Authentic Science Fiction Monthly No. 46 — page 118: what you’re looking at

Machine-transcribed from the original scan — historical spelling and the odd misread are preserved.

HIGHER MATHEMATICS “Let us, for the moment, reconsider some of the theory that I have endeavoured to put before you during the course of my last two lectures. We have seen that the evidence obtained from counting the number of visible stars sug- gests that the umiverse, or space, as it is popularly termed, possesses a negative curvature, rather as the back of a saddle is curved. I shall not bother to run over the mathematical derivation of this finding again, since those of you who were here lasf time will, I hope, have followed the argument quite easily. “We also saw that, as a result of this negative curva- ture, the volume of space within a given radius from any point of reference is greater than would be the case if the space were uncurved.”’ Shifting his attention from the projector, the Professor perceived a glazed appearance about the eyes to left and to right. It was, he supposed, possible that some of his pupils had not taken the trouble to read the textbooks that he had recommended for study during the term. Should he repeat his explanation for the benefit of the glassy-eyed, or assume that all was well and proceed to the next point? 117 He compromised. “IT will ask you to accept, then, that if the space in a given region is negatively curved, then the real volume of that space will be larger than its apparent volume. Conversely, if the space is positively curved, then its real volume will be less than it appears to be.” Perhaps a little joke might establish rapport with his audience ? “If you buy a pint bottle of beer, you want to specify that the space inside the bottle is negatively curved, not positively.” It fell flatter than a two- dimensional pancake. He hurried on. “It follows, then, that if we could arrange for the space within a container to possess an infinite negative curvature, then the real volume of that container would necessarily be infinite. This, ladies and gentlemen, is precisely what I have done, and what I hope to demonstrate to you this morning.” The scales could practically be heard falling from the eyes of the occupants of all the rows, front, middle, and back. The nervous student with the Moebius blotting paper tore it comicloooks.conm