“What did you expect to find?”
“Well …”
What had she expected? She could say what she had hoped to find—exactly what she had written to Uncle Edgar.
“I assumed that this room would contain an enthusiastic group of people, combining the forces of their brilliant minds to evolve meaning from an enigmatic signal developed by alien intelligences and transmitted for reception by other sentient beings living many light-years away.”
That had come out far more pompous than she’d intended, but Torquemada took it in stride. He shrugged.
“Then you should be delighted. That’s exactly what you’ve got.” And, when she stared, “Come on, Milly Wu. You’re dealing with the Puzzle Network, not a political convention. How many years were you a Network nut?”
“Nine.”
“How many other Network members did you meet?”
“None.” Milly had sudden memories of a long-ago birthday party and a shy thirteen-year-old boy. “Or maybe one. I had suspicions and I think he did, but we never asked each other.”
“Absolutely appropriate. I’m the odd man out in this place. Most Puzzle Network members aren’t like sheep or bees. They don’t herd and they don’t swarm. It’s a minor miracle getting them within a kilometer of each other, even behind closed doors, and that’s only happening because this is the central point for data receipt and analysis distribution. Everyone is so afraid of missing something, they’ll put up with anything—even proximity. But not personal presence, except at the progress review meetings. I’ve been a member for thirty years. Until I came here I had met only one other.”
“Which one?” Milly was curious to know who else was this friendly.
“Megachirops, alias the Great Bat. But I suspect he’s the most antisocial of the lot.” Torquemada waved a hand. “Bat’s here, down at the end. Try and visit him and you’ll wish you hadn’t. But if you wait you may see him later in the day, in the conference room at the end of the corridor. Then again, you may not.”
“I don’t understand this. What’s the point of coming here, if no one will talk to anyone else?”
“You’ll see how it’s done, as soon as you go to your cubicle. But if you have questions and if I’m still around, feel free to drop in and ask.”
He smiled again, and once more Milly felt the strength of his personality. She started to move toward her own room, then realized that he had ended their meeting so smoothly that she had omitted to ask an important question. While they were talking she had become increasingly convinced that she ought to know who he was. She had seen him before, somehow and somewhere.
She took two backward steps so that she could again see into the open door of his cubicle.
“Do you mind if I ask you one of those questions now?”
“Not in the slightest.”
“What’s your name?—I mean your real name, not your Puzzle Network name.”
“That seems fair, since I know yours. My name is Cyrus Mobarak.”
“Thank you.” Milly retreated along the corridor, which seemed a better reaction than standing and gaping. No wonder his face seemed familiar. She had been speaking with the Sun King, inventor of the Moby fusion plants and one of the wealthiest and most influential people in the System. But here he was simply Torquemada. Within the hierarchy of the Puzzle Network, money and family and influence meant nothing. Ingenuity and imagination were what counted, and all that counted. It gave her a new respect for the unseen faces behind the corridor’s closed doors.
She entered Cubicle 12 and sat down in the single chair. She noticed that the stand to her left was empty. Tastes varied, so apparently each person brought his or her own preferred food and drink. Something to think about before she came here tomorrow, but today she would manage without. There was much to learn, much to do. She couldn’t afford to waste time hunting for food.
The equipment seemed familiar, and as a first move she turned on the console and the dozen displays. The message that appeared on every one was simple and specific: A REMINDER OF AN OPERATING RULE: NOTHING THAT WE RECEIVE FROM ODIN STATION SHOULD BE SENT ANYWHERE ELSE. IT MAY BE SHARED INTERNALLY, BUT MUST BE TREATED AS PRIVILEGED INFORMATION.
Jack Beston had warned her to expect something like this. He argued that conclusions drawn from data were another matter, and could be communicated. Milly was not so sure. She had decided, without getting into an argument with Jack, that she was going to judge each individual case as it happened.
As the displays began to fill with other information, she realized that Cyrus Mobarak—Torquemada, she ought to think of him that way within this environment—had been right. Thoughts, conclusions, conjectures, and results both positive and negative were swapped freely among the group members. Sometimes you could tell the originator of a message, sometimes not. Credit and personal ego did not seem to be an issue.
Milly soon realized something else. This group had been busy while she was in transit from Jovian L-4 to Ganymede, and already they had done an immense amount of work. It would take days, just to absorb their progress.
Milly cleared her mind of all other thoughts, made herself comfortable, and concentrated on the displays. At first she didn’t care about details. On the way to Ganymede she had done her own share of obsessive thinking and decided that the signal, all twenty-one billion digits of it, was too large for any human mind to comprehend except in gross terms. She needed to build up a feeling of general structure before attacking details.
Examining the mixture of facts, conjecture, and statistics on the displays, it was no surprise to find that the Argus, Odin, and Puzzle Network groups were all following roughly the same initial agenda. The signal had arrived as one immense and unstructured linear digit string. Without discovering and imposing order, you had no chance of deciphering message content. Therefore, you looked for rational ways to subdivide the whole into smaller sections.
You could try dozens of different ways. For example, you might examine the statistics of the whole string locally, where a “local” region contained anything from a thousand to a million digits. All the tools of signal processing were available for that analysis. In one common technique, regions of abnormally low entropy—where the next digit could be predicted with some confidence from the group of digits immediately preceding it—could be sought and marked. These might be “start message” and “end message” markers, since it seemed highly unlikely that the whole SETI signal held only one message. You had to remember how much information could be contained in twenty-one billion binary digits. It was like five thousand densely-written books.
But perhaps regions of low entropy were merely a hint to some other kind of information. An entropy analysis had already been performed, but whoever had done it made no assumptions as to its significance. Milly saw a whole library of possible maps, showing the signal divided into pieces and available for her inspection or continued analysis.
Of course, examining the statistical behavior of signal sections was not the only way to seek structure, and it might not be the best way. As a valid but quite different approach, you could scan the entire signal for test sequences that repeated over and over throughout its length. Naturally, a test sequence had to be long enough for its occurrence to provide information. If the whole signal were totally random, then a short sequence such as 1-0-0-1 could be found in it more than a billion times by sheer chance. On the other hand, if you chose a thirty-digit test sequence you would expect to find it only a score of times in a random string of twenty-one billion digits. Occurrence of that thirty-digit string fifty or sixty separate times was so unlikely that you would know you were on to something.
It was easy to say, “Examine the signal for test sequences long enough to be significant,” but the actual task was a monster. A billion different sequences existed with thirty binary digits. You needed to screen for all of them. That work was still going on.
And when you had found a particular sequence too often to believe that it
was the result of chance, what came next? That was another and more difficult question. Perhaps each occurrence of a thirty-digit string indicated a starting point or an end point for an actual message. Then between each thirty-digit string that you found there were sure to be shorter repeated sequences of, say, six to twelve digits. These, particularly if groups of them came in close proximity, ought to form the message itself. In human terms, six binary digits were enough to encode letters of an alphabet, while twelve digits would suffice for most words. Even though there was surely no hope of finding the letters of any human language, it made sense to look for the universals of mathematics. The integers themselves should be easiest of all. Once you knew where each one started and stopped, the numerical value of a binary string was a unique number to within a reflection (should you read the number from left to right, or right to left?). Then you could begin to look for the symbols that stood for equality, less than, greater than, exponentiation, and other common arithmetical operations.
But this brought the interpretation teams face to face with the most vexing question of all: To what extent could you or should you assume that human thinking, human behavior, and human science applied in any way to a SETI message?
How alien was alien? This was the question that gave Milly nightmares. Even within the limited group of workers on Argus Station, she had found two schools of thought. One set—call them the optimists—assumed that any aliens advanced enough to send signals across space must be ahead of humans in every field of science. Moreover, the optimists were convinced that the aliens would have done their absolute best to make their messages easy to read. They would employ no tricks, such as run-length encoding, to reduce the volume of data transmitted and received.
The pessimists said, but wait a moment. These are aliens. Technical and scientific discoveries throughout human history didn’t come in the most convenient or logical order. Archimedes was unlucky. He had the integral calculus within his grasp, and if Arabic numeral notation had been available to him he would have beaten Newton and Leibniz by almost two millennia. Kepler, on the other hand, had been fortunate. The Greeks, from Euclid to Apollonius, had established hundreds of theorems concerning conic sections. When Kepler needed them in order to replace the old systems of epicycles with his own laws, those theorems sat waiting.
Aliens are likely to know different things, because there is no fixed order for discovery. Maybe we have as much to offer them as they have to offer us. Suppose they never invented the alphabet, or positional notation in mathematics? Then their messages could be all ideographs, their numbers Roman numerals. But far more likely they would use something less familiar and comprehensible than either.
Milly had long ago made her own decision as to where she stood. You could not afford to be either an extreme pessimist or an extreme optimist. On the side of pessimism, surely any aliens would be physically and mentally nothing like humans. They were, after all, aliens. Their languages, notations, and order of evolution of ideas would be vastly different. On the other hand, on the side of optimism, surely any alien thought processes must follow the universal laws of logic. Also, anyone who bothered to send messages far across space would want their messages to be not only received, but comprehended.
Once you accepted those two assumptions, you had certain guarantees. To take one simple example, no sensible alien would ever send as part of a message 2 ? 2 = 4 unless there was other independent evidence as to how the symbol? was to be interpreted. The message was too ambiguous. The receiver could not determine whether? stood for plus (2 × 2 = 4), times (2 + 2 = 4), or raise to a power (22 = 4).
If it were up to Milly, she knew exactly how she would build and send a SETI message. First, you defined special symbols that provided start and stop instructions; then you displayed the positive integers, with enough examples, such as sequences of primes, to make sure the receiver could be absolutely sure there was no misinterpretation.
After that came the symbols of common arithmetic, with examples showing how to add, subtract, multiply, and divide. From there it was a short step to negative numbers, fractions, powers, and irrationals. Imaginaries you would introduce using fractional powers of negative numbers. Then on to series of powers, and the elementary transcendental functions such as sines, cosines, logarithms, and exponents. In every case you would give enough examples to be sure there was no confusion. After providing series expressions for the universal transcendentals such as π or e, you would provide a check that all was being interpreted correctly by quoting one of mathematics’ enduring wonders, a formula that mysteriously links transcendental and imaginary numbers with the basic numerical building blocks of 1 and 0:
eiπ=1.
Mathematics was easy, the obvious way to start. After that, Milly would proceed to astronomy, physics, chemistry, and, finally and most difficult, language.
The trouble, of course, was that it was not up to Milly. She was not sending a message. She was receiving one. The difference, in terms of self-confidence, was the difference between being a doctor and being a patient.
The good news was that she was not working alone. People as smart as she, and probably a whole lot smarter, were her allies. The displays in front of her provided an overview of the whole signal in schematic form, subdivided into twenty-seven regions.
Using her console to control the rate at which she advanced, Milly set out to scan the entire length of the signal. The Puzzle Network team had worked cooperatively to attach their analyses to the appropriate regions. The result was like a gigantic snake, of which the string of digits of the signal itself formed a narrow backbone. Here and there, in places where something particularly interesting and significant had been discovered, the snake bulged out like a python that had swallowed a pig.
Milly backed the scan to study Section 7, the fourth bulge, which at first sight was bigger than all the others. The comments were offered in ordered bunches:
* * *
Attoboy: The structure here is odd. High entropy sequences of average length 106 digits are regularly interspersed with low entropy regions each of constant length 3.3554 × 107 digits. Any thoughts?
Sneak Attack: Yes. We could be seeing sections of “text” (variable but roughly equal lengths) that introduce or describe a “picture” (something in image format, with a constant array size). Maybe square arrays of black and white images, each about 6,000 × 6,000 elements?
Claudius: More likely, a gray scale image 4,096 × 4,096 (212 × 212—that supports the notion of binary representations), with 2 bits (4 levels) for each pixel. That fits with the exact size of the low entropy regions, 33,554,432 bits.
Sneak Attack: Could just as well be 2,048 × 2,048, with 256 (8-bit) gray levels.
Claudius: Should be easy enough to find out which. If we assume a particular line length and do cross-correlations of successive lines, the correct line length should jump right out at us when we get to it, because the correlation will be a lot higher. Let me take a look.
* * *
That was all for that cluster of messages. Presumably Claudius did not yet have an answer, or at least not one that “jumped right out.” Milly moved on.
The seventh bulge along the signal’s spine, Section 12, contained remarks similar to the previous one, except for three added comments:
* * *
Megachirops: In this case the low entropy regions have a constant length of 4,194,304 bits, exactly one-eighth as long as in Section 7. Does anyone else find this somewhat surprising?
Ghost Boy: We would probably make them all the same size. The difference may be part of the message, trying to tell us something.
Claudius: Or could these be line drawings?—binary images, black and white with no shades of gray.
* * *
The ninth bulge supported a hypothesis offered early in the history of SETI:
* * *
The Joker: My frequency analysis of this section suggests that we are dealing with base 4 arithmetic, rather than the base 2
binary we have seen elsewhere. The temptation to interpret this as a biological description in terms of strings of four nucleotides is strong.
Attoboy: Beware of anthropomorphism. But I agree, the temptation is strong. I will try to correlate this section with everything in the genome library.
* * *
Not surprisingly, Attoboy had not yet reported results from that effort. The task was a monstrous one. The library to be examined held complete genomes for more than two million species, everything from humans and oak trees and mushrooms to the smallest and simplest viruses. No one, no matter how optimistic, would hope for an exact match. It would be a miracle (and enormously relevant to the universal nature of life) if anything correlated at all with a living creature from Earth. But Attoboy was right, you couldn’t afford not to look.
Milly worked her way on through the signal, section by section. The exercise was giving her a strong inferiority complex. The results that she was seeing had been performed so quickly, and offered such powerful evidence of ingenuity—what could she possibly contribute? The team had already established the existence of unique start and stop sequences, each fourteen bits long. Numerical base and reading order were known beyond doubt: integers were base 2 and base 4, with the most significant digit to the right. Sequences of primes and squares and cubes had been discovered, more than long enough to be unambiguous.
When she came to the very end of the signal, with its termination as a repeated pattern of the fourteen-bit stop sequence, Milly at once went back to the beginning and started over. The easy part, following the trail that others had already marked out, was over. Now she had to do something to justify her own presence in the group. Sit, observe, learn, keep quiet; that was all very well—for the first half-day. After that, Milly hoped to bring her own special knowledge and experience to bear. She went to a section near the middle of the signal, where analysis and comments by members of the Puzzle Network were meager and felt tentative. This was a place with special significance for Milly. It was here where she first noticed the oddity that had evolved into the Wu-Beston anomaly, and she had studied it extensively.
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