And quantum theory, with all its now-you-see-it now-you-don't peekaboo elements? He was just as comfortable with that. His brain could now handle everything from Lukasiewicz's three-valued logic, to Reichenbach's infinite-valued logic with its continuous range of truth-values.
Tally permitted himself the luxury of one final test. He turned his mind to Russell's statement of the granddaddy of all true/false problems: "A barber in a certain village shaves all those, and only those, who do not shave themselves. Does the barber shave himself?"
Well, if he doesn't shave himself, then since he shaves everyone who doesn't shave himself, he shaves himself. On the other hand, if he shaves himself . . .
E.C. pursued the endless logical trail, on through the theory of types, meta-set theory, and fuzzy logic. It ate up idle time in a pleasant manner. Only the greater pleasure of a call from Julian Graves could exceed it.
"Tally, I know you are eager to leave, but I have kept you here because I have a task for you."
At last
. After a full day of idleness. Tally switched his circuits from background to turbo mode. "I am ready."
"This will involve colossal amounts of computation. It will possibly exceed your resources."
"We shall see."
Tally was merely being polite. Of course, it had come nowhere close to straining his capabilities. The amount of calculation was gigantic, but he had it completed, checked, and re-checked in a few hours. Now, surely, he would be allowed to leave.
But no. Once again he was obliged to sit in stand-by mode, this time for an even longer period. At last the second call came.
"The results that you provided are most satisfactory. Are you still prepared for departure?"
"I am completely ready. My ship is also ready." In fact, I have been ready for days, while you have brooded over the doings of Professor Lang and Captain Rebka and the results that I gave you. Tally kept the last sentence to himself—another of the many improvements installed in his new embodiment.
"Then you may proceed with your mission. Good luck, and do not forget to keep me informed as to whatever you may discover."
Do not forget
. As though an embodied computer ever would or could forget. "I will keep you informed."
Tally took the final steps to free his own ship, the
Tally-ho
, from its magnetic bonds to the
Pride of Orion
. As he did so, it occurred to him that his current embodiment was perfect, in that it could not be improved.
In a sense he was correct. It could not be improved, because no one had ever managed to define good judgment, still less create a working algorithm to provide it.
Tally had not wasted time while Julian Graves kept him tied to the
Pride of Orion
's apron strings. For three full days he had studied the stellar system to which their last Bose transition had brought them, working with unmatched speed and focus, endless patience, and the powers offered by his new ability to handle multi-valued logic systems.
The members of the expedition party from the Orion Arm were all in full agreement: they had not chosen this destination. It had been fed to them as Bose network coordinates, derived from the log of the Chism Polypheme's ship. When they arrived at an obviously dead system, everyone said, Oh, that's so typical of a Polypheme. It lied, they always lie. But suppose that the Polypheme had lied, and at the same time told the truth? Then in that case the stellar system to which they had come was both the wrong place to find the Marglotta home world, and at the same time the right place.
E.C. could live with that notion. When the
Tally-ho
pulled away from its docking he knew exactly where he wanted to go. Of course, he would eventually head for the edge of the dark zone, just as he had said he would, and hope in that way to arrive at the world of the Marglotta. Before taking his leave, however, there were points of interest right here in this system.
One of them was Iceworld, but Professor Lang had already staked her claim to that. Tally had read every report beamed back from the
Savior
, and he questioned Lang's assessment that no matter what had been done to it recently, the big, hollow world had begun as a Builder artifact. Unlike everyone else on the
Pride of Orion
, he did not reject Darya Lang's idea of a second super-race (perhaps a race of computers?). But didn't it then make sense that they, rather than the Builders, had created Iceworld?
If so, the rest of the system was wide open as a possible hiding place for
real
Builder artifacts. Tally, after analysis that would have taken any human a million years of calculation, had a candidate.
His conversation with Julian Graves on the subject had been less than satisfactory.
"This body." E.C. Tally indicated on a whole-system display a medium-sized planetoid moving in an orbit far out from the dark star that formed the center of the gravitating set of worlds.
"What about it?" Julian Graves glared at the insignificant object, his great bald brow furrowed with impatience or suspicion. Sometimes Tally wondered if Graves approved of embodied computers. "I've never seen a more average lump of rock."
"Councilor, it doesn't rotate."
"I can see that. But it's very common for planets and moons not to rotate. They become tidally locked to some other body."
"Tidally locked bodies
do
rotate. They turn so that they always present the same face to the parent, which means their day is the same as their year. But they rotate.
Everything
rotates, everything in the universe: electrons, protons, atoms, molecules, moons, planets, stars, gas clouds, galaxies—everything but that planetoid in the display."
"Let me see the data." Julian Graves stared at the screen filled with numbers provided by E.C. and went silent for half a minute.
Tally computed tenth roots for the first million integers and waited impatiently. He knew what was happening. Julian Graves had once been two separate entities, Julius Graves and an interior mnemonic twin. The twin had originally been intended as no more than a memory augment, housed in an added pair of cerebral hemispheres inside Julius Graves's big-domed head. The emergence of a second personality, Steven Graves, had been a surprise to everyone. The two had slowly merged, to become Julian Graves, but for certain tasks it was still better to maintain separation.
Like now. Steven had the computational talent, and it was of an order that even Tally had learned to respect. At quiet moments in the past they had indulged in calculation face-offs, and sometimes—to Tally's amazement—Steven Graves held his own. They had discussed it, and decided that although E.C. had better circuit speeds than human neurons by a factor of ten to the fifteenth, Steven compensated for that by the specialized pattern recognition hardware built into the human brain, and by computational parallelism which Tally could not match.
Now Steven must be performing his own analysis of the data. That deduction was verified when Julian Graves blinked his blue eyes, nodded, and said, "Indeed, the planetoid does not appear to rotate with respect to the most distant parts of the universe. But the observations you have provided, like all measurements, are accurate only to within certain confidence limits. We feel obliged to point out that rotational speeds of objects follow statistical distributions. Thus there is a finite probability that a given rotation speed, no matter how small, will be encountered. That is what we are seeing here."
"May I speak?"
But speaking had done no good at all. He had been unable to persuade Julian Graves that the non-rotating planetoid was worthy of investigation. Tally had terminated the discussion before it could go on too long. He was learning the ways of humans. Better to stop talking, take the
Tally-ho
on its way, and offer direct proof to Julian Graves that Tally was right and Steven was wrong.
Unfortunately that might be no easy task. The ship was closing fast on the planetoid, and the observation chamber at the front of the
Tally-ho
offered a direct view of what even E.C. had to admit was an unpromising object.
Tally's find was so small that although gravity could hold it together, it could not impose the spherical shape common to large bodies. From a distance it appeared as an uneven chip of dark rock, about seventy kilometers long and perhaps half that along each of the other main axes. Tally used a high-magnification scope and searched for any sign of the Phages that often swarmed near Builder artifacts. He saw nothing. He performed a routine laser scan of the surface, and read the reflected spectrum. Rock, rock, and more rock. Of course, since the body was not turning on any axis he could examine only one side of it, but when Tally calculated the odds not even he could hold out hope that the other side would be any different.
It was time to give up, accept that Steven Graves was right and E.C. was wrong, and move on to his official mission of seeking the edge of the dark zone and the planet of the Marglotta. Except that while he had been busy examining the reflected spectrum, the
Tally-ho
had continued to close on its target. The navigation equipment would not permit a collision—it was far too smart for that—but when E.C. raised his head and glanced again through the port of the observation chamber, the chip of rock had grown to a great uneven lump that filled the whole sky.
And it had changed. The whole surface, uniform from a distance, was marked by a regular pattern of studs. It looked to Tally as though a meticulous, gigantic, insane, and overactive riveter had been given a free hand on the planetoid. He rejected that hypothesis on the basis of its improbability, and upon giving the surface a closer inspection realized that he had confused bulges with indents. Those were not studs, they were holes. The body was riddled with them. He glanced at the range monitor, estimated the angle subtended by one of the holes, and at once knew its diameter: 2.7 meters. More than wide enough to admit a suited human, but not nearly enough to permit the
Tally-ho
to enter.
So what now?
He had agreed to keep Julian Graves informed as to anything he found, but a message sent to Graves would surely lead to an undesirable result. E.C. would be told to stay where he was until the survival team specialists came to offer assistance. It would do no good to point out that Tally's brain, if not his body, could survive an acceleration of hundreds of gees and temperatures up to four thousand degrees. That was more than could be said for any human, no matter how well trained.
E.C. edged the
Tally-ho
sideways and closer to the planetoid, so that he could shine a beam directly down one of the round holes. The blackness within was absolute, with no sign of reflected light. He wondered how that could be, and what material lined the tunnel. It would surely be all right for him to determine at least that much information. Although Graves had told E.C. to keep the
Pride of Orion
informed, he had not suggested that every independent action was forbidden.
Tally commanded the
Tally-ho
to maintain a precise fifty-meters separation from the planetoid. He put on a suit and went across to the communications console.
I have discovered a planetoid to which some intelligent agent may have made modifications. My signal beacon will direct you here, should you feel it worthwhile to investigate. E. Crimson Tally.
That was enough. He really was beginning to understand how humans thought and operated. Be casual. More was less.
He instructed the console to send his message after a five minute delay. That would give him enough time to leave the
Tally-ho
and make his way to the surface of his find.
As soon as he arrived inside he knew why there had been no reflection from the walls of the tunnel. There
were
no walls. The hole that Tally had entered expanded outward as soon as he was inside. The slab had no interior, it was nothing more than a paper-thin shell surrounding vacuum. He could see tiny circles of starlight, entering through the million other holes scattered all over the surface.
As a possible Builder artifact this was a total failure. It contained no mysteries, and it just sat there and did nothing at all.
Tally was ready to retreat when he noted something slightly unusual. While outside the planetoid, the gravitational force exerted on him had been tiny, hardly enough to notice. That was just as it should be for such a small body. But now that he was inside, his suit had to apply a constant thrust to hold him in position.
He turned off that thrust, and at once began to fall. That made no sense at all; or rather, it made sense only if some invisible object of high density sat at the middle of the lump of rock.
It was still of no more than slight interest, but since he was here he might as well take a look. E.C. allowed himself to drop for a few more kilometers. His suit's inertial system kept a continuous track on how far he had fallen, and just how long it was taking. His conversion of those numbers to a law of force was automatic and almost instantaneous, and it occupied only a tiny fraction of his attention. The results were another matter. They concentrated all his resources. Since he was falling freely he had felt no force on his body, but his acceleration had been increasing exponentially. If he fell for another twenty-six kilometers, the extrapolated value was infinite.
Nothing in nature produces infinite acceleration. Tally knew that very well. It was probable that his computer brain would withstand whatever forces it was exposed to. His body was another matter. It was as weak as any human's. If he damaged another embodiment beyond repair, he would never hear the last of it.
Those thoughts were completed inside a nanosecond. He switched his suit at once to its highest level of upward thrust. His inertial positioning system indicated he was still falling. That was no surprise. It took time to cancel out his downward speed, and start him back up toward the surface. Then he realized that the situation was worse than that. His
acceleration
was still in the wrong direction. The thrust provided by his suit was not sufficient to balance the downward force, and that force increased with every passing second.