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350-Year-Old Newton's Puzzle Solved By 16-Year-Old
First time accepted submitter johnsnails writes "A German 16-year-old, Shouryya Ray, solved two fundamental particle dynamic theories posed by Sir Isaac Newton, which until recently required the use of powerful computers. He worked out how to calculate exactly the path of a projectile under gravity and subject to air resistance. Shouryya solved the problem while working on a school project. From the article: 'Mr Ray won a research award for his efforts and has been labeled a genius by the German media, but he put it down to "curiosity and schoolboy naivety." "When it was explained to us that the problems had no solutions, I thought to myself, 'well, there's no harm in trying,'" he said.'"
We all had that moment in school when a teacher would pose an "impossible" problem, thought to ourselves "Well, they've never faced ME before!", spent a few minutes toying with it and finally giving up. This kid...did not.
Kudos all around! The rest of your life will, unfortunately, now no longer live up to something you accomplished when you were 16.
The article itself is mathless. It doesn't tell you what the solution was, or even present the exact problem that was solved.
Can anyone actually find the problems in question somewhere? I've been scouring Google and the whole thing is very vague -- no story really goes into depth about the actual problem he solved and how.
Concepts of mathematics (calculus) are actually very simple.
Most confuse the trivia of solving problems (knowing many rules) and how to apply them with understanding of basic mathematical principles.
Teach your kid about 'x' and abstract thinking in relation to rates of change. The rest follows quite naturally. (IMO).
..don't panic
German media praise math geniuses, while american media praise hollywood actors/actresses (read: human rubbish) and reality show weirdos. In the US a "genius" is someone who makes millions, especially with lower education and without being able to do anything. That's "free market economy", and "supply and demand", right?
"The land of the free and of the brave" (with some fat on the belly).
...go to the source! The German articles I've scoured seem to have a little more information about the problem itself and what he actually accomplished. The oldest one only records that he "claims" to have solved them (earlier this month), but so far no actual data. Close.
http://www.enso-blog.de/jugend-forscht-drei-arbeiten-aus-ostsachsen-beim-bundeswettbewerb
http://www.morgenpost.de/vermischtes/article106358144/16-jaehriger-Schueler-loest-uraltes-Mathe-Problem.html
http://jugend-forscht-sachsen.de/2012/teilnehmer/fachgebiet/id/5
Text is in German. It all stems from a Youth Research competition he entered into back in March of this year. This is, so far, the best summary I've found -- there is a paper, apparently, but no link just yet.
'Two problems in classical mechanics have withstood several centuries of mathematical endeavor. The first problem is therefore to calculate the trajectory of a body thrown at an angle in the Earth's gravitational field and Newtonian flow resistance. The underlying power law was discovered by Newton (17th century). The second problem is the objective description of a particle-wall collision under Hertzian collision force and linear damping. The collision energy was derived in 1858 by Hertz, a linear damping force has Stokes (1850) is known. This paper has so far only the analytical solution of this approximate or numerical targets for the problems solved. First, the two problems are solved fully analytically. For the first problem will be investigated further using the analytical solution, the physical behavior of the system and set up outline solutions for generalized models. For the second problem is carried out in order to increase efficiency and convergence control a semi-analytical optimization. Finally, the analytical results are compared with numerical solutions so as to validate accuracy and convergence to numerically."
The problems he solved are not NP. They are essentially calculus, but they are both very nasty calc problems, and the traditional way to solve calc problems is using newton approximations until the answer is close enough to what you want. An analytical / precise way to solve these problems is extremely useful to the physics folks, as the solution will probably also lead to better models of particle motion.
-=Geoskd
I wish I had a good sig, but all the good ones are copyrighted
Andrew Wiles solved Fermat's Last Theorm with paper only, as he despised the use of computers in writing mathematical Proofs. Another famous example is Grigori Perelman who solved the Poincaré Conjecture - with hundreds and hundreds of pages of mind-numbingly dense mathematics vs computer search.
You forgot a lot of things:
-gravity is not a constant vector force downward. It is a radial force inward toward the center of the Earth, and its intensity varies with altitude.
-air resistance is not constant either. It depends on air pressure which varies with altitude as well.
-air resistance is not perfectly proportional to v^2, especially at transonic and supersonic speeds.
-if the projectile is spinning, it may cause a net aerodymamic force in a direction other than -v. Like a curveball.
-the earth is a spinning frame of reference, which results in various annoying effects.
-the air is not necessarily stationary. Wind exists.
and so on.
But we don't know whether this dude accounted for any of this stuff or not, because the goddamn article doesn't tell us.
These stories about overwhelming acts of personal genius, especially stories that lack the details of the alleged act, are, without memorable exception, false. But we all like a good story about an under-caste upsetting gray hairs and the established order of things.
Think about that for a moment. A story supposedly lionizing science lacking the most basic facts that would permit substantial verification, or falsification, of that science. This is just flash journalism at work.
No. The problem is to determine the trajectory from the initial position and velocity. A human tracks the ball as it moves, which is a completely different problem.
I was not a prodigy, but a really smart kid who was in many environments with prodigies or near prodigies.
My experience has been that most pre-teen children with this history don't understand the material very well, and there tends to be a lot of exaggeration about it. Smart kids are good at mimicking things and that is all that is really need to "do" the first year or two of college math.
Occasionally, but very occasionally you get someone really young who later goes on to do decent, or even more rarely great things, like Norbert Wiener or Terry Tao. But I would like to hear those people give their opinions of the depth of their understanding at that age.
I knew Nadine Kowalsky, who in HS would essentially just remember everything she heard in class and got 100 on every exam. (She wasn't the only one though. I knew a number of other people like that though that didn't do as well as Nadine did.) She later went on to get a Ph.D. from Chicago and published her thesis in the Annals of Math. That is a journal most mathematicians can't get a paper in. Like publishing in Nature or Science. Nadine was the real deal, but sadly she died of cancer not long after finishing her Ph.D. But I don't believe that Nadine was doing calculus until she was 15. And that was certainly on purpose. She, and her parents apparently, knew what was a good idea to do, and not to do, with a super smart kid. (This last sentence is conjecture on my part.)
But I think most cases of pre-teens you hear about are really not what they are made out to be. Once you get to 12 or 13 those, I think things do change a lot.
I was doing advanced Geometry and Algebra at age 8, yes I'm a slow fool compared to this kid. but it's mostly the quality of teachers (his dad) and the willingness to keep giving a kid what they want and challenging them.
The american school system is designed to DISCOURAGE this. Smart kids are told to be happy with the A they got without trying. If they challenge their teachers knowledge they are told they are wrong. Mostly because Grade-High-school education in the USA is simply following a lesson out of a book and not teaching it from an expert. the Gym teacher teaches computer class, The English teacher teaches Chemistry, and all of it creates a ho hum boring as hell experience for the children.
Here in the USA we do NOT want geniuses, we want good factory and office workers. Mediocre will not challenge authority.
yes I am jaded at the education system here. I was one of them that got bad grades because the teachers were idiots. I challenged my math teacher who could not believe that a kid can do multiplication and simple geometry in his head. I proved it on several occasions, but I was given failing grades for not doing the busywork of writing it all out. Plus I refused to learn his technique. It sucked and was harder than what I was using that came from college text books. So I ended up being a pissed off moody kid hating the education system because all I saw was idiots and morons trying to tell me they knew more than Me and I knew that they were wrong. I was reading at a 14th grade level when I was 12 years old. I read 1984 and understood the concepts and hidden meanings. I was devouring Vonnegut with a passion. I was told that the books were "too grown up for me" Everyone talked down to me and all it did was piss me off.
Sadly I did not have rich parents, so I had to suffer through the waste of time that the American Public School system is. College I slept through and aced it, at least they were not morons requiring me to turn in worthless busy work. It was in college where I ran into real education, educators that actually knew what they were talking about and would actually hold a discussion with me and help me learn more.
This is the problem here in the USA. If you are smart, you have a sack put over your head to slow you down to match the rest of the other students.
Do not look at laser with remaining good eye.
Of course it's a different problem.
The first is a prediction from a known initial state, the second is an exercise in analytical approximation that just means you have to get your hands to reach the same position in space and time as the ball, based upon a continuous stream of information of ever-increasing accuracy about the relationship between said hands and the ball over time.
Wildly different exercises.
The principles of differential equations are also simple and there are many simple physical systems that can be used to demonstrate them in a way that is easy to grasp. Even by relatively young children.
The idea is not to confuse the understanding of principles with their applications, as those can be (and are) horribly complex.
Math is not hard. Math is very elegant and simple. Much like language, the same words that are in children's books also comprise the classics.
..don't panic
Here in the USA we do NOT want geniuses, we want good factory and office workers. Mediocre will not challenge authority.
I've shared this and I'll share it again (and again...) but when I was in third grade I had an asshole, authoritarian teacher who I believe was only at my school for a couple of years. He was a lazy, arrogant, abusive asshole. When one was done with one's work one was to literally lay one's head down on one's desk and wait quietly for the other children to finish. I was in trouble on numerous occasions for "looking at the other children". I wrote so many lines I had wrist problems before I ever owned a computer or even discovered masturbation.
Sadly I did not have rich parents, so I had to suffer through the waste of time that the American Public School system is.
I went to a private school for a couple of years, before my parents broke up and there wasn't enough money because my dad was a deadbeat. I was about to be learning algebra, I was learning Spanish (I had great retention back then, and I never forgot some of the words I learned back then... though "ferrocarril" does have a fantastic ring to it, no?) and so on. Then I was placed literally into kindergarten due to my age and went from actually learning at a satisfying pace to being told lies about American colonization, making flags out of construction paper and placing Dead-President's-Head's stickers on them, and the like. After a year of that I spent two weeks in first grade before being bumped up to second, where I was still doing work inferior to what I'd been doing in my previous school.
This is the problem here in the USA. If you are smart, you have a sack put over your head to slow you down to match the rest of the other students.
Especially if you are smart, but your parents are dysfunctional and can't teach you how to blend in because they know fuck-all about how social situations work.
College I slept through and aced it, at least they were not morons requiring me to turn in worthless busy work.
Alas, I discovered life about the same time I went to college for the first time and besides, by that time I was prejudiced against education. What really shat upon my educational aspirations at that time, though, was a counselor who suggested I take a fully practical case load and save my electives for later. If I could remember who that was, I would send them a picture of my asshole right now. Hated it. Made school just a big bore of a chore. Most counselors don't give one tenth of one fuck about you as a person or even as a student, you're just a convenient unit that can be used to fill out slightly empty classes. What, am I bitter? Why do you ask?
Now I have a two-year degree from going back to school much later, but it wasn't convenient for me to matriculate to a four-year at the time and now what do I do with this extra piece of paper? It's too crisp to be good bumwad.
"You're right," Fisheye says. "I should have set it on 'whip' or 'chop.'"
I have to agree with your comment about learning DE, I failed differential equations the first time I took the class (a D-grade) I was taking engineering course work at the time that required them - and what they actaully "meant" clicked in an electrical networks class - when I took the class again (my university had a 1 time grade forgiveness policy) I got an A - it seemed trivial and simple the second time around in a different context. I general I have mathematics makes mroe sense to me personally when I can relate it to a real world problem - Mathematics taught as rote learning is a horrible thing - some of us can't do it that way....
"Here in the USA we do NOT want geniuses, we want good factory and office workers. Mediocre will not challenge authority."
Exactly. And I tell you, is the same thing here in Brazil.
Religion: The greatest weapon of mass destruction of all time
...it does publish great papers, but does require something of a personal connection to get into... Same for The Proceedings of the National Academy of Sciences
Actually, this isn't so true of PNAS any more. One of the previous editors decided in the late 1990s to raise the quality prestige of the journal by accepting more papers through a traditional peer-review route, as opposed to NAS members "communicating" or "contributing" articles (which would often have minimal peer review). This was very successful, and now most articles in PNAS get in through the front door, and they're slowly eliminating the back doors. The overall quality is pretty good - not as high-impact as Science or Nature or some of the top specialty journals, but it's definitely a journal that researchers are excited about publishing in if they can't get into the top tier. The fact that they're not part of Elsevier or one of the other big commercial publishers, and their open-access fee is very reasonable, is an added bonus. (Disclaimer: I've published there, so I'm not entirely unbiased.)
Now, as with any journal, knowing the right people always helps - sadly, this is true at any level.
Exactly. As a kid, I had a dog that understood when I threw a ball up on the roof of our garage, which caused it to disappear from her sight, that it would roll along the slope of the roof and and reappear further down the roofline. She actually got fairly good at predicting where the ball would reappear, repositioning herself along its path over time so she would meet it at its eventual drop point. Does that mean my dog understood calculus, or solved Newton's problem? Well, she recognized a pattern and was able to apply a repeatable solution.
That tells me that the brain is capable of recognizing complex patterns around us, and is actually already very capable of deriving and applying practical solutions. ("So easy a dog could do it.") Applying abstract mathematical models to them, however, is not so easy.
What I'd be most interested in in this whole saga is "what methods did his father use to teach him math?" Obviously they were highly effective.
John
The number of times I read rants against (maths) teachers for holding back students and then halfway through it they drop "just because I don't show my working!" bombshell.
Teachers are doing this for your benefit, not theirs. If you can hand in your homework with just the answers and get them all correct, great, but if you hand in the homework and get some wrong, the teacher won't have any idea where you went wrong, whether you used the wrong method when solving it or if you just made a simple error with the arithmetic. 99.9% of kids, even the ones who think they don't need to show their working because they know to do it, will at some pointstruggle with something and need help.
The UK exam system drills this into you pretty early, only 1 mark out of 3 or 4 being awarded for the correct answer, the rest being awarded for the method used. By the time you get to A-level (High school) maths, you're even given the answer beforehand and asked to "show that x = 5".
Ultimately the working out is usually more important in maths than the answer. You won't win a Fields medal for "Fermat's late theorem : it was correct. The end"