"You can have the reward," Oridin said. "Take him away. He's a nuisance."
They found Caddo in the lounge of Oridin's house chewing on a book of logarithms. His mind was gone. He could only babble figures. His fingers twitched with cramps from writing with a pencil and punching the keys of the calculating machine. Every spark of vitality had been taken from his body. The batteries of his force armor had burned out.
"What's the matter with him?" the captain asked.
"He wanted too much," Oridin replied. "I gave him a simple little formula for success, but the formula ceases to be simple as the definition for success grows more demanding. Had he sought perfection, Caddo would have seen that even this was unrecognizable, although the certainty was only halfway to infinity—"
"Sorry, Mr. Oridin, but I'm not a mathematician," the captain said.
"There's nothing difficult in the formula. It proves that certainty is unrecognizable. You'll have to admit that a goal, to be reached has to follow a path and that path is determined by two points. The beginning is one and the second one makes the ultimate objective certain. Therefore the second point is certainty. But certainty is unrecognizable—"
Oridin brought forth his formula and allowed the captain to read it. The patrol officer blinked his eyes and scratched his head. Oridin wrote his formula out:
J = (a + 1) times infinity/2
"J is certainty, a our starting point and 1 is unity, or perfection," Oridin explained. "Our starting point is close to zero, but not zero. But for convenience we'll say that it's a fraction so close that we can call it zero. Then certainty, J, is one-half of infinity, which you'll have to agree does not approach infinity and may be well within the realm of human comprehension, although we will not recognize perfection because we do not know what number is halfway to infinity. Caddo overlooked the fact that he went further and further into the transinfinite with each number he added to his equation, for there are an infinity of numbers between any two whole numbers and any two fractions and their sum is always infinity."
The patrol captain already was muttering to himself and Oridin hurried him out of the house and into the patrol ship with his prisoner.