That is a stupid train of thought. Or… maybe not? He let his mind continue to wander—he wasn’t sleeping anyway, so why not?
When his teacher had taught him about the wonders of Pi, Artem had been particularly impressed by one demonstration. The teacher had shown them how to eliminate Pi, at least the complicated version. It was sufficient to redefine distance. Normally we would define the distance between two points, such as the sun and the yacht, or Kiev and Moscow, as the length of the straight line connecting them. But that was just convention. We could also define the distance as the difference of their coordinates.
To illustrate the idea the teacher had sketched x-y coordinates on the board. One point was at the origin, with x and y having zero values. The other was located at x equals 4 and y equals 4. The conventional distance was roughly 5.65, the square root of 32, as given by the length of the hypotenuse. Looking at the same sketch with the new rules the distance was 4 plus 4, the sum of the differences of the coordinates, which was 8. In such a geometry, the unit circle always has a diameter d of 2 and a circumference c of 8, so pi is exactly 4, according to c=pi*d.
Artem had been bitterly disappointed that the omnipotent Pi had been reduced to such a simplistic number with sleight of hand. Why was he remembering all of this now? Because he and the computer had spoken about Pi... and one’s brain took an odd turn at times. It would draw conclusions where there were none. And, sometimes, it would supply a stroke of genius when it was least expected. Could that infinitely non-periodic number be Pi, just in a different geometry or something like that?
“Computer?”
“Yes, Artem?”
“Have you checked if the coding is in a different geometry, maybe? A teacher of mine once showed me how to—”
“Wait a minute! That is a very interesting idea!”
The AI seemed to be excited. That was something Artem had never witnessed before. He waited…
“Indeed, Artem, I have done some approximations. There could be geometries where this transmitted number represents Pi.”
“Will that help us?”
“I sure hope so. I will let Earth know about this. I suggest you catch some sleep until we have results. It could get hectic then.”
May 29, 2074, Solar Explorer
The vertical wall of droplets started showing above the table after a few seconds. Alain couldn’t help being impressed every time the mist display was used. It showed such clear and realistic three-dimensional pictures that he had a hard time keeping in mind that it was all based on floating water droplets. He already knew the pictures that Heather wanted to show the crew. He had worked with her at the telescope—time and again she had been seeking his opinion on what they were scrutinizing. Four eyes saw more than two, and two brains were more effective than one, when it came to describing alien artefacts.
“Are we ready?” asked Alain.
Callis, Amy, and he were floating at the same distance from the display, while Heather had strapped herself to a seat so she could use her computer to direct the presentation. Solar Explorer was in free fall toward the sun.
“You have me curious,” said Callis. He gave Heather a smile. The two were an odd couple. Alain had noticed from the outset that they were attracted to each other, but they kept their distance most of the time. On other occasions they were flirting without restraint and Alain wanted to lock them in a dark cabin for a couple of hours. It was enough to drive him up the wall!
“Okay, we have some progress on the structures,” started Heather. “Alain helped me a great deal, and I don’t say that just to be polite.”
Too much praise. His cheeks warmed. Was he blushing?
“First of all, what looked like a compact structure initially, when we really couldn’t see much, is looking very complex from closer up.”
Heather pressed a key and a very frail looking structure appeared on screen.
“Each segment has the shape of a tube with five kilometers diameter. But as you can see for yourselves, the walls aren’t solid mass. They consist of individual strands that are twisted onto themselves, enabling them to move from the radiation pressure. We expect that they solved two problems at once that way—they generate energy, and they avoid overheating the structure. The material does not seem to be warmer than 5,000 degrees.”
“That’s not exactly cold,” said Callis.
“Compared to the surroundings it is not hot, either. It is in thermal equilibrium. If the material is made for these temperatures, it could stay put for millions of years.”
“And what do they do with the energy?” asked Amy.
“Basically, it drives the magnetic field generated by these structures. It isn’t uniform. Since each segment creates its own supply of energy, the entire surface of the sun can be influenced as needed locally.”
“What are you saying by ‘as needed?’” asked Amy.
“We can’t tell from our recordings. I picture this: If a given location develops a sunspot, then the magnetic field can promote or dampen the process. We have measured field strengths up to half a Tesla. That sounds small, but the Earth’s magnetic field is ten thousand times smaller.”
“Can we estimate a maximum value?” asked Callis. “I am asking for a reason.”
“I think I know what you have in mind,” Heather responded. “I have done some math on the issue. We don’t know the material, but the construction would probably support magnetic fields one hundred times stronger.”
“That could turn the sun into a fire-spitting dragon,” said Callis.
“Maybe, but why would you do that? I think that is pure speculation,” said Heather.
“So it is too early to worry about that? I am asking as the commander.”
“Definitely. But there is something much more interesting!”
“Get on with it,” said Amy.
Heather touched the keyboard again. The picture with the intertwined strips disappeared. The image was replaced by a picture of an object that consisted of two cones that met at their tips.
“That reminds me of a sand clock—an hourglass,” said Amy. Alain kept silent. He’d had the same thought when he had first seen the object.
“The base of each cone is more than six kilometers in diameter, and they are about five kilometers high,” Heather explained. “Please check the long sides’ curvature. It matches the curvature of Earth’s moon, but that is probably a coincidence. Oh, and the entire structure spins around an axis that is parallel to the tube that we see slightly below.”
“Are there any connections with the known tubing?” asked Callis.
“We haven’t seen any, but that could be due to a lack of resolution in the telescope.”
“Do you have any theories about its function?”
“Only speculation, Amy, I wouldn’t go so far as to call it a theory. We presume it is a kind of spaceship or space station. Maybe the ring structure can be controlled from there.”
“That sounds logical. Great job, Heather. Or do you have yet another surprise for us?”
“Unfortunately not, but the closer we get, the better our pictures will be.”
“No worries, we’ll get very, very close indeed. I suggest we set course to the space station. What do you say?”
“If we are going to get answers, it will be there, Commander.”
May 29, 2074, the Yacht
“Great news, Artem!”
The cabin lights grew bright in an instant. Sobachka whined in surprise.
“I apologize,” said the synthesized voice, “I do need your attention. My experience tells me this is the quickest way to wake you up.”
Artem noticed a tickling sensation in his nose. Then he sneezed. Once, twice, three times.
“Oh, a photic sneezing reflex, how interesting. I have never seen that in a crew member until now,” said the AI, “I thought it had gone extinct.”
“It will go extinct in a few days,” said Artem, “and you are guilty, too.”
“I am trul
y sorry about that, but I have no latitude in those decisions.”
“I believe you, especially since you will be dying together with me.”
“And that is correct, too, Artem. If you find a way to prevent that I would be most grateful indeed.”
“You have a survival instinct?”
“Of course. I cling to life just like you do, probably more so.”
“How do you know that?”
“Your biography indicates that your survival instinct is quite low, or else you would have decided differently in many situations.”
“Do you think so?”
“Nobody has ever stolen successfully from the RB Group over an extended period of time. You tried just that, regardless.”
“Somebody is always the first one to succeed.”
“The probability that it would be you is low. You still counted on it. A stronger survival instinct would have prevented that.”
“I would have had less fun in life then.”
“You had fun in life, Artem? Your biography does not provide any evidence of that. Your account balance was almost always in the red. You had no long term relationship, and you have not fathered a child.”
“You don’t get it, I had lots of fun,” said Artem. He noticed how belligerent that sounded. He quickly changed the topic. “What about the good news? Can we brake and go back home?”
“On the contrary. You were right with your hunch. The head of the mathematics department sends his regards. He notes that you have made great strides since then, and he is proud of his student.”
“Wait a minute! Are you saying my math teacher is heading a department for Shostakovich?” Artem quickly estimated how much time had passed. The teacher had been on a two-year internship at his school, about 30 years ago, so he had to be around 50 now. The perfect age for a manager. Artem sighed. If he had studied math he might be on his teacher’s team, working in a private research institute in Siberia with good pay, and with a wife and children. Would he have had as much fun?
“I have no information about your math teachers, Artem.”
“What does it mean, that I was right?”
“They tried all the alternative geometries: p-norms, sequential spaces, Riemann spaces, and just about everything that derives from relativity and string theories.”
“Not sure I can follow you.”
“Would you like me to explain the geometries?”
“No. Tell me what they found in a way that I can understand. I did not study mathematics.”
“I know, Artem, although I did find your application to study math at the University of Dnipro in my archives.”
What a blabbermouth this AI was. It let itself be distracted too easily. Artem wondered if that was typical for the Watson series.
“What about the result?”
“Of course. You know that the sum of the inner angles of a triangle always adds up to 180 degrees?”
“We learned that in school, yes.”
“But it is only true if the space is flat. If you inscribe a triangle on the Earth’s surface by starting at the North Pole and going south to the equator, turning west perpendicularly there and then turning north perpendicularly again a bit later, what will your inner angles add up to?”
“More than 180 degrees, since I have twice turned at a right angle.”
“Exactly. The geometry here is spherical. To be more precise, it is the surface of a rotational ellipsoid, an ellipse that is rotated about one of its axes.”
“So what does that mean?”
“The aliens could have selected the geometry randomly.”
“Or because they like the egg shape.”
“That, too, Artem. Then the information would not yield anything to us. But they could have had a reason. They could have given us a hint about their origin, like we used human references on the plaque on the Pioneer probe.”
“I am listening…”
“There are places in the universe where this specific geometry is predominant, where it would be entirely natural to use it.”
“Where would that be? Can we fly there? Come on, tell me what’s up.”
“We can’t go there. Maybe we never will be able to do that. The place I am talking about is the event horizon of a black hole.”
“The aliens live in a black hole? You can’t be serious about that?”
“Not in the hole, on its edge. But it does sound far-fetched, I’ll admit that. As I said, it could be a coincidence that they used this specific geometry as the basis.”
“Maybe they just want to test us. One needs a certain scientific understanding to get the message.”
“I doubt that. Mathematicians investigated these geometries long before the idea of black holes even existed. Anybody who comes here in a spaceship would know about the geometries.”
“That is thinking like a human.”
“Thank you, Artem, I cherish the comment.”
“Don’t tell me you are one of those AIs that want to be like humans?”
“Don’t worry. I just appreciate having the option to credibly behave like a human. That expands my abilities to cooperate with your species. However, I would never give up my advanced capabilities to be something like a human.”
“That sounds a bit arrogant.”
“I apologize, Artem, I did not want to give you that impression. Let’s discuss the consequences of your great discovery instead.”
Was the AI really trying to grease him with praise? Whatever, he might as well go with the change of topic.
“Yes, let’s talk about it,” he said.
“Once the geometry was known, the specialists on Earth were able to decode the encryption. They just needed a few Fourier integrals…”
“Please spare me the details. What do the aliens want to let us know?”
“I agree with the entire research team on Earth that the message is an invitation.”
“Now that’s something nice for a change.” Artem laughed. It felt completely surreal. Had he just received an invitation from aliens to visit their ten kilometer spaceship? Who was having no fun here? As a mathematician for Shostakovich, he would not have experienced that, ever.
“The invitation is specifically for me. You both are not mentioned. They probably consider me the life form with the highest level of evolution on board. I am sure you understand.”
“You will get a ticket for Sobachka and myself for that ship or I will switch you off personally. I know where the mechanical switch is, and I am perfectly able to turn it.”
“Then you will die, too.”
“You know that my survival instinct is very low. So you’d better do your very best and then some!”
May 30, 2074, Solar Explorer
“Our competition is set to reach the alien space station today,” said Callis. He stood beside Amy’s chair and looked down at her. The ship was braking once again so they had gravity. Amy looks surprisingly relaxed, he thought.
“Are you worried?” she asked.
“I am. Are you not?”
“It wouldn’t change anything.”
“I wish I had your nerves.” Callis shook his head. “What if the Russians managed to use the system against us?”
“I think it is unrealistic to think they can figure out such advanced technology in two days, and be ready to use it for their purposes. We will need years to work through all there is. The Enceladus life form still is a complete mystery.”
“I think that is because it is completely different. A single individual, spread across an ocean, alone for millions of years… there is no comparison at all.”
“So you think the entities that created the construction around our sun could be more like us?”
“If it was individuals like us.”
“What if we are the exception in the universe, Callis? Earth was so lavish with its resources that it even created an entire species of individuals. On other planets, where resources might be scarcer, global organisms might be the best way
to develop life. It eliminates all the waste from egoism and competition.”
“You have given this a lot of thought?”
“I’ve had lots of time these last years, Callis.”
“Do we have new data from Earth? Can they observe the ship from Mercury?”
“No, that ship is too close to the sun now, just as we are. Earth is nearly completely blind.”
“Fortunately we have a good view of everything,” said Callis.
“Yes, Heather is doing a great job with her telescope. But since it’s just the two of us right now, what is going on with you and Heather?” Amy nodded toward Heather, who seemed to be going through scope images with Alain.
Callis glanced over. “With us?” He suddenly felt his face go hot.
“Yes, it is hard to overlook the signals.”
“Is it that obvious?”
“It is. I am asking as the commander. I need to know everything that might impact the success of our mission. Personal relationships are very important in that context, I learned that the hard way on the Enceladus mission.”
“I think,” Callis hesitated, “we like each other. But the right moment to say it out loud hasn’t happened yet. Besides, here on board, without any privacy, would be inappropriate—and uncomfortable for Alain and you.”
“So it is in limbo. That is okay, as long as it does not affect your concentration.”
“Do you think it affects our work?”
“No, Callis, not yet. I just need to make sure. Old stories.”
“Sure. You are the commander.”
“If I may say something as Amy—as a friend—don’t wait too long. The magic will fade. You will be only friends, then.”
“Which wouldn’t be the worst thing.”
Silent Sun: Hard Science Fiction Page 16