Can NP-complete problems be solved efficiently in the physical universe?
I survey proposals including soap bubbles, protein folding, quantum
computing, quantum advice, quantum adiabatic algorithms,
quantum-mechanical nonlinearities, hidden variables, relativistic time
dilation, analog computing, Malament-Hogarth spacetimes, quantum
gravity, closed timelike curves, and "anthropic computing." The section
on soap bubbles even includes some "experimental" results. While I do
not believe that any of the proposals will let us solve NP-complete
problems efficiently, I argue that by studying them, we can learn
something not only about computation but also about physics.