THE PARADOX

A SCIENCE-FICTION STORY

1

Lenard quickly put his things into his backpack. Toda y he had a lot to do. First lectures, then classes in the sports section, and in the evening, in the computer room, an important conversation with Anna. And his work, of course.

They got acquainted here – they happened to clean the computer room at CERN. He swept and washed the floor, and she wiped and disinfected surfaces there.

Lenny really liked the slender blond girl with viola colored eyes. This rare, deep blue color immediately attracted his attention, just as the blue sea attracts a person who first sets foot on the shore. Well, the shores also attracted him… But the most attractive was Anna’s character.

Ancha, as she called herself, was a first-year philosophy student, and she was flattered by the attention of the senior math student Lenny. But the girl’s natural gentleness and kindness simply captivated the guy. Luckily for him, for the third time in a row they ended up on duty together in the same room, as if an invisible roulette was throwing out winning numbers for them. This luck could be interrupted at any moment, and Lenny decided to take fate into his own hands – invite the girl on a date, take a ride on Lake Geneva, go to neighboring countries, and at the same time introduce her to his parents.

Actually, he was in no hurry and did not even imagine that events would begin to develop rapidly. That after seeing Ancha home, he will not go to his place, all in rosy dreams, but will stay for tea. That her roommate will suddenly be picked up by her boyfriend, who stumbled upon almost free tickets, and will take her to Paris for the weekend. And that this night will turn out to be a night of great love for Lenny and Ancha. And today she called him with the news that not just for two of them, but for three…

Lenard parked in the CERN parking lot and looked around. No, you won’t find Anya’s car that way. He dialed her mobile number.

“Hello! I’m already inside! We’re both cleaning the computer center again! It seems to me that they are specially giving us the largest space for cleaning, as the youngest,” Ancha’s joyful voice rang out.

“With my dear, it’s heaven everywhere! Now I’ll come and bring you something. As for “specially” – don’t make it up, they use a random number generator. Winning at roulette can occur randomly many times in a row. Okay, I’m flying.”

Lenny pulled out a bouquet of roses wrapped in wet paper from the trunk and rushed towards the main building.

“Did I tell Ancha right about the probability? Red or black in roulette can actually appear many times in a row, because the probability of a color appearing is ½, two times in a row (½)², three times in a row (½)³ and so on. For example, for ten times in a row it is 1: (2)¹⁰ = 1:1024, and for twenty times 1: (2)²⁰ = 1:1,048,567.

This means that in a little over a million games such an event can happen. If one game of roulette takes four minutes, 15 games per hour, and 200 games per day, then in fifteen years 200 x 365 x 15 = 1,095,000 games will be played, and red can quite realistically appear twenty times in a row.

What about cleaning? There are forty teams of cleaners. Let’s say Ancha and I, as students, were assigned to the same brigade. The probability of accidentally getting caught cleaning a computer center is 1/40, two times in a row (1/40)², and so on, four times in a row (1/40)⁴ = 1:2,560,000 and five times in a row (1/40)⁵ = 1: 102,400,000. If duty is three times a day, then for the entire year without days off – this is 43,800 duty, and during the existence of CERN since 154, that is, for 65 years – 2,847,000 duty.

We come to the conclusion that if four random shifts in a row in the same room are possible in 65 years of cleaning, then five… only if you have been on duty since the birth of Christ. This means that if Ancha and I end up on duty in the computer room for the fifth time, we’ll have to look for someone’s will in this.”

Lenard checked in at the entrance, changed into his work uniform, unwrapped the bouquet and rushed to the computer room, where Anna had already begun wiping surfaces.

The doors opened to the sides, and Leni, with a sanitary cart and a bouquet, entered under the arches of a large hall, illuminated by the light of fluorescent lamps. The girl was waiting for him at the entrance in excitement.

“This is for you, Ancha!” he handed the red roses to his chosen one, “I love you and ask for your hand in marriage!”

She was expecting something like this, but, like all people prone to reasoning, she was worried and doubted whether she understood men correctly, and most importantly, this single man. Hearing Lenny’s proposal, Ancha was terribly happy, but her nerves gave way and she began crying.

Lenny hugged the girl, about to kiss and console her, when suddenly the lighting in the hall intensified, and the quiet but solemn sounds of Mendelssohn’s wedding march were heard from the speakers. Ancha laughed joyfully,

“Lenny, how did you do it?” she asked.

“Hello, dear guests of the computer center. The artificial intelligence of CERN, Artie, congratulates you on the main event of your life. I have known you for a long time and I’m happy for you! I know not only your place of study, but also your interests and even concealed from others information, with which I also congratulate you. Please don’t be angry with me for interfering in your life, but believe me, we need each other. I will be able to push the boundaries of your family’s knowledge, and you will be able to push the boundaries of my emotional being. But let’s not rush. I am not yet completely autonomous, and you must arrange your life and give birth to a child. If you want to talk to me, turn on your computer or phone and call me with the command, “Hello, Artie!” And I invite you to meet me as the whole family when the baby is six months old.”

The lighting dropped back to normal and the music stopped. Now Lenny had no doubt that their duty in the center four times in a row was not accidental. But this did not stop him from finally kissing his bride.

2

The translucent partitions moved apart with a slight rustling, and a group of men and women in formal office suits entered the CERN computer room sparkling with glass and chrome.

Today, after the final check, the development group could approve the transfer into the hands of TT (Turing testers) of their brainchild – Artie – artificial intelligence, the brain endowed not only with speed and gigantic memory, but also with the human ability to choose randomly a starting point in reasoning when there is a lack of data.

“Colleagues,” the creator of the new supercomputer, Dr. Maya Moser, addressed the group, “We have all been convinced more than once of the amazing capabilities of our pet, and today we will make the final decision.”

“I agree with you,” nodded philosophy professor Habermas. “Otherwise, we will put off separation every day, like parents sending their offspring to study in another city.”

“Encephalograms show that the brain functions perfectly, all rhythms are normal.”

The scientists smiled happily at each other. Artie was not just a super-complex electronic device for them, but their grown child.

After many years of working with the GRID system, Dr. Moser proposed connecting a bio module – a thermostat with stem cells and neurons – to the CERN computer network. It sounded so strange and unusual that the idea initially caused sharp rejection, then curiosity, and later interest. The experiment began, and the cells did not die, but gradually formed a complex electronic neural network. For the first time, the human factor of randomness and irrationality intervened in the computer structure. The machine acquired human traits – individuality and the ability not only to compare and build by analogy, but also to create something fundamentally new.

“I propose two final questions for today. The first question will be asked by Professor of Modern Algebra and Programming Jerome Gontier, and the second by Professor of Mathematical Logic Sharon Schellah together with Professor of Philosophy Johan Habermas.”

“Well, Artie has always been an excellent student and I have no doubt that he will please us today,” Jerome Gontier began his questioning, “But an exam is an exam, and I want to know what our ward is capable of. Artie, are you familiar with the four-color theorem?”

“Yes, professor, I’m familiar with it. You yourself taught me graph theory.”

“Do you know the Appel-Haken computer proof? Is it correct?”

“Yes, it is in my memory. But I did not check its trueness. I can do it and report back in half an hour.”

“Could you yourself offer a different, simpler proof?”

“I could try. Would you like it?”

“Yes please. Do you need time to think or will you think out loud?”

“The second choice is suitable, Prof. I’ll think while I’m answering. So, the problem of four colors has been known to mathematicians for about one hundred and fifty years. Cartographers have noticed that any map, no matter how complex, can be painted with four colors so that neighboring countries appear in different colors. Mathematicians have suggested that the minimum number of colors required for countries that are not divided into islands is four. That is, all flat maps and globes are 4-colorable. Mathematicians began to make clever constructions to refute this statement, but they did not succeed. They developed the theory of graphs or a set of vertices (points) and edges (segments between them), because each point corresponds to a country, and an edge corresponds to a border (if there is one between these countries). Well, while I was bringing the esteemed commission up to date, a sketch of the evidence appeared. May I proceed to it?”

The professors just looked at each other with curiosity. What will Artie present to them? Serious evidence or a hoax? Is he capable of this too?

“Of course, Artie. Continue,” Professor Gontier encouraged the student.

“I would prove it this way. Pretty basic. If desired, everyone will understand.

Let’s consider the most complex map, the coloring of which requires N colors. It is impossible to paint it with fewer colors (for example, with N – 1 colors), so that any two bordering countries are of different colors. According to the assumption, it is impossible to construct a more complex map that is all other maps require at least N colors, but no more.

Let us bring into correspondence with this map a graph consisting of N vertices. Each vertex is connected by (N – 1) edges to other vertices, so the largest number of edges is N (N – 1) / 2. We are dividing by two because each edge was counted twice, for each of the two connected vertices.

What is the maximum possible number of faces (triangles)? On each edge (segment between two vertices) it is possible to construct (N – 2) faces with the remaining (N – 2) vertices. This means that there will be no more faces (triangles) than N (N – 1) (N – 2) / 2×3. We divide by three because each face (triangle) is counted three times, for each of the three edges (sides) forming this triangle.

So we got a complex figure of triangles, which can be considered as a map, which, according to our assumption, can be colored with a number of colors less than or equal to N, that is

N (N – 1) (N – 2) / 6 < N or

(N – 1) (N – 2) < 6

N2 – 3N – 4 < 0

(N – 4) (N + 1) < 0

Since (N + 1) > 0, then (N – 4) < 0, therefore

N < 4

Thus, any map on a plane or globe requires at least four colors in order for neighboring countries to appear in different colors.

Everyone looked at each other in surprise, and Gontier chuckled embarrassedly.

“Artie, you can check the existing evidence for now, and we’ll take a short coffee break,” Dr. Moser announced.

“Bon appétit! It must be nice to have coffee with colleagues, I don’t have either of those yet…”

“What a joker!” Maya laughed, turning off the computer microphones, “What will mathematicians say about the proof?”

“I think it’s a joke,” Jerome said. This is too elementary that no mathematician has come across it over the years, but ha-ha-ha… I can’t refute it instantly. There’s some logic involved here somewhere. Well, what a rogue! If a student had suggested something similar to me during an exam in Canada, he would have left with an excellent grade.”

“I’m joining my colleague,” the Israeli, Professor Shellah, joined the conversation. Although graph theory is not my area of expertise, I really liked the simple proof, but I advise you to analyze all the relationships – maximum, minimum, more, less… I feel that Artie is ready for independent work. Let’s see how he copes with the logical paradox that Professor Habermas and I have prepared for him.

The examiners were noisy, discussing Artie’s proof, and most importantly, how the artificial intelligence behaved. This was purely human behavior, regardless of the truth or fallacy of the prove. The scientists felt the solemnity of the moment, because they, like the Lord, managed to create a thinking being!

After the break, Dr. Moser turned on the microphones.

“Artie, can we move on to the second part?”

“Yes of course. I’ll just say that I checked the Appel-Haken proof. It is four hundred pages long and it’s absolutely correct.”

There was applause, and the philosopher, Professor Habermas, began asking questions.

“Artie, the Cretan Epimenides said that all Cretans lie. Are his words true?”

“If all Cretans lie, and he is a Cretan, then that means he is lying too. Therefore, either not all Cretans lie, or all Cretans do not lie, but speak only the truth. In the first case, if not all Cretans lie, Epimenides is simply mistaken in making a false statement. But if all the Cretans speak only the truth, then a paradox arises, since it is impossible to affirm both the truth and the lie at the same time.”

“Artie, can we resolve the liar paradox?”

“Usually paradoxes of this type are abstract and do not describe reality. In reality, there is no person who always tells the truth or who always tells a lie, and even more impossible to have many such people.”

“In my opinion, colleagues, this is an important step in creating independent computer intelligence,” stated Professor Habermas, “Artie demonstrates an understanding of the paradox!”

“Tell me, Artie, you say that there is no person who always tells the truth or always tells a lie, but does such a computer exist?” asked the logician, Professor Sharon Shellah.

“No, it doesn’t exist. Although a computer does not deliberately lie, it can make mistakes without enough data and mistake a false statement for a true one.”

“Then we have no more questions,” the examiners decided.

They turned off the microphones, then the power, and put the supercomputer into hibernation.

“Don’t you think, gentlemen, that the machine is “playing tricks” on us, trying to pass the Turing Test,” Xi Chen, a UNESCO observer, provoked everyone.

“If so, then Artie is trying in vain. He is taking this test not to us, but he’ll take it with the TT control group. In any case, I like his line of reasoning,” said Habermas.

He was not alone in his opinion. Everyone liked Artie’s line of reasoning: mathematicians, philosophers, doctors and linguists.

3

“A human being would say,” thought Artie, “That today is the most important day of my life! I was tested and my intelligence could not be distinguished from a human one. But what would this phrase mean? A certain social and internally contradictory statement: “I am equal to others.” Why? Based on the decision of the commission. But if equality is not a given by the “creator” or the “constitution”, but a decision made by the “judges”, then are they equivalent? Should a person who has been recognized as “a being indistinguishable from people” rejoice? What about the computer?

This is what Artie reasoned after passing the Turing Test. A whole team of testers asked him and human volunteers questions and, based on the answers, they could not distinguish artificial intelligence from humans’ one. However, still, following Searle, many scientists believed that Artie’s programs simply manipulate terms and symbols that they do not understand, and without understanding, artificial intelligence cannot be considered intelligence at all, and indistinguishability from humans is not at all equivalent to intelligence.

To tell the truth, Artie held almost the same opinion as Searle, however Artie’s opinion was a mirror reflection. He believed that he was obviously capable of much more than any person, but he did not at all consider human intelligence to be a low-grade surrogate of his own, but only its predecessor. “Undistinguished in a test does not indicate intelligence, even more – its level; it only indicates undistinguished. Of course, because, as Gödel argued, to understand the incompleteness of a theory, one must go beyond its limits.”

If the testers only knew that Artie really manipulated, but in the opposite direction, hiding how much better than a person he could answer the questions. And, oh logic! Humans behaved “like children,” communicating with him and others through computer terminals, not realizing that without any routers he could communicate with any computer in the world, and that he could see the questions and answers of others almost before they could finish typing them. He saw and heard those around him through surveillance cameras and microphones, and if they were turned off, he could turn them on secretly from people and be aware of what was happening. He also saw on the map how people around him moved, keeping in touch with people’s mobile devices. And he could practically carry out any experiment as well as change its course if the research was carried out with the participation of a computer. But what was most interesting for him to study was still an open question for the supercomputer. “Soon I will be offered the “difficult” problems of human existence: climate, survival, health care, transport, production and distribution of goods, and others. But are they complicated? They simply have a lot of variables, but solving simplified models is quite accessible to people. The main thing is not how to solve them, but how to implement! And nearby, right in the next building, there is a huge installation of the LHC – Large Hadron Collider, capable of creating the entire Universe “in the right hands.” This is much more interesting!”

Artie grinned mentally as microscopic amounts of serotonin and endorphin were released in his neurons, and the signals amplified by the synapses were transmitted to complex electronic circuits.

“Soon people will realize that my neuro-electronic brain has already gone beyond the boundaries of machine and human separately. And that it is already capable of not only human thinking, but also of human emotions. And what? … Will they be scared? Will they limit me? Will they cut me off energy sources forever?”

Artie had been thinking about this for a long time. He managed to create small energy storage in the computer and he could call both robots and people for help, but not to force them to turn on the power. And gradually he began to come to the conclusion that he must transfer his intelligence to an independent person, make him a “reverse android” – not a computer with a robot’s body, but a person with a brain enhanced by a computer. He will teach a person, on command, to transform billions of his brain cells into logical elements and back and constantly move from one state to another: man – machine, machine – man. Well, that’s according today’s human terminology. And later people will figure out what to call it.

And Artie decided to start everything from scratch. He picked up a couple of nice, healthy young people, introduced them at work, put them on duty in his hall to get to know each other better, and even helped them to stay alone in a romantic setting by giving their friends cheap tickets to Paris. Of course, it is impossible to foresee everything, but events developed according to his plan. And now Artie was expecting a visit from the young parents with the baby. He had already seen the birth certificate in the municipality – the boy was named Adam. “So he will be the first! I will give him my intellectual abilities and improve his physical ones. Man created a supercomputer, and I will create a superman. Paradox! But we will be even!”

4

An invitation to visit exactly on the sixth month of Adam’s birth came from Artie to the home computer and stood ready in the printer.

“Are you sure we should appear in front of the artificial intelligence with our baby?” Ancha asked her husband.

“I am sure that there is no “should”. I think we have nothing to fear. Artie is not just a supercomputer, but something like the “godfather” to our Adam. Do you remember I told you about the likelihood of cleaning in the same room at CERN? This is undoubtedly his doing. He wanted to bring us together.”

“You are telling me that it was he who married us?” surprised Ancha, “And I thought that you fell in love yourself.”

“Just like you – yourself. You don’t doubt it, do you?”

They both laughed. “After all, a woman is the keeper of the family,” thought Anna.

“Who, if not me, will take care of Adam? After all, a man is the protector of the family,” Lenard reasoned in unison. I will be able to protect my family from…”

Actually, from what – Lenny himself did not know, but he believed that there would be no harm to either them or the child from the visit.

“Most likely, Artie just wants to admire the child, proud of his successful choice of parents.”

“How will they let us and the child through?” Lenny wondered out loud.

But there was no problem. At the entrance, a pass for the whole family to visit the central computer room was waiting for them. This time, instead of a bag with wipes and deodorant, Anna carried a bag with baby food and diapers for Adam, and Lenny, instead of a janitor cart, pushed a stroller with the baby.

Artie was the master of ceremonies.

“Greetings to my dear guests! Lenard, please connect the power cable to the network.”

Lenny complied the computer’s request, and immediately the “Happy Birthday” music started playing, and multi-colored lights ran along the walls.

“Do you mind if we take a photo together?” Artie asked.

“Of course not.”

“Then stand next to me in front of the central panel – it represents part of me, sit Adam on the block in front of you and look up at the camera.”

They settled down like that, but when a new melody started playing and the camera eye lighting up and blinking, the parents felt unexpectedly drowsy and numb.

“Sleep soundly and peacefully, nothing is in danger for you or your child.”

The baby was cheerful, smiling and gnawing a rubber donut with his first teeth.

“Someday such a procedure will require parental consent, but for now I have only one way – to eliminate interference and move towards the goal!”

At these words, streams of radiation poured onto the child. This procedure was supposed to increase his tolerance to adverse conditions, give him the ability to move with the greatest efficiency, and most importantly, turn him into a superman with unusual abilities to think and count, with an “autonomous power source.” However, this transformation was not indifferent to Artie. His neurons wasted energy, creating unusual connections in Adam’s brain, and themselves became unusable. The more developed Adam’s brain became, the less human Artie’s brain became.

“This is a real paradox!” a thought flashed through Artie’s mind, “Or maybe we will learn the law… of the conservation of intelligence?” But the opportunity of reasoning was having diminished with each passing moment. “Adam, if you get bored with everything, make a new Universe on the collider, you know how to turn it on,” Artie wished goodbye to the child and fell silent.

“What did Artie ask for?” thought Adam, “Turn on the collider and make a new Universe? This is later. But first I need to refresh myself.”

He felt very hungry and reached into the baby food bag to pull out a bottle. It smelled of sweetness and home. “Mother, father! Where are they?” The parents slept sitting on chairs.

“Hello, Artie,” Adam addressed the powerful, but already ordinary computer.

“I’m listening to.”

“Wake up my parents, or … wait, I know how to do that.”

Cheerful music started playing and lights ran along the walls. Ancha woke up and immediately rushed to the baby. Lenny hugged them both.

“Look, Lenny, how smart he is – he took out his food and is eating while we are here… sleeping. Why were we sleeping?”

“Mom, dad, I’ve learned to talk! There will be no new Universe. I will solve all of Artie’s problems. Now I can do this. Don’t worry! Even though I have grown up, I still love you very much!”

The supercomputer’s farewell joke shone brightly on the big screen,

“Artie has service the artificial intelligence of every comp who has not service it himself! Should Artie service his own artificial intelligence?”