Latent Variables

We were all faking it. 

Walking through the nearly empty University of Washington campus as if everything were ok, James Deaning our way as we crossed the street without looking both ways–no need when there are no sounds of cars or buses. The streetlights were on, strange but not when you consider the flexibility needed in the Pacific Northwest. It was hours yet before nightfall on a Tuesday afternoon, but the brownian motion expected on a university campus was just . . . not.

Saul walked with the two girls he’d recently met, one of which he was warmly aware he was attracted to. One was studying geology and the other environmental engineering.

“Where to?” he said.

“One of the libraries, one of the geology libraries,” said Amber. “We’ve been getting together with some other people and talking about–” and here she pointed up with her chin while keeping her eyes on him.

The other girl, whose name he didn’t remember, led them through the front door of the Health Sciences building. They walked like they belonged through the empty lobby and as they approached the elevator Saul realized the signage. They were in the building where medical students studied using real cadavers. Why would a geology library be in this building? Had the building been this cold a moment ago?

He walked into the elevator a little anxious. Amber pressed the B3 button, down at least three floors. In a building containing dead people. He tried to control his breathing, his heart beating down to his arms and legs.

When the doors opened all he saw was concrete. The two girls exited and made to go right. The other girl, was her name Eve?, turned and said, “it’s ok. We’re ok here.” Saul followed and saw that he was in a hallway that extended to the right and to the left, nothing but concrete.  A memory of a zombie movie with a prominent cinder block wall. He followed the girls. 

It was a long hallway. Concrete was good for sound reflecting, he remembered, meaning that so long as there was line of sight you could easily hear voices even at a distance. No line of sight, though, meant you would likely not hear someone who was just around the corner. Why was he thinking of this? Was there someone just around the corner the world could not hear or see? His mind meandered.

At the end of the hallway they turned right again. A large glass window invited him to the Earth Sciences Library. The girls went in. He waited outside. Beyond the glass he could see two dozen people sitting on couches, chairs, leaning on walls, looking at giant oversized books, atlases. 

He could also see two LCD screens on the walls, one showing a news station and the other showing a split view of the LASCO Coronographs that everyone around the world had become experts at these last few months. A black circle at the center obscured the sun to block its glare, but all around you could see the sun’s corona, solar flares, ejecta. And there, just coming into view, inside Mercury’s orbit and in an impossible orbit perpendicular to the ecliptic, were the dots.

Saul could feel the shared horror even out here in the hallway. Some of the people in the library were staring at the screens, fear thinly veiled. The others carried hushed conversations intended to distract them from feeling the edge of the cliff. He could tell they were hushed because their lips barely moved.

The only other time Saul had felt something similar was after 9/11, when everyone walked around for days and weeks in a stupor, eyes glazed and dread weighing them down. He’d worked as a cashier at the time and when ringing up customers he had asked, “are you handling it ok?” They knew what he meant. Some could respond. Most could not. Some seemed grateful that someone saw them. A mild form of triage, he supposed. What was happening now was worse, because it was impending, because it was imminent. It affected everyone, everywhere. And it had yet to actually happen.

He entered the library and tried to smile, like everyone else, faking it.

***************

Man is by nature a social animal. Saul smiled with his mouth and his eyes and spoke with a low, but clear voice. He asked questions of each person he talked to, asked if they were handling it ok, and actively listened when they tried to articulate what they didn’t realize was primal dread. He asked about their work and their families and their pets. Some were put at ease by this small chance to feel normal, and some startled and looked angry. How dare he try to distract them from worrying about this end of the world? 

He eventually found Amber, zeroing in on the outline of her body leaning against a wall, and thanked her for inviting him. “But why are we here?” he said.

“Eve?” said Amber, calling the other girl, the environmental engineering student, over.

Eve, oddly, repeated what she said at the elevator. “It’s ok. We’re ok here.”

Saul relaxed his shoulders and she continued. “We’re here to listen to a theory,” she said.

“About?”

“About that,” she tipped her chin up and to the right at the television where graphics showed the projected path of the dots across the surface of the sun. 

“A theory,” he said.

“Yes.”

“Why here? Why this building? Why the building that contains cadavers? Why three stories down?”

Amber and Eve giggled. “Feeling a little like a buried corpse?” said Amber. “A little too on the nose?” said Eve.

*************

Someone turned off both of the televisions. Everyone started walking towards one end of the library. There was a large screen and an older man standing in front of it. He might have been a staff member, maybe not a professor, but someone used to lecturing.

A woman, also someone who looked like they could be staff, spoke. “Welcome, everyone. Mr. Yeager asked for the floor this week. Before he starts I’ll say that there has been no new activity these past seven months. The dots are still orbiting the sun in an orbit perpendicular to the ecliptic, around 25 million miles, which is about 10 million miles inside of Mercury’s orbit. No one, as far as we know, has posited a credible theory as to what they are or how they are able to maintain such a seemingly impossible artificial orbit.

“Most theories worldwide have focused on game theory, specifically cooperative and competitive. Those who study game theory have convinced most nations that if we share less information then this entity cannot use it against us. So we watch, but we don’t hail them.” Her face darkened. Everyone knew what she was thinking. If the dots were an intelligence, and if they were playing a game, this display of an artificial orbit was essentially a fear tactic. 

“This meeting,” she continued, “is just for thinking aloud. A reprieve. Please don’t be negative. You are all part of the university in some capacity, you are academic. Approach this as such. Thank you.” She sat.

“Thank you, Dr. Darnielle, Sarah,” said the man. “I appreciate your time, everyone. My name is Albert Yeager. I work for the math department here focusing on combinatorics. Combinatorics focuses on the arrangements and combinations of objects. Probability lies within the scope of my field.

“The first thing I want to do is acknowledge some of the feelings some of us are having. There is a lot of fear, here and out there. There is a lot of apprehension and distrust and . . . melancholy. I would go so far as to describe it as an existential crisis en masse. It is terrifying. I assure you, I am not here to make fun of those feelings.”

“Here goes,” he said. He looked around the crowd, you could see his body language shifting, ramping up to speak on topic but still oddly subdued. “It’s not aliens. It’s not. It can’t be.”

Saul looked sideways at Amber and Eve.

Mr. Yeager continued. “It can’t be aliens. And I’m going to explain why, mathematically.”

Saul could see and feel people squirming. No one said anything. 

“First, I am talking strictly about aliens as envisioned by the general populace. Meaning they are somehow humanoid, and though they have technology far beyond ours that they can somehow communicate with us directly, on this plane.” Like a lecturer he paused to see the effect of his words. “Think of it this way, there very likely are aliens like that, but just as likely extra-terrestrial life could be mold or hive-mind oriented, or super intelligent but not conscious, and I mean conscious in the way that we perceive ourselves to be.”

“I believe that the probability of aliens being here in our solar system, now, is so unlikely that if it were real,” he paused, “it would instantly and concurrently prove the existence of God.”

*************

Instantly several people rose out of their seats, voices raised, some swearing. A couple of them walked towards Mr. Yeager with threatening body language. Others made straight for the library doors. Within moments the woman who had introduced him, Dr. Darnielle, placed herself between Mr. Yeager and the others. Saul thought he could make out what they were saying. She mouthed the words, “I don’t think this is a good idea, Eric.” He couldn’t make out what Mr. Yeager said to her. She considered it, then spoke to the people who had approached Mr. Yeager. Once everyone settled, she waved for him to continue.

“I started by saying that I am not making light of this phenomenon. And I was sincere. I wish for you to consider what I must say.”

In total seven people left. Saul sat on the nearest couch, making sure that he was slightly touching Amber’s arm.

“I’ll start with some background math,” he said. He wrote a large zero and a large one on the board behind him and pointed to one and then the other as he spoke. “Probability is expressed as a number between zero and one. The closer something is to zero the less likely it is to happen. The closer it is to one the more certain it is to happen. Tomorrow’s sunrise? I’d say 0.99 repeating. The sky turning purple? About 0.000001. You get the idea.”

One of the audience spoke up, “Eric, you know as well as we do that there were reports of these things approaching our solar system years ago, right? As horrifying as it seems, every nutjob who ever claimed to be abducted by aliens doesn’t seem to have been that nutty!”

“I know,” Mr. Yeager said. “I know the evidence is to the contrary. I followed those news reports the same as everyone else. But I am telling you, it is not possible for these things to be aliens. Not here. Not now. Please. Let me lead you to my conclusion.”

“Eric,” said another woman’s voice. “The pictures. The dots are not man-made. They arrived in our solar system. Even now they are maneuvering in a way that cannot be natural and that we sure as hell cannot replicate.”

Grumbles about this.

“Please, everyone, let me continue.”

“Keep going,” said Dr. Darnielle in a more hushed tone. “This may not be the most fun any of us have had in a while, but I’m curious.”

Mr. Yeager bowed slightly. “Thank you, Sarah. He reached into his pocket. “Here I have a die, a number cube. Pretty universal when talking about probability. If I roll the die on this table, what is the probability that it will come up, say, the number two?”

Saul said, “One out of six.”

“That’s right,” said Mr. Yeager. “One out of six. The truth is if I roll it on the table it can come up one, two, three, four, five, or six. But only one of those times will be the number two, so one out of six possibilities. In terms of percentages, one divided by six is zero point one six repeating. That’s 16%.” He erased the board completely and then wrote 0.16666 . . .  with 16% next to it. “As far as probability is concerned that’s actually pretty good. Closer to zero, but way better than Vegas odds! If someone tells you you have a 16% chance of winning the lottery you buy a ticket immediately!”

He erased the board again and turned on the projector and an image slowly started to materialize. It was a number line.

“Imagine that this mark all the way on the left represents the beginning of time, the universe, everything.” He took three steps to the right mark and said, “this mark represents this moment. Today. Tonight. The line connecting them represents all time from the beginning to now. 

“Those wonderful Vegas odds from a moment ago? One out of six? There were six possible outcomes.” He clicked on his laptop and lines appeared. The entire line on the board was now marked in such a way that there were six equal parts starting at the beginning of the universe to now. 

Mr. Yeager continued, slowing his words for emphasis. “If it holds true that the age of the universe is 13.8 Billion years then each of these six sections has a value of 2.3 billion years.”

Saul looked around the table. He could see wheels turning, even in those who were pretending not to be listening too closely. He could see that some were mental-googling already, making intuitive leaps.

A man at the back frowned. “You’re going to say that even with a 16% probability they likely could have come to earth 2 billion years ago.”

“That’s right,” Mr. Yeager said. “Even with the very good odds of 16%, it means aliens could have arrived here tonight or up to 2.3 billion years ago. If you’ll indulge me further, I invited a friend to join us tonight, a geologist, Amber. Can you tell us what the earth was like 2.3 billion years ago?”

Amber went to the board and nodded at the line that marked the beginning of the 6th segment of the line. “That,” she said, “we call The Great Oxidation Event.” She paused. “Most of the land masses had formed a supercontinent, Kenorland–”

“Like Pangea?” said a woman near the front.

“Sure, but that came much later. Kenorland happened about 2.7 billion years ago. Not the first supercontinent by the way, and still others happened before Pangea. By this time,” she pointed, “Kenorland was already starting to break up. There were inland oceans already. But The Great Oxidation Event is believed to have happened here. It’s a big deal. Life as we recognize it started here. There was plenty of life before, millions of years before, even photosynthesis. There was oxygen in the air, but not a lot. This is when biologically produced dioxygen started to actually accumulate in the atmosphere. Most of the stuff living around that time died off, but the rise in oxygen is what eventually allowed the development of multicellular forms. Like us.”

“Thank you, Amber,” said Mr. Yeager. “The point being,” and here he gestured to the others in the room, “is that even though there are very good odds, 16%, that aliens could have visited us here during this ⅙ portion of the universal timeline, that’s still a gigantic sized chunk of time covered, and that it’s entirely possible they could have shown up tonight or when multicellular organisms were just starting to arise.

“Watch closely. We’re going to zoom in on just this last segment that we’re in. Remember, it’s a whole 2.3 billion years, representing 1/6th of all time. And now I am also going to further break this segment into six new equal parts.” He was typing as he was talking.

The image did zoom in until only the last segment was visible. The label Great Oxidation Event appeared near the left of the image. More lines appeared, creating a total of six new segments.

“Cutting this segment into a further six sections means each one is 1 of 36 segments,” he said. He looked around and waited to see if anyone needed clarification on this. It took Saul just a little bit longer to imagine cutting each of the six segments into a smaller six segments and understanding that there would indeed now be 36 little segments.

Here he pointed at the last segment of the new line. “One out of 36 is the probability now, in a universe that is 13.8 billion years old, this means that each of these new segments now has a value of 383 million years .  .  . Amber? Could you tell us what the earth was like 383 million years ago?”

A man at the back piped up, “Now was it Pangea?”

“No,” said Amber. “Pangea came later still. This time it was a supercontinent called Gondwana.” Everyone in the room listened intently. Amber began to talk in a low tone, almost to herself.

“The first forests covered the world. Flowers won’t exist for many millions of years, but forests are everywhere. There aren’t large land herbivores, so the plants just cover everything. They shape the world . . . It’s odd. When we think of a jungle we can’t help but also imagine bird sounds, the leaves and twigs breaking, the insects, the snakes, the howling animals, the mating calls, the cacophony of sounds . . . but not now. Plenty of ocean life, and I remember something about fish with jawbones starting around this time.”

Mr. Yeager took a beat while conversations died down. He could see that they were all now plainly rooted in their seats. No one would leave now. Three of the people who had left early were now returning, no doubt brought back by their friends’ frantic texting and messaging. Their brains were engaged. The mental gymnastics were in swing. What more do thinkers ever want?

“One 36th,” he said. “Or, just under 3%.” He waved his hands toward the timeline on the board. “There is now a 3% chance that aliens could arrive on Earth now. But they could also arrive 383 million years ago when the world was green, before large animals even walked around, and when fish first started showing up with jawbones.”

He looked around. “Continue?” None of them had to nod. “I’ll repeat the process. We’re going to zoom in once again and show only the last section, the 1/36th which includes us. And once again we’ll break it up into six new equal parts. This will result in a line with individual sections now worth 1/216th.” Again he typed as he spoke.

“In a universe that is 13.8 billion years old, that means that each of these tiny little segments has a value of just under 64 million years. By the way, that is a little less than half of 1%. The probability is becoming less likely.” Mr. Yeager gestured to Amber.

Amber resumed. “66 million years ago is when we clock the extinction of the dinosaurs. So this is about two million years of recovery later.”

Saul could see people trying to recall what they’d heard via nature shows or documentaries what the world must’ve been like after the asteroid that punched into the Yucatan peninsula. 

“Mammals already existed about 20 million years before this event, and the consensus is that the extinction event, while creating vast niches for mammals to move into, didn’t really result in significant diversification. The first primates didn’t show up until 55 million years ago, around here,” she pointed near the second tally mark. “So, mimicking what you’ve been saying; there is a 1/216th chance that aliens could show up here today, or a 1/216th chance that aliens could have shown up 11 million years before even the first primates–”

“Hold that thought!” said Mr. Yeager. He looked around the room. “I’m sure everyone here has the pattern down now. So let’s speed it up.” Once again the image zoomed into the last segment and more tally marks showed. “Take the last segment, again, and split it into six new parts.”

The audience had picked up on the pattern and a man who’d been leaning against the door read from his phone, “Each segment is worth 1/296 which is equivalent to 0.0007%, and encompasses ten million, six hundred sixty-six thousand years.”

Saul saw that several people were tapping away at their phones, not in a distracted way, but in a way that suggested they were fully engaged, either performing searches or calculations. Those not on their phones were staring at Mr. Yeager as well as Amber who was still looking at the projector screen.

Amber, in a low voice, continued, “This world would have looked familiar to us. Warmer global temperatures, but tending towards cooling, the Sahara desert was green, actually green. Mountain ranges came up. Changes in ocean currents redistributed nourishment worldwide which finally accelerated evolution. The megalodon was in the ocean and mammals spread throughout the world. Here we saw the precursors to horses, elephants, giraffes, rhinocerotids, and primates like we said earlier.”

Saul was very much aware of two things just now. One, Amber’s obvious intelligence was intoxicating. And two, he could clearly feel the empty space where she’d been sitting next to him some minutes ago.

Dr. Darnielle raised her hand. “Mr. Yeager, if I may?”

He nodded.

“Tell me if I am understanding you. You are suggesting that if we continue to narrow the window of probability in which the dots we are seeing inside the orbit of Mercury are proof of alien intelligence, that that probability would be so astronomically small that the only possible explanation would be, what . . . divine intervention?”

“Yes,” he said. “But that, Dr. Darnielle, is only the first part of this mathematical proof. Allow me to continue.” To the room he said, “here is a breakdown of the probabilities that we’re seen so far.” He tapped at his computer and a list showed on the screen.

2.3 Billion years → 16%

383 Million years → less than 3%

64 Million years → less than 0.5%

10.6 Million years → 0.0007%

“You can already see the probability getting smaller. It is literally approaching zero. The smaller it gets the more unlikely. Not impossible, but more and more improbable. I’m going to extend the table now.” Again he tapped the computer. 

Everyone’s eyes were glued to the screen. They could not look away if they tried. The list grew, one line at a time, triggering memories of historical eras, then historical figures, then perhaps their own family histories, eventually arriving at spans within their own lifetimes, then within their immediate memories, close enough for them to touch, until finally it arrived at this very night.

2.3 Billion years → 16%

383 Million years → less than 3%

64 Million years → less than 0.5%

10.6 Million years → 0.0007%

1,773,000 years → 0.0001%

295,500 years → 0.00002%

49,250 years → 0.000004%

8,208 years → 0.0000006%

1,368 years → 0.0000001%

228 years → 0.00000002%

38 years → 0.000000003%

6 years → 0.0000000005%

1 year → 0.00000000008%

2 months → 0.00000000001%

10 days → 0.000000000002%

1.7 days → 0.0000000000004%

6.7 hours → 0.00000000000006%

1.1 hours → 0.00000000000001%

Amber once again sat next to Saul, somehow making the void a little less empty. No one spoke. Some faces looked blank, some anguished, some angry. She leaned into him and whispered, “what do you think?”

He inhaled her breath. “I like his theory.”

She smiled and leaned closer until she whispered in his ear. “But he’s not done yet. And then it’ll be your turn–”

Mr. Yeager cleared his throat. To the room he said, “At the start I assured you that I am not making light of the predicament that the human race is in, and I hold to that. I sense that some of you are starting to at least consider the possibility that the dots, whatever they herald, may be something different to what the majority of the human population thinks.”

“I sense a ‘but,’” someone said into the silence. “Well,” they said, “now that you’ve rattled our collective cages, toss us some bananas.”

Mr. Yeager gestured to the list on the screen. “The probability of aliens, the kind which we envision as being technologically advanced but still somehow able to communicate with us, being here tonight, is infinitesimally small.” Another dramatic pause. 

Dr. Darnielle picked up the cue, “but not small enough to warrant a deux ex machina.”

“No,” said Mr. Yeager. “The probability is one hundred billionth of a percent. The probability will continue to approach the asymptote on our timeline, which in real world terms means it is impossible for them to be here. 

“And if you’re still not convinced,” he looked in their eyes, “consider that all of this math we’ve been looking at only accounts for probability in terms of time, and not also of space.”

*************

A cascade of connections, tripping over one another faster than the last, pushing against the walls of rational thought louder and louder and LOUDER. Such is when thinkers make intuitive leaps.

Eventually, “it’s still compound probability, right?–” and “specifically mutually inclusive since you’re talking about two things happening concurrently, time and location–” and “yes, but the permutations are exponentially larger at every single turn–” And on it continued. They took over the room, Mr. Yeager forgotten at the far end. Their voices rose, others stepped out into the hallway and started to make phone calls.

Saul looked around until he came back around to Amber. She was looking him in the eye. She nodded her head at the front of the room. “You’re up.”

Her body heat left as she stood. He stood. He made his way to Mr. Yeager.  

“You must be Saul,” he said.

“Yes, sir,” he said.

“Amber said you and I should meet.”

Saul looked at Amber. “Now I know why.”

For a moment neither of them talked. They listened to the conversations around them. 

“I like your theory,” said Saul.

“Thank you.”

“There’s a problem with it.”

“Please.” Mr. Yeager waved his hand at the board.

“When you introduced yourself you said you worked in combinatorics, focusing on the arrangement and combinations of objects. Combinatorics is generally regarded as one of the most challenging fields in mathematics. You showed that the probability of this event occurring was so improbably small that the only way for it to occur is through divine intervention. You then said that if one did not believe you, then to consider that the vanishingly small probability we had spent time discussing only accounted for time, and not space.”

“What part do you disagree with?” said Mr. Yeager.

“I don’t disagree with any part in particular,” said Saul. “I said there’s a problem with it.”

An outside observer would have first noticed the various people spread out around the library enthusiastically discussing their topic, some desperately texting, messaging, posting, yelling into their phones. An outside observer would also have noticed that the televisions, which had been showing the LASCO coronographs nonstop for months, hard been turned back on and now showed computer generated imagery comparing Mercury’s typical orbit 7 degrees off of the ecliptic as well as the dots’ orbit which was exactly 90 degrees perpendicular to Earth’s ecliptic. Eventually an outside observer would have noticed that the small group of people at the far end of the library, standing stock still as they spoke.

“Please tell,” said Mr. Yeager.

Saul continued. “You have adequately shown that the mutually inclusive probability of aliens showing up here and now and able to communicate with us is tantamount to infinitely improbable. But when dealing with numbers that large (or in this case infinitely small) scale comes into play.”

The group consisted of Mr. Yeager, Saul, the two girls, Amber and Eve, and Dr. Darnielle who had coordinated the meeting. They listened as Saul spoke, no nodding or slouching, no sounds.

“After all,” said Saul. “The hardest lottery in the world right now is Italy’s SuperEnalotto, with a probability of 1 in 623 million of winning the main prize. But the thing is, as unlikely as that probability is, people have still won.”

If any of the other people in the library or the hallway had looked in their direction they may have thought it strange that a group of people stood still among all the hubbub. As it is, they were too caught up in themselves, their own attempts to make themselves seem in the know and projecting to their social circles their superior mindpower. So none noticed.

“1 in 623 million is nowhere near as improbable as–” said Mr. Yeager.

“It’s a question of scale,” said Amber.

“That’s right,” said Saul. “Scale. At the scale of these numbers there really is not much practical difference.”

“I disagree–” said Dr. Darnielle.

“You disagree for intuitive reasons,” said Eve.

“The fact is,” said Saul. “Far fewer than 623 million people play that lottery, and yet there have been winners. That should not be possible.”

“I don’t like what you are suggesting. Are you saying that the probability of this event happening,” he indicated toward the television, “notwithstanding the mathematical improbability, is actually more likely to happen?”

Saul nodded.

“Son, who are you? Are you a student here? What do you study?” said Mr. Yeager.

“I study physics,” said Saul. “Cosmology. Gravity.”

Recognition showed on Dr. Darnielle’s face. 

“You,” said Dr. Darnielle. “I read your paper, your theory on gravity and entropy.”

Mr. Yeager looked surprised. “Sarah, what are you talking about?”

“Scale,” said Dr. Darnielle. “He posits a theory that explains why galaxies formed in less time than cosmological models suggest it should have taken.”

“I’m sorry, what do you mean?” said the older gentleman.

“I mean,” said Saul, “that current models suggest a timeline for how long it should take for galaxies to form. Evidence has shown galaxies that formed only a few hundred million years after the big bang, far sooner than they could have formed. The only way this could have happened is if there were another external force helping the formation along, something we can’t see–”

“Are you talking about Dark Matter?” said Mr. Yeager.

“No, I’m talking about gravity. Extra gravity. Gravity that has leaked into this universe. From another universe. From many other universes, in point of fact.”

“Think of it,” said Amber. “An infinite number of universes where galaxies formed at the same location, at the same time, their gravity leaking into one another, affecting their formation, advancing time frames, keeping stars at the spinning edges from being flung off into the void. Millions of years instead of billions.”

The professor and the doctor stared at the young people in shock. 

“Yes,” said Saul. “An unlikely event made more likely via leaked gravity.” He lowered his voice slightly. “But it goes farther than that. I also deal in probability. You see

7.29.2024 – Present