Over the past decade Kim has described a very new way of looking for patterns in the seemingly patternless world of rational numbers. He’s described this method in papers and conference talks and passed it along to students who now carry on the work themselves. Yet he has always held something back. He has a vision that animates his ideas, one based not in the pure world of numbers, but in concepts borrowed from physics. To Kim, rational solutions are somehow like the trajectory of light.


Thinking about how physics, basically reality, is connected to an abstraction like mathematics or computer science can be pretty mind-blowing.

My absolute favorite mind-blower is computation. There are several wildly different models of computation computation works, but they're all equivalent to each other: they do the same thing, they have the same limits. The limits of what can be computed are built into the universe – computation is a property of reality.

Considering that the whole concept of doing what we do with mathematics is built into our cosmology, and that mathematics is the only tool we have for it, it's not all that surprising this link was found. Is it an artifact of some deeper structure, or "just" a sort of byproduct of how we've done physics so far?

posted by rrrrr: 84 days ago