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Georgia Teen Stumbles On New Theorem 289

dread minerva writes "Proof that the kids are alright: The Atlanta Journal-Constitution published the following article about Josh Klehr, who discovered a math theorem while sitting in study hall one day in eigth grade. The theorem is now known as the Klehr-Bliss Theorem and a paper on it is being published in The American Mathematical Monthly."
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Georgia Teen Stumbles On New Theorem

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  • by isaac ( 2852 ) on Wednesday March 14, 2001 @03:58PM (#363099)
    I think this explains why girls do better than boys when younger, but worse later, in education. Girls are good at doing routine tasks. It has been scientifically shown that they have a higher boredom threshhold. However, boys desire stimulation, and so the pre teen education system disadvantages them.

    I'd love a citation on this.

    I know you're just a bullshit troll, but I'm still calling you out on the bogus gender stereotypes.

    Just so this isn't a one-sided game, here's an article [] from US News about how women now outnumber men in higher education. And here's [] a report from the US Department of Education's Education Statistics Quarterly that suggests that girls continue to excel in verbal skills relative to boys at all ages, and that there's no statistically significant difference in their achievment in math and sciences.

    Kinda shoots down your central assumption ("girls do better than boys when younger, but worse later, in education").

    Any response?


  • by sconeu ( 64226 ) on Wednesday March 14, 2001 @04:02PM (#363102) Homepage Journal
    And some of the most obscure set theory stuff, the Banach-Tarski Theorems, which were thought to be completely abstract actually help describe the Eightfold way of quark theory.

    Other "useless" stuff, but of more interest to /.'ers: Number theory was thought to be the "queen of mathematics", unspeakably pure. Of course, now it's the workhorse of crypto.
  • She made the news because of her age, in reality her study was far from perfect. The study ultimately was inconclusive at a decent level of signifiance, failed to protect itself from outside variables, and was obviously biased.

    While it may have been 'good for her age', she really proved nothing, claiming she 'proved' something is just sensationalism. It did make a good 60 minutes piece however, because no one is going to go out and say 'oh, her work was worthless' on national tv.

  • It certainly looks like it. Anyone know what "the nine-point circle" is? Sounds like something from some upper-level geometry course. *shrug*

    From the article: He draws a triangle, labeling the midpoints of the three sides with black dots A, B and C. Then he draws perpendicular lines through each of the midpoints until the lines meet at a point inside the triangle, point E.

    He knew from his class work that the algebraic formula for perpendicular lines involves the negative reciprocal of a certain number. So he decided to see what would happen if he didn't make it negative. He did that for each side of the triangle and came up with three new lines that were not perpendicular but still intersected at a new point inside the triangle.

    So a real brief primer here: Drawing perpendicular bisectors of the sides of a triangle will yield the in-center. (You draw lines perpendicular to the sides of the triangle, and you do so from the midpoint of these sides. They intersect at a point inside the triangle. Drawing a circle with the center here with the proper radius will yield a circle that's tangent to all three sides of the triangle.)

    If you take the slope of a line, the "certain number" in the article, and take the negative reciprocal of it, you get the slope of a line that is perpendicular to the original line.

    Basically what this kid (I can call him kid, can't I? Not meant derogatorily) did was instead of taking the negative reciprocal, he just took the plain reciprocal. This number has no real bearing in the world of algebraic geometry (or whatever it's called), AFAIK. This is probably why no one really looked there before. When he played around with THESE lines, he found they intersected at a different point. Apparently drawing a circle of a certain radius from here will yield something, but that's where I get hazy.

    The interesting thing to me is that this kid (good kid!) did something off the wall. As they say, a little bit of knowledge is a dangerous thing. :) No one really would try this because the reciprocal of the slope of a line doesn't really yield anything useful.

    So, I'd like to give props not only to the student, but for the teacher as well, who was willing to look at something the student did, recognizing it, and nurturing it. That's a good story for our edu-ma-cation system, don't you think?

  • The article notes that he attends a public school.

    Where did you see that? Paideia [] is *not* a public school. It's a private school, one of the more selective (read: difficult to get into) schools in the Atlanta area. The tuition is over 10K a year.

  • by Alomex ( 148003 ) on Wednesday March 14, 2001 @04:10PM (#363115) Homepage
    I hope he gets an A in math for the rest of high school.

    Don Knuth solved a math problem at the beginning of the school year in High School. He got an A on the course and was excused from any extra work.

  • Damn, where are my modpoints when I need em?!?!
  • Did his teacher push the "Independent Thought Alarm" button?

    The children there must be overstimulated. Maybe it's the colored chalk. Afterall, that colored chalk was forged by Lucifer himself.
  • by spoonyfork ( 23307 ) <> on Wednesday March 14, 2001 @05:47PM (#363124) Journal
    That article reads like a story on the onion:

    Geekboy average Joe grocery-bagger astounds mathematician PhD's with a doodle from study hour.

    Squeezed in the margin of his geography text book under a crude replica of a Limp Bizkit logo, a weird triangle with intersecting lines gives hope to millions of parents that their kid might actually do something meaningful.. even if the kid doesn't fully understand what they've done.
  • If anyone can go to the American Mathematical MOnthly website [] and find an article by Klehr or Bliss or both I'd appreciate you letting me know.
  • I'm smart, and I'm 6"3' and weigh 195lb's.
    you pick on me, you gonna be walkin wit' 3 shoes,
    2 on yo feet, and 1 up yo a$$
  • All that this proof says is that the three skew lines always intersect. This is an interesting fact, but I can't see how it's hailled as a big new theorem. It feels more like a correlary to theorem which states that the perpendicular bisectors of a triangle's three sides all meet at a unique point (which is either the center of the circumscribed or inscribed circle [I'm sorry I don't remember, someone correct me]).

    What would be really cool is if this point had some sort of significance - like generating the center of [circum|in]scribed circle which I mentioned before.

    Eventually, a mathematician in the Netherlands used Josh's result in his own work and prepared an article for academic publication.
    That's what I'm really curious about. Does anyone have any info on that publication?

  • Social skills are important too. My greatest fear is that I'll end up working at some commercial research lab and my years and years of brilliant work will never see the light of day. If you cant convince people that what you think is worth something then you might as well sit in your room and drool all day.
  • see [] definition #1: Characterized by or consisting of two parts or components; twofold.

    If you view all choices as having only two possible answers, that's what I'd call a binary worldview.

  • by Anonymous Coward
    I hated people like you in highschool.

    You were the ones that sat in the corner giggling, often playing supid 'card' games; disrupting the class. When you got into trouble with the teacher for things such as disrupting the class, or being a kiddie on the computer, you blamed it on 'being smarter than the teacher'. You rarly ever were, even in the specific subject, and you lack of social skills, reason and understanding of human nature certainly made you much dumber than the teacher. Its also notable that that this was why you had no friends outside the dirty group of three of four friends that you had.

    So to all of the highschool kids on slashdot, look at yourself, and if you even remotely fit any of these characteristics get help now.

    Stop pretending that you better than everyone else, and actually look at why your not.

    please don't moderate me down because you disagree.
  • by _outcat_ ( 111636 ) on Wednesday March 14, 2001 @04:20PM (#363137) Homepage Journal
    "Girls...have a higher boredom threshhold."

    As a female, I tend to disagree with this.


    Okay, I'm bored now.

  • "Of course, I have no idea what Godel did in his younger years, I just
    know he proved the incompleteness of formal systems, especially
    Principia Mathematica."

    Oh the horror! You spend ten years writing two volumes of mathematical logic to prove 1+1=2 and someone writes a short paper that says all of your work is worthless since any sufficiently complicated system is provably incomplete!

    No wonder Bertrand Russell had nightmares that his books would be ignored in the future.

  • shit, I'm impressed. I've often wondered why the political environment we first expose our children to is a tyrany or dictatorship, and then wonder why they dont appear to be able to function in our democratic republics. Maybe if we truely believed in democracy we could find a way for children to participate.
  • by phutureboy ( 70690 ) on Wednesday March 14, 2001 @04:22PM (#363142) Homepage
    The school he goes to (Paideia) is actually quite cool. It is kinda a free form private school. From what I remember they really don't have many grades or announced tests. Kids are encouraged to learn at their own rate, and many gifted kids go their when they out pace their regular classes. It is kind of a neat place. They actually encourage creative thinking instead of kicking you out or arresting you!

    You might be interested in Sudbury Schools [], which are modeled more or less after the original Sudbury Valley School [] in Massachusetts.

    The schools are run as a democracy, with students, parents and staff voting in the weekly school meeting on things including hiring and firing of staff. Students of all ages are able to mix freely, and there is no mandated curriculum. Never been to one, but they do seem to have more than a few good ideas.

  • Yes, any two meet in a point. Any three only rarely meet in a point.

    Here's some non-parallel lines that still don't meet at a point: x = 1, y = x, y = 2.

    To go back on topic... maybe the kid in the story is a math whiz after all...

  • our society is fucked up. I'm a computer geek, I work at a computer company. I want to talk to the women who work here because I have met so few females in the computer industry. I like to hear everyone's opinion, everyone's outlook because I believe it improves my own. What do I get in return? People naturally assume that a girl couldn't have anything worth while to say and that I could only have biological reasons to be talking to them.
  • by rgmoore ( 133276 ) <> on Wednesday March 14, 2001 @04:24PM (#363146) Homepage
    I guess I'm saying that rather than bitch about how someone doesn't really understand medical science, why not make a difference instead? So yeah, therapeutic touch folks definitly can't isolate a problematic area of the electrical field. The whole point of the study was to say, "Nyah, nyah, you're just a bunch of crazy flakey people!"

    I guess I disagree on this point. Debunking quackery is a valid and valuable scientific service. It might not be as great as developing a new treatment, but it's important for people to know whether or not the treatment they're seeking is actually likely to help them. After all, if somebody decides to go to a quack, they may not seek help from somebody who can actually do them some good.

    I honestly believe that most of these therapeutic touch therapists are interested in helping people, even if their science is a bit wacky. If that's true, they're far better human beings than Emily and her parents, who are more interested in wholesale discreditation of theories than separating the truth from the lies.

    I think that you're really wrong here. The problem is that the advocates of theraputic touch have no science. There's no credible scientific evidence that theraputic touch has any positive health benefit. There are no peer reviewed, placebo controlled, statistically tested, double blind studies to determine the efficacy of theraputic touch. AFAIK there aren't even any lousy, uncontrolled studies, just a bunch of anecdotes. That's not science, it's just a bunch of pseudoscientific garbage with about as much scientific credibility as faith healing.

    Now compare that to the tests that this girl and her parents carried out. You are quite correct in claiming that they set out with the single goal of debunking theraputic touch. What you miss is that any study that has a reasonable chance to debunk the theory also has a chance of turning up a reall effect. If the practitioners had actually been able to do what they claimed and detect the girl's energy field, they would have been able to produce a positive result and the study would have produced evidence in their favor- which is exactly what they need if they really want to get anywhere scientifically and medically. An interesting counterpoint is acupuncture; skeptics tried very hard to debunk it but couldn't. Eventually they became convinced that there was a real effect, figured out what caused it, and have helped to develop it as a theraputic technique. That's what science is about.

  • I recently heard about an article, and later saw a documentary, on an interesting thing going on a few schools:

    the lack of math for the first several years of elementary

    In fact some schools won't start until 5th grade. Why? Basic math was boring students. Instead, increased time is spent in conceptional sciences, with enough math taught to make a few aspects understandable.

    In the 4th and 5th grades then an applied math is taught, and the students are given a basic knowlege of geometry. The result?

    By 8th grade these students have far accelerated above their peers in both Math and Science. As you can imagine the results are fairly debated right now, but many agree that teaching applied math, or math using some applied techniques, gives faster advancement to students than the dry grindish elemtary school stuff.

  • Wow it sounds like someone has read some Simon Singh. But generally that concept is credited to Von Neumann specifically about not being able discover anything new in math after 30. It should be pointed out that Von Neumann said this because he was a cocky ass 20 year old and as he got closer to be a cocky ass 30 year old this magic age tended to get higher. To my knowledge there isn't any actual data to support Von Neumann's claim but mathmatician tend to like to continue concept just because Von Neumann was such a cool guy (how could the inventor of the computer and game theory not be a cool guy)
  • "School voucher programs are bad because it imposes a blanket solution (vouchers vouchers everywhere) to a problem that only exists in certain areas (poorly funded inner city schools)."

    The problem with your argument is you fail to show how school voucher programs would prove to be detrimental to schools outside the set of "poorly funded inner city schools."

    I am glad that you can comprehend how they would benefit inner city children, but at the same time I would like to know how vouchers would not be a pareto-optimum solution.

    The larger problem you face is, how are you going to prove that social-welfare is not maximized when competitive markets prevail?


  • by jafac ( 1449 ) on Wednesday March 14, 2001 @03:37PM (#363150) Homepage
    Public schools are little more than federally funded daycare for working parents, and consumer indoctrination.

    If you gave kids 3 hours of study hall, they'd hang out and socialize.

    School voucher programs are bad because it imposes a blanket solution (vouchers vouchers everywhere) to a problem that only exists in certain areas (poorly funded inner city schools).

    Plus, just because one genius kid shakes up the math world doesn't mean that the school was successful, just the kid. Schools' success shouldn't be measured based on how many geniuses they happen to have enrolled, they should be measured based on tests showing improvement in student knowledge and skills over time.
  • Was I, now? I have never claimed to be better than anyone else. Smarter, maybe. Better, no. I rarely disrupted class. When I claimed I was smarter than the teachers, it was not because I got in trouble. It was because they could not understand the material they were supposed to be teaching, when I could understand it just from reading the book. I am now in my second year of college, and am taking more advanced math and science courses than all but 2 or 3 of my teachers ever did. The funny thing is that my classmates told me I was smarter than the teachers far more often than I told anyone else the same thing.

    Admittedly, I am not an outgoing person. This does not make me dumb. As for friends, I had no "dirty group of three or four." I tended to associate with others who thought for themselves. There are more people like this than you might think. My friends included other geeks, several potheads, and even 2 guys on the football team.

    My reason and understanding of human nature are no worse than yours. You read one 3 line long post on slashdot, and you think you know who I am. I will not venture to guess what you were like in high school, as that cannot be told from a single comment.

    You say you hated people who had few friends, or played card games, or disrupted class, or played with computers, or said they were smarter than teachers. Where the hell do you get off hating a person because of these things? Did you ever actually get to know these people? Just because they don't act like you and your friends does not give you, or anyone else, reason to hate them.

    As for your suggestion to get help, I must say that I agree. If any students reading this do fit any if those characteristics, find someone who will help you immediately. Find someone who will help you learn. Find someone who will help you get access to computers. Find someone who will help you resist the pressure to conform, to stop acting smarter than the teachers, to sit down and shut up. Find someone who will help you pursue your interests, and never let someone like this anonymous coward discourage you.

  • Taking the normal reciprocal is sort of like reflecting the line over the line y=x. (That's exactly true if the line has no intercept, and almost true if it does. In the latter case you have to imagine your origin on the line.)

    Not a big deal, but phrasing it that way helped me visualize what he was talking about.

  • by King Babar ( 19862 ) on Wednesday March 14, 2001 @06:17PM (#363163) Homepage
    The teacher then walked towards his office to read for an hour, when young Carl Gauss announced "I'm done!!! The answer is 5050." Flabbergasted, the teacher demanded to know where Carl got the answer. Turns out that Gauss discovered the formula

    sum = (n(n+1)/2)

    Thus began the career of a brillian mathematician.

    Basically right, except you leave out the really important part, which is where Gauss explains his work and makes it accessible even to his teacher. How he did this was to argue that the sum of the numbers from 1 to n is half of twice that sum. Okay...we can go for that. But then he points out that this double sum can be written as n terms that combine the ascending and descending series like this:

    (1+(n)), (2+(n-1), (3+(n-2), ... ((n-1)+2), ((n)+1)

    Now, each of these terms has the sum (n+1), and there are n such terms since there are n terms in the original series. So the double sum is just n*(n+1), and the sum we want is just half of that.

    And that is why he's Gauss, and you're not. :-)

  • As long as you understand the theory of the equastion, I feel the calculator is fine. Assuming you continue with a math/science background, you will find that understanding the concepts behind the formula useful. You will ask yourself the same thing going through calculus and transform analysis. Cool stuff, but understanding the idea is the most important part. Even if you forget the actual formulae, if you have learned the concepts, it will be much easier to relearn/remember the formulae.

    Sorry, kind of verbose but hope it helps. Good luck.

  • I thought that "all public schools are bad" was right-wing propaganda. Otherwise, why would the republicans be so strong in supporting vouchers? (so their rich Christian constituents won't have to pay tax to support crappy inner-city schools where they don't have to send their kids anyway).

    Then there is the Libertarian stand; all public schools should just plain be abolished, so only the rich can afford an educa- no wait, not just the rich, we'll ALL be rich because the IRS will be off of our backs! Yes, that will solve ALL of our problems!
  • I'm not sure if quite everything in math has practical applications, it's just that it's generally very difficult to predict in advance whether any particular mathematical development will or won't be useful. There are many, many branches of mathematics that were viewed as being too esoteric to have any practical use when they were developed, only to have applications spring up later. Noneuclidean geometry is a good example; it seemed useless until it turned out that it was critical for General Relativity. The same thing with a lot of linear algebra for quantum physics and number theory for computer science.

  • I thought of some new mathematical formulas that made mathemathics easier for me, I explained them to my math-teacher when she asked why I skipped my homework again and she was really astonished. She used them untill my final exams.
    Ok, I really don't remember the details unless I'm going to dive deep into my old books.
    But these kind of discoveries really depend on the teachers who will have to guide them, if they won't do that a student will never going bring forward a discovery. I think most teachers will find such a thing amusing and perhaps handy for fellow students when they can think of a way of using it. But it's really exceptional when they will put the effort of discussing it on usenet and making an article of it in a science paper.
  • The problem with your argument is you fail to show how school voucher programs would prove to be detrimental to schools outside the set of "poorly funded inner city schools."

    Because it directly takes away money from the entire public school system. Currently, even parents who decide to send their kids to private schools must pay school taxes. In my understanding of Bush's proposal, they would get this money in the form of vouchers to put wherever they want, in this case the private school. So in the end it becomes a tax cut for the rich to the detriment of public education everywhere.

    The larger problem you face is, how are you going to prove that social-welfare is not maximized when competitive markets prevail?

    Sorry, I'd rather keep corporate competitive behaviour out of my public schools. You've asked a larger question than can answered with a couple quick quips, so I'll leave it at that.

  • It's not that hard. He took the perpendicular bisectors of the sides, and instead of giving them both the inverse and negative of the slope, he gave them just the inverse (so they're no longer perpendicular to the side, just a reflection about a slope=1 line through the midpoint).

    They still pass through the midpoints of the sides they're reflecting. This also works if you use the negative slope, but you get a different point in the triangle (the negative-slope lines are a reflection about a horizontal line through the midpoint).

    The well-known theorem goes something like "the perpendicular bisectors of all three sides of a triangle meet at a single point". Substitute "inverse-slope" or "negative-slope" for "perpendicular", and Hilbert's your uncle.

    I don't know about Morley (except it's the brand the CSM tokes) and I don't know what it has to do with parallel lines and nine-point circles and pentacles and runes...

    This kid's discovery is astonishingly simple. Like it's something that someone really should have found before. Like it's something that maybe several people have found before, and never bothered to publish because it was so simple it must have been discovered, published, and lost to the obscurity warehouse where all grade-school theorems go to die.

    "Insert something here about watery bints distributing swords."
  • I guess I'm saying that rather than bitch about how someone doesn't really understand medical science, why not make a difference instead? So yeah, therapeutic touch folks definitly can't isolate a problematic area of the electrical field. The whole point of the study was to say, "Nyah, nyah, you're just a bunch of crazy flakey people!"

    I just think it's pathetic when the whole point of your study is showing someone else is wrong, rather that searching out new truth. You can tell that the study is biased because it focuses on the psychological practice, not the science that is or isn't backing up the practice.

    It's possible that humans are physically healthier when their bio-electrical fields are near other humans, regardless of "hitting the right places" or not. Or maybe people just feel better psychologically when they think someone else is nearby. So it's still possible that therapeutic touch therapists are helping patients, even if the therapists don't understand the real reason for this.

    This is similar to understanding that the earth is round, but thinking it's round because "God likes round things," not because "sufficiently large masses assume the compact shape of a sphere under gravitational pressure."

    I honestly believe that most of these therapeutic touch therapists are interested in helping people, even if their science is a bit wacky. If that's true, they're far better human beings than Emily and her parents, who are more interested in wholesale discreditation of theories than separating the truth from the lies.

    Whatever... I hope you excuse me while I spend time learning how to treat people with Love and Respect, not hatred and disdain. :/

  • by tenzig_112 ( 213387 ) on Wednesday March 14, 2001 @02:38PM (#363189) Homepage
    She debunked "theraputic touch" through a double-blind study while she was in sixth grade (that age is a rough guess). No one had ever bothered (or dared) challenge the validity of the practice. Sometimes it takes someone several years shy of a driver's license to shake up a feild of science.

    Say what you will about this. But what amazes me about this story is that this kid took the initiative to check on whether the idea was novel or not. I think we can all learn a little from that.

  • by grappler ( 14976 ) on Wednesday March 14, 2001 @03:45PM (#363190) Homepage
    It's the nine point circle, which is neither the circumscribed nor the inscribed circle.

    The nine point circle includes:

    o the midpoints of the three sides
    o the feet of the three altitudes
    o the midpoints of the lines joining the orthocenter (there the three altitudes meet) to the vertices.

    The easiest way to find it is to simply take any of these three groups (say, the midpoints of the three sides) and find the circle that touches those three - the circle that circumscribes the triangle formed by those three.


  • by caffeinated_bunsen ( 179721 ) on Wednesday March 14, 2001 @02:38PM (#363191)
    Anybody know what the theorem actually states? The article was quite vague in that area, even for mainstream press. I'd really like to know some details of the discovery.
  • by MO! ( 13886 ) on Wednesday March 14, 2001 @02:38PM (#363192) Homepage
    He was not suspended, expelled, or arrested for "Thinking While In Highschool"!
  • the lack of math for the first several years of elementary

    In fact some schools won't start until 5th grade.

    What do you mean by the word "math"? I assume you don't mean the basic skills like addition, multiplication, etc. Learning that stuff is much easier when you're very young (just like learning new languages is). It's boring, but without that you're handicapped latter on.
    In the 4th and 5th grades then an applied math is taught, and the students are given a basic knowlege of geometry. The result?

    By 8th grade these students have far accelerated above their peers in both Math and Science.

    Again, what do you mean by "math" in "accelerated above their peers in math"? How is it measured? In particular I'd have a major problem with this theory if it's still talking about applied math. What I'd like to know is how these students are at the more pure mathematics (what's normal for that level? Advanced geometry and algebra?).
  • Amazing how far things can go when you're not paying much attention. It seems like good ideas pop up when you let your conscious mind relax and just play around with a medium, be it geometry or sculpture or code. In drawing classes they try to get you to "loosen up", which doesn't mean crudely but simply without worrying about an end goal. I think this is definitely an example of that; just playing with the math.
  • by Anonymous Coward
    "I'm pretty damned smart. Anything I don't know, I can learn in relatively short prder." [emphasis added]

    This pretty much speaks for itself.
  • >I can attest to that.
    >I discovered this same thing while working too >late at night.
    >I was writing code to find the circle through >three points.

    Ha! I can top that
    I (re)discovered the Hertz/Einstein photoelectric Effect in first year physics class at the U of P in '76 (nope this is not a troll )

    We were doing some lame lab involving spectroscopy and he/ne tubes in boxes. We had to record the voltage on the tube as part of the error in the experiment. Except I noticed that that when the box that the tube was in was open it took a little less voltage to make it glow then when the box was closed.

    So I call over my physics prof and showed him what was going on but he tells me to just get with the lab and stop fussing over things like that.

    I didn't understand the significance until next semester when we learned about the quantum effects and relativity --Dooh!

    The bad news is that I eventually flunked out of college.... the good news is that I make a chunk of change doing software and drive a Vette....still though...I should go back one day ...I suppose...

  • Despite the image of the grey-haired, spectacled mathematician, most math scholars agree that if you don't make your big discovery while your mind is still young and 'squishy'. In that respect Andrew Wiles (who proved Fermat's Last Theorem) is considered an abberation for making his major contribution in his 40's

    *sing* I'm a karma whore and I'm okay....
    I sleep all night and I work all day
  • I love it. It's a great story and shows how simple and naive approaches can discover new things right under our noses. But in the end, Josh's own words sum things up... (quote from the article)

    As for his contribution to mathematical science:
    Does his theorem have any interesting practical applications to everyday life?

    "Uh, no. Not really."
  • This has got to piss off some maths dudes who have been working all their life to get a theorem named after them, only to have a 8th grader get one.
  • I saw a show on TV where they discovered a 6,000 year old body frozen in some mountain. This guy had accupuncure marks on him.
    For 6,000 years people have been using accupuncture without a double blind stury or scientific peer review, or a statistical tested studies. Only thing they had was anecdotal evidence.

    That whole time accupuncture actually worked dispite the lack of scientific evidence.

    Just because there is no study that meets your expectations that does not mean it's not true.
  • by euroderf ( 47 ) <a@b.c> on Wednesday March 14, 2001 @02:42PM (#363218) Journal
    It is wonderful that some children can excell so at Mathematics. A sublimely creative genre, mathematical prodigies have included some of the best Mathematicians we have ever known, such as Goedel.

    However, mathematics is, on the surface, a rigourously boring subject. What enables these children to see its inner beauty?

    I think that mathematics is taught incorrectly in our schools. For pre teens, the education system is a Gradgrindish experience, and they are asked to remember many boring but worthy facts. This is a shame, because it happens at the time when they are at their most creative and curious.

    Only later, when they are in their final years of school, are they taught in a creative and interesting way.

    I think this explains why girls do better than boys when younger, but worse later, in education. Girls are good at doing routine tasks. It has been scientifically shown that they have a higher boredom threshhold. However, boys desire stimulation, and so the pre teen education system disadvantages them.

    If only our schools education system saw learning as a voyage, a journey of exploration, rather than a means of inculcating our children in corporate dronery.

  • by Grendel Drago ( 41496 ) on Wednesday March 14, 2001 @05:07PM (#363221) Homepage
    [I don't care if it's a troll, damn it.]

    No, I actually was. Smarter than everyone else if you count standardized tests, smarter than ninety-seven percent of my class if you count rank. I was the kid who begged my math teacher to go on to the next chapter when we finished the curriculum early, when everyone else just wanted to play TriBond. When everyone I talked to said the infinitude of primes was unproven,.damn it, I did it myself. And, of course, found out that I'd duplicated Euclid's work, and hit myself in the forehead for how simple it was.

    I lacked social skills. I didn't understand people; I didn't understnd myself. And I had no pride whatsoever in myself. I refused to sing my own praises, because people would accuse me of being conceited. I'm only now learning to say "I'm pretty damned smart. Anything I don't know, I can learn in relatively short prder." Ego had never been a problem. Lack of geek pride was.

    -grendel drago
  • by caffeinated_bunsen ( 179721 ) on Wednesday March 14, 2001 @02:42PM (#363222)
    Holy shit, you're right! He even showed that he's smarter than his teacher(s), and has yet to recieve punishment. I tells ya, that place needs more discipline. If we let our kids spend all day in school thinking, there's no telling what could happen to our country.
  • by alewando ( 854 ) on Wednesday March 14, 2001 @02:42PM (#363223)
    The article notes that he attends a public school. This raises an interesting conundrum.

    A successful school is, by definition, one that succeeds in engaging its students in academic pursuits and gives them the intellectual growth they need to succeed in the world. But education takes time and effort, as everyone knows.

    If education monopolizes a student's time to the exclusion of all other activities, then he won't be able to develop these new and exciting discoveries. He'll be proficient in the knowledge of yesteryear, but he won't be able to look ahead to the future; for his nose will be constantly buried in a book.

    This is why it's imperative for schools not to spend too much of students' time on homework. A half hour of homework per night and three hours of enforced studyhall periods would go a long ways towards giving students the time and the environment to make these wonderful discoveries. Some will spend it doodling, as the article noted, but that's the price we pay for a sophisticated environmentally-holistic educational approach.

    Public schools are already making great strides in giving our students these opportunities, but private schools lag far behind (and public schools are starting to join them). This is why it's more imperative than ever that we oppose school-voucher programs. Students must be kept in the environments where we're already seeing successes like Josh's.
  • by Khopesh ( 112447 ) on Wednesday March 14, 2001 @05:18PM (#363227) Homepage Journal
    Here [] [] is a more visual definition of a nine-point circle for people like me who are much more visually oriented.

    THIS is the kind of news that should be reported, not "some guy shot some clerk on the other side of this state" or "it might snow in [distant state] tonight."

  • Wasn't Gauss, he of the famous first grade Gauss's Theorem, the first thing they teach you to prove by induction, the prodigy you meant?

    Of course, I have no idea what Godel did in his younger years, I just know he proved the incompleteness of formal systems, especially Principia Mathematica

    -grendel drago
  • I don't understand this because I was pretty useless at maths in school and because it was 16 years ago as well. Many braincells have been killed by beer since then.
  • by Anonymous Coward on Wednesday March 14, 2001 @07:26PM (#363238)
    I'm the Adam Bliss mentioned in the article. You'll just have to take my word for that, I guess. I'm really from Lawrenceville, not Norcross. Nowadays I attend Harvey Mudd College [] in Claremont, CA (where Zach Walters told me I was on Slashdot... Thanks Zach!). I noticed a few things in the threads below that I'd like to clarify.

    First and foremost, I don't think the theorem is actually called the Klehr-Bliss theorem. AFAIK it's the van Lamoen theorem, since he was the first to furnish a full proof. Lou Talman [] had a quicker (and simpler) proof that was purely geometric, but I believe it was found to be flawed. I was working on a brute-force algebraic manipulation, but Floor van Lamoen carried essentially the same technique to its completion before I was able to. You can read about his proof here [].

    Josh's conjecture was pretty accurately summarized in the article. The point E mentioned is actually the circumcenter, the center of the only circle passing through the three vertices of the triangle. Also, it is not exactly correct to say that the lines through A, B, and C intersect in "a point" inside the triangle. The three lines are concurrent (they all pass through a common point, a rare thing for three lines to do), but Josh's slope-reciprocal construction is really just a reflection about the line y=x in the coordinate plane, and changing the orientation of the coordinate axes relative to the triangle makes the point of concurrence wander around inside the triangle. The kicker that I noticed is that as it wanders, it stays on the nine-point circle, or Feuerbach circle of the triangle. I've actually found that there's a lot more to be said along these lines, and to my knowledge none of it has been published.

    For the public/private thread... I think that Josh was and is attending a private school (Paideia, an excellent school by the way) though I attended a public one (Collins Hill... not too bad as public schools go).

    Not only does the theorem have little to no practical value, it also is of little interest to mathematicians. I've always thought of it as simply a little ditty in triangle geometry. I haven't yet read van Lamoen's article in the AMM, but I believe he mentions it only in passing.

    And yes, it is vitally important to have an encouraging mentor. Steve Sigur, Josh's teacher, is a great guy and an excellent math teacher. I don't mean this to trivialize Josh's accomplishment--it's also vitally important to have a creative mind and be willing to explore--but Mr. Sigur deserves the real praise here.

    I'd also like to take this opportunity to shamelessly plug The Geometer's Sketchpad []. It's a great piece of software that dynamically creates geometric constructions. It's excellent for visualization. I used it to see the generalizations I was after, and I think Josh was using it when he first made his conjecture. If you've any interest in geometry--or are willing to have some anew--you should check this out. You can download a free sample version.

    Anyway, I just wanted to post and settle a few things... If anyone has any questions, you can post them here or email me (I'm abliss at Thanks for your attenton!

  • I think this explains why girls do better than boys when younger, but worse later, in education.

    I think this explains that you're trolling. Have you done any study of this problem? Based on my experience [] as a middle & high school math teacher, personal reading [], and literature reviews [], it's pretty clear that math gender issue can be explained very effectively by social factors []. Peer pressure and media influence shunt girls into supporting roles and focus them on appearance over accomplishment.

    scientifically shown that they have . . .

    Show me the money, euroderf. Any post that claims "science has shown" something without providing a valid URL should be modded down immediately.

  • Josh then gets tutored by a Fields Medal winner (and resents it), gets mental health counseling from a washed up math genius now working as a professor at a local community college, and then he falls in love with a Harvard student whom he gives up his promising math career to chase after.

  • In my discrete math class a few years back, my professor taught me a story about Gauss, when he was a kid.

    He was in an arithmetic class, and the teacher wasn't in a good mood - it was a Monday or something. So he made the kids add up every integer from 1 to 100. The kids groaned and started working on this long, tedious problem. The teacher then walked towards his office to read for an hour, when young Carl Gauss announced "I'm done!!! The answer is 5050." Flabbergasted, the teacher demanded to know where Carl got the answer. Turns out that Gauss discovered the formula

    sum = (n(n+1)/2)

    Thus began the career of a brillian mathematician.

  • School voucher programs are bad because it imposes a blanket solution (vouchers vouchers everywhere) to a problem that only exists in certain areas (poorly funded inner city schools).

    Actually, inner city schools tend to be well-funded. The terrible Washington, D.C. system has one of the highest per-student spending in the country. Throwing billions of dollars at the Kansas City schools [] didn't improve them at all.

    In fact, extensive studies have shown that there's very little association between school funding and student performance.

    See Does Money Matter [] or the work of Eric Hanushek []

  • by artdodge ( 9053 ) on Wednesday March 14, 2001 @02:47PM (#363252) Homepage
    A quick search on altavista turns up some work connected with Adam Bliss: []

    The extremely vague statements in the article look similar to what is presented there...

  • by hugg ( 22953 ) on Wednesday March 14, 2001 @05:30PM (#363253)
    That's two independent thought alarms in one day! Remove all the colored chalk from the classrooms!!
  • Oh, but assuming all blacks act black, wear gold jewelry and play loud rap music is an improvement?

    From one side: we're all one big multicultural family and color doesn't matter! From the other: we're all different and must have pride in our 'heritage'.

    Pfft. I know you're ragging on consumerism, but this is something that pisses me off to no end.

    -grendel drago

  • Interesting. There was a very similar experiement performed with reading, many years ago.

    IIRC, the parameters were a class of kids was not taught to read until ~4th grade. After about 9 weeks of instruction, these kids were vastly out-performing the control group which had received standard reading instruction from kindergarten on.

  • Interesting. I always understood it better graphically:


    ...and so on up to 100 lines. Then you mirror it about the diagonal edge and get


    Hey - the width is equal to the height + 1! Multiply width and height, divide by two...

    I find it far more likely that, in reality, this is how Gauss explained it. For something this simple, the equation usually comes after the concept.
  • Learning that stuff is much easier when you're very young (just like learning new languages is). It's boring, but without that you're handicapped latter on.

    Do you actually have evidence for that, or is it one of those "everybody knows" sorts of things?

    And, frankly, is the the issue even relevant to whether it should be taught to kids in schools?

    Seriously, when I was a kid (elementary school, jr high) I did a lot of peer-tutoring in math, because I witnessed for myself how damaging most math classes were to my peers' mathematical intuitions (which in young kids starts out pretty good). I seriously mean to say that the majority of those classes were egregiously counterproductive, ingraining in kids terrible habits of mind and attitudes about the behaviour of abstracts, which greatly interfered with their ability to pursue real mathematics.

    I really don't think that, even if arithmetic is more easily learned when very young, we can trust the classroom to impart that skill without savaging all but the brightest students' facility for true mathematical abstraction.

  • Well, depends where you look. I mean, I wouldn't consider national college admissions as any indication of academics. It merely means that they continued school after high school.

    If you look at gender statistics at the top schools, there is a slight male bias. In engineering, it is a pronounced male bias. That is the "top" academic achievements.

    Indeed, if women are proportionally continueing onto more education, but the top schools are evenly divided or slightly male heavy, then it reinforces his belief that men are doing better.

    Indeed, there are many reasons that would explain a higher attendance of females than males while still supporting his assertion.

    For example, at lower income levels, a male is more likely to leave academics for exmployment. That will bias the results towards women.

    Crime and incarceration rates are higher among males, and heavily pronounced among black males. This biases the results towards females.

    Tight economy (we're still under 5% unemployment) makes this a better time to be in a job market. Assume a working class recent high school graduate, do they attend the local community college or take a job with decent wages. Community college can now wait.

    The stereotypical MRS degree, girls off at school seeking spouses. This will result in non-academically oriented females continueing their education while their male counterparts are unlikely to do so. This also biases it towards female.

    He was discussing academic performance along gender roles. You through out a meaningless trend (meaningless to this debate, not in general).

    To put it in Slashdot terms, we're argueing about a portion of Linux's design, and someone points out that Linux is more stable than Win95... and claiming that this was debating.... Oh wait... that happens daily...
  • There are lots of reasons.
    1) studies cost a lot of money. Most practitioners of alternative medicine simply can not afford to do the studies (compare what your doctor drives to what your massage therapist drives).
    2) Most studies in the US are underwritten by medical companies which have a vested interest in keeping non chemical treatments out of the market.
    3) Most non traditional medicine is knowledge based and not material based. By this I mean instead of needing expensive chemicals for treatment they rely on nutritional or herbal methods. As a result wealth does not concentrate on a few manufacturers but gets diffused amongst many practitioners. As a result no political power is gained which might influence government or universities to conduct the research on their own.
    4) Most of the alternative medicines are designed to work slowly over time. They concentrate on undoing bad habits that have taken years to establish. Their argument is that damage done your body through years of abuse (alcohol, coffee, cigarettes, sugar, junk food, pesticides etc) has to be cleaned out. There is no magic bullet which will flush your body of accumulated junk. The process will take a long time and will involve helping your body at the same time abstaining from these products. There is simply no easy way to do a scientific study on such long term techniques especially because the subjects are not likely to stick to them very long (ever try to give up coffee?).
    5) Most people who do peer review in scientific journals are totally ignorant of these subjects. Simply put they are incapable of doing a peer review on accupuncture or massage or herbalism.

    For example: lets say that it is my opinion that yoga is the single most effective medicine ever invented. If pacticed regularly it will eventually make you much healthier and resistant to disease not only of the body of the mind too. If everybody did an hour of yoga every day there would be a drastic decrease in all kinds of illnesses including mental ones.
    Now what kind of a scientific study could you do to test this? Who would pay for it? Who could peer review it?

    Also keep in mind that many of the techniques used by doctors or conventinal medicine also have not been tested scientificaly. Just recently a first of it's kind study was done that concluded that electro shock therapy did not work!. How long have they been doing that to people and just now they get around to doing a study which concludes that it does not work.

    Finally: Just because scientific studies have been done that does not mean that the product actually works or is safe. How many drugs have been recalled? Even after years of study and peer reviews evidence comes up that says this is dangerous stuff. Weather this is for medicine or pesticides it's scary. Of course some of this is due the corruptibility of the current scientific methodologies by vast amounts of money.

    In conclusion:
    Just because it has not been scientifically proven or no studies have been done it does not mean that it's not effective.

    just because it has been scientifically proven does not mean it's effective or safe.

    It is very hard and expensive to do scientific studies.

    The process of scientific proof is corruptable by big money and can not always be expected to produce truth.
  • Not all smart kids get picked on. Believe it or not, there are smart kids who are popular.

    Yes! It's true, it *does* happen. There are even, dare I say it, popular but not so smart students who tolerate and accept smart kids.

    I know, that's not a binary view of the world, but sometimes the world ain't binary. ;-)

  • by Raindeer ( 104129 ) on Wednesday March 14, 2001 @02:50PM (#363276) Homepage Journal
    A Fields Medalist winner (Nobel prize for math) won the medal for his research on knots. Knots as in knots in rope. He made very nice models of it and all his colleagues agreed the math involved was very interesting, beautiful etc. Problem was that nobody had any real life application for it. Years after first having started the research the professor receives letters from genetic researcher who used his math for their calculations on the human genome. Morale: Maybe Josh doesn't know what to do with it, but that doesn't matter, maybe somebody else will think of a good way to use it.


    See you all at HAL 2001 []

  • A clarification.

    It's not that I presume the medical establishment is corrupt it's just that they are motivated by profit like everybody else. Like most people they take the path of least resistance. If Bill Gates got interested in this stuff and paid for research who know what we could find out. Until then there is simply no profit in doing research or funding studies. Maybe the insurance companies could be persuaded but even then it's kind of a crapshoot for them.
  • Consider that different people might think of things differently.

    E.g., I find the explanation in terms of the summation of reflected terms, i.e.:
    k:=1->100 of (k + (100 -k))/2
    to be much clearer. That you may find the diagram easier is not unreasonable, but please accept that others think differently.

    Caution: Now approaching the (technological) singularity.
  • Excellent points, all five.

    In any example, like yoga or accupuncture though, you assume that the medical establishment is so corrupt that they are unable to change radically if a new method comes about. Perhaps your cynicism is justified, but if accupuncture or yoga really were 100% of everything they were hyped to be sometimes, medical and insurance companies could make millions or billions more.

    I tend to believe that the main reason scientific studies on these practices haven't been conducted en masse is more related to the specific practices in question. You give yoga as an example. You are so right when you mention that its not a cure all magic bullet but rather a chance in lifestyle. Basically, yoga's benefits are beyond scientific. Practicing yoga daily (besides the physical strengthing of bones, muscles, joints) has many benefits (you mention mental strength) that would not show up in any type of medical test. Methodology is a major issue.

    So really though, alot of the so-called fringe practices really aren't scientific - they cant be proven/disproven using the traditional approaches to science. My major problem with the whole situation is when people claim that they are medically proven, when in fact, the evidence is ancedotal. Regardless of how substantial that evidence is, it still isn't medically proven or scientifically proven.

    I am one of the most avid believers in non-medical approaches to curing certain problems. A while back I would have been declared manic depressive and fed full of pills, but I choose a differen route and cured the underlying causes of the depression. However, I could hardly say that moving to a new town or getting a new job was "medically and scientifically proven to end depression" because in fact, they are not.

    So thats my beef really, when patently non-scientific or non-medical practices claim indeed to be medically proven.
  • Well, given a choice between reading about a hotshot young kid who invented, and then proved, a theorem on his own [...] or yet another high school student with an assault rifle and a terminally bad attitude, which would you prefer?

    Well, what kind of assault rifle?

    Rich ;)

  • For 6,000 years people have been using accupuncture without a double blind stury or scientific peer review, or a statistical tested studies. Only thing they had was anecdotal evidence.

    Yep, and for a long time they also believed that bleeding patients was a great general cure all. They even had elaborate theories explaining why you should bleed a patient under some circumstances, give him purgatives under other situations, and the whole nine yards. They had tons of anecdotal evidence to support their beliefs. Do you recommend that we re-establish bleeding as a therapy because people earnestly believed that it was valuable?

    The point is that (placebo effects aside) believing earnestly in a therapy doesn't make it effective. Having an actual biomedical mechanism of action makes it effective. It's true that people have to have theories about what treatments will be effective before they can study them, but it's also important to do the study before making great claims of effectiveness. In the case of accupuncture, there was an actual underlying mechanism there to be discovered when people looked for it, and in discovering it they've been able to make significant refinements over the traditional practice. But that was only possible because the practitioners worked with scientists rather than saying, "Oh you're just trying to debunk us." It's also interesting to note that a lot of the improvements have not been adopted by "alternative medicine" practitioners in the US, who appear actively opposed to scientific confirmation and adaptation of their system. I honestly think that they're just as afraid of being confirmed and co-opted by the medical establishment as they are of being debunked. Instead the advances are being used in China, where accupuncture is considered part of conventional medicine.

  • Why do we care how old the guy is? Why does that have any weight on how good/valid the Theorem is? If it is an important theorem, then we should talk about its importance, and not how far away the author was puberty.

    If it is just a mundane discovery with little usefulness, I don't think we should make it a carnival show just because some young person proved it.

    _ _ _
    I was working on a flat tax proposal and I accidentally proved there's no god.

  • Still, he says, "It required a kid like Josh, who tries hard, likes to think and can perceive a whole complex of potential answers to find a new truth."

    Looks like that school had not drummed the creativity out of the kid yet.

    which is a damning comment on the quality of the education system.

    Watch it be practical for something like warp drive design.

  • I think this is hella cool, but the slant in the article seemed a bit anti-intellectual. like they were trying to tell the kid "good work, son, but remember that's only book-larnin." I dunno, maybe it was just me.
  • I don't have the reference in front of me, but John Gribbin refers to it in Schroedinger's Kittens []. Essentially, the rules for disassembling a unit sphere and reassembling it into two unit spheres models some nuclear process (which I cannot remember).

    If you'll post a (spam-proof) email, I'll send you the relevant quotes from the text.
  • Well, that's because there was no flaw in the proof of his theorem. And he didn't even use the dreaded "choice axiom []" nor the sacred number 18. You have to remember that the kids in yesterday's story [] only got into trouble because they used list context in a situation where it wasn't appropriate.
  • you missed my point. The kids won't be leaving public school, they already have and attend private school. What will be leaving next is their money, which their parents have already decided to pay above and beyond what they pay for public school taxes. Now they can get those back. It looks to me like a pretty clear cut upper vs. lower (money) class question, and while I fall in the upper, I'd rather not have even more idiots running around. I don't think this is the proper solution and I think it would contribute to an extended widening of incomes and opportunities for U.S. families.
  • Two things: the first is about fear and commercial research, the second is about light.

    When I graduated in the mid-late 90's I feared I'd be riding the internet sea in liferaft, jumping from company to company and watching my stock values plummet. I didn't want to be on that track... I wanted into research.

    By sheer luck (and being in the right place at the right time), I found a research engineering firm that wanted me (despite that thing called my "GPA"). Commercial research is very rewarding. If your company bids on contracts which you find interesting you will have an absolute blast. There's a lot of freedom with what you do. You can pick and choose what you work on (for the most part). You get to order the really expensive toys and make salesmen gawk when you give them a *slight* idea as to what you are doing (yes its partially their job to be in awe, but we've caused some show stoppers - "10,000 Amps??? Are you doing lightening research?" ). You get to design freakin' awesome circuits (if you're Electrical or CompE). You get to figure out communications protocols and techniques (if you are a CompE or CompSci). You learn to play with DSPs (CompE or CompSci). You get to play with big mechanical devices and use words like "bushings" (any of the above and especially MechE). Whatever it is that you do, you learn respect and appreciation for the entire team's effort (at least in retrospect).

    I know of no other job where I can cause a small electrical fire, slam an 80 pound weight into a wall (in a very unique way), fling pieces of food product across a room, and play with a milling machine in the same day...

    I see the light of day... I see it on my drive in to work and I see it on my ride home. When I first started I even had a window... but then we absorbed some more PhDs - and they like their windows (they're photosynthetic). Plus as a contract engineer, all of my contract time is billable, and the company has to compensate you for your time working (80 hours one week means I can take the next week off - if I really want to)

    Plus I see the outdoors on weekends (I'm an avid backpacker and pseudo-tree-hugger). Its not quite like college where you could even do your homework outside, but their are many rewards.

    Everyone I work with has good social skills. Those that don't learn them quick (or don't get hired).

    Whatever a company asks us to design is going to see the light of day. Companies rarely throw money at us with the intention of not using the final product or the knowledge gleaned from the research. I've worked on distributed power systems, sensors, industrial robotics, motors, magnetics, and several other things. Hefty amounts of design go the mechanical, the electrical and the software components of each project. Whatever your discipline, chances are there is a place for you on a project.

    We even have a bunch of math and physics guys who come up with all the theoretical modelings for our projects...

    Oh, but my paycheck is not anywhere near what an IT guy makes. Unless I go back to school I won't see six figures for a long while, but that's not what I'm really interested in. I do what I do because I love the work.
  • I don't think this study disproved the general concept. As you said there are lots of other factors that CAN'T be controlled for in a double blind study. What was tested were the claims the therapeutic touch practitioners themselves made, namely they CLAIMED they could sense fields even without seeing the person, through cardboard, whatever. Those claims were refuted to some confidence interval. That doesn't "prove that therapeutic touch is fake" or that "people can't sense bioelectric fields". It just proves that the people practicing therapeutic touch are either misinformed, ignorant of what they are really doing, or in some way think they can do something that they cannot. Which sheds some light on the general likelihood of the rest of their claims being accurate. It "proves" that their perception of what they do is not really what they do. Whether what they do helps people or not, this study says nothing about.
  • by Ted V ( 67691 ) on Wednesday March 14, 2001 @02:54PM (#363309) Homepage
    A slight correction. Emily Rosa did not prove that "theraputic touch" doesn't provide medical benefits. She proved that practitioners of it could not detect the proximity of another human due to the presence of their bio-electrical field (which definitly does exist, by the way). All her study showed was that the conscious human brain cannot reliable sense nearby electrical fields. It didn't prove or disprove that altering things in and near a human's electrical field have any other impacts on the human.

    Think about this analogy. Even though I can't consciously tell how much Vitamin C is in the food I eat, the Vitamin C still affects my physical health. A study that shows people can't detect how many vitamins are in their food does not prove that vitamins are (or aren't) nutritionally helpful.

    If people want to further study the bio-electrical field using scientific methods, great. Maybe we'll find better health that way and maybe we won't. This study just deals a blow to the nut-cases who don't use scientific backing for their therapy, but would they care about that study in the first place?

  • Actually, my experience with Paideia is that it is (like many private schools) a combination of the gifted and rich. It is a good school that always came in force to the science and math competitions.

    The girls I've met who went there were liberated and sexually adventurous. ;) Josh, take note: this is one of the few schools where an accomplishment like this can be translated into romantic success.

    Paideia, in the sciences, is very good. They encourage creativity and hard work. It pays off in college, where you start maybe a year or two ahead of everyone else. In the social sciences and humanities, though, they are as bad as my (public) high school, maybe worse. They are very dogmatic-- do it their way or you're ignorant-- and they tend to be worse in that the students get to college thinking that they are way ahead of their peers. Until first semester's literature grades come in....

    Paideia is very expensive, but worth it if you're looking for a good education. Be careful about dating their alums, though.

  • What is often left out of the Emily Rosa story is that her father was a PhD researcher at a university. While the work _was_ good, and it _was_ funny, it's been pretty well documented that Dad had a big hand in the discovery process.

    But the News is always looking for a good headline...
  • In other words, now it's time to rest on his laurels? Coast the rest of the way through high school?

    It would be really nice to believe that his [high] school might be providing him with work that's stretching him to the limits and really flexing his mathematical brain muscles.

    It would also be really nice to believe in Father Christmas.

    I remember getting told off at [high] school, because we were supposed to show (i) that something was true for any rectangle, and then (ii) that the same thing was true for any square, and for part (ii) I just said "this is implied by (i) because a square is a rectangle". Apparently I was supposed to blindly work through the argument again.

    Teachers sometimes don't realise that laziness is the mother of mathematics, and hence aren't aware that spotting generalities is important.

    So no, you're right, now isn't the time for him to rest on his laurels. But if he wants to learn to be good at actual mathematics, then maybe he should buy a good book (e.g. "What is Mathematics" by Courant and Robbins, updated by Ian Stewart) and bunk maths lessons to read that instead.

  • I know this article is about young minds in math and science. Even though Therapeutic Touch is a whole other can of worms, it's good to see that Emily has a sense of humor about the relative (un)importance of her research. In her speech at the 1998 Ig Nobel Awards ceremony, Emily stated:

    "Scientists shouldn't have to spend a lot of time and money testing really far-out ideas. I had an excuse for doing the first basic research on TT: I was just learning about science, and I only spent ten dollars."

    The Ig Nobel award for Science Education went to Dolores Krieger, Prof Emerita of NY Univ. and founder of TT. The host gave the award with the comment that TT is "a method by which nurses manipulate the energy fields of ailing patients, by carefully avoiding physical contact with those patients." He added that since Dr. Krieger "could not (or would not) be with us tonight," the prize will be accepted on her behalf by Emily Rosa. Emily gave this acceptance speech:

    "My career in science started off with such promise. At age four, I was successfully conducting parent behavior-modification experiments. Within a few short years, I was obtaining dramatic results in studying the effects of oatmeal porridge on the respiratory system of the common goldfish.

    "But by the time I entered fourth grade, my career was definitely languishing. You can appreciate that grant money was tight, and my peers - they weren't taking me seriously. Always just kidding around. But I was concerned; I had yet to get even one paper published in a major medical journal. Then I heard about Therapeutic Touch and NYU Prof. Dolored Krieger, who introduced the practice to nursing back in 1972.

    "Apparently realizing it was mere child's play, they saved all the basic research on TT for future generations to do. Imagine, 15 years before I was even born, Professor Krieger and NYU were giving me my first really big break. I can't thank you enough, Prof. Krieger (who is not here)."

    I was going to add some comments on TT, but everything I would say has already been said much better than I could do:

    Therapeutic Touch: Responses to Objections to the JAMA Paper []

    - MFN

  • by Deanasc ( 201050 ) on Wednesday March 14, 2001 @03:07PM (#363327) Homepage Journal
    I hope he gets an A in math for the rest of high school. How I would love to be in his math class and hear him say to his teacher "when you come up with law of mathematics on your own then you can tell me my math homework is wrong!"
  • Still, I can't help making the point that it doesn't take a genius to realize that any 3 independant lines in two-space are bound to meet in a point. Just call me cynical, I guess.

    Apparently, it does take a genius. (Hint: lines x = 1, x = 2, x = 3.)

  • Actually I am familiar with the work. Ms. Rosa is from my home town, and actually my mother was at the time (and still is) the chairman of the local board of education, so I heard a lot about the incident. Ms. Rosa did a very good double blind study that did not directly refute the theraputic claims of theraputic touch but rather refuted the underlying claim that practitioners could sense the energy fields of their subjects. Actually, from what my mother has said it sounds as though she did the actual experiments but that the study was really designed by her parents who are well known skeptics of this kind of thing. Her parents also apparently helped out with the statistics. Her study wound up being published in the Journal of the AMA, again with her parents as co-authors.

  • When I was in High school a new geometry computer program came out that allowed you to rapidly visualize triangles and other geometric shapes, keeping certain variables constant while rapidly changing others and seeing the resulting shapes. From this you could quickly visualize generalizations and relations that appeared true in 'experiment' and then set out to prove them from first principles.

    The year after this program came out there were several new theorems discovered by High School students with the assistance of this program. Kids in my school thought perhaps we had discovered some new theorems as well, but did not bother to research further beyond our text books (Usenet was not available to us at the time).

    This kid's theorem is not all that big a deal - Geometry is a fairly accessible mathematical topic for kids. I imagine that most mathemeticians, if they had really needed this result in their work could have derived it on their own, it's just that noone has needed it thus far, or bothered to document their derivation in the literature. Plus this makes a good headline.

  • Um, what? I don't think I understand your point. Are you saying that less instructional hours are a good idea? Or that private schools provide more instructional hours?
  • by crashnbur ( 127738 ) on Wednesday March 14, 2001 @03:12PM (#363345)
    You see, this is precisely the kind of news that I hate reading. The kind where they make a big deal out of something someone did just because someone was there to take the next step for them. I, too, played with all of those theorems and numbers when I was in my earlier math classes. And I, too, played with that number and those triangles. But did I show anyone? No. No one around these parts cares about such things. I have attended so-called National Schools of Excellence since the second grade, and none of them really care! They only care about being in control and producing higher standardized test scores - nothing more. They don't care about establishing connections for us. They don't care about furthering us. They just want us to get up and out and make them look better.

    Josh, if you're out there and just happen to be reading this, count your lucky stars, and thank that teacher of yours. My teachers would have either not cared or taken credit for themselves.

  • I'm reading the book with Feyman's talks and lectures (some of them) called "the joy of finding stuff out" or something similar, and he also mention the work of eacly 20 century mathematician ... forget the name... Hilbert? Anyways, this guy went off and worked out all these therories about how vectors and matricies that appeared to have no use whatsoever. Until quantuum mechanics came around, and Pauli had to reinvent much of it.

    Now Pauli was a smart guy, so a lesser intellect might have looked up Hilbert's stuff rather than reinventing it.
  • The schools gain for every kid that takes a voucher to opt out, but lose for every kid that already WAS out of the existing system. This is a net gain of resources for the schools if enough kids leave.

    This would only work if the numbers you quoted were accurate. And I'm gonna need more than word for convincing. This does combat one of the major problems with public school, large class sizes, but I don't think it is a good one.

    Your next paragraph needs some serious backing up, because my experience is pretty much completely opposite. How can lower class kids gain by having less funds for their school? And your private school data, and profile of typical students is totally contrary to what I have observed.

    because the local public school is a scary violent place where little learning occurs.

    And taking away another slice of the social class and their school taxes is going to help this how? Or do you wish public education to be written off as a lost cause?
  • I didn't, I just didn't put as much effort in. Getting the extra three points in every class would have required twice as much work as was needed to fly through the tests and do nothing extra on the labs.

    Yep, I was lazy.

    -grendel drago
  • by NonSequor ( 230139 ) on Wednesday March 14, 2001 @03:14PM (#363364) Journal
    No, she debunked one of the central tenets of therapeutic touch. The practitioners of therapeutic touch claimed that they could sense the bio-electric field and know where it was out of whack and could manipulate the field in these areas to fix the problem. Apparently they only thought they could sense this field and were only touching random parts of the body, so even if there was some place where the bio-electric field was out of whack they would only find it by chance. All of this makes it highly unlikely that therapeutic touch can do anything.

    "Homo sum: humani nil a me alienum puto"
    (I am a man: nothing human is alien to me)

  • by Spoons ( 26950 ) on Wednesday March 14, 2001 @03:51PM (#363380) Homepage
    The school he goes to (Paideia []) is actually quite cool. It is kinda a free form private school. From what I remember they really don't have many grades or announced tests. Kids are encouraged to learn at their own rate, and many gifted kids go their when they out pace their regular classes. It is kind of a neat place. They actually encourage creative thinking instead of kicking you out or arresting you!
  • by David Eppstein ( 306415 ) on Wednesday March 14, 2001 @03:22PM (#363387) Homepage
    The Monthly article in question appears to be "Morley Related Triangles on the Nine-Point Circle", by Floor van Lamoen, Amer. Math. Monthly vol. 107, no. 10, Dec. 2000 [], pages 941-945. The introduction says: "We identify two points M and H on Euler's nine point circle CN, found as intersections of three reflected lines. M and H each depend on the direction of a set of parallel lines. Posing the condition that M and H coincide for a certain direction, or that MH is a diameter of CN, we find two equilateral triangles in CN homothetic to Morley's famous trisector triangles."

Every program is a part of some other program, and rarely fits.