Dr. Klaus Wasterno went to Captain Luce in his quarters and said, “I must understand more clearly the mechanics of the changes in course.”
Luce propped himself up on one elbow. “Why?”
“Because I think I know what they do in that ship that follows us, captain. And if I know clearly what they do, then we can take a further step and they cannot catch us.”
“Stick to your arithmetic, doctor. I’m commanding this ship.”
Doctor Wasterno beamed jovially. “It occurred to me that certain appreciation would accrue to the first commander to successfully evade the Gaice when trapped.”
Luce was immobile for long seconds. “Have you got something?”
“First tell me one thing. While in superspace our course is irregular, but speed is constant. And I know that the course pattern for the superspace period is set in advance. But how is that done?”
“We assume superspace to be three-dimensional for the purpose of our evasive action. So we take one of the tapes and punch it at random with a stylus and feed it to the automatic pilot. As each hole in the random tape reaches the pilot beam light shines through onto the plate and sends us off in a random direction at a previously unknown angle. There is no chance of a pattern, you see.”
“This is a problem, captain, in infinities and also in the theory of randomness. I suspect your method is no good.”
Luce scowled.
“It was devised by some of your people, doctor.”
“It fails to work, thus it must be no good. That is a starting point. If we were dealing with a weak infinity, aleph sub zero, a number progression, they should catch us in minutes. For a stronger infinity, aleph sub one, such as the points within a cube, it should take them longer, but they should be able to solve the problem. But here we are dealing with the strongest infinity yet known, aleph sub two, the diversity of geometric forms, and if it were completely random they should never anticipate or catch us at all. Mathematically I can prove that it is impossible for them to catch us if the evasive tactics are random in the pure sense. Thus there is pattern. When we find the cause of the pattern, we know how to avoid making that pattern.”
“It’s definitely random,” Captain Luce said.
“Have you a record of what evasive action we have taken?”
“Certainly. On the automatic log, expressed in numerical terms. Angles and degrees from the established reference point — Sol.”
“I must look at those figures. And you must do one thing to give me time to learn what I must learn. Have three persons prepare the next tape. The first to punch not very many holes and the second more and the third to fill the tape.”
“That doesn’t make sense,” Luce objected.
“Captain, if you would just do it—”
“All right, all right!”
The lack of integral calculators forced Wasterno to select the simplest possible relationship to prove his point. He decided that the interval, the frequency of the shift from super-space would give the best results when plotted.
In twenty hours he was satisfied with what he had discovered. He took his chart to Captain Luce. He had drawn it in the form of a frequency distribution. The curve was regular.
Luce took it. “What’s all this?” Fane and Holzer moved inconspicuously closer. They looked over the captain’s shoulder at the chart.
Wasterno took on a lecturer’s mannerisms. “As the shift from superspace to objectivity is instantaneous we can assume that we have a problem on the same order as determining the number of points in a line. An aleph sub one infinity. This tabulation resulted from the tapes that you yourself prepared in what you thought was a random fashion, captain. If it were truly random there would be no discernible pattern. Now assume that on the Gaice ship they have prepared such a curve, that they have automatic equipment which will produce within itself this sort of curve and advise of the greatest possibility. You see here that the greatest probability, with you preparing the tape, would be an interval of one hour, seventeen minutes and eleven point eight six three seconds. If I were on the Gaice ship I would adjust my own pattern to this chart with a greatly increased probability of anticipating the evasive movement of this ship.”
“But I punched the tape at random!” Luce complained.
“You thought you did. Evidently the act of punching a tape at random is impossible for a human. You punch with certain individual characteristics that can be sorted out, in much the same way as it is impossible for you to completely disguise your handwriting. I used the simplest relationship. I believe they can also detect the greatest probability in the new courses selected. Once the fact of individual detectable patterns’ is admitted, it is not difficult to see how a relatively simple electronic calculator could consistently correct for each new datum and be so geared to the drive of their ship that their course would be automatically set for the greatest probability of duplicating our next move.”
Luce’s jaw tightened. “Then the answer is to have all seven of us prepare the tapes. Destroy the pattern. We’ll try that and see if it works.”
“It will work well for a time,” Wasterno said, “because It will give their equipment a flood of new data to absorb and correlate, but sooner or later their equipment will discover a pattern in tapes made by the seven of us. It is inescapable. It will make their task more difficult, but not impossible, as we cannot avoid, even with seven working together, a pattern which will be the result of the amalgamation of our individual patterns. But I suggest we do it until we can discover some way of punching the tape which will be purely and mechanically random.”
“Dice are supposed to be pretty random,” Holzer said.
Wasterno thought that over. “No. We can’t measure them accurately enough for precision. And they might have to be rolled ten thousand times before we’d find a deviation from randomness based on some tiny inaccuracy In weight or dimension. Their equipment would find such a flaw before we did.”
Luce, sour and embittered, was retired eight years later with his unchanged rank of commander. Fane was killed in that vast and indecisive battle which so weakened the Gaice that they withdrew to their home galaxy. Dr. Klaus Wasterno died on the return trip of the Oberlin from the 23rd Island Universe, his heart weakened by the strain of eluding, for the first time, a Gaice pursuit. What happened to Cantor and Simmins is not known. Lorrky is in command of a light scout ship which makes periodic patrols with impunity deep Into Gaice-held space.
Oddly enough, it was Holzer who was honored. On Corinthia there is a heroic bronze statue which shows Holzer on one knee, crumpled currency in his left hand, a wry smile on his rugged face as he looks down at the small ivory cubes in front of him.
The principle, of course, as stated in Wasterno’s report, is that there is no discernible pattern and thus a complete randomness in any numerical listing obtained by using any device which selects a digit by chance and then is not used again for any other digit in the listing.
It is laughable to think of those seven men making, throwing, melting and recasting those thousands upon thousands of dice so as to obtain the random ten-digit numbers which, translated into direction and interval, were then punched on the escape tape.
Now, of course, it is a simple matter for Captain Lorrity once pursuit starts. The process Is completely automatic and so geared to the drive that even the tape has been discarded.