Non-Computability and Intractability: Does It Matter to Physics?

Over the last sixty years there has been a stream of impossibility results from mathematics and theoretical computer science announcing undecidability, noncomputability, and intractability. Should these impossibility results be of concern to physics? Two of these impossibility results are discussed: Should noncomputability be of concern to physicists? Should intractability be of concern to physicists? The answers to these questions are influenced by which abstract model of computation is used. Physicists who have thought about this seem to favor the Turing machine model, but the real-number model might be more appropriate. Should physicists consider alternatives to the Turing machine model of computation?