"Don't be so down in the mouth about it. You've got me convinced there is an answer; let's figure out how to find it. In the first place the three natural radioactive series are out, aren't they?"
"Yes — at least we had agreed that all that ground had been fully covered before."
"O.K.; we have to assume that previous investigators have done what their notes show they have done — otherwise we might as well not believe anything, and start checking on everybody from Archimedes to date. Maybe that is indicated, but Methuselah himself couldn't carry out such an assignment. What have we got left?"
"Artificial radioactives."
"All right. Let's set up a list of them, both those that have been made up to now, and those that might possibly be made in the future. Call that our group — or rather, field, if you want to be pedantic about definitions. There are a limited number of operations that can be performed on each member of the group, and on the members taken in combination. Set it up."
Erickson did so, using the curious curlicues of the calculus of statement. Harper nodded. "All right — expand it."
Erickson looked up after a few moments, and asked, "Cal, have you any idea how many terms there are in the expansion?"
"No — hundreds, maybe thousands, I suppose."
"You're conservative. It reaches four figures without considering possible new radioactives. We couldn't finish such a research in a century." He chucked his pencil down and looked morose.
Cal Harper looked at him curiously, but with sympathy. "Gus," he said gently, "the bomb isn't getting you, too, is it?"