“Whatever this creature is,” Gea said dryly, “the body of ‘Morag Poole’ responds to our sensors, every one of them. It has mass, volume, an internal structure. It is in our universe. It is no hallucination, and no ghost, in the sense of the word as I understand it.
It is really there.
”
But who
was
this? Gea snipped out a little volume around Morag’s head and blew it up until it was life-size, a disembodied head with a serene, somewhat vacant expression. Gea overlaid this with an X-ray image of the skull within, and she compared it to images of Morag from her medical records and my own personal archive. Rapidly we were taken through a point-to-point matching of facial structures, of the deeper bones. All this was completed in seconds. The implication was clear: any forensic scientist would have concluded that the face in our image was indeed Morag.
“But,” Gea said, “there are anomalies.”
The Morag creature was dense, massive, in fact about twice my weight. Gea had been able to measure that by studying seismic echoes of her footsteps. The sense I’d sometimes had that Morag was somehow more
real
than me and the rest of my world seemed to be borne out. But Gea’s sensors had detected only flesh and blood and bone, and it wasn’t clear what form her invisible mass took.
For all her intense reality, the sensors had no clear record of where Morag had come from, or where she had gone to. It was as if the myriad artificial eyes just looked away, and she was gone.
As Gea went through all this, Rosa watched Tom carefully. She seemed fascinated by his reaction, his emotional state. Tom was expressionless, but even that was eloquent, I thought.
Rosa said at last, “Whatever we are to make of all this, one thing is clear. The visitations are now part of our consensual reality. Michael may indeed be crazy, but we can’t explain away his experiences that way anymore.”
“Thanks,” I said warmly.
“Well, personally I’m awed,” Sonia said. “Scared.”
“Me, too,” Shelley said. “It’s a ghost story suddenly coming true.” But she didn’t sound scared, or particularly awed, and neither did Sonia; they sounded curious. I was impressed by the resilience of their minds, the minds of a soldier and an engineer. It wasn’t just their professions that gave them such strength, I suspected, but a deeper robustness of the human psyche.
I said, “There’s no reason to be afraid. If strangeness spooked us we’d still be competing for gazelle bones with the hyenas out on the savannah. We’ll deal with this—”
Tom turned on me. “That’s typical of your bullshit, Dad. What we’re trying to deal with here is
my mother.
Or rather, that thing that looks like my mother. And all you can come up with is some fucking pep talk about walking out of Africa.” His voice was controlled but brittle.
Rosa said evenly, “We all need ways of coping with this, Tom. You must find your own path, as your father is finding his. This is a reality Michael has accepted for some time, I think. But now suddenly this is real for
you.
You were even able to approach your mother—”
“It wasn’t my mother,” he snapped.
Rosa nodded. “Very well. You were able to approach
the visitor
closely, to inspect her, as I hadn’t been able to in Seville. What did you feel?”
Tom wouldn’t reply. He shot me a resentful, pitying glance.
As for me, I truly believed that this visitor
was,
on some level, Morag, it really was her. I had always believed that. So how was I supposed to feel? I had never known that, not since my first visitations as a child. My reaction was to figure it out, try to make sense of it. But maybe I was the weak one; maybe the true, strong reaction was actually Tom’s, his devastated weeping on the plain; maybe he felt the reality of this return, its strangeness in ways I was incapable of.
Shelley’s hand crept over mine.
Rosa had been concentrating her own studies on Morag’s speech. She played us a sample. Once again a disembodied head floated over our tabletop; once again I saw that beautiful face, those full lips. But Morag spoke strangely and quickly, a string of syllables too rapid to distinguish, her tongue flicking between her lips.
Rosa froze the image. “There is no known human language detectable in this signal. And yet we can detect structure . . .”
She told us, somewhat to my surprise, that there was a flourishing discipline in the study of nonhuman languages.
It had originated in questions about animal communication. The songs of whales and whistles of dolphins were obvious case studies, but so were the hoots and screeches of chimps and monkeys, the stamping of elephants—even the dull chemical signaling of one plant to another. But how much information was contained in these messages? Even if you couldn’t translate the language, even if you didn’t know what the whales sang about, were there ways of determining if there was any information in there at all—and if so, how much, how dense? This was a discipline that in latter years had been useful in helping us figure out the sometimes cryptic utterances of our more enigmatic artificial intelligences—and, I thought, it might be useful someday if we ever encountered extraterrestrial intelligences.
Rosa waved a hand, and the air filled with graphs. It was all to do with information theory, she said, the mathematics of sequences of symbols—binary digits, DNA bases, letters, phonemes. “The first thing is to see if there is any information in your signal. And to do that you construct a Zipf graph . . .” This was named after a Harvard linguist of the 1940s. You broke up your signal into its elements—bases, letters, words—and then made a bar graph of their frequency of use. She showed us examples based on the English alphabet, presenting us with a kind of staircase, with the usage of the most commonly used letters—
e, t, s
—to the left, and lesser usages represented by more bars descending to the right. “That downward slope is a giveaway that information-rich structure is present. Think about it. If you have meaningless noise, a random sequence of letters, each one is liable to come up as often as any other.”
“So the graph would be flat,” Sonia said.
“Yes. On the other hand if you had a signal with structure but no information content—say just a long sequence of
e, e, e,
like a pure tone—you’d have a vertical line. Signals containing meaningful information come somewhere between those two extremes. And you can tell something about the degree of information contained by the slope of the graph.”
Sonia asked, “What about the dolphins?” She glanced apologetically at Tom. “I know it’s nothing to do with your mother. I’d just like to know.”
Rosa smiled. “Actually the analysis is a little trickier in that case. With human languages, it’s easy to see the breakdown into natural units, letters, words, sentences: you can see what you must count. With nonhuman languages, like dolphin whistles, it’s harder to see the breaks between linguistic units. But you can use trial and error. Even dolphin whistles have gaps, so that’s a place to start, and then you can expand the way you decompose your signal, looking for other trial break markers, until you find the breakdown that gives you the strongest Zipf result.”
Sonia asked, “And the answer?”
Rosa waved a hand, like a magician. A new line on the graph appeared, below the first and parallel to it. “Dolphin whistles, and whale songs and a number of other animal signals, contain information—in fact they all show signs of optimal coding. Of course knowing there is information in there isn’t the same as having a translation. We know the dolphins are talking, but we still don’t know what they are talking about.”
“We may never know,” said Sonia, her voice tight. “Now that the oceans are empty.”
Gea rolled back and forth, friction sparks flying. You wouldn’t think a tin robot could look so judgmental.
Rosa said brightly, “As far as Morag is concerned we aren’t done yet. There is a second stage of analysis which allows us to squeeze even more data out of these signals.”
As I’d half-expected, she began to talk about entropy. The Zipf analysis showed us whether a signal contained information at all, Rosa said. The entropy analysis she presented now was going to show us how complex that information was. It makes sense that information theoreticians talk about entropy, if you think about it. Entropy comes from thermodynamics, the science of molecular motion, and is a measure of disorder—precise, quantified. So it is a kind of inverse measure of information.
Rosa showed us a new series of graphs, which plotted “Shannon entropy value” against “entropy order.” It took me a while to figure this out. The zero-order-entropy number was easiest to understand; that was just a count of the number of elements in your system, the diversity of your repertoire—in written English, that could be the twenty-six letters of the alphabet plus a few punctuation marks. First-order entropy measured how often each element came up in the language—how many times you used
e
versus
t
or
s.
Second-order and higher entropies were trickier. They were to do with correlations between the elements of your signal.
Rosa said, “If I give you a letter, what’s your chance of predicting the next in the signal?
Q
is usually followed by
u,
for instance. That’s second-order entropy. Third-order means, if I give you two letters, what are your chances of predicting the third? And so on. The longer the chain of entropy values, the more structure there is in your signal.”
The most primitive communications we knew of were chemical signaling between plants. Here you couldn’t go beyond first-order Shannon entropy: given a signal, you couldn’t guess what the next would be. Human languages showed eighth—or ninth-order entropy.
We talked around the meaning of this. The Shannon entropy order has something to do with the complexity of the language. There is a limit to how far you can spin out a paragraph, or even an individual sentence, if you want to keep it comprehensible—though a more advanced mind could presumably unravel a lot more complexity.
Sonia asked, “And the dolphins?”
Sadly, the dolphins’ whistles showed no more than third or fourth-order Shannon entropy. They beat out most primates, but not by much.
“I guess they were too busy having fun after all,” Sonia said wistfully.
Tom had glowered all the way through this. Now he asked, “And the signal from the mother-thing? What does your analysis tell us about that?”
“It passes the Zipf test,” Rosa said. “And as for entropy—”
She laid a new line on her graphical display of plant, chimp, dolphin, human languages. Sloping shallowly, it tailed away into the distance of the graph’s right-hand side, far beyond the human.
“The analysis is uncertain,” Rosa said. “As you can imagine we’ve never actually encountered a signal like this before. Human languages, remember, reach Shannon order eight or nine. This signal, Morag’s speech, appears to be at least order thirty. We have to accept, I think, that Morag’s speech does contain information, of a sort. But it is couched in a fantastically abstruse form. As if it contains layers of nested clauses, overlapping tense changes, double, triple, quadruple negatives, all crammed into each sentence—”
“Jeez,” Shelley said. “No wonder we can’t figure it out.” She sounded daunted, even humbled.
It wasn’t a comfortable thought for me either. The bright new artificial minds, such as Gea, would surely have scored more highly than us on a scale like this—but at least we made them. This was different; this was outside humanity’s scope altogether. Suddenly we were going to have to get used to sharing the universe with a different order of intelligence than us.
“And,” I said, wondering, “it’s coming out of the mouth of my dead wife.”
Again my words sparked Tom off. He stood up, pushing back his chair. “No,” he shouted. “
It’s not her.
That’s the point—can’t you see? Whatever is animating that fake shell, whatever is producing these alien words,
it is not her.
” And he stormed out of the room, without looking back.
Sonia hurried after him, with a mouthed “Sorry” to me.
The meeting broke up. I was left with the patient VR image of Rosa, and the graphs that scrolled in the air around her.
I apologized for Tom.
“Give him time,” Rosa said. “After all it is a strange business. His mother is trying to talk to you. . . .”
“If it is Morag.”
“
You
believe it is, don’t you? But we face this odd mixture of emotional power—she is your wife, after all, and Tom’s mother, there can hardly be stronger emotional bonds—coupled with this strange symbolic overcomplexity. She has something she needs to tell us, that seems clear, but she doesn’t seem to know how to do it.”
I had no answer. I just sat there, my head and limbs heavy; I felt simply overwhelmed by all I had learned.
Rosa watched me carefully. “Are you all right?”
“I think so. It’s all a lot to take in.” I rubbed my temples. “So much is going on, so fucking much. I’m trying to push forward the hydrate project. I’m trying to deal with Tom, and John, and everybody else. Even Shelley. Even
you.
And I have this business of Morag, which only seems to get stranger and stranger. I don’t want to hurt anybody, Rosa. Especially not Tom.”
“I know that,” Rosa said gently. “You think you are weak. Don’t you, Michael?”
I shrugged. “What else should I think?”
“You are buffeted. You are surrounded by epochal events in our history; you are at the center of an extraordinary storm. And at the same time you are being subjected to these extraordinary manipulations and messages.”
I forced a smile. “Messages from beyond the grave?”
“From somewhere else, certainly. We may yet learn there is some connection between all these different sorts of strangeness in your life, and things will get more complicated still.”
Just as her brother had hinted, I thought uneasily. But I had enough conspiracy theories in my life.
Rosa said, “But in the middle of the storm
you keep going,
Michael. You keep trying to do your best for everybody. You know, you remind me of Saint Christopher.”