The scientist looked so inexpressibly gloomy as he offered this conclusion that a pall of hopelessness settled over Weinbaum in sheer sympathy. “You don’t look as if you expected that to uncover anything new.”
“I don’t. You see, Robin, things are different in physics now than they used to be in the twentieth century. In those days, it was always presupposed that physics was limitless the classic statement was made by Weyl, who said that ‘It is the nature of a real thing to be inexhaustible in content.*
We know now that that’s not so, except in a remote, associational sort of way. Nowadays, physics is a defined and self-limited science; its scope is still prodigious, but we can no longer think of it as endless.
“This is better established in particle physics than in any other branch of the science. Half of the trouble physicists of the last century had with Euclidean geometryand hence the reason why they evolved so many recomplicated theories of relativityis that it’s a geometry of lines, and thus can be subdivided infinitely. When Cantor proved that there really is an infinity, at least mathematically speaking, that seemed to clinch the case for the possibility of a really infinite physical universe, too.”
Wald’s eyes grew vague, and he paused to gulp down a slug of the licorice-flavored aquavit which would have made Weinbaum’s every hair stand on end.
“I remember,” Wald said, “the man who taught me theory of sets at Princeton, many years ago. He used to say: ‘Cantor teaches us that there are many kinds of infinities. There was a crazy old mani’ “