WHAT LIES BEYOND THE MOUNTAINS?

Up to Turing power, all computations are describable by suitable programs, which correspond to the prescription by finite means of some rational parameters of the system or some computable real numbers. From Turing power up we have computations that are not describable by finite means: computation without a program. When we observe natural phenomena and endow them with computational significance, it is not the algorithm we are observing but the process. Some objects near us may be performing hyper-computation: we observe them, but we will never be able to simulate their behaviour on a computer. What is then the profit of such a theory of computation to Science?