https://www.youtube.com/watch?v=tRaq4aYPzCc
There's a strange number system, featured in the work of a dozen Fields Medalists, that helps solve problems that are intractable with real numbers. Head to...
P-adics
Having watched this and Numberphile’s explanation, I was pretty intrigued about how this may be applied to other problems. As I understand it, seems like the ability to restrict the search field to rational solutions could be extremely helpful for areas of research where continuous distributions are applied to necessarily discrete outcomes, especially in terms of saving compute resources and processing larger data sets.
Anybody have insight about how this performs computationally? Benchmarking “simple problems” like the one in the video? Numerical instability?
Disclaimer, not a math guy, so maybe this is a nonsense idea and I’ve misunderstood something along the way.
I watched this when it came out a few weeks ago and I just could not follow along. I'm a bit ashamed about since I use math for a living, and since I've taken and done well in done graduate level physics courses, including electricity and magnetism. But I just do not understand anything more than looking at the numbers to the left of the decimal rather than to the right. But all of the formalism just whizzed right by.
I watched this when it came out a few weeks ago and I just could not follow along. I'm a bit ashamed about since I use math for a living, and since I've taken and done well in done graduate level physics courses, including electricity and magnetism. But I just do not understand anything more than looking at the numbers to the left of the decimal rather than to the right. But all of the formalism just whizzed right by.