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Even the concepts of “places”, “paths”, “action”, “distance” (and, for that matter, “two”) are ultimately just mathematical abstractions. The fact that we privilege some abstractions as more “real” than others is a byproduct of familiarity, not fundamentality.

Common misconception. Newtonian gravity (no spacetime) *also* allows a massless particle to be affected by gravity: in 1801, von Soldner calculated the trajectories of such particles by taking limits as M->0. Interestingly, the deflection is exactly half that predicted by GR.

Alright, NYC peeps: a few of us (∞-modal, Phoebe Klett, etc.) are planning to meet up in Central Park next weekend - probably Sunday, weather permitting - to do some recreational math, discuss our favorite problems/theorems, etc. If you're interested, let me know ASAP!

Proof of concept that high-resolution, shock-capturing methods can indeed be used to solve the (vacuum) Einstein equations in a stable fashion. Simulating a binary black hole inspiral using a novel, modified form of the first-order, flux-conservative Bona-Massó equations.

“Modified gravity” is a psyop. Everything* is general relativity if you violate enough energy conditions. * assuming your metric is at least twice differentiable

Many happy returns to the inventor of my favorite geometry, my favorite coordinate system, *and* my favorite class of metric perturbations. Truly a legend.

This is precisely why one should go easy on oneself about procrastinating on writing. If there’s resistance, it’s not (necessarily) laziness: it may well be that you just don’t quite have things straight in your head yet. Keep thinking. It’ll come.