Wednesday, April 13, 2016

An 8-dimensional and then a 24-dimensional analog of Kepler's sphere-packing conjecture, widely believed to be true (and actually used for error-correcting codes), were proven true last month, with the major breakthrough due to Maryna Viazovska. (Hales proved the original conjecture in the 1990s.) I noticed that the paper on dimension 24 has Abhinav Kumar as a coauthor. On my dorm floor way back when, Abhinav was a "greater math god" and I was a "lesser math god."

P.S. Why does that paper talk of "+1 eigenfunctions"? What's wrong with "fixed point"?

Thursday, April 07, 2016

In the asymptotically safe gravity proposal, quantum gravity is weaker at high energies. In this proposal, gravity is both weaker and less quantum (meaning the effective Planck length (but not the Planck mass) is smaller) at high energies.

Imagine that "everybody wins" mathematically, i.e., it is proven there are elegant mathematical models consistent with observation and unifying all of fundamental physics, including an asymptotically safe gravity model, a string theory model, loop quantum gravity model, maybe other models I don't want to take the time to mention, and maybe even an "unquantizing" model like in the link. Which theory will win the parsimony contest? Since parsimony is not the same as mathematical elegance or beauty, I'm not confident that the most parsimonious theory will also become most popular.