Is this geometry ever realized? Strictly it is not the geometer's business to ask or answer this question. But research develops two viewpoints. There is always the man who indulges in the pursuit of facts for their sake alone, and equally the man who wants to see his new facts lead to something else. One great mathematician is quoted as enunciating a new theory of surpassing mathematical beauty with the climacteric remark "And, thank God, no one will ever be able to find any use for it." An equally distinguished contemporary, on being interrogated concerning possible applications for one of his most abstruse theorems, replied that he knew no present use for it; but that long experience had made him confident that the mathematician would never develop any tool, however remote from immediate utility, for which the delvers in other fields would not presently find some use. If we wish, however, we may inquire with perfect propriety, from the side lines, whether a given geometry is ever realized. We may learn that so far as has yet been discovered there are no elements for which all its postulates are verified, and that there is therefore no realization known. On the other hand, we may more likely find that many different sets of elements are such that the postulates can be interpreted as applying to them, and that we therefore have numerous realizations of the geometry. As a human being the geometer may be interested in all this, but as a geometer it really makes little difference to him.