“No matter how far mathematics progresses and no matter how many problems are solved, there will always be, thanks to Gödel, fresh questions to ask and fresh ideas to discover. It is my hope that we may be able to prove the world of physics as inexhaustible as the world of mathematics… If it should turn out that the whole of physical reality can be described by a finite set of equations, I would feel disappointed.”
– F. J. Dyson. Infinite in all Directions. London: Penguin Books, 1990, p. 53.
The idea that Gödel’s logical insights might reflect deeply upon physics is fascinating. I am still working hard to wrap my cortex fully around the logic and the theorems but, as I understand it, applied in this context of physical laws this suggests that there would always be further and deeper iterations and recombinatory organisational constellations of physical models and theory. This strikes me as absolutely and utterly beautiful.