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Georgia Teen Stumbles On New Theorem
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."
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?
-Isaac
I am not a lawyer, and this is not legal advice. For Entertainment Purposes Only.
Ummm, maybe many people who have survived cancer had this treatment, so what? Many of them drank kool aid too. Kool Aid cures cancer!!!
PEBCAK
Finder of the any key.
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.
/.'ers: Number theory was thought to be the "queen of mathematics", unspeakably pure. Of course, now it's the workhorse of crypto.
Other "useless" stuff, but of more interest to
General Relativity: Space-time tells matter where to go; Matter tells space-time what shape to be.
Your expectations are too high.
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If you think big enough, you'll never have to do it.
I myself have a hard time balancing the two approaches. I'm just out of high school now, and I work as a programmer and am majoring in Math and CS. I had this idea of being one of those really "creative" people who just links concepts together and makes it all work, like I'd done on my brief forrays during school.
Problem was, I had only just recently learned much unix shell stuff. I knew all about TCP/IP but had never actually implemented anything with a socket interface. I knew C and C++ really well and had written several kinds of algorithms and data structures, but didn't know any libraries for system calls, graphics, networking, GUIs/widgets, or anything else.
You can be good at math/logic and have all kinds of conceptual knowledge of the stuff, but I'm not going to be able to do anything until I am handy with the tools of the job. Then maybe the creative juices can flow.
--
Vidi, Vici, Veni
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 is known that the sum of the internal angles of a triangle is 180 degrees
See, you can prove theoremsIt is known that a straight line (sum of internal and external angles) is 180 degrees
Take out the common angle, and you're left with the sum of the internal angles, an equals sign, and the external angle
Proven
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?
Where the wind blows, the tumbleweed goes.
Something like 10,000 mathematics theorems get proved and published each year, IIRC.
Interesting, since i was smart and picked on, but did none of those things. I was a nice person, and got along w/most people, mainly b/c i didn't say much in school. if i am a little arrogant now, its as result of being picked on, not the reason i was picked (in case you're wondering, its b/c i came into public school late in the game). I suspect the reason 'these people' leave with a chip on their shoulder is because they have the knowledge that they will amount to something, while the morons that picked on them will be asking 'do you want fries with that?' for the rest of thier lives.
Any two lines (even in 2d space) do not meet in a point.
I pondered over the information in the article, started reading the postings and found a URL to the "proof" of the theorem, looked at it, came back to slashdot, went back and looked at it again, and then came to write this.
It really isn't anything spectacular. No wonder the kid didn't think it had any actual application. And please don't say, "you never know where this could be used in the future!" I've looked at it, it made sense, but ultimately it's just doing the same thing in a wardback kind of way. (backwards is the wrong term)
What you are doing is creating any line that only touches a corner of the triangle and then drawing parallels that go through midpoints of the various sides. Then you reflect points over the line to form a rectangle and you amazingly have a diagonal for a rectangle.
What I want to know is what the hell was wrong with taking perpendicular lines through the midpoints rather than creating an arbitrary line and making a box by reflecting points and creating a diagonal? The old system works, the kid was dinking around and found something countless others have probably "discovered" but got lucky enough to have a teacher who took interest in.
I'd thank the teacher if I was the kid.
This thing really isn't newsworthy.
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.
If you're still at CalTech and ever run into a guy named Isaac See, tell him Stan says hi through the Internet void. :)
Eighth grade is high school in some school districts. (It was for me.)
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.
So a theorem happens like that, while staying in Study Hall. Knew I was missing out on something in Middle School
blah
I am in the 10th grade and am struggeling through Algebra2 (because I had a crappy teacher for the first 1/2 of the year).
Anywho, I was wondering, what is peoples opinion of using a Program on a caclulator to solve a formula for you, or do you feel as if you should work it out the hardway?
Such as I designed a program for the Quadratic formula to where it would just ask a? b? c?
and you entered in the #'s.
I know how to do the formula, and in fact can recite it from memory, but how do you feel about this being used in schools, instead of having to work out a boring formula to do just a small part of a problem, when you already know how to?
Damn, where are my modpoints when I need em?!?!
The only "creative" math is that done at a graduate level. Unless you are talking about Education, then you are dumb and insulting to people that like math.
As a mathematician who has done some research, I hated the question about "practical applications" because people would lose sight of the beauty in the math and the proof. While it's nice to have these practical applications in mind when you do work, it's not what's important in the mathematics. That's the true beauty of mathematics: it can live in its own world and still function; it is a true art. Mathematics, like art, doesn't have to be practical, but it never hurts if it is.
-Jellisky
Like elliptic geometry?
Laws do not persuade just because they threaten. --Seneca
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.
Portable versions of Firefox, GIMP, LibreOffice, etc
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.
Speak truth to power.
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.
I honestly believe that most of these therapeutic touch therapists are interested in helping people, even if their science is a bit wacky.
Whatever... I hope you excuse me while I spend time learning how to treat people with Love and Respect, not hatred and disdain.
Which shows you respect a patient more? To fool a person into believing something false or to reveal a practice as quackery?
Isn't scamming people in their last days the ultimate sign of disrespect?
Maybe our definitions of Respect are different.
Dancin Santa
yep, it's called a "strawman"
How we know is more important than what we know.
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.
:wq
If it's so astoundingly easy, why did nobody do it first? Why didn't YOU do it?
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Obfuscated e-mail addresses won't stop sadistic 12-year-old ACs.
Win dain a lotica, en vai tu ri silota
I remember hearing that story in school as well, and the formula seemed obvious to me before I saw what it was - there's fifty pairs of numbers that add up to 100 (0+100, 1+99, ... 51+49) plus 50. Or 50*100 + 50 = 5050. I doubt Gauss was the first to discover that formula, as it was so simple - either that, or I'm a maths genius. It's a nice idea, but I don't think so.
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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$$
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.
That's what I'm really curious about. Does anyone have any info on that publication?
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"Of course, that's just my opinion. I could be wrong." --Dennis Miller
But people that say they're freakin' geniuses and smarter than 97% of the population don't impress me one ioda. They just come off as insecure.
SEO Copywriter. Just Say ON
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.
How we know is more important than what we know.
If you view all choices as having only two possible answers, that's what I'd call a binary worldview.
Read the EFF's Fair Use FAQ
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.
Thus showing how ridiculas our current system of learning is. Imagine if some horribliy important theroum has been published of which just you reading it could lead your mind onto the right path to discovering something with highly practical applications.
Heya, only got 10k per year * papers to sort through!
Need help treating your acne? Come here!
"Girls...have a higher boredom threshhold."
As a female, I tend to disagree with this.
....
Okay, I'm bored now.
Angry IT woman in big clompy boots. And talking lint!.
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.
I'd call this flamebait. Not all public schools are created equal. Similarly, not all private schools are created equally. It's ridiculous to make sweeping generalizations about the quality of educations available public or private schools, and then make a philosophical/political statement about school vouchers.
I think school vouchers are a great idea for a lot of the public schools. And simply labling them all bad is nothing more than left-wing propaganda. This kid's school is obviously doing a good job. And if his parents had vouchers, there's an excellent chance he would still go to this school. Or maybe he would go to a better one. But the point is that he and his parents would be free to make that choice for themselves. Isn't freedom what this country's about?
I've only heard one argument against school vouchers that makes sense to me. That's the idea that if parents used vouchers to send their kids to christian schools, then the government would be sending strings-attached money to the schools, increasing the liklihood that the government would try to regulate the schools, and forcing the schools to lose focus on what their goals are.
I can tell from past experience that the slashdot moderators are most likely liberal and democrats. :-) Feel free to moderate me into oblivion.
Disconnect your television. Do your own research. Draw your own conclusions. They're probably lying. Don't be a sheep.
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.
"sweet dreams are made of this..."
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.
How we know is more important than what we know.
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.
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you gotta hand it to him though.. that was beautiful.
How we know is more important than what we know.
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.
How we know is more important than what we know.
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 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.
There's no point in questioning authority if you aren't going to listen to the answers.
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.
------ 24.5% slashdot pure
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?
Sigless.
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.
These are my friends, See how they glisten. See this one shine, how he smiles in the light.
Am I wrong; or by the standards applied in the USA, the process of applying this theorem can be patented?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~ the real world is much simpler ~~
--- -- - -
Give me LIBERTY, or give me a check.
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.
Bugrit! Millenium hand and shrimp!
I discovered this same thing while working too late at night.
I was writing code to find the circle through three points.
The formula is pretty simple, but I was sure I was getting bogus results (& I was), so I re-wrote the thing from scratch, using first principles.
Of course it being 2am, I forgot my negatives on the perpendiculars.
The fact that these lines meet at a single point, is a PITA! I was getting a result, that from the output of the program (just a set of co-ordinates) looked right, but the point was not equidistance from the original three vertices.
You know, if I'd done that a couple of years ago, I could have been famous.
But at least this kid had the energy to say, "Wow".
All I thought was: "Hmm, I wonder why that happens, Oh well, back to work"
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Read more of this story at Slashdot.Read more of this story at Slashdot.Read more of this story at Slashdot.
Maybe part of the reason for his continuing creativity was that he always worked cooperatively. He is named as co-author on literally thousands of papers, to the point where mathematicians talk of someone's Erdosz number in the same way that film buffs talk of a Bacon number: how many hops it takes to get from a particular mathematician to Erdosz through mutual publication.
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Dunx
Dunx
Converting caffeine into code since 1982
Its a tried and tested technique
Consider pythagorus and other early scholars
who sat around playing with geometry and came
up with all sorts of theorems and the like.
"Watch it be practical for something like warp drive design. "
yeah dood! or new photon torpedos for fighting off the borg!
Not a big deal, but phrasing it that way helped me visualize what he was talking about.
I was one of "those" people in High School. I was bored with the curriculum and yes I was smarter than the so-called teachers at the school who could never answer my questions. I read the text book which was and I'm sure still is unheard of. I played cards because to put myself forward would have made me a social outcast. I resent it when people just assume that people like me had no social skills when all somebody like you can do is put down someone else. If being able to do that equates to social skills, I'd rather be an introvert.
Or maybe it's because Erdos was always on speed, was completely uninterested in sex, and had no life besides math. I kid you not, the man was very strange.
I challenge his assertion, provide links to reputable sources to back up my claim, and I'm moderated down as a troll?
Truly sick.
-Isaac
I am not a lawyer, and this is not legal advice. For Entertainment Purposes Only.
The medians (i.e. lines connecting the vertex with the middle of the opposite side) interesect at the centroid.
The perpendiculars do not.
My second question is: Why doesnt everybody understand this?
I think you might be a bit confused yourself.
I learned this formula in elementary school, the teacher said Aristotle discovered this when he was a kid, and I think my algebra teacher said the same thing about Napier. Wierd.
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. :-)
Babar
...
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 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.
A year ago I would've been with you, repeating the "uh huh, *cough* bullshit *cough*, I'll just wait until I see a scientific study" rallying cry of the skeptic... I've since learned that it behooves me to refrain from automatically dismissing ideas from the realm of possibility. Progress would be iceberg-slow if every "scientific" advance was contingent on "peer reviewed, placebo controlled, statistically tested, double blind studies." On the contrary, a great number of rapid advances are made in leaps and bounds, which can later be explained using the "scientific method". I don't care that there's no science behind theraputic touch, I only care that in the past it's worked for me (hey, it was free, why not give it a try?).
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Learn the rules so you know how to break them properly.
www.teslabox.com
This kid sits down one day and discovers something simply by thinking outside the box. The established mathematicians couldn't be bothered, or it never occured to them to look for it because they're entrenched in their methods and their own problems.
And who knows about it's utility. I'm not a mathematician... but it does deal with triangles. The first thing that popped into my head was: "I wonder if this could somehow be used for 3d rendering"
I really have no clue as to it's utility, but that's not important here. It's the mere fact that it was accomplished.
-- kwashiorkor --
Leaps in Logic
should not be confused with
-- kwashiorkor --
Leaps in Logic
should not be confused with
Jumping to Conclusions.
Girls are good at doing routine tasks. It has been scientifically shown that they have a higher boredom threshhold.
:)
Sounds very interesting. Do you have a link or something to this study? I would really like to show it to my girlfriend
Just remember that vitamin C has been proven to be good for you by many scientific studies.
There is currently no evidence that shows that "theraputic touch" provides medical benefits, and there is evidence that it doesn't provide medical benefits. Therefore any claims that "theraputic touch" provides medical benefits are extraordinary.
Extraordinary claims require extraordinary proof.
--Fac Iustum Nec Time-- --Veritas Prevalibit--
...was a puddle of drool on my desk.
---Technology will liberate us if it doesn't enslave us first.
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!
These are my friends, See how they glisten. See this one shine, how he smiles in the light.
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.
There's no point in questioning authority if you aren't going to listen to the answers.
What was tested were the claims the therapeutic touch practitioners themselves made, namely they CLAIMED they could sense fields even without seeing the person
If that's what they claimed, and that's what the experiment explicitly aimed to disprove, then I hope they took care about my first point(distance issue). Anything claiming to be scientific should be as thorough as is reasonably possible. I know she's just a kid, but like I said in another post, if she's getting published, then I'll rip it to shreds if the experiment has holes in it. (Just as I would rip to shreds anyone who spouts off "theories" without any proof or at least some sound reasoning to back them their claims).
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"People who bite the hand that feeds them usually lick the boot that kicks them"
Higher Logics: where programming meets science.
Minor nits to pick. There could be several such points (consider the distance from (0,2) to Cos(x)).
Also, you need to check points of discontinuity, or discontinuity in the first derivitave. Consider the distance from (-1,-1) to sqrt(x) and from (0,-1) to abs(x).
But the basic idea is good.
JET Program: see Japan, meet intere
Thanks for pointing that out -- that is pretty damn funny...
there is no thing
what else could you want?
Sorry for the double post...
;-). Linux has alot of anecdotal evidence concerning it's stability and performance, yet little hard data to corroborate it. Do you think any less of the linux kernel when some preliminary tests show it doesn't quite perform as well in certain areas as originally thought. I don't think so, since it works beautifully for you(alternately, you can insert whatever other OS you use as none of them have much hard data for performance and stability). This is the identical situation except applied to medicine.
Which sheds some light on the general likelihood of the rest of their claims being accurate.
I wouldn't even go that far, because this evidence has no bearing whatsoever on the validity of the practice. You cannot draw any such conclusions(though I know why you're tempted to and why most people would). What this practice has going for it is anecdotal evidence. People say it helps them, the therapists have a theory for why it works, but there has been no significant/accepted scientific study in this area(AFAIK). So anecdotal evidence is all they've got.
This situation is very similar to where linux currently stands(to draw a tangential analogy...have I got your attention now?
Some very rough and preliminary tests showed that therapeutic touch did not work as they originally thought it did. Big deal, they think and test more and come to a more complete and robust theory. Happens all the time. It's called science, but from what I've heard of this science fair experiment, these results are being used to debunk "quackery". People should learn to think more, react less.
-----
"People who bite the hand that feeds them usually lick the boot that kicks them"
Higher Logics: where programming meets science.
It's been a while since I read the paper, but IIRC the experiment was very simple. The practitioners claim to be able to sense the electric fields (and in fact not just their existence but enough detail about them to figure out what's wrong with the patient and correct it) through clothing and without touching the patient. To test this, she had a box covered with dark cloth into which she could put her hands. The practitioners were then supposed to sense her hands through the cover. I can't remember if it was that she stuck one hand or the other into a box with two regions and they were supposed to tell which box had a hand in it, or whether her hand was sometimes in the box and sometimes not.
In either case, the test was of a much simpler ability than the practitioners claimed, and something that they could have gotten right by chance half the time. They were just about exactly as good as you'd get if they were just plain guessing. IIRC, they actually got it less just less than half the time, but not statistically significantly different from a random guess. It's not absolutely conclusive, but it is pretty damning; the practitioners showed no obvious signs of an ability that they claim is crucial to their practice.
There's no point in questioning authority if you aren't going to listen to the answers.
If you take any three lines (not parallel), and shift them around without changing their slope, you can make them intersect at a point (unproven, intuitive, verrrry scientific).
So indeed, you do need to know which point to use.
Now, there are three (four?) theorems about interesecting lines in a triangle. Medians, perpendicular midpoint, all that. And it seems at first glance that all of these may have a partner in "non-negative reciprocal theorem" space.
Anyone with time on their hands?
- AnoniMoose Cowherd
are the anal retentive folks like you often constipated? wtf is wrong with you, belabouring semantics in such a bitter and extensive manner?
not to mention the numerous semantical errors found within your own thesis. fool.
But I think the most insulting aspect of your little belinked tirade is the implication of surety, that you simply must be right in your beliefs because 'blah blah blah, valid science'. This is pure foolishness- you've clearly no idea the damage that 'scientific method' has caused the world. And it is nit-picking like this what re-enforces the torture. Look around you. the soul of western civilisation is utterly bankrupt. from prozac to hell mouth, tampon ads to trailer trash, our entire populace faces implosion. and the meat of the matter lay in so-called 'scientific method' robbing us of our very humanity, be it through denying us our important capacity for superstition or industrializing our bread and butter.
knowledge without wisdom is about the most contemptible and evil trait going. congratulations.
::I will not moderate my opinions for your stinking karma
That is what you are supposed to do to smart kids, isn't it?
I think that euroderf is right about the way that math is taught in school, at least in High School anyway. When i was in HS, math concepts were taught without any eplanation. We were told that in order to do this, you must do this. It always involved doing it in some long drawn out way, and it always seemed really hard. It wasn't until i got into a College Algebra class that the instructor showed us simple formulas for what had been hard and obfuscated in HS.
HS teachers also have a stupid way of doing assignments and tests. My HS algebra II teacher would lecture, and then give us and assignment. and then he would hardly ever give us the oppourtunity to ask questions. Then the test would take 2 hrs to do because it would be 30 problems. College is so much easier actually. You spend half the hour learning why you couldn't do some of the homework from the previous day, and then the rest is new stuff, and our tests are like 8 problems that are hard, but since we've already beat the subject to death, then if you paid attention you whip through them.
----------------------
Opportunities multiply as they are seized. --Sun-Tzu
This may be cool, but it really isn't that exciting. I have a friend who published his first theorem when he in fourth grade. I guess the real interest in this story is that Mr. Khler wasn't really all that smart.
-- Nerds on toast in the new millenium
I can ask the kid at school tomorrow. He goes to my school.
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.
OK take a triangle (call the points p,q,r). Draw a perpendicular line from each line to its opposite point (say going from line [qr] to point p, and so on). These intersect at the centroid of the triangle (known geometric theorem).
A line has the equation ax + by + c = 0, and its slope (m) can be expressed as -b/a. The line perpendicular to this has the slope a/b (negative reciprocal refered to in the story).
What the new theorem says is: make the new slope -a/b (the non-negative reciprocal). And find one line using each slope. There's a new point, heretofore undiscovered, at their intersection.
What the story doesn't say is what point to use. Every line needs a point and a slope to find its equation. Do we use the original points (p,q,r) and the new slopes, or the new slopes and the points at the intersections of the old perpendicular lines and the original lines of the triangle
My second question is: Why doesnt everybody understand this? It does only take 8th grade maths to get, maybe 10th grade if you weren't in the advanced class. I know that nobody where I'm from (shameless plug: Ireland) can get into college without knowing this, because several questions of the exams that everybody takes are based on this. It may take a genius to discover this (I question the use of the word genius; I'm putting it down to boredom and curiousity), but everybody above the age of 15 should get this, and you 13 year old 133t h4x0rs who read this, this should be well within your comprehension.
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.
--
+&x
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.
--Blair
"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.
-Ted
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.
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.
--
Vidi, Vici, Veni
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.
Bugrit! Millenium hand and shrimp!
He was not suspended, expelled, or arrested for "Thinking While In Highschool"!
I AM, therefore I THINK!
Why's that revolutionary? Any course on Galois Theory will teach you how to create any geometric construction that's possible [and how to tell if it isn't, like squaring the circle]. Granted, most high-school kids don't know Galois theory, but it's not "new maths" in any sense.
I don't think doodling is something that we conciously do. In general when a person doodles thier mind is in a completely different place, working over some problem, or thought, or feeling.
Sometimes the thought can be trivial, which is good - it's pleasing, possibly relaxing, to think about things we want to think about. Sometimes the thought can be much more useful.
Personnally I am not a doodler, I'm a pen twiddler. When I have to solve a problem, or design a new system etc then I sit back in my chair, pen in hand, disconnect my brain from the outside world and twiddle away.
I've had many Eureka moments twiddling my pen, I'm sure many people have had Eureka moments doodling too.
--- James Sleeman
NZ Electronics Enthusiasts: Check out my Trade Me Listings
How could girls have a higher boredom threshold, math is the most boring activity.
You miss the point completely. Everyone is trying to figure out how it CAN help you. It's just every avenue that is explored just yields more failure.
At some point you are going to have to consider the possibility that perhaps none of these therapies are beneficial.
Except that would make you have to admit that your BELIEFS aren't real SCIENCE.
Sigs are awesome huh?
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.
-- "Sucks to your ass-mar"
From the article:
"He's tried to explain it to me," says his father, Harvey Klehr, a political science professor at Emory University. "But I still don't really understand it."
Apparently neither the reporters, nor me understood it.
Could someone please explain or even enounce this new theorem?
Kilroy was here!
>I can attest to that.
...I suppose...
>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
----- In Your Cubicle No One Can Hear You Scream...
You're saying it's "a damning comment on the quality of the education system" because he hasn't lost his creativity?
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
In Soviet Russia, hot grits put YOU down THEIR pants.
Ummm.. I hope he learns some calculus and trig.... Geometry is nice, but most math related careers require a bit more.
Do not go gentle into that good night. Rage, rage against the dying of the light.
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."
http://www.parentssource.com/article.3.00.html
Jumpstart the tartan drive.
Maybe the Scientists and Engineers who thought 'Computers Sucked' should look up the Klehr kid who came up with a new Geometry theorem while doodling on a notepad in study hall. Perhaps the new discovery tool of choice will be crayons and standard rule paper? (Probably better than Windows on a PC anyway)
Legalize the constitution. Think for yourself question authority.
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.
-- Cheer, Cheer, The Red and the White.
We were actually given this problem in school when I was about 8. I had a maths teacher who liked to try and make us break a few limits. Needless to say, none of us figured it out, but it reassures me to know that there are at least some teachers who don't just force kids to rote learn.
Now, if only the rest of my teachers had managed to keep that kind of attitude.
mick
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.
War is necrophilia.
Here's how I remember the story from one Usenet thread on comp.lang.c a long time ago...
(Dejanews isn't fully functional at present, so the exchange is more or less how it happened.)
One poster wrote in the little anecdote you just related, about Carl Gauss discovering the formula n(n+1)/2. Another poster followed up with this version:
Soon another poster (Kaz Kylheku?) wrote in with his version of the story:Quality without creativity is pompous; creativity without quality is infantile.
You know well you can't make it alone... you can't make it alone.
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.
--
It seems the job of the school is to:
1. produce a productive member of society.
2. Encourage further learning and development.
I think schools for the most are failing at these two points. The real test is not a quantitative measure of a students performace, but broader questions of is our society a success? In what areas is our society failing? Because ultimately we are all a product of the system of which the schools are only a part.
World Socialist Web Site
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.
Actually, you can't prove Theories -- you can only disprove theories, or show that they work every time you try -- but you can't prove that they are always right. A law (in the scientific sense, not the mathematical) is simply a theory that has stuck around for a while. Laws are not proven either. Newton's "Laws" of motion were eventually found to be the limiting cases (for velocities here
"That's not even wrong..." -- Wolfgang Pauli
Here [http://www.csm.astate.edu/Ninept.html] 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."
Use my userscript to add story images to Slashdot. There's no going back.
What I meant to say was this: Actually, you can't prove Theories -- you can only disprove theories, or show that they work every time you try -- but you can't prove that they are always right. A law (in the scientific sense, not the mathematical) is simply a theory that has stuck around for a while. Laws are not proven either. Newton's "Laws" of motion were eventually found to be the limiting cases (for velocities much less than the velocity of light) of Einstein's special theory of relativity. Laws aren't proven any more than theories are -- Newton's "Law's" are approximations of a more general "theory" -- special relativity. If you want to read more, I wrote up a page on this a while back: you can check it out here if you want.
"That's not even wrong..." -- Wolfgang Pauli
Why is my comment offtopic?
And Mr RTFA Anonymous Coward, try it for yourself, with the coordinates given in this example.
Ie: (x1,y1; x2,y2; x3,y3) = {0,-1; 1,1; 2,0}. You get an intersection point at {-16/5, -11/10}.
How about you try things for yourself instead of believing everything you read?
Sometimes I just despair of this fucking place.
--
I vote for "would not have cared" as most likely. My personal experience? While trying to integrate the Bell Curve (a known impossible problem) as a spare time project, I accidentally invented my own technique of integration. It turned out I was reinventing a technique that used to be commonly taught, but to find that out I had to pore through old textbooks at the Stanford Math Library. (My public-school calc teacher was no help and high school kids didn't have Usenet access in 1983.)
crashnbur, you'll be a much happier math genius if you worry less about being worshipped by the authority figures around you -- it ain't gonna happen. The important thing is to impress yourself and find some friends who think the same things are cool that you do, so you can learn from one another.
I play Nerd-Folk!
A sack full of good intentions is worth an empty sack. I forget which rule of acquisition that is, but it definitely applies in this case. The TT practitioners may very well be far better human beings than Emily. That, however, means exactly dick.
So let's look at what we have. we have a theory which makes some claims which can be falsified by a schoolgirl. This means that the people who came up with it did not bother to test it. What this means is that TT practitioners around the globe are using their boundless good intentions in a way that is at the very least extremely suboptimal and may even be valueless or counterproductive. Lots of good people wasting their efforts when they could have been doing genuine good in ways that have been proven. Let's see, good people trying to do good work but accomplishing or at least nothing measurable. That to me sounds like all their good intentions are just paving the road to hell. You should instead focus your venom on the people who gave them the road they are paving.
I'm sorry if this is a bit harsh, but one thing that really bugs me is people and organizations who feel justified in either lying or fudging data in support of a good cause. Emily, with her wicked act of tearing down the illusions of good people without replacing them with something constructive, has done more good than any TT practitioner ever has. I'll take her kind of evil over your kind of good any day.
pornking
An easier explanation is that there is additive symmetry around 50. In other words, 49+51=2*50, as does 48+52...1+99. so 50 + 49*100 + 100 = 5050. Then again, I guess kids learning addition can't really multiply, but I'm sure Gauss could (this is the anecdote my discrete math gsi told us).
replace 'berserkeley' with 'berkeley' to respond via email.
Eh, sorry. I guess I would rather hear about new innovations, or that gas prices are dropping again, or that the stock market isn't crashing...
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 freeshell.org). Thanks for your attenton!
..or you'll go blind.
thanks mom.
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.
-S
--- What parts of "shall make no law", "shall not be infringed", and "shall not be violated" don't you understand?
I was one of two people in advanced classes that also played football. Oddly enough, I was never picked on. So I guess the moral here is be smart and freakin HUGE!!
I really hate Dan Patrick.
It makes you wonder how many such discoveries are made each year, only to go unnoticed.
My teachers would have either not cared or taken credit for themselves.
Or they would have failed to recognize that it was an important discovery in the first place. That would have been the case with my high school trigonometry teacher, who used to stand like a deer in headlights whenever we'd ask a question not covered in the text. To her credit, at least she was humble enough to ask the calculus teacher (who was brilliant) when she didn't know something.
so what makes this one special? Is it an important theorem, is it beautiful, will it help with the discovery of further theorems? Does it solve a well-known open problem? "Now named the Klehr-Bliss theorem" named by whom? Are other mathematicians talking about it? Obviously, the reporter knows nothing. Why, then, should we even read this uninformed chatter?
Theorems and Theories...not the same thing.
A .png is worth 2KB (1k words? Erm, sorry.)
But seriously... this is interesting, though maybe not interesting enough for me to want to take the time to try to duplicate the kid's theorem (without any formulas given) and draw a picture for myself. How lazy is the paper that they can't waste a column-inch (even on their Web posting) on a simple illustration or two?
--
--
I don't want to rule the world... I just want to be in charge of mayonnaise.
Don't steal my line!
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.
Meldroc, Waster of Electrons
http://home.wxs.nl/~lamoen/wiskunde/concur.html
The extremely vague statements in the article look similar to what is presented there...
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
Laws do not persuade just because they threaten. --Seneca
Comment removed based on user account deletion
"You don't think science knows everything, do you? Can't there be things outside the realm of scientific knowledge?"
-- reminds me of a quote from a James Morrow novel.
"Science has all the answers, we just don't have all the science."
I gotta get a tight tension on...
Vince Lombardi summed it up quite well:
'I'd rather be lucky, than good.'
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...
Although vague, I believe the formula is to find the inverse point of any point in a triangle... By not inversing the reciprocal on the formulae for parellel lines, he finds the inverse of the point created by the perpendicular lines off the sides of the triangle. Pretty neat napkin trick.
"I've seen plays that were more exciting than this.
Honest to god... Plays!" Homer Simpson
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.
War is necrophilia.
Ok, this is the proof of some things we have always done. Try and see it'll work! We do it while coding: add-more-code, gcc, add-more-code, gcc, delete-the-bad-code, gcc ... finaly the math guys found out about it. Now, we'll see a hole lot more OpenSource math. "Uh, well, its not quite a Lema, but nobody proofed it wrong, so it may work." Acctualy a Ph.D guy with the uni in Zurich tiped me off, that much math research is done that way ...
--
42 cows on a 42km road on their way to 42.org
so what?
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. ;-)
Read the EFF's Fair Use FAQ
use Bielefeld.pm
--
Vidi, Vici, Veni
kids aren't all bad.
I believe one of the basic assumptions of euclidean geometry is that parallel lines do not intersect. Euclidean geometry is pretty much the norm, so it's not unreasonable to assume that's what's being used.
Ask Sarah Flannery, who was 16 when she wrote a paper showing her "Cayley-Purser" algorythm to be faster and as secure as RSA. This latter claim proved false, as Sarah herself found out through more research with Michael Purser and William Whyte.
The young man in the article seems to be just as lucky as he was brilliant. Ms. Flannery focused her interest and intellect with incredible results.
Math: it's not just for Cowboys.
"All the ladies who crack RSA keys Throw your hands up at me..."
What bio-electric field??? That's my first impression as an electrical engineer. The human body is hardly ferro-magnetic or anything like that. There may be slight charges as with anything else, but as it is mostly organic, those charges are extremely minute. If they were significant, the study would be easy: just hold a measuring device close to the body.
But that's just the first problem. The other issue is that humans simply aren't equipped with senses (neural or otherwise) to detect electro-magnetic fields. This isn't surprising. There are many things we cannot detect even though they may be real, and affect us for better or for worse. We cannot detect radio waves, x-rays, gamma rays, etc.
There is a third problem beyond the first two above, and that has to do with "manipulating" such a field. There is simply no evidence to suggest that humans can manipulate electro-magnetic fields. Hello! Otherwise, I could simply deflect the next radio wave that came my way.
I will not deny the fact however, that it sometimes feels good to have someone around you. It feels good to have some people very close to you. It feels good to be cared for. It feels good to our bodies to get a massage. We can also sometimes feel the presense of a person: we can see them, we can hear them, we can feel their body heat. We have senses for these things, and sometimes, their outputs are pleasant. By the way others touch and interact with us, we can pay attention to each other, and share our emotions. This however, does not mean that there is an electric field that can be felt and manipulated, and that such a field is the cause of the afore-mentioned effects.
Alright, enough said. Like they say, "A word is enough for the wise." Use some common sense. You have a brain. Don't put your precious time, energy, or money into foolish things. Some fallacies are very easy to recognize.
But it also directly takes away students from the entire public school system, with the result that in every voucher proposal I've yet seen the public schools would be likely to end up with more resources per student after vouchers than before them. If the public school system is spending $7k per student and you let kids opt out with a $3k voucher, the public schools are $4k richer per student leaving than before. The more kids leave, the better the situation for the remaining kids.
I play Nerd-Folk!
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.
War is necrophilia.
Comment removed based on user account deletion
Well, what kind of assault rifle?
Rich ;)
You must be a fundy. Science is the most precious thing we have. The "Scientific Method" has turned out to be our greatest friend, protecting us from credulity and proving to be the only reliable tool for understanding ourselves and our world. And you wonder we defend it so vigorously?
Who ever said paks could spell, anyway?
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.
There's no point in questioning authority if you aren't going to listen to the answers.
99th percentile in everything... What a life
I was one of those you hated also. I went around thinking "The world doesn't understand the genius" until I came to the same epiphany as pizza man in Death by Pizza; Its not that the world doesn't understand the genius its that the genius doesn't understand the world.
My brother had his fingers slammed in his book for reading ahead. Another brother was sent home when a teacher got mad at him for not listening in class. When she quized him on the subject (even through in a few questions about what she wasn't talking about) and he answered them all she just got angry and sent him home for the day.
So I was going to be revenge on teachers. I learned to be a real middle finger up at society. Until I learned that being that way was really easy. A dummy could do it, in fact all my friends that were doing it really were dumb.
So I learned that school was a place where I could learn to be in control rather than curse those who were in control. A place where I could get what I wanted. From then on, I have cooperated with the world and found it a much better place (and me a lot less of a genius) than before. I'm much happier now. Much happier.
C'mon. Kids are as alright as the rest of society is or isn't. This does not require proof.
This kid had the "eureka moment" that defines mathematicians. I hope he pursues pure math, because he's sure to be a valuable asset to the field.
-Legion
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.
That's a lousy analogy.
The whole idea of therapeutic touch is that trained practitions can *feel* and *manipulate* the
so-called bio-electrical field of the body, and
that by doing so, can affect the healing process
of the body.
Her study demonstrated conclusively that TT practioners were full of it. Not only could they not distinguish a healthy bio-electrical field from
a sick one, but they couldn't even tell if a body
was there or not.
The vitamins analogy is totally backwards. The key
difference? The tole of perception. When you take
a vitamin, it is in some sense, the active party.
You, the patient, are inactive, and the vitamin
acts on your body. You are a passive participant.
In therapeutic touch, you have two people involved:
the patient, who is essentially passive, and the
practitioner, who is active. The *active* party
in therapeutic touch cannot perform their activity
without being able to perceive that which they
claim to manipulate.
Rosa's study looked at the active party, to see
if it was possible for them to perceive that
which they claimed to be able to perceive. And
they couldn't.
Any ongoing discussion of TT needs to explain either (A) what it was about the experiment that
prevented the practioners from be able to perceive
the fields that they claim to be able to perceive,
or (B) how therapeutic touch can possible work in
the absence of any ability to perceive the fields
being manipulated.
(B) is clearly out of the question: the practioners
of TT are quite clear about the fact that they
are *feeling* the fields, and using that perception
of the fields to guide their activities. So it falls to (A), and I have yet to see a remotely
convincing argument for it.
Feel free to prove me wrong - I'd be delighted
if something as simple and comforting as TT could
actually work. But the evidence against it is
pretty darned powerful, and in the years since
Rosa's study, I haven't heard anything that made
any sense.
Yeah, I know what you mean. Oftentimes something like this is 99.999% being in the right place at the right time. I can't say I ever played around with geometry like that (I can't draw a figure with a pencil to save my life, but I could probably draw you a good portrait of my math teachers from memory), but I can think of equivalent cases which burned my toast just as badly. (The one that really pissed me off was some folks with a bad case of "Backstage Mother Syndrome" got media attention for their kid who read at the age of 3ish...She wound up with a full scholarship to Oxford. As near as I and my family can figure, I was reading before I was three, and the only way I -- or a lot of folks like me -- will ever get anywhere near school at Oxford is if we win the lottery or something. Gee, I wish I had attention seekers-by-proxy for parents, too.)
:P
So, yep. I know where you're coming from there. I wonder how many other Slashdots and Slashdaughters out there have had similar experiences... I mean, this *is* a very "high side of normal" to "normal side of high" kind of place, intelligence-wise (usually), which is one of the reasons I hang out here.
Also, I just dig typing "break" tags.
?!
I'm not a geek, I'm just a clever script.
What I found out so far:
The intersection of the three lines (drawn from the midpoints of the sides) do indeed meet a single point each time. This I have shown analytically. To do the same, solve for the slope (a) for each segment. Then calculate the y-intercepts (b) for each equation ymid - xmid/a. Finally take any two of the resulting equations, and solve for a common x. You can check that all three combinations yield identical x. Then substitue x with the a and b of your choice, and you get y = a*x+b. Unfortuneately, it appears the point will never always be inside the triangle in this interpretation. For example, try (x1,y1; x2,y2; x3,y3) = {0,-1; 1,1; 2,0}. You get an intersection point at {-16/5, -11/10}.
Black holes are where the Matrix raised SIGFPE
Well, if you were a rational person and especially if you were a scientist, you should never have discounted the possibility in the first place. The whole point of science is objective evaluation and not biased opinion. So on these grounds, I agree with Ted V(the above poster) when he said that Emily's experiment didn't prove anything except that some of the things the therapists were saying weren't valid. Does that mean the therapy as a whole is invalid? Not at all. And if you believe that the whole thing is a quackery on no proof(as the experiment did not attempt to prove any such thing), then perhaps you should reevaluate your approach to these kinds of issues(not speaking to you directly, but to people in genereal). Allow me to quote a previous comment of mine(since it's pertinent to this discussion):
I'm sure that neither of these two possibilities were taken into account. It's very difficult to design an experiment that would satisfy everyone, but to me, anyone claiming to do any kind of science would do more than just a one-sided job like this experiment seemed. Science should be thorough, not biased. I know she's just a kid, but shit, she got published for christ's sake. If you're going to get published, then I'm going to bash you if I think you fscked up(even a little).
-----
"People who bite the hand that feeds them usually lick the boot that kicks them"
Higher Logics: where programming meets science.
It all started when he was reading a slashdot article.
His theorem states:
The noise on slashdot is inversely proportional to the number of trolls.
any practical use?
"sure, post only noise for a week, and the trolls should go away..."
Moderators: I'm a kicktoy, please mod me down, the buzzing noise you hear is the capitalists trying to opress us...
__________
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.
"It is a greater offense to steal men's labor, than their clothes"
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.
General Relativity: Space-time tells matter where to go; Matter tells space-time what shape to be.
Really? It sound to me like they were doing both. They were able to discredit a theory by separating the truth from the lies. (I guess it might be more accurate to say that they were separating some specific lies from the general body of truth. But that's really just semantics.)
Intention certainly has it's value, as do love and respect. But action is what produces results.
Last night I went to kiss my wife goodnight. In the dark, I bumped my nose into her open eye. My intent was show affection. The results were that she was in a lot of pain and crying for several minutes. Her understanding of my intentions of my Love and Respect *eventually* helped her to feel somewhat better about the whole situation. But the action of it was that I poked her in the eye and that hurt her a great deal.
In a related story, the IRS has recently ruled that the cost of Windows upgrades can NOT be deducted as a gambling loss.
hell yeah. you wake up in a start to someone's snoring (your own) and your cheek is stuck to the desk in a puddle of drool. ahh... memories... of course i remember all the interesting face-imprint patterns kids with sweaters would get. "Wow, the stitching on that guy's sweater is immaculate. Look at the waffle pattern indented into his forehead!"
The REAL sam_at_caveman_dot_org is user ID 13833.
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?
-Ted
Checking back to one of my old tests from grade 9 math, I actually lost marks for forgetting to use
I guess this just goes to show that most "great" discoveries start as simple mistakes. I guess the major difference is that his was in study hall, while mine was on a test, huh?
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.
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.
perl -e 'fork||print for split//,"hahahaha"'
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:
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:
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
"Slow down, Cowboy! It has been 3 years, 7 months and 26 days since you last successfully posted a comment."
Your a fuckin racist bastard. I hate people like you. IF that was intended as a joke, itz not funny.
Think for yourself Question authority Throughout human history, as our species has faced the frightening, terrorizi
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!"
I've hit Karma 50 and gotten a Score:5, Troll... I win!
"Homo sum: humani nil a me alienum puto"
(I am a man: nothing human is alien to me)
My only political goal is to see to it that no political party achieves its goals.
My boss told me another similar one; a special form of a ship's wake that does not spread out behind the ship, but remains parallel to the direction of movement of the ship. I can't remember the name, but it was named after the guy who first noticed and described it, probably in the region of a centry ago. The reason for this specific behaviour of the wake had to do with the shape of the channel the ship was in. Apparently, nobody could figure out a use for this somewhat esoteric theory for quite a long time - until the development of fiber (or fibre) optics - apparently light travelling through a fiber can exhibit the same behaviour, and is quite useful for minimizing refraction within the fiber.
Cool - care to elucidate? I gotta admit I don't like the thought of basing the universe on very strong AC :-)
perl -e 'fork||print for split//,"hahahaha"'
I learned this particular lesson back in 10th grade. At the time we were doing something with ellipses. Whatever it was involved finding the distance from the origin to an arbitrary point in order to figure out something else (sorry I'm not more specific, it's been a long time since this happened). Since it didn't matter what point you picked on the ellipse, I just picked a point at the intersection with one of the axes. This simplified the math considerably, reducing the calculation to one-dimensional (since the other dimension was just 0). A few minutes after I confirmed that this worked, the resident teacher's pet raised her hand and told the teacher that she found another way to do the problem. She then went on to explain the exact same approach I took (she used the other axis, but the concept was the same). Now, I didn't particularly care that someone else thought of the same thing. After all, it was rather obvious. The problem was that everyone thought she was a genius because of it. I was left with the knowledge that I had come up with an idea that impressed other people, even though they didn't know what I had done.
The moral of this story is that the loud and annoying people get all the credit, while the rest of us just get whatever we give ourselves. Of course, the loud and annoying people are also more likely to make fools of themselves...
The best you can do is show that is works in the general case. There are always problems that either don't work with any given Theorem or turn out to be a horrible carnival of yuck. (You can, however, prove a Law, but that's a question left to philosophers.) The hard part is in the discovery.
---
ECHELON is a government program to find words like bomb, jihad, plutonium, assassinate, and anarchy.
Does proof by insuction count?
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.
-josh
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 have a hard time believing that these excerpts where written by a fourth grader. Any fourth grader who writes that well shouldn't be in fourth grade any more. The more I read about this one the more I think the parents used their daughter to create some sensationalism and get their own opinions out to a wider audience
Well, Emily was 12 years old when she appeared at the Ig Nobel Awards. And she didn't claim to have written her own material! In any case, you can hear her yourself on NPR at:
1998 Ig Nobel Prize Ceremony
I think she obviously had the support and assistance of her parents, but it's clear that she is a very bright girl and has a promising future. The science project was completely her idea. She was originally going to do a probability of picking M&M's blindly from a bowl, when she saw a videotape her mother (a registered nurse) was watching as part of her research on Therapeutic Touch. She said "I wonder if they can really do that?" :)
- MFN
"Slow down, Cowboy! It has been 3 years, 7 months and 26 days since you last successfully posted a comment."
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.
Any 3 independant lines in two space are bound to meet? What exactally is this "two space" that makes these things true for it when they would not be true in two dimential space?
Binary applies to numbers. Smart students wouldnt say "binary view," they would say bifurcated.
As of right now they can't THINK of an application. I remember reading somewhere that EVERYTHING in Math has a real life application, and that the search was on for a theory that had NO applicaion in real life. So far, AFAIK, they haven't found one and surely a theorem about triangles does have a real life application.
Every rule has an exception, and this is the only rule with no exceptions! Huh? -- Spatch
Every rule has an exception, and this is the only rule with no exceptions! Huh? -- Spatch
Excellent post. Moderators, please mod this up!
Here we go. Gribbin talks about it in Schroedinger's Kittens, but also discusses it on his web page.
Hope this helps....
General Relativity: Space-time tells matter where to go; Matter tells space-time what shape to be.
Public schools tend not to be racially or economically diverse because they only admit people who live in that school district and the districts themselves are segregated racially and economically. Here's a link to a 1996 Cato Institute study on What Would a School Voucher Buy?. From the executive summary:
At the time they did the study, there were many private schools in San Francisco that charged less than $1500/year, and even a few that charged around $1000/year. The poor families that send their kids to such schools would benefit from the vouchers. As for the kids going to scary violent places, vouchers help in several ways: (1) some parents can remove their kids to better schools, thus bettering the experience for the kids who leave. (2) The loss of kids makes for smaller classes with less than proportionate loss of resources, so the kids left behind get more teacher attention and the schools can spend more on books or whatever else they need per student. (3) The bad public schools stop expanding and might even diminish to the point of being closed down. (4) the good public schools attract more students and expand or are copied and improved upon.(1) and (2) deal with the current problem; (3) and (4) change the dynamic so that future kids have a better situation than the current ones.
More specifics: the major California voucher proposal a few years back was designed by a teacher who had worked in a $1000/year school that catered to poor black families in East LA; the vouchers were designed to help more poor families afford schools like hers, and the vouchers were to be for an amount that was about half what the california school system was then spending. (IIRC, it was a $2600 voucher at a time when average California spending was $5200.)
I play Nerd-Folk!
No, I'm pretty glad for the medical science right now, since I still have my balls in a sling from a sudden testicular torsion last weekend. Seeing stiches on your scrotum isn't nearly as weird as you'd think it would be.
Damn it, that's not divine retribution!
Besides, I never said I knew jack about medicine or law. How much easier is it to say "No you can't!" than "I can!" -- and how much easier is that than the actual action? Why did everyone replying to my post assume I thought I was the Nietzschean Antichrist? Is someone not bowing and scraping and apologizing for their talent such a threat?
-grendel drago
Laws do not persuade just because they threaten. --Seneca
A few clarifications though: The proof is a nicer, shorter proof of a known theorem. It is important to understand the difference between a proof of a new result (where the truth or falsehood was not known beforehand) and a proof of an existing result (where it the result was known, but perhaps using a complicated method or advanced results from some other work on other questions.) New proofs of existing results are important if they are improvements of earlier proofs, as in this case, but there is a different flavor to them. Clever approaches that were not seen on the first proof can sometimes surface later; there is a remarkable example of a result (not that far removed from the field of this work) that when first proven in the 1800s, took several hundred pages- modern proofs can prove the same result in three lines (the impossibility of a finite projective plane embedded in the xy-plane authentically, if you are curious.)
Thus it is worth noting that the article mentioned appears in the American Math Monthly, which does not tend to publish hard-core new research results, but instead elegant, elementary proofs of known results. Just meant to clarify; this is a remarkable result (and let me repeat the earlier plug for the Geometer's Sketchpad- quite a remarkable piece of software...)
It's psychosomatic. You need a lobotomy. I'll get a saw.
The article itself was muddled. Looks like the student drew a line from the midpoint of each of the vertices... Yeah, good. Rather than drawing lines perpendicular to each of the segments of the triangle (negative reciprocal of the slope of each line), he simply took the number's reciprocal. Did all this kid simply figure out was that the three lines met at a point? What is the genius of that? Nothing in comparison to the two students a couple years back that proved how to geometrically split a line into segments of five. I've love to see the actual journal article when it comes out. I think they're just staking this point within the triangle as theirs just to take away the credit from someone who actually finds a relevant use for this point. Doing this in threespace on the other hand... That might be interesting.
/^[A-Z0-9._%+-]+@[A-Z0-9.-]+\.[A-Z]{2,4}$/i
nice troll, got me, it's this thing about "vocally reject popular culture" that really pisses me off. That's because popular culture is stupid. Popular culture is a result of people who can't think for themselves, who have set themselves up for a lifetime of pointless commercial servitude. People who look at a Nike commercial and say, "wow, cool shoes, Michael Jordan wears them, so I'll buy them". People who see a Brittney Spears video and say "wow, she's so popular and pretty, she must be the greatest musician in the world otherwise she wouldn't be getting that much attention. I want to be popular and pretty too, so I'll surround myself with her merchandise, maybe some of that will rub off on me".
Popular culture walls itself off from people who don't very actively participate in it. You're either IN or NOT. It's no wonder that "smarter people" don't struggle with this, the ethics and logic of embracing Disney and McDonalds (admittedly in favor of Star Trek and Mountain Dew). The rejection of these people by popular culture, the struggle, all of that will create emotions, which are sometimes hard for young people to deal with. (bang, you're dead). So, yes, it's partly a moderation of arrogance that is needed, but in most cases, that's not enough, it's people forcing themselves to embrace something they may be deeply philosophically opposed to.
Say black people. Replace "arrogance" with "blackness" (black culture, speech, dress, etc):
If they were smart, they would moderate their blackness, and people would like them more.
See? Just act like a white person, be an uncle tom, and white society will accept you. Don't act black. Don't wear gold jewelry. Don't play loud rap music.
This is not the fault of the geek with principles.
These are my friends, See how they glisten. See this one shine, how he smiles in the light.
and my circle method! If you have some curve C defined by x(t) and y(t) and you want to find the nearest point (x,y) to C, simply draw a circle with radius r such that it intersects C at 2 and only 2 points and the center is at (x,y). The point on curve C whose linearization is the inverse-reciprocal of a line drawn from the center to the circumference is the nearest place on the curve to that point (in other words, imagine a line drawn from the center that extends to the circumference of the circle. Imagine it sweeps around like a radar line. When it intersects the curve C, and the slope of the point of intersection on the curve is perpendicular to that radius line, then that point on the curve is the closest to (x,y)).
Granted in subsequent calculus classes I was shown how completely useless that method is, but since I developed it in high-school with only a knowledge of derivatives, I think it's pretty cool...
Si hoc legere scis nimium eruditionis hebes