ... he needs some project that will teach him what intellectual work is. Because the brilliant kid unchallenged by school who goes to university and suddenly and disastrously discovers he never learnt how to think as work is a stereotype for a reason. (I speak as a smart kid who went to a very good school in Australia and experienced this disaster.)

[-]Darmani13y60

I know at least four people who started college by age 15. They're not "kid" geniuses anymore though -- the youngest is 16 and slowly going through college part-time, while the oldest is in his 30s and a full math professor at Arizona.

I don't know about the upbringing of the other three, but one attended a program where taking classes mutliple grade-levels ahead is the norm (though no-one else learned calculus in 3rd grade), and attended Canada/USA Mathcamp during the summers of his undergrad.

I second the Olympiads. Terry Tao famously represented Australia at the IMO at age 10, so he's definitely old enough.

[-]Dmytry13y50

He needs to be doing something challenging on his own, like studying math. Doing something is as much about having the drive to challenge yourself, as about having the smarts. Smart people who don't challenge themselves don't get anywhere, they do perform well on IQ test but they never develop intelligence for things outside the IQ test. It's like having good athletic genes, vs becoming a world champion. (edit: or actually worse, because in intellectual field you altogether can't rely on others to challenge you).

[-]dbaupp13y00

Your point is very good, but I think this post is more about the social (rather than intellectual) development of the kid in question.

[-]Dmytry13y00

I was more referring to him not being challenged by the school system.

Socially - surely one could find online smart individuals to talk with, about common interests, and I'm sure he wouldn't care so much about the age gap. People with interest in computer graphics, programming, and/or mathematics contact me routinely, and I am not even particularly visible. Some are just interested kids. Dunno what his interests are though. edit: if he has a hobby, he could met other smart individuals through it. He can participate in some contests - now with the internet one can do it worldwide - though contests are kind of a distraction.

[-]dbaupp13y00

Yes, finding smart individuals is the goal of this post, and it appears that he has people who aren't his age to talk to.

However, real-life (i.e. meat) friends of a similar age (and similar intellectual ability & background) are probably the most important friends: for young people, an age gap of 2 or 3 or 4 years can mean a huge gulf in experience and physical development; so that they will always be the "baby" of the group, even if they are intellectual equals. This means that things like, for example, dating and sex don't really work (maybe not particularly important for the kid in question right now, but it is likely to be more relevant in a few years).

[-]Dmytry13y00

Well, its not very possible to help with real life aspect of it, without being from this town. The genetic solutions are easy to propose for that disabled kid, not so much for that smart kid.

Still, consider: 1 in ~1000 kids got IQ of ~150 or better *, so if there's several thousands kids his age in that town there got to be someone about as smart, now how to go about meeting them, well local math competition can do, or the like. The question is - what does this kid actually do? What interests him?

which is about the point where IQ tests begin to lose meaning.

[-]brilee13y30

I'll second the "smart kid" summer camps, and trying to work up the ladder of olympiads.

I'd say lesswrong is a good website for him, as well as artofproblemsolving.com

[-]Alex_Altair13y30

Jake Barnett has become somewhat famous recently, although I doubt he's available for personal friendships. I hope you've introduced your friend to the sequences, or at least HPMOR!

[-]pragmatist13y240

From what I've seen and heard of Jake Barnett, he's a very bright kid being overpromoted to an unhealthy extent. I remember reading news articles that casually mention that he's debunked big bang theory. Watching Youtube videos of him explaining his supposed "expansion" of the theory of relativity shows that he has a worse than rudimentary understanding of the theory. I also recall watching a TV show where they had Jake solving a math problem in the background while his parents chatted with the interviewer. I don't remember the details, but anyone with a college-level math background would have realized that he was applying methods that would work on similar problems, but for fairly obvious reasons would not work on this particular problem. The interviewer ignored the fact that the problem wasn't actually being solved and instead expressed great admiration at the fact that the kid was writing Greek letters on a chalkboard.

The Jake Barnett trajectory is exactly what smart kids should be avoiding.

[-]Alex_Altair13y00

I'd like to see that particular video. I'd paid attention to what he actually said and wrote in other videos, and didn't catch any problem. Plus he is actually doing work for Indiana University, which is a pretty serious accomplishment. Plus he got published in Physical Review A. It is possible that we are both correct and that he learned enough between our observations.

[-]pragmatist13y100

Here's the video: http://www.youtube.com/watch?v=hBW4S9xcTOk

He starts solving the problem at the 9:50 mark.

It is quite possible that he's improved markedly since then, and if he's a university student and published in Phys. Rev. A then I would guess he has.

[-]Alex_Altair13y120

[-]Jayson_Virissimo13y00

I am extremely worried to see him in the context of Glenn Beck pushing Christianity. As far as I know, his ideas to disprove the Big Bang have nothing to do with religion, and I sure hope he hasn't written the bottom line. And you're right about the integral test.

If I remember correctly, the Big Bang model was first proposed by a Catholic priest and was initially dismissed as an attempt to sneak religion back into cosmology. If he was engaging in motivated cognition to defend his faith, then wouldn't he not try to "disprove the Big Bang"?

[-]pragmatist13y10

The Catholic Church has enthusiastically supported the Big Bang model since the '50s. But there are strains of fundamentalist evangelical Christianity that don't think the theory is consistent with the Bible and so reject it. The Young Earth Creationist website "Answers in Genesis" is an example: http://www.answersingenesis.org/articles/nab2/does-big-bang-fit-with-bible

In America at least, if I knew a person was very religious, I would count that as evidence against the claim that they believe the Big Bang occurred. If I remember correctly, surveys show that a majority of Americans don't believe in the theory, and I suspect this is largely because they think it is in tension with their religious beliefs.

While the Big Bang may be a better fit for theism than the steady state model, it is a worse fit than the claim that the universe came into being a few thousand years ago with essentially the same physical structure it has now.

[-]Alex_Altair13y00

Christians don't have the criterion of making sense.

[-]Jayson_Virissimo13y40

Christians don't have the criterion of making sense.

Some of them do. In any case, it seems clear to me that the Big Bang model is coherent with theism, but the steady state model is not (or, at least, is much less so).

[-]wedrifid13y40

Christians don't have the criterion of making sense.

I am not comfortable with this generalization - particularly when applied across all ages and the Christian being discussed was right.

[-]RobertLumley13y10

Beck said "show us what you showed me in my office" implying that he'd been shown the problem before.

But it should be fairly obvious to any calculus student that that series doesn't converge since the limit as it goes to infinity isn't 0... It doesn't even exist. Sine and cosine functions are an immediate red flag to this, all you need to do to look at it is a simple order of magnitude analysis.

Nevertheless, I'm sure he's very smart. But I'm not sure he has much common sense if he didn't see that right away. I'll also echo Alex's sentiments below...

[-]Dmytry13y00

[-]pragmatist13y30

I just realized you're probably asking about the relativity video, not the interview video. I searched for it on YouTube but can't seem to find it any more. It was a video of him talking about an error in standard presentations of the theory. I suspect he took the video down after learning more about relativity.

ETA: Found it. Most of what he says here just sounds like nonsense. The fact that the video is no longer on his own channel does suggest that he's come to realize this.

[-]Solvent13y40

I hope you've introduced your friend to the sequences, or at least HPMOR!

Of course.

[-]hesperidia13y20

There are places on the Internet, if one is so inclined, to socialize and talk shop with other intelligent kids.

I'd recommend the ones I came from, like Gifted Haven and Cogito, but the former is a tiny community (really nice, but there are maybe a dozen regulars, total) and the latter requires talent search scores (although I might be able to bend an ear if you can't find one).

From what I've seen the AoPS community looks pretty good, but I have no personal experience.

[-]John_Maxwell13y10

Also, http://groups.google.com/group/lesswrong-highschool

[-]FiftyTwo13y10

Not quite on your original topic, but my own experience of intelligent and gifted children is that if they get into the mindset that they are different from other children at an early age they tend not to socialise with them, and never learn full social skills as they grow up, which are extremely important for adulthood. I think people (particularly on LW sadly) underestimate the importance of generalised social skills, and how much can be learned from interacting with people who are less 'intelligent'*

While meeting other 'gifted' kids with similar life experiences would definitely be good as you've said, it would also be good to see if you can arrange for him to have activities with other kids his age. One possibility might be to find activities where he's not operating at a much higher level than them (maybe sport/arts/music?) so he can interact without that being a barrier. Remember however clever he is, developmentally and psychologically he's still 14 and has a lot more in common with people his age than adults.

*(Scare quotes as there are a lot of issues with defining general intelligence, and it doesn't necessarily correlate that well with academic success at that age.)

[-]Solvent13y00

I absolutely agree, and try to convince him of this regularly.

[-]VincentYu13y00

If he is considering or interested in a career in academia – especially in science or math – he might want to start doing research over the summer. 14 is young, but not too young to start. Besides the obvious benefits from getting experience and publications, this is also what he needs to do to win the major high school/undergraduate research awards (I don't know about Australia, but in the US, these awards are: Siemens, Intel, Goldwater).

Getting started on a successful research project in high school is not trivial, and is impeded by a lack of information from the typical educational sources one encounters before college. One way is to independently find a faculty member who is willing to act as a research advisor; it is probably best to find someone who has prior experience with this (a publishing record with high school students as co-authors would be very promising – if they care about this, they will mention it in their CV or webpage).

Another way to start, which worked for me, is to get involved in summer camps that give students research opportunities. I know there are quite a few in the US, and most of these accept international students. I believe the most prestigious and competitive science/math program is the Research Science Institute at MIT (according to one of faculty mentors: "The typical RSI student is comparable to the very best MIT sophomore physics major."), but it seems like they only accept students going into their final year of high school study (i.e., rising high school seniors).

Some summer math camps offer research opportunities to returning students. I did research as a second-year student at the Honors Summer Math Camp (HSMC), and I can attest that good research work gets done there – since 2006, at least four research papers get selected each year as semifinalists in the Siemens Competition. All students who are invited back for a second year are assigned a research project and faculty mentor if they wish to be. Ross and PROMYS are similar in math content to HSMC (i.e., number theory for all first-year students), but I'm not sure what research opportunities they provide. [Edit: Just remembered that HSMC only offers research projects to US citizens because these projects enter the Siemens Competition, which unfortunately only accepts submissions from US citizens... This might be worth keeping in mind for international students.]

Regarding age: I can only speak about HSMC as I am only familiar with that, but I expect other programs not to differ too much. HSMC recommends applicants to be at least rising high school sophomores, but I know there were several rising freshman who were probably 14 during my second year there. Some of these young students went on to be regional finalists in the Siemens Competition for research done during their second year there. So some 15 year old students certainly have the ability to produce a good research paper.

Regarding research: There are pretty much limitless problems in math that can be approached by someone with only a (pre?)undergraduate-level knowledge of a single field. But it would be very helpful to have a mentor who can pick out suitable problems and provide any necessary guidance. Computational fields in the sciences may also be suitable for students with some programming skills. This is what I worked on for my first research project – I simply wrote a simulation of gas diffusion in nanocomposites, ran that for a month on a supercomputing grid, co-authored the results in a research paper, and that was enough to be selected as a regional finalist in the Siemens Competition. Before that project, the only programming experience I had was from my first summer at HSMC, so one could get started very quickly on a successful computational/programming project.

[-]MixedNuts13y00

I know a French 10-year-old. Too young and too far away?

[-]nathantodd6310y-20

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[-][anonymous]13y-40

I cannot say that I know such a kid genius in person. However, you and your friend might both be interested in this recent article about a young genius: The Boy Who Played With Fusion.

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[+]hermanalvarez5010y-60

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