The Emperor's New Mind

according actually algorithm amplitude answer Argand plane argument atoms behaviour big bang binary black hole brain calculation Chapter classical complex numbers complicated concept consciousness consider cortex described device digits direction effect Einstein's electron energy entropy equations Euclidean example fact field finite formal system geometry Gödel gravitational Hamiltonian Hilbert space idea infinite initial kind light cone linear superposition low entropy Mandelbrot set mathematician measurement momentum motion natural numbers neuron Newtonian normally notation objects observer operation particle particular perhaps phase space photon physical physicists picture position precise principle probability problem procedure propositions quantum mechanics quantum theory question real numbers recursively enumerable referred region relativity Riemann sphere Schrödinger's equation second law seems sense simply slits space-time special relativity spin square state-vector strong AI suppose tape theorem things tiles Turing machine Turing test universe vector viewpoint wavefunction WEYL world-lines