What is this Newton unsolved problem?

[davey2222]

http://www.foxnews.com/world/2012/05/27/german-teen-solves-300-year-old-mathematical-riddle-posed-by-sir-isaac-newton/

 

Does anyone know what is this problem that was unsolved for 300 years, and the other part about 'bouncing' problem?

[D H]

It's bad science reporting bouncing around from one media outlet to another with no one checking the facts. This story is all over the media (just search for it at news.google.com). Fox is just late in the copying game here.

 

The first problem is that of a ballistic trajectory with quadratic drag, [imath]\ddot{\vec x} = -\kappa ||\dot{\vec x}||\, \dot{\vec x} + \vec g[/imath]. This is known not to have a closed form solution in the elementary functions. Just because a problem doesn't have a closed form solution doesn't mean it isn't solvable. Kepler's problem (the elliptical orbit of a planet) does not have a closed form solution. Most real-world problems don't have a closed form solution. This particular problem has been solved over and over again. Calculating ballistic trajectories was one of the key factors that motivated the development of digital computers in the 1940s.

 

The student claimed to have found "the first fully analytic solution of a long unsolved problem." He didn't. He instead expressed the solution as a ratio of infinite series. That's a variation on a standard freshman calculus trick: Turn everything into an infinite series. Someone should have told this student that an infinite series representation doesn't count as an analytic solution. Someone should have told the news media not to add even more hyperbole to the story.

Edited May 30, 2012 by D H

[davey2222]

Thanks.

[Brent]

I haven't been able to track down the kid's actual solution yet, so all I have to go on is what you've said. The method you described would be the power series method or Forbenius method, which is used all over the place for things like orthogonal polynomials (Legendre polynomials, Laguerre polynomials, Bessel functions, etc.). Is there something more to his solution? Could you please provide a link to his work?

[D H]

There is no link to his work. This was a competition for high school age kids. There is no publication of his results.

 

There is an image:

http://m.static.newsvine.com/servista/imagesizer?file=boyle6DB47079-0C04-F6B6-85A6-C21F964A3A06.jpg&width=600

<Aside: What is this BS: I am "not allowed to use that image extension on this board"? Oh well. You can click the link.>

 

This is a known result. It's also not that useful. It's for velocity rather than position, and it's implicit rather than explicit. He also offered a solution for position, but this was in terms of a series. Neither solution is not a closed form solution in the elementary functions. There are tons of problems that cannot be expressed as closed form solutions in the elementary functions. This is one of them. This particular problem, is not an unsolved mystery.

 

The above image is from Alan Boyle's Cosmic Log, http://cosmiclog.msnbc.msn.com/_news/2012/05/28/11920006-16-year-olds-equations-set-off-buzz-over-325-year-old-physics-puzzler. Alan Boyle is one of the very few reporters who got this story correct.

 

Wikipedia is another place that got this story correct. The wikipedia entry on Shouryya Ray has been deleted. Here's the discussion on the vote to delete: http://en.wikipedia.org/wiki/Wikipedia:Articles_for_deletion/Shouryya_Ray, and here are a couple of blog articles by a wikipedia editor on this subject: http://thorehusfeldt.net/2012/05/29/shouryya-ray-and-the-press/ and http://thorehusfeldt.net/2012/06/05/shouryya-ray-closing-remarks/.

 

Part of the problem stems from Shouryya Ray's initial misinterpreting "not solvable in the elementary functions" to mean "unsolvable". For example, [imath]\int_0^x \exp(-(t^2))\,dt[/imath] is not solvable in the elementary functions. That doesn't mean it's unsolvable, period. Big difference.

 

A much bigger part of the problem stems from very bad reporting. Reporters for the most part are drooling idiots when it comes to science, math, and technology.

Edited June 6, 2012 by D H

[veritaz]

Reporters provided information about an event that happened but not necessarily how it happened so whatever detail that we need to know is murky. This in part showed why you placed them as drooling idiots. It is up to the experts and those in charged of following up the said report and place it in a proper tangent to define the detail.

 

Information that we received daily today whether we need or not are massive in scale and the average person simply could not absorb all the 'clutters' as they go about what to do with 'this and 'that' and often provide negative response or lack of interest of that information, what was known as junk. It's about how much attention that information will get.

 

Until someone highlight that information, for example and just an example, in the headline of 'The truth about Blackhole', be in the proper place and time because what we know and already knew is biased since our immediate concern is WHO presented this information, thus, by personally confirmed on the issue until we delve deeply upon it. It's really up to the informed, skilled and educated person to provide more workable solving solution, if there is.