Page:Popular Science Monthly Volume 58.djvu/274

266 actual measurement departs from two right angles, the fact of the non-Euclidean character of our space would be established at once. But no such triangle has been discovered. Even the largest, which are concerned in the measurement of stellar parallax, do not help us, and it does not seem possible to get larger ones. Nevertheless Clifford and others have shown that some physical phenomena, which require the conception of elaborate and complex machinery for their explanation, are capable of very simple explanation upon the hypothesis of a fourth dimension. Then, too, in the domain of pure mathematics several phenomena find a ready explanation upon the basis of such an assumption. In the theory of curves we constantly make use of the assumption that a curve may return into itself after passing through infinity, which is only another aspect of the same hypothesis. In fact, without this aid our processes of generalization, so important to the development of modern geometry, would be sadly hampered. Professor Newcomb has carried this matter to its logical conclusion and has deduced the actual dimensions of the visible universe in terms of the measurement of curvature in the fourth dimension. In such a space it becomes actually possible for a curve with infinite branches to pass through infinity (so-called) and return into itself. Upon this hypothesis our universe is unbounded in the sense that however far we travel we can never reach its limits, for it has none, but it is not infinite. Just as we can travel forever on the surface of the earth without reaching any limits, but that surface is not infinite. But even supposing that all this is true, the question still presses home: What is beyond?