Drawing inspiration from physics, he thinks of rational solutions to equations as being somehow the same as the path that light travels between two points.
What does this even mean? This looks like fancy words for "Kim used lines in his solution".
The earlier article that the article links to says a bit more about this. It's still pretty far from concrete, but it does say a bit more. When they talk about the path that light travels between two points, they're talking about the principle of least action.
Going by the earlier article, the idea seems to be roughly like the following. You associate to each point the fundamental group based on that point. All these fundamental groups then live in some larger space, and the ones based at rational points will minimize some quantity analogous to action (or, if we're thinking of light, time).
That's basically the best I can figure just based on the earlier article.
It's something like, (and please don't try too hard to understand my description here, I watched the video over a year ago, and you've got Feynman at the link) imagine a photon is a particle going in all directions, and has an arrow inside it spinning at a rate of 10^15 revolutions per second, and the probability that light goes from its origin to a particular destination is the amplitude of the sum of all the internal arrows of the all the possible paths between the origin and the destination.
Even if this is not what the article is referring to, its a reminder that for a lot of people, light doesn't move in straight lines.
Finally, the series linked series of lectures are amazing, if you have a layperson's interest in Physics then this will take your knowledge to a new level.
Maybe it means something along the lines of "instead of thinking of those equations as curves in a flat space, he thinks of them as lines in a curved space". Disclaimer, I know nothing about number theory.
Comments
What does this even mean? This looks like fancy words for "Kim used lines in his solution".
The earlier article that the article links to says a bit more about this. It's still pretty far from concrete, but it does say a bit more. When they talk about the path that light travels between two points, they're talking about the principle of least action.
Going by the earlier article, the idea seems to be roughly like the following. You associate to each point the fundamental group based on that point. All these fundamental groups then live in some larger space, and the ones based at rational points will minimize some quantity analogous to action (or, if we're thinking of light, time).
That's basically the best I can figure just based on the earlier article.
Maybe its referring to the way Feynman describes light travelling, for example in this lecture.
https://www.youtube.com/watch?v=kMSgE62S6oo
It's something like, (and please don't try too hard to understand my description here, I watched the video over a year ago, and you've got Feynman at the link) imagine a photon is a particle going in all directions, and has an arrow inside it spinning at a rate of 10^15 revolutions per second, and the probability that light goes from its origin to a particular destination is the amplitude of the sum of all the internal arrows of the all the possible paths between the origin and the destination.
Even if this is not what the article is referring to, its a reminder that for a lot of people, light doesn't move in straight lines.
Finally, the series linked series of lectures are amazing, if you have a layperson's interest in Physics then this will take your knowledge to a new level.
This is just another guess, but it might refer to something of this nature: http://www.analyzemath.com/calculus/Problems/minimum_distanc...
Maybe it means something along the lines of "instead of thinking of those equations as curves in a flat space, he thinks of them as lines in a curved space". Disclaimer, I know nothing about number theory.