THE EXOANTHROPIC PRINCIPLE

by Carl Frederick

Those who ask big questions must be prepared to accept the answers….

Colin plopped the last of the cardboard boxes onto his desk at the Institute for Distant Communication: Alien Intelligence Group. He smiled. If Bing, his new colleague, was to be believed, the IDC:AIG had more syllables in its name than it had research scientists. Not that his presence would make a difference in that regard; he was a mathematician in a den of physicists.

He cast a glance at his bookcase—empty, depressing, like a deserted beehive—then pulled open a few boxes of books and populated a shelf and a half. In one of the boxes, he found his Brigit’s Cross plaque. Kicking off his shoes, he grabbed the plaque, climbed onto his desk, and set the Brigit Cross on the molding above the window.

Just then, the phone rang. Colin dropped to his knees and rummaged on the cardboard-strewn desk for the phone. He found and answered it.

“Colin!” came Bing’s voice, his excitement apparent in even one word. “I think maybe at long last we’ve got something. Come on down, if you would.”

“Of course,” said Colin. “Where?”

“Farcast lab.”

Colin chuckled. “As I said, where?”

“Oh, right! One flight down. Room 302.”

Darting through the door into the Farcast lab, Colin saw Bing Robinson and two others whom he didn’t recognize standing over a desk gazing intently at a large computer display. From a speaker on the monitor came a pervasive hum, as if from a defective fluorescent fixture. A chirping sound, like the twittering of finches, interrupted the hum at regular intervals. Although Colin couldn’t identify much of the room’s instrumentation, he did notice an old line printer in the rear of the lab. Buzzing in rhythm with the chirps, it disgorged a waterfall of continuous-feed paper to the floor. He was surprised that a modern laboratory would still use a line-printer. But then, this lab didn’t look particularly modern.

The scene, particularly the hum, brought to mind his visit as a boy to his mother in the hospital. He pushed away the memory and walked forward.

Bing turned at his approach. The others did as well—but only briefly before returning their gazes to the monitor. Bing drew them away to make introductions. Katya Shirova was an experimental physicist and Neville Fox, a theorist. The two were cordial but clearly had other things on their minds.

Bing grabbed a sheet of printout from the desk and thrust it into Colin’s hands. The sheet held only rows of dots. Colin stared at them:

… ….. ……. ……….. …………. …………….. ……………….

… ….. ……. ……….. …………. …………….. ……………….

… ….. ……. ……….. …………. …………….. ……………….

“I’ll save you counting them,” said Bing. “They’re three, five, seven, eleven, thirteen, seventeen, and nineteen.” He nodded toward the speaker. “The chirps you hear are that sequence at high frequency. Blips separated by short pauses and longer pauses between the numbers.”

“Are you…” Colin struggled to take it in. “Are you saying you’re receiving extraterrestrial signals?”

“Certainly looks like it,” said Bing.

“Maybe not be so quick with conclusion,” said Katya, turning from the monitor. “You remember LGM.”

“LGM?” said Colin.

Neville swiveled into the conversation. “LGM. Little Green Men. That’s what some astronomers called pulsars when they thought that only an intelligence could be the source of such regular pulses.”

“I think,” said Bing, “that these prime number sequences are from an intelligence.”

Smiling, Neville glanced at the monitor. “Actually, so do I.”

“This is wonderful!” said Colin. “Absolutely fantastic!”

Bing and Neville gave slow, shy smiles, the way children might when given an unexpected compliment. Katya looked pleased as well.

“We really don’t have much,” said Neville with a self-deprecating shrug. “Some prime numbers, only seven of them.” He shrugged. “The sequence repeats approximately every 15.5 seconds. The hum frequency is 142 Hz, almost exactly—”

“The hum?” said Colin. “Is it from the same source?” Again, he pushed that long ago hospital visit from his mind.

“Most likely,” said Bing. “Sort of a carrier—or an indicator that we should stick to this wavelength.”

“And that wavelength?” said Colin, eager to show he was conversant in SETI matters, “Twenty-one-centimeter, neutral hydrogen, I imagine.”

“No, not radio waves,” said Neville. “Actually we scan through frequencies and polarizations of coherent gravity waves.”

“What?” Colin felt his eyes widen in wonder. “I didn’t know you could do that.”

“Oh, we physicists can do a lot,” said Neville, lifting a cup from the desk, “given enough money—and enough coffee.” He pointed at the printout Colin held. “And voila!”

Colin looked down at the printout. “Interesting that they don’t consider one or two as prime.” He blew out a slow breath. “They probably define a prime as an integer with no integral divisors less than itself. Makes Fermat’s Last Theorem easier to state.”

In thought, he gazed absently at the monitor speaker. “I wonder if the hum frequency is arbitrary.”

Katya cocked her head. “Arbitrary?”

“Let’s assume it is,” said Colin. “And also assume the time between transmissions is also arbitrary. By arbitrary, I mean chosen for convenience, or rather for ease of representation. And further, assume the Axiom of Choice.”

Bing and Neville exchanged puzzled glances.

“You know,” said Colin, softly as if to himself. “We might be able to deduce something.” He fingered an imaginary piece of chalk. “Let’s call their basic unit of time a … a ‘woof’ and take that as the time between transmissions. A transmission every woof.” He looked away at an imaginary blackboard. “Then in cycles per woof, the hum frequency would be 142 times 15.5, approximately.” He narrowed his eyes in thought. “Which would be … 2201.” He paused. “Ah, how about this?” he said after a few seconds. “If they picked an easy number for the frequency, as we might pick 100hz or 1000hz then, if we let A be the base of their number system, their equivalent would be A squared or A cubed or perhaps A to the fourth—which would have to be approximately 2201.”

Stealing a glance at his listeners, he saw signs of their eyes glazing over. He had to admit taking some small satisfaction in getting that result from physicists.

“So,” Colin continued. “Trying base six, we’d have 6, 36, 216, 1296. Nope. Nothing anywhere close to 2201. Trying seven, 7, 49, 343,”—he paused—”and 2401. Closer, but still no cigar. Eight gives 8, 64, 512, 4096. No good. For nine, 9, 81, 729, and”—again a pause—”6561. A strong no. Ten won’t work of course. Eleven gives 11, 121, 1331. Not even close—”

“That’s fine,” said Neville, taking off his glasses. “We get the idea.”

“And twelve,” said Colin, ignoring the interruption but noting the little furrows of bite marks on the temple-tips of Neville’s glasses, “gives 12, 144, 1728. Closer, but no. Thirteen gives 13, 169,”—yet another pause—”and 2197. Ah good. That’s only four off from 2201. Well within measurement error, I should think.” He let out a long breath. “Yes,” he said, with finality. “My guess is that they have a base thirteen number system.”

“You’re kidding,” said Bing.

“It would imply an odd biology,” said Neville. “A fingers per hand issue.”

“It’s the best I can do, I’m afraid,” said Colin with a smile to Bing. Again he gazed at the printout. “3, 5, 7, 11, 13, 17, 19,” he said, distantly. “It’s too bad we can’t send them 23 as a reply and see what happens.”

“Oh, but we can,” said Bing. “Or we will be able to once we’ve cooled down the Farcaster.”

“We just don’t have enough liquid nitrogen left to cool the gallium arsenide emitter,” said Neville. “Jake, our lab technician, has taken the van and a Dewar to the university to borrow thirty liters or so. He should be back in half an hour.”

“What I meant,” said Colin with a chuckle, “is send a reply and see how they react—without waiting the, I don’t know, the hundreds of years of light travel time.”

“Not a problem,” said Bing in an amused voice. “Round-trip signal delay is negligible.”

“Excuse me?” Colin, wide-eyed, wondered if Bing was kidding.

“I do hope they keep transmitting,” said Neville.

“Wait a minute. Wait a minute.” Colin felt suddenly thrust into the Alice in Wonderland tea party. “What do you mean, the delay is negligible?”

Katya gave Bing a puzzled look.

“Sorry,” said Bing. “I didn’t have time to brief him yet.” He turned to Colin. “Primitive as this place looks,” he said, “we’re actually doing some cutting-edge physics here.”

Colin threw a glance at the printer.

“Our legacy printer?” said Bing. “Yeah, primitive, but there’s something comforting about hard copy you can tack to a wall.”

“Please,” Katya cut in. “Perhaps brief him in your office. I need do transmitter calibration before Jake comes with nitrogen.” She smiled at Colin. “I will enjoy to talk later.”

Bing stood. “Fair enough.” Turning to Colin, he said, “But let’s use your office. Mine’s a mess. And maybe I can help you move in.”

“I would have imagined,” said Colin as he walked back to his office with Bing, “that having detected an alien intelligence, you’d be much more excited.”

“I’m afraid to be excited,” said Bing. “We’ve been burned before. We’re pretty sure we’ve eliminated all mechanisms for pranks now, but…” He shrugged. “Katya almost died from the embarrassment—which is why she’s so cautious now. It’s lucky we hadn’t released the news to the media.”

“And that’s why you’re not doing it now,” said Colin. “Yes?”

“That and not wanting the project taken away from us just when we start chatting with our aliens.”

“Speaking of chatting,” said Colin, “you were kidding, right? When you said the signal delay was negligible.”

Bing shook his head. “I wasn’t.”

For the sake of conversation, Colin slowed his walk toward the stairs. “But Einstein said nothing can exceed the speed of light—not even information.”

“Well … yes and no.” Bing gave a grunt of a chuckle. “You have to be very, very careful when making a statement about physics. It’s as if the universe takes any little loophole it can find and acts on it.”

“But what does this have to do with the speed of light?”

“Well, ‘nothing goes faster than light’ was first taken to mean matter.” Bing spoke in synchrony with his tromping up the flight of stairs. “But the distant galaxies in our expanding universe go, in effect, faster than light. Of course they’re going directly away from us so we can’t see any light from them.” He looked over his shoulder, as if to see if Colin was following him, both literally and figuratively, then went on, “So then people said the idea applied to information.” They went through the fire door to the fourth floor. “But quantum entanglement,” said Bing, scarcely pausing for breath, “implies instantaneous transmission of information of some strange sort. So now one says that no message can be transmitted faster than light.”

Bing waited as Colin opened the door to his office. “But even here there’s wiggle room.” Bing followed Colin into the room, took a quick glance around, and then laughed. “And that’s not a comment on the clutter in your office.”

“You’re most kind,” said Colin as he cleared off a chair for Bing.

Bing sat. “Anyway,” he said with the enthusiasm of a kid, “if the information is stochastic in nature, which means we’re not certain of the message contents, then there’s the possibility of superluminal transmission. But the big loophole, the one Project Farcast makes use of, is that if the receiver of the message can’t tell where the message came from, then it’s allowed to have traveled faster than light.”

Colin circled around his desk to its chair. “That’s a little hard to believe,” he said as he sat.

“It doesn’t violate Einstein,” said Bing. “Tachyons and all that.”

“Are you saying that tachyons actually exist and you’ve actually been able to detect and manipulate them?”

“Well, no. Not directly. But Gell-Mann’s Law says that if something is not forbidden by physics, it must exist.” Bing laughed. “Gell-Mann proposed it as sort of a joke, but it’s predicted a lot of good stuff.”

“Stuff?” said Colin.

“Like tachyons. In theory, they interact with, and only with, gravitons. And so…” Bing spread his arms in a pantomimed “ta-da.” “And so using focused, coherent gravitons, we’ve been able to modulate and demodulate those theoretical tachyons. And so we’ll be able to transmit stuff to these aliens—we think.”

“You think!”

“It’s the best I can do, I’m afraid,” said Bing with a smile.

“But that means you’ve no idea where these aliens might be?” said Colin.

“Absolutely none. They could be across the galaxy, although probably not—farther is more probable. They could be across the universe or even off in another pocket universe. Especially as the speed of light isn’t even a defined concept when going from one pocket universe to another.” He looked quizzically at Colin. “You do know what pocket universes are, don’t you?” He didn’t wait for an answer, but pointed to the plaque above the window. “What is that?”

“That?” Colin followed Bing’s gaze. “That is a representation of Saint Brigit’s Cross.”

“Doesn’t look much like a cross to me.”

“Well, it is. Saint Brigit made it out of rushes on short notice.” Colin noticed his new colleague’s baffled expression and tried to explain. “We Irish often hang one over a doorway to bring luck.” He lowered his gaze from the cross to the window below it. “Snow,” he said in a tone of disgust.

“Hardly unexpected,” said Bing, “in New York City in January.”

Colin glowered at the unwelcome whiteness. “Maybe Saint Brigit will bring the good luck of an early spring.”

Bing laughed. “You know,” he said. “Niels Bohr used to tell the story of friends who had a horseshoe over their door for luck. Bohr asked them, ‘You don’t genuinely believe in that, do you?’ and they answered. ‘No. Of course not, but we’ve been told it works whether you believe it or not.’”

Colin forced a thin smile. “My belief,” he said evenly, “might be a bit more spiritual.”

Bing looked at first astonished, and then mortified.

“Oh, come,” said Colin in some amusement. “I’m sure you’ve run into believers before—even among you physicists.”

Bing’s expression morphed to sheepishness, and then to inquisitiveness. “Look,” he said. “I’m sorry, but I—”

“It’s all right.” Colin spoke more abruptly than he’d intended.

“But I wonder,” Bing went on, tentatively. “Do you … Are you a creationist?”

“You mean do I believe God created the universe? Yes, I do. Absolutely. Without doubt.”

“It must be good to believe in something absolutely,” said Bing with an almost wistful expression. “What faith I have, I place in science.”

“There are many degrees of creationism,” Colin said almost by rote; he’d had this conversation many times before with scientists. “I believe God’s creation of the universe followed the precepts of science. After all, he created science.”

“But what gives you the certainty?” Bing insisted. “Is it because you believe, as I’ve heard creationists maintain, that the eye, for example, is too complicated to have happened purely through evolution?”

Colin gave a rough laugh. “The evolution of the eye? Irrelevant! I’ve no problem with evolution. But just look around you.” He gestured, expansively. “That proves the existence of God.”

“What?” There was a challenge in Bing’s voice. He gestured as well. “You mean your desk, the bookshelves, the blackboards?” He nodded toward the window. “Or do you mean the Earth, the sky, the flowers, the—”

“To hell with the flowers,” Colin barked out. “I hate flowers. I have allergies. What I mean is the fine structure constant, Planck’s constant, the properties of the elementary particles, and most critically, the cosmological constant.”

“You know a lot of big physics words,” said Bing in a voice at the boundary between anger and jest, “considering you’re a mathematician.”

Colin, rising to anger despite himself said, “If the cosmological constant were minutely different from its God-given value, then life and even chemistry would be impossible.”

“Ah, the anthropic principle,” said Bing with a sigh. “The idea that the probability of a livable universe developing by chance is essentially zero. The idea that only God could have created such an unlikely universe.”

“Yes. Most definitely yes,” said Colin. “There can be no other logical solution.”

“Look,” said Bing. “You can believe in anything you like—as long as you don’t confuse belief with science.”

“Damn it, this is science,” Colin growled. “The fine-tuned value of the cosmological constant. There is no possible way it could have happened by chance.”

“In fact, there is,” said Bing, clearly suppressing anger.

“Do tell me.” Colin’s voice dripped sarcasm. “I’m all ears.”

“I’m sorry if I’ve offended you,” said Bing. “I didn’t mean to. Let’s discuss this like intelligent beings.”

Colin gritted his teeth, then decided he’d not let Bing take the high ground alone in the issue of Christian charity and forgiveness. “I’m sorry as well,” he said, struggling for a smile. “I’m afraid I have something of a temper. A congenital condition, I’m afraid.” Colin knew he was being disingenuous. He was not about to tell Bing that when his mother was taken from him, his faith had wavered. He’d challenged God to provide a reason to believe in Him and, years later, when he was old enough to understand it, God provided the cosmological constant.

“All right,” said Colin with a sigh. “Let’s hear your explanation of how our universe can exist.”

“Not my explanation, exactly,” said Bing with no lingering hostility in his voice. “It’s Leonard Susskind’s formulation of string theory. Susskind says that up until a few years ago, there were only five or six possible Calabi-Yau manifolds: solutions to the string theory equation describing the universe. Now they estimate that there are over ten to the five hundred solutions—a googol to the fifth.” Bing’s eyes all but glowed with fervor. “And most of these solutions might actually exist as distinct pocket universes in a vast megaverse. A vast landscape of possible solutions—of universes. Each of these universes could have different values of the physical constants and could even have different numbers of uncompacted dimensions. So, by virtue of there being so many universes, some of them will, by chance, be right for us. And we’re in one of those.”

“Come on,” said Colin. “Be serious. Different numbers of dimensions? This Susskind is crazy.”

“Oh,” said Bing, “you know him then, do you?”

“Do you really consider this physics?” said Colin. “My God! Ten to the five hundreds of universes with differing physical constants—and differing dimensions?”

“Well, all universes have ten dimensions, we think,” said Bing, “or eleven if you accept m-brane theory. But some of them are compacted, folded, too compact to measure. At a scale of ten to the negative thirty three centimeters or thereabouts.”

“What the hell is a compacted dimension, really?” said Colin, making no attempt to keep incredulity out of his voice. He was actually glad though, that they were getting away from theology. He was pretty sure Bing felt the same way.

Bing looked at him with a puzzled expression.

“I mean to say that I have only a layman’s familiarity with the term. I’m a specialist in information theory and complex analysis, but I’m not a differential geometrist or topologist.”

“It’s actually easy to visualize,” said Bing. “Imagine this office having a 3-dimensional coordinate system—we’ll use polar coordinates.” He touched the tip of his nose. “To specify the coordinates of my nose, you’d need two angles and a radius line from the corner of the room—the origin of the coordinate system—to the tip of my nose.” He twitched his nose like a rabbit. “But string theory says there is no such thing as ‘points’ in space, so that radius has to be thought of not as a line, but as a very thin rod. And with a rod, there’s another dimension—the angle around the rod. QED, a 4-dimensional coordinate system. Of course, in a universe of six or seven compacted dimensions, things get a lot more complicated.”

Colin stared with amused incredulity. “This sounds like fiction—just another way for some physicists to try to deny the existence of God.”

“No,” Bing protested, “just taking the need for God out of physics. You can have God. It’s no problem.” He paused. “Although, for reasons of physics, I think any god would be restricted to the particular pocket universe he was in.”

“What?” Despite himself, Colin laughed. “No! You’re missing the whole idea of God. God is not a localized phenomenon.”

“Sorry.”

Just then, the phone rang. Colin, thankful for the diversion, answered it. When he hung up, he announced, “Jake is back with the nitrogen.”

Bing jumped to his feet. “Great! Let’s go.” Colin stood as well, but more slowly and with dignity.

“You know,” said Bing, glancing at the door in obvious impatience, “after a couple of years trying, this is the first signal we’ve ever received. I think you’ve brought us luck.”

“Oh?” Colin couldn’t help smiling. “You don’t genuinely believe in that, do you?”

“Touche!” Bing chuckled. “Perhaps I do. We physicists tend to be superstitious—ritually superstitious.” He started for the door, but Colin asked him to hold up a moment.

“I’ve heard it said,” said Colin, solemnly, “that two people can’t become true friends until they’ve had a knock-down, drag-out, shouting argument with each other.”

Bing nodded, then stuck out his hand. “Friends?”

Colin clasped it. “Friends!” He paused. “But I still believe.”

“No problem,” said Bing. “Belief isn’t subject to science or rational thought.”

“Descartes was a rationalist,” said Colin. “And he did prove the existence of God—using logic and rationality.” He urged Bing on toward the door. “Simply put, a belief in God is more rational than a belief in science.”

“I think that’s backwards,” said Bing looking over his shoulder, his serious expression contradicted by a crack in his voice. “You’re putting Descartes before the horse.” He darted through the door.

Colin threw a glance to the ceiling. “Give me strength!”

Colin, following Bing into the Farcast lab, again heard the hum. Even though it indicated the alien presence was still transmitting, he found the sound disquieting.

He saw Katya fiddling with some equipment next to the display monitor. Then he noticed that the line printer had streamed more paper to the floor. Apparently the prime numbers were still coming through. Neville, standing next to the printer examining the printout, caught Colin’s gaze. “Strange, in a way,” said Neville. “The data stream is absolutely constant.”

“In what way, strange?” said Colin.

“I would have expected some noise in the data stream,” said Neville, his eyes on the printout, “some suggestion of stochasticity. The fact that it’s missing suggests that the source is very distant—implying a total uncertainty of its position.”

Bing walked up. “Evidence perhaps that the signal might be from another pocket universe?”

“Quite possibly.”

“This is great!” Bing turned to a rack-mounted instrument cluster next to the printer. He peered at a circular dial calibrated in degrees K. The needle stood at 270. “Brr,” he said. “It’s cold on the roof.”

Neville glanced at the dial. “About twenty-six or twenty-seven degrees Fahrenheit. Yes. A bit chilly.”

“I thought Jake had gotten the liquid nitrogen,” said Bing.

“He’s just gone up to the roof with it.”

“You really believe in these multiple universes?” said Colin, annoyed for some reason at how matter-of-factly his colleagues discussed the issue.

“I don’t disbelieve in them.” Neville gave a tight-lipped smile. “I gather you are a skeptic.”

“I’ve never been called that before.” Colin nodded. “But pocket universes, higher dimensionality. Yes. I admit having difficulty believing it.”

“Well, our aliens could possibly be in a … in a galaxy, far, far away. Where have I heard that phrase before? But the megaverse is so much larger than our universe, I think the odds of the signal coming from another pocket universe are much greater.”

“As I said, I have trouble with the idea.”

Neville chuckled. “Then I guess you don’t think much of … oh, I can’t remember who did it, but of the calculation that a god cannot exist in only four uncompacted dimensions.”

“What?” Colin shot Bing an exasperated glance.

Again, Neville chuckled. “Sorry,” he said. “I ran down to my office for some aspirin and couldn’t help hearing some of your philosophical disputations through the wall.”

“Ah,” said Bing, pointing to the temperature dial. “There it goes.”

Colin turned his gaze to the dial and watched as the needle vibrated and moved slowly counterclockwise. “How low will it get?”

“Nitrogen boils at 77.2 degrees Kelvin,” said Bing.

“It’s cooling down now, Katya,” Neville called over to the Farcaster control console. “Should be ready in about ten minutes.”

“I ready now,” Katya called back.

Fifteen minutes later, Neville sat gazing at the monitor with his finger on a pushbutton. Colin standing with Bing and Katya behind, noticed that the finger shook.

“This is it,” said Neville, softly. “I hope we’re…”

“Go for it,” said Bing in a voice softer still.

“Udachi!” whispered Katya. “Good luck!”

Silence pervaded the lab—save for the hum. Then Colin heard the chirps and saw the string of primes ending in 19 displayed in white on the monitor.

“Here goes,” said Neville. He pushed the button twenty-three times in quick succession. His pulses displayed green on the monitor.

They stared in silence at the monitor. After five seconds or so, Neville said, nervously, “God, I hope I actually sent twenty three.”

“You did,” said Katya with a smile. “I counted on monitor.”

Then, at about the fifteen-second mark, there came a chirp and the monitor displayed:

-.- .-.-. .

“A response!” Neville shouted.

“This is great!” said Bing. “We’re communicating!”

“But what it mean, I wonder,” said Katya. “Short blips and long blips.”

They stared at the screen until, about fifteen seconds later, another chirp came:

.-.-. ..

Fifteen seconds later came nothing. But then after another fifteen seconds, they saw,

.-.-. …

“What do you make of that?” said Neville.

No one answered.

About forty-five seconds later came the next transmission:

.-.-. ….

“It’s got to be a message about time,” said Bing after about half a minute. “The short long short long short might mean the LGM will transmit its next message in n time units, and the short short short short is the number of time units.”

“Could be,” said Neville. “Yes. Delay of n time units. Good.”

The next message came a little over one minute later:

.-.-. …..

“Looks like you’re right,” said Neville. “Each transmission comes with a delay one woof later than the last.”

“Yeah.” Bing threw a glance to Colin. “Looks like you’ve added woof to our vocabulary.”

“I wonder,” said Neville, pointing to the -.- .-.-. . higher up on the screen, “what that initial symbol might mean, the dash dot dash.”

No one answered.

The chirps came in at an ever slower pace until, after the delay associated with the .-.-. ………… transmission, they received:

——

“What do you make of that?” said Colin, rhetorically.

After five minutes of no transmissions, Bing said, “Maybe they’re waiting for us to respond.”

“Quite possibly,” said Neville, “but we can only send dots.”

“Then I think we should send the next prime.”

“Twenty-nine,” said Colin.

“Okay.” Neville pushed the button twenty-nine times. A few seconds later, an answer came:

-.- ——

After staring at it for a minute or so, Colin said, “My guess would be that dash dot dash means ‘acknowledged’ or ‘correct’ and dash dash dash dash means ‘over.’”

“I agree,” said Neville. He pulled open a drawer and withdrew a lab notebook. “I think we’d better start a dictionary.”

“What we send our new friends now?” said Katya.

“I suggest we send nothing,” said Bing. “Not until we can send dots and dashes, and at the speed they’re sending them to us.”

“Agreed.” Neville glanced at his watch. “But, damn it, it’s after five, and a Friday. I’m sure everyone but us has bailed for the weekend. We’ll have to do it ourselves.” He furrowed his brow and looked off into the distance. “Bing and I can do the computer programming,” he said to no one in particular. Neville stood. “Katya,” he said. “Can you whip up something to drive the transmitter from a computer data stream?”

“Da. Of course. I am experimentalist.” She glanced over at a lab bench. “Must solder connector and configure microprocessor chip.” She headed for the bench. “You must give me data as USB-IV.”

“Done,” said Neville. “Let’s get going.”

In spite of the camaraderie of the small group, Colin had no doubt as to who was in charge.

“Neville,” said Colin. “I can help with the programming. I’m good at that sort of stuff.”

“Terrific,” said Neville. He darted to a phone and, with great solemnity, ordered delivery of a couple of pizzas.

“It will take many hours,” said Katya. “Will our friends wait for us?”

“Don’t think about it,” said Neville.

Colin, aware again of the hum, did think about it. In the rush to communicate, he’d almost forgotten the monumental significance of the event. And he wasn’t really interested in talking to this alien presence about physics, or even mathematics. He wanted to discuss important things with them.

Late that evening the Farcast lab lay strewn with empty pizza boxes reflecting bright from the ceiling fluorescents. The air held a rich amalgam of aromas: pizza, people working hard in close quarters, and the incense-like smell of Katya’s rosin-core solder. The soft hum persisted—ubiquitous, constant, uninterrupted by chirps for many hours.

The programming had gone well; now, rather than receiving and displaying dots and dashes, they could display words—that is, after they had deduced them and stored them in the program’s dictionary.

“All right,” said Neville, “I’ll send ‘acknowledged’ and ‘over.’ Agreed?”

All agreed and Neville made the transmission.

Almost instantly, came the reply:

acknowledged 5—3 -. 2 over

“Ah,” said Neville. “Now we learn arithmetic. Dash dot must be plus, and dash dash represents equals.”

“Or maybe,” said Colin, “dash dash means minus and dash dot means equals.”

Neville stared at the monitor. “Good point,” he said after a few seconds. “Let’s hope they’ll clarify it for us.”

“Interesting that the response came so fast,” said Bing. “Maybe we’re important. Maybe they have a person, creature, whatever, watching our transmissions full time.”

“Unless,” said Colin, “this is all CAI, Computer Assisted Instruction.”

Neville chuckled and then again sent the “acknowledged,” “over” pair. Once again, the response was quick.

acknowledged .-.—3 -. 2 -. 1 over

“What’s this?” said Neville.

“They’re testing us, I think,” said Bing. “Dot dash dot might be a question mark.”

“Testing? Are they, indeed?” Neville stared at the screen. “Looks like they’ve done this before. They’re telling us that dash dot can’t mean equals.” He glanced over his shoulder at Colin. “Yes?”

“Yes,” said Colin. “So it seems.”

Neville entered “acknowledged 6 over.”

acknowledged .-.—3 -. 1 over

“Seems you were right, Bing,” Neville entered “question mark,” “plus,” and “equals” into the dictionary definition table. Then he entered “acknowledged 4 over.”

acknowledged—= 3 .- 3 over

“I guess you passed the test,” said Bing.

Neville nodded. “And now we know minus and zero,” he said as he entered the new symbols into the dictionary. “Good progress.” He keyed the usual reply.

acknowledged 1 0 = 6 + 7 over

“What’s this?” said Neville. “Ah.” He turned to Colin. “You were right,” he said in an astonished voice. “Our Little Green Men have a base thirteen number system.”

“Apparently.” Colin was astonished as well, but tried not to show it. It’s good for these physicists to know humility from time to time. He smiled. “And it does show that, to some degree, the … the LGM think the way we do.”

“Oh,” said Neville, “I wouldn’t be so quick to anthropomorphize them.”

“The anthropomorphic rather than anthropic principle, maybe,” said Bing, lightly.

Colin shot him a glance before answering Neville. “At any rate, I think it means it’s likely we’ll be able to comprehend their thought processes.”

“Maybe so. Maybe so.” Neville keyed the reply.

acknowledged ? = 8 + 9 over

Neville turned to the others. “More tests on simple arithmetic. Sort of tedious after all the excitement.” He whipped off his glasses and rubbed his forehead. “We can probably be more productive in shifts. Why don’t you guys go out for some real food? I’ll carry on here until you get back. Then, I’ll grab a late dinner.”

Bing, Colin, and Katya agreed and headed for the door.

“Oh,” Neville called after. “And bring back some tea for me, if you would. English Breakfast, milk, no sugar.”

In a booth in Tom’s Restaurant, an all-night eatery just around the corner from the institute, Colin, Bing, and Katya waited for their food.

“Without set of common referents,” said Katya, “I not see how we really can communicate with aliens.”

“I assume that if our friends really exist,” said Colin, “they’ve probably done this before. We’ll just have to let them take the lead.”

“Unless,” said Katya, “technological civilizations very rare and we their first.”

Colin nodded. “The blind leading the blind,” he said, thoughtfully. “I hope not.”

Bing sighed. “And if they’re in another universe, we won’t even have a common language of particle properties to help us. I can’t see how we could hope to learn any physics from them in that case.” He turned to Colin. “It must be even worse for mathematics, a human-created rather than nature-created discipline.”

“To the contrary,” said Colin. “Not that I believe in these multiple universes, but—”

“We not believe, either,” said Katya. “It is hypothesis. Theory.”

“Fine,” said Colin. “But, even in your hypothetical other universe, I’d expect mathematics to be more—if I may modify a superlative—more universal than physics.” He was conscious of raising his head—angling his nose to an arrogant height. He self-consciously lowered it again. “I look forward to discovering their mathematics—wherever they are. And I think we could find something of a shared language based on number.”

“To what end?” said Bing.

“Well, for example, I would like to know if they’ve managed to prove Goldbach’s Conjecture.”

“I more am interested in real world,” said Katya. “Physics.”

Bing tapped the top of his water glass with a spoon, exciting standing waves on the surface of the water. “Yes,” he said with a sigh, and staring morosely at the waves. “There is so much we could probably learn from them—if only we had the language.”

Colin nodded. “Most interesting to me though, would be their philosophy.” Bing smiled, softly. “Belief in God?”

“Why not?” said Colin, defensively. “It’s an important question.”

“I not believe existence of God is important question,” said Katya.

“Me neither,” said Bing.

“What?” Colin swiveled to glare at Bing. The man was like a child. Most physicists were like children. “How can you say that? It’s the most important question.”

“But not to you, surely,” said Bing. “You already believe you know the answer.”

The comment hit home. Colin never could expunge a tiny twinge of doubt. When, as a boy, his mother had been taken from him, he couldn’t accept that it was the will of God. God couldn’t be that mean. He remembered the hospital room and the hum of the heart monitor—and how he felt when the hum stopped. The overwhelming loss. The silence. He felt himself begin to sweat.

“More important question is,” said Katya, looking on him with an expression of compassion, “where is food?” She smiled genially—Colin realized Katya was trying to lighten the mood, to ease the pain she’d somehow detected—then Katya waved toward an approaching waiter. “Easy answer. Here comes food now.”

Colin smiled. This Katya has a true soul.

“It’s not an important question to me,” said Bing as the waiter placed a platter of fries and a cheeseburger in front of him. “Because I can’t believe in a god so small-minded that he’d send someone to hell just because the guy didn’t believe in him.”

The waiter gave him a funny look and hurriedly moved more plates to the table.

Bing picked up a French fry and pointed at Colin with it. “And anyway, isn’t it more honorable to do good things in the world because it’s the right thing to do, rather than to do them because if you don’t you’d wind up as toast?”

“That’s not the way faith works,” Colin said in a louder voice than he’d intended. “God is … the compass for the world.”

The waiter took her tray and hurried away.

“Dear God, if there is a god,” said Katya, her face and voice showing gentle amusement, “thank you for food”—she picked up a fork—”and thank you for restaurant.”

Colin forced a smile, but inwardly, he fumed—convinced that Bing’s atheism was easy, not struggled with, a physicist’s limited view of the universe. Colin couldn’t help feeling superior; his belief came with constant effort, constant questioning.

Obliquely, Colin glanced at his dining companions bantering with each other like kids. He gestured at the two of them with a fork. “You guys are more alien to me,” he said, “than even our LGM.”

Katya raised her eyebrows and turned to Bing. “I think I am insulted,” she said with an expression of mock hurt.

“No, Katya,” said Bing, lightly. “I’m sure it was meant as a compliment. That’s the way I take it, anyway.”

Colin gave in; he couldn’t help laughing. “Hopeless!” he muttered under his breath.

Neville leaned back and took a sip of his English Breakfast tea through the little hole of the paper-cup cover. “They’ve taught me their multiplication and division signs and also decimals,” he said in a tired voice. “Or should I call them thirteenimals, perhaps?” He took a second sip. “So far, very conventional arithmetic. I’d expected something more … more alien.”

“Where are we now?” said Bing.

Neville nodded toward the monitor. “See for yourself.”

The last line of text on the screen showed:

delay woof 100

“That 100 is 169 in decimal,” said Neville, “a delay of almost forty-five minutes.”

“I wonder why?” said Bing.

“We’ll know soon enough.” Neville glanced at the time display at the lower right of the monitor. “In about ten minutes.”

“Maybe their sense of time is different,” said Katya. “Maybe they need more time than we to think.”

“Interesting idea,” said Neville.

Ten minutes later, the hum was interrupted by a burst of chirps. The monitor showed:

“Whoa!” said Bing. “What’s this?”

“I think,” said Katya, her eyes on the screen, “maybe they send raster.”

“Yes.” Neville slapped the desktop. “You’re right. Acknowledged here should be a carriage return.” He turned to Bing. “Can you get this back from disk and modify its output—sending it to the screen as well as the printer?”

“Easy.” While Neville stood and stretched, Bing replaced him at the keyboard.

After a few minutes, Bing blew out a breath. “This should do it,” he said, hitting the Enter key. The screen cleared and then displayed:

over

Bing stood and stepped to the side.

“Gentleman,” said Neville, sitting again at the console. “To the resolution limit of the data, I declare this a circle.”

“Thirty-nine by thirty-nine pixels,” said Colin, having counted them.

Neville glanced around. “All right then,” he said. “Let’s see what else they have for us.” He entered “acknowledged” and “over.” The monitor showed another jumble of dots and dashes with carriage returns, and the line printer spewed paper at a furious rate, littering the floor with an ever-growing pyramid of paper.

“Perhaps a finer raster.” Neville turned to Bing. “Yes?”

“Yes.” He leaned in over the keyboard. “I’ll switch the display from text to graphics mode.”

As Bing keyed the changes, Neville said, “May as well turn off the printer also. No need to waste any more trees.”

Bing nodded. After a minute or so, he said, “Done! I’ll redisplay from disk.” He pushed a button with a flourish and the monitor displayed another circle, this time at a high resolution. “Over” appeared at the bottom of the screen. This circle looked perfect. Bing again relinquished the chair to Neville.

“I always think there is something mystical about circle,” said Katya.

Colin nodded; he’d felt that way as well. “My guess,” he said, peering at the perfection on the monitor, “is that the raster is 2197 by 2197. 1000 by 1000 base 13.”

“Could be,” said Bing, staring at the screen. “Close to that, at any rate.”

“Fine, then,” said Neville. “Next!” He keyed “acknowledged” and “over.”

A flurry of raster images scrolled up the screen faster than the eye could follow. They seemed to be a sequence of circles: smaller to larger and then to smaller again, terminating as usual with “over.”

Once more, Bing replaced Neville at the keyboard. He called up the set of images from disk and displayed them one by one—giving something of the effect of a circle coming close and then receding.

“Any thoughts?” said Neville.

“Da,” said Katya, after a few seconds. “It look like it is maybe representation of sphere.”

“I concur.” Neville looked to Bing and Colin. “Do you agree?”

“Yes.”

“Definitely.”

“Right,” said Neville. He entered “CR over.”

Another rush of circle-like raster images danced up the monitor screen. They kept coming and Colin wondered if they’d ever stop. After almost a minute of dizzying scrolling, Bing, by unspoken, tacit agreement, replaced Neville once more at the keyboard.

When the scrolling finally stopped, Colin felt dizzy from having watched it. He sat. Neville and Katya did as well.

“This,” said Bing, with emphasis, “might take a little longer.”

More than an hour later, very late into the night, Bing sat up straight from the keyboard and stretched. “It’s a raster of rasters of rasters,” he said in a weary voice. “A sequence of spheres.” He splayed his fingers over the keyboard before resting them on the home-keys. “Here, I’ll show you—sphere by sphere.”

After the demonstration, Neville said, “A sequence of spheres small to large and then to small again. I wonder what it means.”

“Maybe is something about time,” said Katya. “A movie. Sphere come close then go away.”

“But why?” said Neville. “What could they be trying to—”

Bing gasped.

Neville turned to him. “What?”

“That’s not a time evolution,” said Bing at a whisper. “I’m pretty sure it’s—”

Katya gasped as well. “You are right, Bing,” she said almost as softly. “That is only answer.”

Neville looked at the monitor where only a dot showed in the middle of the screen and a question mark and “over” at the bottom. “My God!” he said in a loud whisper. “Intellectually, I knew this was possible, but I didn’t really believe it.”

“What?” said Colin, his speaking voice sounding loud in the lab, which, save for the pervasive hum, was otherwise silent. “What’s going on?”

“It’s not a time evolution,” Bing repeated. “It’s a representation of a 4-dimensional sphere.”

Instantly, Colin saw the truth in the statement—and he knew he would have deduced it himself had it not been unwelcome news. It meant they were communicating with beings from a world of four space dimensions—from another universe. And that meant the megaverse was real and not just some theory of a deranged string theorist. That in turn meant the anthropic argument was moot. We are not necessarily in Leibniz’s best of all possible worlds—not even the best of all possible universes.

Stunned, he became aware of the sound of speech.

“Four space and one time dimension—at the minimum,” said Bing in a voice filled with awe. “From another pocket universe. Susskind was right.” He shook his head slowly, as if trying to clear it of disbelief. “That certainly explains the clean, non-stochastic data.” He stood. Everyone stood. To Colin, the standing seemed almost an act of reverence.

Neville pointed to the question mark at the bottom of the screen. “It’s our turn again.” He rubbed his chin. “They’re asking for our dimensionality, I presume.” He looked from face to face. “Agreed?”

No one had any other explanation.

“I can pull up their 3-sphere off the disk and send it back to them,” said Bing. “It’ll just take a minute.”

“Excellent!” said Neville.

Bing sat and leaned in over his keyboard, engaging in a flurry of programming. His energy contrasted with the overall air of happy exhaustion. A minute or so later, he looked up over his shoulder at Neville. “Just give the word.”

“The word!” said Neville with a smile.

With an exaggerated motion, Bing hit “enter.”

Again, a sequence of rasterized circles scrolled off the screen—this time in green, a transmitted rather than received data stream—ending with “over.”

“Their turn,” said Bing.

Neville nodded.

In silence, the four stared at the monitor screen—and waited.

For a long couple of minutes, they waited. Then the screen scrolled up a line and displayed at the bottom:

delay woof 200

“Oh, no!” Bing cried out. “Now an hour and a half delay. Why the hell do they need to take so long?”

“I do not like to wait either.” Katya rubbed her eyes and suppressed a yawn.

“Once more,” said Neville, his eyes locked on the message, “it looks like maybe we’ve given them something to think on.”

“I could really use a nap,” said Bing. “I wish I’d kept my sleeping bag in my office.” Colin checked his watch. “It’s nearly dawn.”

“I’m wiped!” Bing said with a long breath. “Adrenaline has its limits.”

“Now that you’ve mentioned it”—Neville also suppressed the contagious yawn—”I’m not exactly ready to run a marathon either.” He brightened. “Why don’t we go down to Tom’s for an early breakfast? We have the time. We have a lot of time.”

Bing and Katya murmured their approval of the idea and started toward the door, but Colin said, “I think, if you don’t object, I’ll stay here and mind the store.”

Bing looked at him for a long moment. “How do you like your coffee—or do you prefer tea?”

Colin chuckled. “Coffee, please. Black. And thanks.”

Colin walked the others to the door then returned to the computer console. He knew he needed food as much as the others, but he needed time alone more—time to acclimate himself to the idea of the megaverse and to try to shoehorn the concept into his belief structure. And most of all, he needed time to test the structural strength of his faith now that one of its supports, the anthropic principle, had crumbled away.

He turned his eyes to the monitor, to the message:

delay woof 200

Staring at it, he gradually accepted the idea that he, Bing, Katya, and Neville had actually made contact with a people from a 4-1 space-time. These people must be superior, great, large; their 4-space could hold an infinity of his 3-space universes. These LGM were something bigger than himself. He yearned to talk to them—to ask them important questions.

He grew aware then, of the hum and listened to it with a feeling akin to veneration. The hum: a mantra, a hymn sung by a universe. He closed his eyes.

He started at the sounds of his colleagues returning. His first thought was that they’d forgotten something, but then he accepted that he’d used the time in timeless meditation. But it had not been sufficient meditation; he hadn’t found answers to any of the big questions. He stared at the monitor—a portal to another universe, a world of creatures much closer than he to the infinite. Over time, they will point me toward those answers.

Colin stood from the console as the others approached. Breakfast had clearly worked; his colleagues seemed re-energized and exhilarated.

“Back and with minutes to spare,” said Bing handing forward a large coffee. Colin received it with thanks.

“Anything exciting happen while we were away?” said Neville.

“No.”

“In … in three hundred seconds something will happen,” said Katya. “Exciting something. We make history!”

The four stared in silence at the monitor until, some three minutes later, the screen scrolled up one line and displayed the message:

delay woof 1 / 0

“What?” said Bing. “What the hell does that mean?”

“I think this is not good,” said Katya.

Suddenly the lab became deathly still. It took a moment for Colin to realize that the hum had stopped. Silence. He shivered. Again, the silence.

“I don’t understand,” said Bing, clearly crestfallen.

“Delay of one over zero,” said Neville little above a whisper. “Infinity. I can’t believe it. I can’t believe they don’t want to talk to us.”

“I think it means our three dimension world can teach them nothing,” said Katya. She raised a finger then pointed it at the monitor. “But,” she said, smiling, “We know you are out there now. We not alone. And if talk to us mean so little, there must be many many out there.”

“I guess it shouldn’t have been a surprise, really,” said Neville, softly as if to himself. “What could we learn from two-dimensional beings? To them, we’d be gods.”

“What do we do now?” said Bing.

“We keep searching.” Neville sighed. “As long as we have funding, we keep searching.”

“Gods,” Colin whispered.

Bing turned to him, heavy concern showing on his face. “Colin. What’s wrong?”

“Nothing,” Colin managed. “Nihil. Nothing.” Afraid that his visage would contradict him, he turned away. “I need to take a walk.”

*

Walking eastward in the predawn, Colin bore the January cold like a penance. A patina of unblemished snow lay on the silent, residential street. He remembered a quiet snow from the past; as a child, he’d prayed for a cure for his mother but his prayers were answered with silence—as from a hum that went dead.

Colin felt a snowflake hit the corner of his eye. It felt like a cold tear. He felt both eyes grow moist. Impelled by snowflakes, he cried for his lost compass, his dead mother—and his god.

As he walked, the sky grew ever brighter until, as the upper edge of the sun’s disk breached the horizon, he was engulfed in a fiery brightness. Emanating from the sun, light poured through the narrow street he trod, bouncing from the white snow, reflecting from the apartment buildings, coruscating from the windows. Stunned at the landscape bleached white by the searing brilliance, he stood in silent awe.

He had read about this: Manhattanhenge—the day when the sunrise aligns with the cavern-like streets of the city. And as the sun rose higher, so did his spirits. As his intellect reemerged from the morass of emotions and memory, he suddenly stopped feeling sorry for himself. Neville was right. We keep searching.