Ratner's Star (36 page)

Notation by sixty.

That had to be it, a positional notation system based on the number sixty. He knew that thousands of years ago two systems of numeration were used in Mesopotamia. Decimal and sexagesimal. The latter used a base of sixty instead of ten. Because the Sumerians had divided the year into three hundred and sixty days, they found the number sixty to be a more workable base in their astronomy. Notation by sixty also had the advantage over the decimal system in all work involving fractions because sixty has more divisors than ten. The vertical wedge used in Mesopotamia to denote the number one was also used for sixty. In the decimal system a given three-digit number is a way of expressing a quantity in terms of multiples of ten. Schoolchildren know that the number three hundred and twenty-four means three times one hundred (or 10
²
), plus two times ten (10
¹
), plus four times one (10°). In sexagesimal notation, the tens become sixties.

The message had been received in the form of fourteen pulses, a gap; twenty-eight pulses, a gap; fifty-seven pulses. He realized now that the total of one hundred and one units was not important. This total viewed differently, as one zero one, or binary number five, was equally unimportant. The fact that one, four, two, eight, five and seven are the digits of a recurring decimal had no significance whatever. The pulse total alone (ninety-nine) and the number of blank intervals (two) were also meaningless.

All that mattered was the original series of pulses: fourteen, twenty-eight, fifty-seven. In notation by sixty these are not three numbers but a way of expressing a single large number. To discover this number it is necessary only to multiply fourteen by thirty-six hundred (60
²
), twenty-eight by sixty (60
¹
), fifty-seven by one (60°). What was being transmitted then was the number fifty-two thousand one hundred and thirty-seven.

A man stood in the open doorway.

This, in our terms, was what the extraterrestrials were communicating. Their natural way of expressing this quantity, since they used powers of sixty, was in the form of the number 14,28,57. There was no reason why an advanced civilization should use a place-value system based on ten. Maybe they'd overcome all the problems inherent in a sixty-system and used it to much greater advantage than we use the decimal method. Of course, it remained for Billy to discover the importance of fifty-two thousand one hundred and thirty-seven. Now that he knew how to interpret the transmission, he could begin the task of decoding it. What did the new value mean? Obviously this constituted the second half of the problem.

For an unreal moment he imagined that the man in the doorway was an extraterrestrial, here to confirm his arithmetic. But there was nothing very exotic about the man and when he introduced himself as Dr. Skip Wismer, a NASA consultant on loan to Field Experiment Number One, Billy thought it a mere coincidence (of the nonexotic type) that he was associated with astronauts. Wismer went on to explain that since he had to pass this way to get to the demonstration, he thought he'd stop by and pick up Billy.

“I'm halfway done with the reason they got me here for. I guess it's okay to take a break.”

“How do you know it's halfway?” Wismer said. “You won't know where the halfway point is until you're able to look back on the entire solution. Since you can't know what's ahead, you don't know how much you've done. This is plain common sense.”

“It's a feeling. Very definitely says half. When I get it this strong I know it's true.”

“You're claiming in effect to be digging half a hole. Can't be done, can it? Besides you're not even supposed to be working on the code. The source of the transmission is what we're primarily concerned with for the time being. In addition to which is the fact that the message was never repeated. Repetition in a case like this is essential. Without it, there's no reason to believe the pulse array is correct. Not to mention the computer retrovert we've just run that indicates error in the receiving equipment. Probably the switch-frequency generator.”

“What's this demonstration you mentioned?”

“The Leduc electrode,” Wismer said.

This didn't sound very promising. But since there was nothing else to do right now, he thought he might as well attend. First there was something he was determined to get rid of, namely the large green pill that Orang Mohole had forced him to accept in his apartments on top of the armillary sphere. He knew if he carried it around long enough, it would get him into some kind of tricky situation. He excused himself, went into the bathroom, closed the door, lifted the top of the toilet tank, dropped Mohole's greenie inside and was about to replace the porcelain lid when he realized something was floating in the water. It was a tiny cardboard matchbox. He took it out of the tank and slid it open. Inside was a tightly folded piece of paper, wet at the edges. He removed it from the box and unfolded it.

Dr. Skip Wismer led him over a footbridge high above a miniature recycled waterfall and then into a sector called Med Comp.

“Large questions come to mind,” Wismer said, “whenever I'm in the presence of someone with your kind of vast mental capacities. For instance, do you believe in someone or something larger than yourself?”

“That takes in a lot of territory.”

“Scientist or not, I sometimes feel overwhelmed by it all. I mean the sheer allness, the sheerness of it all. To cite an example, what do you suppose happens to a person after death?”

“He remains in that state.”

“My wife is dead, you know.”

“Nobody warned me.”

“What kind of system permits this sort of finality?”

“Death?”

“It's so definitive.”

“Buried or cremated?”

“She's in an icebox in Houston,” Wismer said. “Left her body to science.”

“What will they do with it?”

“I hate to tell you.”

“Stick needles?”

“At the very least,” Wismer said. “The whole thing depresses and worries me, not least of all the question of what happens in the first few seconds after electrical activity in the brain ceases forever. Personally I think there's some kind of turning inside out. That's my theory. An unknotting of consciousness in a space of
n
dimensions. A turning outward. Not that I'd say the word. I'd rather commit the act than say the word. Particularly in front of a lady.”

“What word?”

“Evaginate.”

They entered a huge operating theater.

“So what's this electrode we're seeing demonstrated?”

“It's a device that would greatly simplify manned space missions. Probably increase an astronaut's capabilities a thousandfold. Which means I'll be a very interested observer today. Of course I don't know what
they
want to use it for.”

Two men entered the theater. They were dressed in surgical gear—masks, caps, gowns, gloves. Dr. Wismer greeted them and then took a seat high above the floor of the operating theater. The room was full of wires, cables and monitoring devices. There was so much wiring in fact that nine or ten different colors had been used to enable technicians and others to distinguish between the strands. Wires were bundled, twisted and interlaced. They connected various machines, ran along the walls and floor, hung in clumps from a section of ceiling where panels had been removed.

“Ignore this mess,” one of the men said. “It's the equivalent of making prophecies by studying an animal's entrails. Now that we've got the Leduc electrode, all this paraphernalia gets junked. My name is Cheops Feeley.”

“I've heard of your medal.”

“That's not the only thing named after me. There's a science fair, two research centers and a gypsy health clinic.”

“You're a gypsy?”

“Lapsed.”

“I heard your medal's given for work that's crazy in places.”

“Madness content,” Feeley said. “Nobody mentions it aloud but we all know that strict scientific merit is only one of the elements considered. The dark side of the award is what appeals to most people.”

There was a large shipping container in a corner of the room. Billy noticed a scrawny old cat looking out over the top of the box. Cheops Feeley took a long step forward, putting both his hands on the boy's head, probing with his fingertips.

“You've got it, all right. Just as I suspected. I was sure it would be there.”

“What would be there?”

“The mathematics bump.”

“If there's a bump, it never hurt.”

“It's a life passion of mine, skull conformation. Yours is very distinct. Definitely a bump for mathematics. That settles it.”

“Settles what?”

“Everything,” Feeley said. “You're definitely the person we want. The Leduc electrode is only part electrode. It's a bundle of extremely tiny wires able to stimulate and record brain activity. But here's the stroke of genius. These wires are attached to a microminiaturized disk that functions almost exactly as a computer does. But not just any computer. The Leduc electrode has Space Brain capability. And it's small enough to be implanted under someone's scalp. Through a tiny incision that leaves no scars. Once it heals. And the hair grows back.”

All he could see of the men were their eyes, two sets, very steady, green here, hazel there, pinched in by mask and cap. Slowly the cat worked its way over the top of the box, followed by two others just
as mangy. Billy looked up at Skip Wismer, who seemed to have dozed off.

“The Leduc electrodes are in that container to your right.”

“Who's that on my left?”

“That's Leduc.”

The other man nodded. At least, Billy thought, everybody's identified. One of the cats lazily climbed back into the box as three others emerged. Cheops Feeley went over there and lifted out a pink disk with wires attached. Terrific hygiene procedures. Watch him clean it off with some spit.

“We ordered blue and pink. But they only sent pink.”

“Are they different besides color?”

Feeley shook his head.

“Here's our thinking on the matter. You with your enormous powers of abstraction. Space Brain with its unsurpassed superfine computations. A single dynamic entity. With no scars. And hair that's guaranteed to grow back.”

“Sounds familiar, talk of this combination.”

“We have massive backing. The resources of a very powerful cartel. Once the electrode is buried in your head, assuming you agree to such a procedure, all I have to do is notify them and you get paid a generous retainer for a period of time not to exceed the life of the appliance.”

“They want to regulate the money curve, right? That's their only interest in life. The two strange talkers. Tell them my head stays shut.”

“You don't have to decide now. This is just a trial run. I want to point out that subcutaneous implantation is no great problem in and of itself. Although there's a slight inconvenience in this particular case.”

“Cat hairs.”

“Listen closely,” Feeley said. “The problem with the device as now constituted is that it tends to overstimulate the left side of the brain. This will result in an overpowering sense of sequence. You'll be acutely aware of the arrangement of things. The order of succession of events. The way one thing leads to another. This is a side effect of carrying the appliance under your scalp but it's not too great a price to pay for the kind of madness ratio we're getting, not to mention scientific value.
True, you'll find yourself analyzing a continuous series of acts in terms of their discrete components. Eating a sandwich will no longer be the smooth operation you've always known it to be. You'll experience, should you agree to host the electrode, a strong awareness of your hands, your mouth, your throat, your stomach, whatever's between the slices of bread, the bread itself. You might even find yourself in retrograde orbit, so to speak. Bread, bakery truck, bakery, flour, wheat and so on. There is so much involved. Our lives are so dense. The baker's hands, the farmer, his barn, the paint job, the latex, the trees. There is so much and all of it will be apprehended, as you eat the sandwich, should you agree to the implantation, in related sequence. In consecutive order. In proper succession. You'll be involved in a very detailed treatment of reality. A parody of the left brain. But is this reality of yours less valid than ordinary reality? Not at all. You'll be establishing fresh paths of awareness. Taking nothing for granted. Dealing with unlimited data. Every breath you take will be subjected to a thorough sequential analysis. Heart, lungs, nostrils, oxygen, carbon dioxide and so forth. There is so much involved and it's all right there for the asking.”

The scabby cats seeped in and out of the box where the electrodes were stored. Cheops Feeley explained once more that Billy would be given ample time to decide whether he wanted to take part. This was just a test exercise, a dress rehearsal for the actual implantation. The procedure, should he agree to it, would be carried out in a chair-shaped operating table to save time between barbering and incision. He asked Leduc to get the table in question, as a practice maneuver, and then, handing the pink disk or “appliance” to the boy, went to look for a comb, pair of scissors and hair clipper. Finding himself alone with the dozing Dr. Skip Wismer, Billy moved in deliberate stages to the nearest exit. He eased his head out past the door frame and into the corridor, ready to follow it with left foot and leg. Someone was drinking from an ornamental fountain in a circular area about fifty feet beyond the end of the corridor. It was a man, dark-skinned and absolutely naked. Billy was motionless now, watching. As the man raised himself, his hands uncupping from his face, the boy could see that he was white-haired,
although of indeterminate age, and that his chest was painted with geometric figures.