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The concepts of correspondence and commensurability are studied in the light of the Compton effect. We compare the Compton formula for the photon-electron scattering with another derivation in which the electron is considered as a non-relativistic particle. Although based on a less general theory, the second derivation leads to a formula which seems to be more general than the original Compton scattering formula. We show that this generality is only apparent. This circumstance means that the inclusion of additional terms does not necessarily imply more generality. We discuss some difficulties with the concepts of commensurable theories and correspondence, in particular those involving the passage from one theory into another through the concept of a limit of mathematics. We conclude that the problem goes beyond the mere mathematical limit.

This paper concerns the competition among scientifical research programmes. Two different historical moments are considered.  The first moment concerns some aspects of Cartesian, Leibnizian and Newtonian sciences and the second one concerns some aspects of Bohr's and Einstein's conceptions of natural philosophy. In both cases, the categories od space, time and cause constitute the underlying fundamental concepts. Possible similarities and differences between both moments are also explored. It is stressed that the real development of science incorporates, in a very intricate way, conceptions of rival scientific research programmes. Science is much more complex and interesting than simply to say that "this works" or "this does not work".

Einstein said [1] the most incomprehensible thing about the world is that it is comprehensible". On the other hand Bohr wrote [2] "...I advocated a point of view conveniently termed complementarity, suited to embrace the characteristic features of individuality of quantum phenomena, and at the same time to clarify the peculiar aspects of the observational problem in the field of experience. For this purpose, it is decisive to recognize that, however far the phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms".