Brilliant piece on constraint equations. The way Gauss' law forces emergent paterns instead of just limiting possibilities is a counter-intuitive insight that most people miss. It's kinda like how rigidrules in music theory paradoxically create richer harmonic landscapes than total freedom would allow. Though I wonder if the holographic principle's implication for quantum gravity might mean constraint equations aren't just sculpting existing degrees of freedom but actually eliminating redundant ones entirely.
Brilliant piece on constraint equations. The way Gauss' law forces emergent paterns instead of just limiting possibilities is a counter-intuitive insight that most people miss. It's kinda like how rigidrules in music theory paradoxically create richer harmonic landscapes than total freedom would allow. Though I wonder if the holographic principle's implication for quantum gravity might mean constraint equations aren't just sculpting existing degrees of freedom but actually eliminating redundant ones entirely.
That latter point is an amazing insight, that’s what some people seem to find when applying holography in cosmology!