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ssss1 The Turing machine

All the calculations of the values of numerical functions are thus based on the design of Turing machines. We define a general function on a given problem and its effective calculation amounts to defining the set of Turing machines which will represent it.

However, we can proceed in a much more general way by using the differential equations of mathematics. In this framework, we first define functions and constants specifying the elements in relation in a physical system describing a natural phenomenon and we place these functions in differential equations representing the spatial–temporal relations between the observable elements of the phenomenon. We then seek the solutions of these differential equations giving the values of the functions and thus giving the solution of the problem of the relations and movements by comparing with the results of the physical observation to validate the equations. However, this problem does not always offer a good solution in fundamental physics which uses differential equations and partial differential equations representing the relations between the functions which are the characters of the studied problem, because the solution of these equations, if they are indeed calculable, is not always in agreement with the experimental measurements.