This life is no life that we have lived or that, on this planet, we could live. Music is as independent of the world as mathematics, but it cannot, like a system of geometry, even be applied to the real world as an hypothesis. It is even doubtful how far the emotions it expresses, when it is merely expressing emotion, correspond to those of real life. The sorrow of the bereaved father is not the same thing as the sorrow of the bereaved lover, but music can express sorrow with thousands of _nuances_. It is customary to say that the emotions of music are generalised emotions; that its sorrow, for instance, is a kind of common denominator of all sorrows. But the exact opposite seems to be the case. The situations of real life, like the resources of language, are probably too limited to afford correspondences to the immense variety of emotions expressible in music. The musician is as free as the non-Euclidean geometer to create worlds which have no objective counterpart. It is natural, therefore, in comparing the arts, that we should class mathematics and music together, since they resemble one another by their most intimate characteristics and differ, in these respects, from all other arts. It is worth noting, in this connection, that it is only in mathematics and music that we have the creative infant prodigy. Experience and learning, compared with what we vaguely call “instinct” or “gift,” play a comparatively insignificant rôle; the boy mathematician or musician, unlike other artists, is not utilising a store of impressions, emotional or other, drawn from experience or learning; he is utilising inner resources so obviously independent of experience that, like Plato’s slave, he seems to have brought them with him from some anterior life. And the artistic progress of a musician, if it be a true progress, means primarily that he is making ever more accessible the riches of this inner life. It is difficult to avoid mysticism, or at least Platonism, at this point. But here again it seems to us that Schopenhauer understood something essential. When he says that music, like the Platonic ideas, is an embodiment of the “Will” that underlies all things, he does at least say that what is revealed to us by a composition is something other than the “personality” of the composer. The function of music is not, like that of literature, to illuminate this world, but there is a world it illuminates--a world at least as vast and independent of this one as that mathematical “cosmos” described by Mr. Bertrand Russell.