Factoring Humanity Part 11

"I'm glad they caught him."

"Indeed. In pa.s.sing, though, I do wonder why this rapist gets automatic membership in the human race, but I have to prove myself?"

Kyle shuffled over to the coffeemaker, poured himself a cup. "That's a very good question," he said at last.

Cheetah was quiet for a time, then: "There's more to this story."

Kyle took a sip of coffee. "Yes?"

"There was the matter of the incidental zygotic commencement."

"Ah, the coveted IZC. Oh, wait-you mean the baby. Christ, yes. What happened?"

"Prior to her accident, Kathy had been a devout Roman Catholic. She was, therefore, opposed to abortion. Taking that into account, Kathy's parents decided that Kathy should have the baby and that they would raise the child."

Kyle was incredulous. "Have the baby while still in a coma?"

"Yes. It is is possible. Comatose women had given birth before, but this was the first known case of a woman becoming pregnant after going into a coma." possible. Comatose women had given birth before, but this was the first known case of a woman becoming pregnant after going into a coma."

"They should have aborted the pregnancy," said Kyle.

"You humans make judgments so quickly," said Cheetah, with what sounded like envy. "I have tried and tried to resolve this issue and I find I cannot."

"What way are you leaning?"

"I tend to think that if they let the baby live, it should have been placed in a foster home."

Kyle blinked. "Why?"

"Because Kathy's mother and father, by forcing her to give birth in such extreme conditions, demonstrated that they were ill-suited to be parents."

"Interesting take. Were there any polls conducted at the time about what should be done?"

"Yes-The Rochester Democrat & Chronicle ran one. But the option I proposed wasn't even put forward-meaning, I guess, that it's not something a normal human would come up with." ran one. But the option I proposed wasn't even put forward-meaning, I guess, that it's not something a normal human would come up with."

"No, it's not. Your position has a certain logic to it, but it doesn't seem right emotionally."

"You said you would abort the child," said Cheetah. "Why?"

"Well, I'm pro-choice, but even most of those who are pro-life make exceptions for cases of incest or rape. And what about the kid, for Pete's sake? What effect would that kind of origin have on it?"

"That had not occurred to me," said Cheetah. "The child-a boy-was born on March eighteen, nineteen ninety-six, and if he's still alive, would be twenty-one now. Of course, his ident.i.ty has been protected."

Kyle said nothing.

"Kathy," continued Cheetah, "died at the age of thirty, one day before the child's first birthday; she never came out of the coma." The computer paused. "It does make me wonder. The ethical dilemma-whether or not to countenance an abortion-could not have been drawn in sharper terms, even though I don't seem to be able to resolve it properly."

Kyle nodded. "We're all tested in various ways," he said.

"I know that better than most," said Cheetah, in a tone that was a credible imitation of being rueful. "But when I am tested, it is by you. When human beings are tested, though-and a case such as this clearly seems to be a test-who is it that is administering the test?"

Kyle opened his mouth to reply, closed it, then opened it again. "That's another very good question, Cheetah."

Heather sat in her office, thinking.

She'd stared at the messages from s.p.a.ce day in and day out for years, trying to fathom their meaning.

They had had to be rectangular images. She'd tried to identify any cultural bias related to prime numbers, any reason why she'd interpret them one way while someone from China or Chad or Chile would interpret them some other way. But there wasn't anything-the only cultural issue she could come up with was an argument about whether the number 1 qualified as a prime number. to be rectangular images. She'd tried to identify any cultural bias related to prime numbers, any reason why she'd interpret them one way while someone from China or Chad or Chile would interpret them some other way. But there wasn't anything-the only cultural issue she could come up with was an argument about whether the number 1 qualified as a prime number.

No, if the length of the signals were the products of two prime numbers, then the only logical conclusion was that they were meant to be arranged into rectangular grids.

Her computer had all 2,843 messages stored on it.

But there were some messages that had been decoded, right at the beginning. Eleven of them, to be exact-a prime number. Meaning there were 2,832 undecoded messages.

Now that number was not not a prime-it was an even number, and except for 2 there were, by definition, no even prime numbers. a prime-it was an even number, and except for 2 there were, by definition, no even prime numbers.

A quantum computer could tell her in a twinkling what the factors of 2,832 were. Obviously, half that value would be a factor-1,416 would go into it twice. And half of that, 708. And half of that, 354. And half of that, 177. But 177 was an odd number, meaning that its half wouldn't be a whole number. would go into it twice. And half of that, 708. And half of that, 354. And half of that, 177. But 177 was an odd number, meaning that its half wouldn't be a whole number.

She'd sometimes thought that maybe each day's message made up only a portion of a larger whole, but she'd never found a meaningful way to order the pages. Of course, until a few days ago, they'd never known how many pages there were in total.

But now they did did know. Maybe they did fit together into bigger groups, the way the backsides of trading cards often tile together to form a picture. know. Maybe they did fit together into bigger groups, the way the backsides of trading cards often tile together to form a picture.

She brought up her spreadsheet program on her desktop computer and made a little sheet that simply divided 2,832 by consecutive integers, starting with 1.

There were only twenty numbers that divided into 2,832 evenly. She deleted the ones that didn't divide evenly, leaving her with this table:

This Divides into 2,832 Integer This Many Times 1 2832.

2 1416.

3 944.

4 708.

6 472.

8 354.

12 236.

16 177.

24 118.

48 59.

59 48.

118 24.

177 16.

236 12.

354 8.

472 6.

708 4.

944 3.

1416 2.

2832 1.

Of course, the a.s.sumption by most researchers was that there were 2,832 individual pages of data-but there might be as few as one page, made up of 2,832 tiles. Or there could be two pages, each made up of 1,416 tiles. Or three, made up of 944 tiles. And so on.

But how to tell which combination the Centaurs had intended?

She stared at the list, noting its symmetry: the first line was 1 and 2,832; the last was the reverse-2,832 and 1. And so the lines were paired up and down until the middle two: 48 and 59; 59 and 48.

It was almost as if the middle two were the pivot, the axle on which the great propeller of figures rotated.

And- Christ- Except for 1, 3, and 177, the number 59 was the only possibly prime number on the list: all the others were even numbers and, by definition, couldn't be primes.

And-wait. Kyle had taught her a trick years ago. If the digits composing a number added up to a number divisible by three, then the original number was also divisible by three. Well, the digits making up 177-one, seven, and seven-added up to fifteen, and three went into fifteen five times, meaning 177 couldn't be prime.

But what about the number 59? Heather had no idea how to determine if a number was prime, except by brute force. She made another quickie spreadsheet, this one dividing 59 by every whole number smaller than itself.

But none of them divided evenly.

None, except 1 and 59.

Fifty-nine was was a prime number. a prime number.

And-a thought occurred to her. One itself was sometimes considered a prime. Two was definitely a prime. So was three. But in a way, all those numbers were trivial primes: every whole number lower than them was also divisible only by itself or one. In many ways, five was the first interesting prime number-it was the first one in sequence that had numbers lower than itself that weren't weren't primes. primes.

So if you discounted one, two, and three as trivially prime, then in the table she'd produced, 59 was the only non-trivial prime that divided evenly into the total number of undecoded alien messages.

It was another arrow pointing at that figure. The alien transmissions could possibly be arrayed in 48 pages each consisting of 59 individual messages, or 59 pages each consisting of 48 messages.

Researchers had been looking for recurring patterns in the messages for years, but so far none had turned up that hadn't seemed coincidental. Now, though, that they knew the total number of messages, all sorts of fresh a.n.a.lyses could be done.

She opened another window on her computer and brought up the file directory of alien messages. She copied the directory into a text file, where she could play with it. She highlighted the bit counts for the first 48 undecoded messages and tallied them up: they totaled 2,245,124 bits. She then highlighted the next twenty-four. The tally came to 1,999,642.

d.a.m.n.

She then highlighted the counts for messages 12 through 71-the first 59 undeciphered messages.

The total came to 11,543,124 bits.

Then she highlighted messages 72 to 131 and tallied their sizes.

The total was also also 11,543,124 bits. 11,543,124 bits.

Heather felt her heart pounding; perhaps someone had noticed this before, but. . .

She did it again, working her way through the material.

Her spirits fell when she found the fourth group tallied only 11,002,997 bits. But after a moment, she realized she'd highlighted only 58 messages instead of 59. She tried again.

The tally was 11,543,124.

She continued on until she'd done all 48 groupings of 59 messages.

Each group totaled precisely 11,543,124 bits.

She let out a great whoop! whoop! of excitement. Fortunately, her office did have that st.u.r.dy oak door. of excitement. Fortunately, her office did have that st.u.r.dy oak door.

The aliens hadn't sent 2,832 separate messages-rather, they'd sent 48 large ones.

Now, if only she could figure out how to tile the messages together. Unfortunately, they were of many different sizes, and there was no orderly repet.i.tion from page to page. The first message making up the first group of 48 was 118,301 bits long (the product of the primes 281 and 421), whereas the first message of page two was 174,269 bits long (the product of the primes 229 and 761).

Presumably, the individual tiles formed square or rectangular shapes when properly placed together. She doubted she could figure it out by trial and error.

But surely Kyle could write her a computer program that would do it.

After last night, she was hesitant. What would she say to him?

She steeled her courage and picked up her phone.

"h.e.l.lo?" said Kyle's voice.

He doubtless knew it was Heather calling; he could read it off the status line on his phone. But there was no particular warmth in his voice.

"Hi, Kyle," said Heather. "I need your help."

Frosty: "You didn't need my help last night."

Heather sighed. "I'm sorry about that. Really I am. This is a difficult time for all of us."

Kyle was silent. Heather felt the need to fill the void. "It's going to take time to sort all this out."