He stared at them for a long time, his lips moving occasionally, as though he were doing some rough calculations in his head. Finally, he said, without lifting his eyes, "What's Bliss doing?"
"Sleeping, old chap," said Pelorat. Then, defensively, "She needs sleep, Golan. Maintaining herself as part of Gaia across hyperspace is energy-consuming."
"I suppose so," said Trevize, and turned back to the computer. He placed his hands on the desk and muttered, "I'll let it go in several Jumps and have it recheck each time." Then he withdrew them again and said, "I'm serious, Janov. What do you know about psychohistory?"
Pelorat looked taken aback. "Nothing. Being a historian, which I am, after a fashion, is worlds different from being a psychohistorian. Of course, I know the two fundamental basics of psychohistory, but everyone knows that."
"Even I do. The first requirement is that the number of human beings involved must be large enough to make statistical treatment valid. But how large is 'large enough'?"
Pelorat said, "The latest estimate of the Galactic population is something like ten quadrillion, and that's probably an underestimate. Surely, that's large enough."
"How do you know?"
"Because psychohistory does work, Golan. No matter how you chop logic, it does work."
"And the second requirement," said Trevize, "is that human beings not be aware of psychohistory, so that the knowledge does not skew their reactions. But they are aware of psychohistory."
"Only of its bare existence, old chap. That's not what counts. The second requirement is that human beings not be aware of the predictions of psychohistory and that they are not-except that the Second Foundationers are supposed to be aware of them, but they're a special case."
"And upon those two requirements alone, the science of psychohistory has been developed. That's hard to believe."
"Not out of those two requirements alone, " said Pelorat. "There are advanced mathematics and elaborate statistical methods. The story is-if you want tradition-that Hari Seldon devised psychohistory by modeling it upon the kinetic theory of gases. Each atom or molecule in a gas moves randomly so that we can't know the position or velocity of any one of them. Nevertheless, using statistics, we can work out the rules governing their overall behavior with great precision. In the same way, Seldon intended to work out the overall behavior of human societies even though the solutions would not apply to the behavior of individual human beings."
"Perhaps, but human beings aren't atoms."
"True," said Pelorat. "A human being has consciousness and his behavior is sufficiently complicated to make it appear to be free will. How Seldon handled that I haven't any idea, and I'm sure I couldn't understand it even if someone who knew tried to explain it to me-but he did it."
Trevize said, "And the whole thing depends on dealing with people who are both numerous and unaware. Doesn't that seem to you a quicksandish foundation on which to build an enormous mathematical structure? If those requirements are not truly met, then everything collapses."
"But since the Plan hasn't collapsed-"
"Or, if the requirements are not exactly false or inadequate but simply weaker than they should be, psychohistory might work adequately for centuries and then, upon reaching some particular crisis, would collapse-as it did temporarily in the time of the Mule. Or what if there is a third requirement?"
"What third requirement?" asked Pelorat, frowning slightly.
"I don't know," said Trevize. "An argument may seem thoroughly logical and elegant and yet contain unexpressed assumptions. Maybe the third requirement is an assumption so taken for granted that no one ever thinks of mentioning it."
"An assumption that is so taken for granted is usually valid enough, or it wouldn't be so taken for granted."
Trevize snorted. "If you knew scientific history as well as you know traditional history, Janov, you would know how wrong that is. But I see that we are now in the neighborhood of the sun of the Forbidden World."
And, indeed, centered on the screen, was a bright star-one so bright that the screen automatically filtered its light to the point where all other stars were washed out.
32.
FACILITIES for washing and for personal hygiene on board the Far Star were compact, and the use of water was always held to a reasonable minimum to avoid overloading the recycling facilities. Both Pelorat and Bliss had been sternly reminded of this by Trevize.
Even so, Bliss maintained an air of freshness at all times and her dark, long hair could be counted on to be glossy, her fingernails to sparkle.
She walked into the pilot-room and said, "There you are!"
Trevize looked up and said, "No need for surprise. We could scarcely have left the ship, and a thirty-second search would be bound to uncover us inside the ship, even if you couldn't detect our presence mentally."
Bliss said, "The expression was purely a form of greeting and not meant to be taken literally, as you well know. Where are we? And don't say, 'In the pilot-room.' "
"Bliss dear," said Pelorat, holding out one arm, "we're at the outer regions of the planetary system of the nearest of the three Forbidden Worlds."
She walked to his side, placing her hand lightly on his shoulder, while his arm moved about her waist. She said, "It can't be very Forbidden. Nothing has stopped us."
Trevize said, "It is only Forbidden because Comporellon and the other worlds of the second wave of settlement have voluntarily placed the worlds of the first wave-the Spacers-out of bounds. If we ourselves don't feel bound by that voluntary agreement, what is to stop us?"