After lunch the three and their guest went back to the clubhouse. Cargraves spent most of the afternoon spread over the bunk, telling stories of the early days at Oak Ridge when the prospect of drowning in the inescapable, adhesive mud was more dismaying than the ever-present danger of radioactive poisoning, and the story, old but ever new and eternally exciting, of the black, rainy morning in the New Mexico desert when a great purple-and-golden mushroom had climbed to the stratosphere, proclaiming that man had at last unloosed the power of the suns.
Then he shut up, claiming that he wanted to re-read the old H. Rider Haggard novel he had found. Ross and Morrie got busy at the bench; Art took a magazine. His eyes kept returning to his fabulous uncle. He noticed that the man did not seem to be turning the pages very often.
Quite a while later Doctor Cargraves put down his book. “What do you fellows know about atomics ?”
The boys exchanged glances before Morrie ventured to answer. “Not much I guess. High-school physics can’t touch it, really, and you can’t mess with it in a home laboratory.”
“That’s right. But you are interested?”
“Oh, my, yes! We’ve read what we could — Pollard and Davidson, and Gamov’s new book. But we don’t have the math for atomics.”
“How much math do you have?”
“Through differential equations.”
“Huh?” Cargraves looked amazed. “Wait a minute. You guys are still in high school?”
“Just graduated.”
“What kind of high school teaches differential equations? Or am I an old fuddy-duddy?”
Morrie seemed almost defensive in his explanation. “It’s a new approach. You have to pass a test, then they give you algebra through quadratics, plane and spherical trigonometry, plane and solid geometry, and plane and solid analytical geometry all in one course, stirred in together. When you finish that course- and you take it as slow or as fast as you like -you go on.”
Cargraves shook his head. “There’ve been some changes made while I was busy with the neutrons. Okay, Quiz Kids, at that rate you’ll be ready for quantum theory and wave mechanics before long. But I wonder how they go about cramming you this way? Do you savvy the postulation notion in math?”
“Why, I think so.”
“Tell me.”
Morrie took a deep breath. “No mathematics has any reality of its own, not even common arithmetic. All mathematics is purely an invention of the mind, with no connection with the world around us, except that we find some mathematics convenient in describing things.”
“Go on. You’re doing fine!”
“Even then it isn’t real- or isn’t `true’ -the way the ancients thought of it. Any system of mathematics is derived from purely arbitrary assumptions, called `postulates’, the sort of thing the ancients called `axioms.'”
“Your jets are driving, kid! How about the operational notion in scientific theory? No . . . Art-you tell me.”
Art looked embarrassed; Morrie looked pleased but relieved. “Well, uh . . . the operational idea is, uh, it’s building up your theory in terms of the operations you perform, like measuring, or timing, so that you don’t go reading into the experiments things that aren’t there.”
Cargraves nodded. “That’s good enough — it shows you know what you’re talking about.” He kept quiet for a long time, then he added, “You fellows really interested in rockets?”
Ross answered this time, “Why, er, yes, we are. Rockets among other things. We would certainly like to have a go at those junior prizes.”
“That’s all?”
“Well, no, not exactly. I guess we all think, well, maybe some day . . .” His voice trailed off.
“I think I see.” Cargraves sat up. “But why bother with the competition? After all, as you pointed out, model rockets can’t touch the full-sized commercial jobs. The prizes are offered just to keep up interest in rocketry — it’s like the model airplane meets they used to have when I was a kid. But you guys can do better than that — why don’t you go in for the senior prizes?”
Three sets of eyes were fixed on him. “What do you mean ?” Cargraves shrugged. “Why don’t you go to the moon with me?”