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ings, inhuman or super-human, from the heart of an abstract science. I wonder, sometimes, whether the appreciators of art and of mathematical solutions are not even more closely allied. Before we feel an aesthetic emotion for a combination of forms, do we not perceive intellectually the rightness and necessity of the combination? If we do, it would explain the fact that passing rapidly through a room we recognise a picture to be good, although we cannot say that it has provoked much emotion. We seem to have recognised intellectually the rightness of its forms without staying to fix our attention, and collect, as it were, their emotional significance. If this were so, it would be permissible to inquire whether it was the forms themselves or our perception of their rightness and necessity that caused aesthetic emotion. But I do not think I need linger to discuss the matter here. I have been inquiring why certain combinations of forms move us; I should not have travelled by other roads had I enquired, instead, why certain combinations are perceived to be right and necessary, and why our perception of their rightness and necessity is moving. What I have to say is this: the rapt philosopher, and he who contemplates a work of art, inhabit a world with an intense and peculiar significance of its own; that significance is unrelated to the significance of life. In this world the emotions of life find no place. It is a world with emotions of its own. To appreciate a work of art we need bring with us nothing but a sense of form and colour and a knowledge of three-dimensional space. That bit of knowledge, I admit, is essential to the appreciation of many great works, since many of the most moving forms ever created are in three dimensions. To see a cube or a rhomboid as a flat pattern is to lower its significance, and a sense of three-dimensional space is essential to the full appreciation of most architectural forms. Pictures which would be insignificant if we saw them as flat patterns are profoundly moving because, in fact, we see them as related planes. If the representation of three-dimensional space is to be called "representation," then I agree that there is one kind of representation which is not irrelevant. Also, I agree that along with our feeling for line and colour we must bring with us our knowledge of space if we are to make the most of every kind of form. Nevertheless, there are magnificent designs to an appreciation
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