[SGVLUG] Teenager solves Newton dynamics problem

[Dustin Laurence]

On 05/29/2012 02:07 AM, Steve M Bibayoff wrote:
>
> Thought it was interesting. Need to follow the links to see original
> story, which doesn't give much details. But the problem is here:
> Teenager solves Newton dynamics problem
> http://math.stackexchange.com/questions/150242/teenager-solves-newton-dynamics-problem-where-is-the-paper

That mostly says that it's overblown by the media, which I suppose is to 
be expected.  It's like tree squirrels reporting about nuclear physics. 
  Exceptionally stupid tree squirrels.

If that's remotely accurate, it was very clever mathematics, but not 
Earth-shaking or terribly relevant to physics.  One of the better 
comments points out that a closed-form solution that requires numerical 
evaluation to do anything with is no more useful than simply solving the 
differential equations numerically.  True, and in fact it can be much 
less useful because we know an enormous amount about solving DEs. 
Directly attacking the equation of motion of a system is the general 
technique that "always works," can be approximated and manipulated in 
various ways, and so on.

Exact solutions are more important in a field like General Relativity 
mainly because the numerical treatment is obscenely hard, hard as in 
simply could not be done when I was a grad student.  (To give you 
computer people a flavor of why that's so, consider the fact that to do 
GR numerically you must evolve the coordinate system as part of the 
equations of motion, and that that evolution generically goes degenerate 
so that the numerical representation of perfectly finite quantites 
diverges.)  Newtonian dynamics is more sane, and my guess (and 
definitely only a guess) is that his solution is much harder to work 
with than the equation of motion.

N.B.: I didn't try to follow the mathematics myself, so I'm simply 
summarizing bits of the thread.

The lone genius beating the establishment is a cultural meme, and the 
media is a slave to the lens they peer through.

Dustin