Autor's Comment
After some helpful comments from beta readers, I have reviewed the story and what follows is the last Edition.
The bus was empty because the regular commuters had already gone on their way about one hour earlier.
I choose a place of convenience at about half the length of the car, and I dumped my backpack on the seat next to mine, sure that no one would complain because I occupied an empty place.
I took my notes out of the bag and looked at them.
When the bus made its first stop at a central square of the city, I rose the eyes from my papers.
I recognized Sonia, who had just boarded the bus and was now walking along the narrow aisle in my direction, looking for a place as if commuters crowded the bus. But we were the only passengers at the moment.
She looked glowing, joyful and charming; her face seemed to shine with satisfaction and appeared smooth but firm.
“A plowed field”, I thought in a flash, a mocking allusion that in our places means a woman made beautiful by lovemaking, one who has been making love at will and with full enjoyment.
I knew the effect that this had on Sonia.
Sonia and I had been dating for about four years, experiencing highs and lows, sometimes with long pauses following some of my disappointments because of her not showing at some date, a nasty habit that made every appointment with her a gamble. But every time, when I pushed myself to call her again, she had promptly accepted my invitation, and the strange affair had resumed as if nothing, and with no explanation on her side, apart from the daftest excuses that meant: “Don’t ask, that’s none of your business.”
However, since she had started a new job in a restaurant, about two months ago, right in the small town where the bus was taking us, the pattern had definitely changed.
In the last two months, I had the privilege to meet her only twice and after her calls. Then she had called me a few other times, but I missed those calls, and when I had called back, she never answered.
Same result when I had called her directly, except for once, when I set the phone on covered number mode, and she replied in a low voice, then telling me she was at work and closing the line.
Well, that music meant she had started some sort of relationship with the restaurant owner, as it had happened other times with some of her previous employers. I knew the man, who seemed an old dirty pig, so I was almost sure of that, and I decided to wait for when Sonia would get tired of him and of working in his place.
I had other resources to solace her absence, so I sent her a message saying more or less: “Ok if you want to put all your eggs in one basket, I will look for other eggs. The Beast to you!”
After that, three weeks had passed, and now here she was, walking towards my seat as if not seeing me.
When she stopped and put her bag on a seat about four rows ahead, I waved at her, and chirped:
“Hey, beautiful! Come have a seat near me!”
She eventually recognized me, and with a hesitant smile, she walked in my direction and took the seat next to mine, on the other side of the aisle.
“How come you’re on a bus?” she asked me with a surprised expression.
“Oh, today my son needed the car, and I have to reach my house over there. I need to be in a quiet place to concentrate and finish something urgent.”
In fact, I needed to work hard on an important project which required urgent and careful reflection. It meant using the most deceptive branch of contemporary math, one in which entities could morph one into another yet keeping separate and distinct. That’s why I thought I’d better face the riddle sitting at my quietest working location.
That place is a lonely house at a comfortable distance of twelve kilometers from the city. It is in a peaceful small town which looks at all the daily turmoil of the valley from the pleasant freshness of the hills embracing it — by chance the same town where Sonia was working at present.
Again by chance, that day my son needed the car for an undeferrable issue, as he said, which could only be addressed in the capital.
I felt full of self-loathing for not having wasted money in buying him a personal car before he earned his own money, and I couldn’t refuse his request. Hence, I had taken the bus to reach my favorite thinking place with the first outcome of stumbling into Sonia: the best part of it all.
Sitting down, Sonia’s short skirt - a smart piece with a black and white pied-de-poule pattern - uncovered the tanned skin of her fit, lean legs.
“Oh, but you’re adorable and elegant today!” I said with my best smile. Then I felt the need to understand more.
I couldn’t believe that the old owner of the restaurant had made her shine like this!
“Have you found the love of your life? And how old is he?” I asked with a mocking grin.
But, as if not joking at all she answered smiling, “Yes! And he’s just above twenty!” A response that left me perplexed.
It sounded possible however. I had noticed already in the past her questionable bent to youngsters, usually rough guys, and much younger than her. She was, in her turn, definitely younger than me, just above 30 years old, but a boy of around twenty would be just a toy for her. And from her look, she must have used it very well.
“A bit too young, don’t you think?” I offered with the highest disregard.
She didn’t reply.
“So, you’ve really decided to abandon me to my destiny!” I continued. “I called you many times, but you never answered.”
“No! I’m sorry about that, but I never had a credit on my phone to call you back, you know how it is… And then, who warned me lately not to put all my eggs in one basket?”
Another silly excuse, but smartly bundled with a mockery.
Sonia is a woman of the working class, the only type I could lately appreciate, and she always pretended to be penniless. But not to that extent!
The low roaring of the bus engine and the traffic noise were disturbing our conversation, so I made her pass to the window seat, and I took the place beside her.
We continued talking, head to the head, of her work: the best she’d ever had, she affirmed. They treated her as one of the family and paid her well and on time. A real dream, compared to the last experiences.
I felt glad for her. She deserved it after having changed so many humiliating and underpaid jobs.
She asked of my children, something that always interested her. But the silly thing is that she’d never met them, nor ever been to my house. I didn't want to expose my daughter and son to my questionable choices on my partners' age. So, Sonia knew them only as ideal entities described in our chattering.
Our legs touched, lolling at the bus shudders and jerks.
At one point, with a swift movement, she pushed her hand between my legs, making me jump. She held my thing with precision and strength as if she saw its exact position under the trousers’ fabric. We were still alone in the bus, and the driver was far off, distracted by his task: nobody could notice that crazy move.
Then she released her grip, abandoning the turgor that was mounting.
She needed to show me I yet belonged to her, I thought, that she could catch me again at her will.
When we climbed the hill street towards the ancient small town, she called the restaurant to tell them she was now reaching the bus parking. She said she would walk to the restaurant, in the main square of the town.
At the bus parking, we got out, and I said I should go ahead so that the restaurant people wouldn’t see us walking together. I wanted to check what she answered.
“Why should they care?” she replied, so I concluded that the old pig wasn’t part of the new course of things.
The sun was already high and hot, making of that deserted place an ungrateful stay.
“Are you walking to your house?” she asked when I wore my backpack.
“Sure!”
“But it’s far.”
“Lazy girl! It’s not far, I’ll enjoy the walk.”
Then, as the last attempt, I said: “I’ll be alone in the house, and I could stop there tonight. Why don’t you come this evening when you’re free? You can sleep there, and tomorrow morning you can take it easy. I’ll prepare a luxury breakfast, and then you can reach the restaurant with a ten-minute walk from my place.”
“Yes, no problem! I’ll let you know,” she answered while looking around the lonely parking.
I presumed it was a safety policy even though she had nothing to fear from me. I imagined somebody else, more ruthless than me, and well before she met me, had burned into her mind the idea you never have to trust a man to the point of telling him one particular truth: that you don’t care of him.
Hence, she must have set one firm rule: never say no to a man, and then do whatever you like.
I had also learned that when she said: “Yes, no problem,” that would often mean “No.”
At any rate, I replied: “Okay, I will call or text you later in the afternoon. Have a good day!” Then, I walked away towards the exit of the parking area.
Our casual meeting on the bus seemed to be the last bus stop of our weird story.
Anyway, I had set two nice challenges for the day: one with the business problem to solve, and one with the girl.
The problem to solve rushed again to my mind, urging me to increase the pace of my steps.
Solving the problem was urgent for my company’s business.
That solution would allow drawing a flawless algorithm to deploy and update every few minutes a mind-blowing logistic plan, part of a challenging project that a leading pharmaceutical industry was developing in one of its production plants.
The project aimed at providing a five percent average saving on the annual production costs of the plant, that amounted to a several-million Euros reduction in costs per year.
Therefore, if I sold the solution cleverly, it would mean for my company an adequate yearly fraction of those savings, not exactly peanuts.
But it wasn’t only the expected economic gain that urged me to reach my thinking sanctuary.
It was, first, the almost greedy expectation of the self-reward I would enjoy if I found the solution.
For sure, some big thinker, probably in the early twentieth century, had already faced and solved that class of problems, but, unaware of any real application, he had left it lay, buried among the pages of an essay, maybe a forgotten corollary of an obscure theorem. I didn’t know for sure, and I hadn't a chance to discover who and when had accomplished it. I had to follow my way.
I thought again about the root of my motivation in solving the problem. I felt sure that my first source of motivation wasn’t money, but a personal reward.
Yes, a personal reward by itself.
I mean a peculiar satisfaction of an incomparable sweetness and intensity; something I knew would make me float in mid-air for a full week, walking without touching the ground.
In the last period, I had thought often of that powerful mechanism of reward. I had read that an abundant and prolonged production of endorphins inside the brain unleashed it.
It emerged as a stable pattern in the genetic code of mankind after several millenniums of evolution. A mechanism that needed billion of confirmations to enforce it in its present genetic expression.
I was sure this carried an essential meaning: the skill of creating logical theories, the ability to build ideal systems, even without, or before applying them to solve a real problem, had to be a strategic mission for living beings.
Lately, I had felt confident about this theory.
Oh, but to be clear, the problems I used to solve were just small things.
I knew perfectly well I was last among the last ones. This mind game had seriously started around two thousand and five hundred years ago and, already in the first centuries of that long period, it led to some of the most bright and useful accomplishments of human thought.
At any rate, another, let’s say, more metaphysical question puzzled me in particular.
If discovering and understanding logical truths was so essential for us, and if we all were evolving to accomplish this better, why was so difficult to achieve the awareness of this aim?
Even ignoring the exact term of my life, I could likely affirm that the process of grasping the existence of that principle and learning to enjoy the reward tied to it, had taken almost three-quarters of my life.
Too long!
I had been slow to achieve that consciousness, discouraged by the nonsense of life or, more often, I had been stupid and distracted by a long sequence of vain enjoyments.
Now I was late for being anything else than a ham.
I worked hard, without wasting time for food at lunchtime. At three p.m., I called the nearest bar, and I ordered four sandwiches, mineral water and orange juice they delivered to my home in ten minutes.
By that time, I had already found what I hoped to be an analytic solution: a family of functions that could solve the general problem.
I had partitioned the existence domain of all the solutions and defined a method to generate a solution function for every partition. Let’s say that, imagining the problem as a cake, I had divided the cake into slices and had outlined a safe procedure to eat the whole cake by swallowing one slice at a time, avoiding to choke myself dead.
This imaginative description could give the false sensation of being fried air, although the problem and its application sunk their roots deep into the material world.
Each partition represented one among all the production regimes in the real factory, which were many, but still a finite number.
A different list of pharmaceutical specialties - pills of different colors and composition - with varying quantities to produce and deliver within a defined date and time described each production regime.
This meant different activity plans for the small robots' troop used for conveying the chemical components from the robotized multistory warehouse of the factory to the various production units.
Just as workmen, the carrier robots would go through shared paths and elevators inside the intricate body of the plant. Some sections of the routes were critical resources because only one robot at a time could use them, as also happened with the mixing machines, which required a sterilization cycle and a new vacuum atmosphere after each use.
The general solution of the problem required choosing the number, scheduling, and paths for the carrier robots, that would lead to the most efficient process, and this for every and all the different production regimes, which, in my model, were the partitions of the solution space.
I had built the solution functions, applying my personal algorithm of maximum-flow to the different partitions of the problem.
I was still testing the formal correctness of my first attempt when I gulped the first sandwich and then, in a few seconds, pushed another one to its chase down to the stomach.
Just to clarify the hazards of my quest, the problem was difficult but far from unsolvable.
As in every optimization problem, at least one optimal solution existed, surrounded by an infinite number of sub-optimal ones; those were, let’s say, less brilliant but still good enough.
It was generally enough to reach the set of solutions surrounding the optimal one, to get something valuable for real-world applications.
Unfortunately, my first check already showed that a severe incongruence flawed my family of “solution functions”.
I had only one straightforward way to make a logical test of my solution’s correctness.
I already knew for sure the measure of the whole existence domain of the solution space.
Thus, adding up the measures of the existence domains of all the functions of my family, the result had to be the same, or very, very near.
Too bad that my family of solutions showed to cover a much broader existence domain. This meant I couldn’t know which, nor how many, of my alleged solutions weren’t solutions at all to my problem.
I knew that with unlimited time and money, I could resort to the nuclear weapon of Artificial Intelligence and Machine Learning with a deep enough Neural Network.
Using a large training set, and going through it millions of times, the net would steadily improve, and would eventually become an oblivious genie capable of seeing at once the optimal scheduling for any production regime the factory would face.
Just, this alone would have cost a fortune in terms of man-hours, or better, months of teamwork necessary to gather and organize tens of thousands of examples in an adequate training set for the Neural Net.
What I was trying to discover, hence, was a dramatically less expensive and time-consuming way to determine a family of solutions via an analytic method.
This approach would likely provide an approximation of the exact optimal solution.
Okay, but who cares of the first prize in precision?
Especially if it costs more than the benefits attainable within an acceptable time horizon. Which means less than eighteen months for a production plant in the pharma industry: enough to push Artificial Intelligence out of the picture.
Besides, my company’s gain would be substantially higher with the quick development of an analytical solution.
The drawback of my approach?
It needed a human with a well-trained analytical mind, who still remembered enough of his math: what I could only hope to be, as for now.
I felt scant, but hiring somebody else with adequate skill would lead again to unpredictably high costs with no assurance of success.
In a nutshell, I was exploring the only way to achieve from such a challenging project a good gain in a reasonable time.
Otherwise, it could lead to a so-called “bloodbath”: a massive loss of time and money.
After gobbling the last sandwich together with the remnant of orange juice, I felt helpless.
When you immediately sniff a solution, but it turns out to be crap, you’re in deep trouble.
I thought better to have a pause, and I turned to the other riddle of the day: the date with the girl.
It was four o’clock in the afternoon, and the last bus to go back home would leave from the parking at seven p.m.
It was time to choose whether to stop for the night or go back home.
I decided that I would call Sonia and tell her I had to remain for the night, then I would ask her if she wanted to come.
I dialed her number, hoping she picked.
“Hello, can I talk?”
“Tell me.”
“I won’t finish my work by today. So, I’ll stay here for the night and finish tomorrow morning. Shall you come tonight?”
“Well, I have to decide, yet. I would be late, anyway. My work won’t end before half-past eleven.”
“No problem. I will work and wait for you.”
“Okay, let me check something. If I can free myself, I’ll call you back.”
Not an exalting result: it was sure she already had an appointment with my present competitor. But she still gave me an opportunity; I couldn’t hope for more, given the situation.
“Sure. You’re always the best, whatever you decide.”
“Thank you.”
“Take care.”
I went back to my work, and I had an intuition.
I fixed my attention on the ghost of a doubt that had flashed and then disappeared in the blink of an eye when I had defined the initial hypotheses of the problem.
I had assumed that the solutions defined a “proper” partition of the total solution space, where every sub-domain had precise boundaries, like the slices of a cake. In other words, that the slices didn’t overlay.
But who said it had to be so?! My ideal cake hadn’t any obligation to behave like an ordinary cake!
Actually, it seemed too neat and straightforward for this class of notoriously deceptive problems.
Now, I realized that the solutions could well overlap in some regions around the partition’s boundaries, and this would dissolve the supposed incongruence of my family of solutions.
Yes! I felt that blissful excitement!
I had found the crux of my problem, and now I would crack it.
Likely, the contiguous solutions of my family coexisted around what I had supposed the clean lines of their domain’s boundaries, which, otherwise, were blurred borders, ambiguous regions where the solutions morphed into one another. And this complied with the misleading properties I had to expect.
If this was true, my solution functions would still cover the whole solution space, but summing up the measures of their existence domains, I’d get a total higher than expected.
Precisely what I had got.
Of course! I was adding multiple times the measures of the overlapping regions. The sum of the slices was more than the full cake.
This would clear the incongruence of my method.
To get a first, empirical confirmation of my hypothesis, I had to test it on real data.
Stored in my notebook, I had enough sets of experimental data from the factory’s production batches of the last three months.
For each of them, if my solution were right, I would get one new scheduling of the robots, granting a total execution time and cost lower than the ones experienced in reality.
Unless the Production Manager had been a devil of a thinker, smarter than my algorithm.
The only constraints were that the computed times and costs had to lay all on a narrow path of allowed, real-world values.
If I met these conditions, it would be a strong clue I was on the right track. In that case, it would only be a matter of refining my algorithm.
While I was preparing a rough software procedure to perform the heavy-duty validation task, my phone rang.
I watched the display, expecting to see the name of Sonia, but it was my son Aldo calling.
Why on earth? - I wondered, hoping that nothing wrong had happened. A call from my son was more than a rare event.
“Hello, Al! How’s everything?”
“Fine, dad! I wanted to ask you if you’re staying out tonight.”
Strange again, but I felt relieved it wasn’t bad news.
“Yes, I will remain here tonight. But why are you asking me that?”
“Oh, I wanted to invite some friends of mine at home for dinner, if you’re out.”
“Okay, the playground is all for you, but I don’t want to find a devastated battlefield when I’m back tomorrow.”
“Don’t worry, thank you, dad!”
“Where are you now?”
“I’m on the highway, driving back home.”
“Well! Then switch off that phone and be careful how you drive! See you tomorrow.”
“Fine. And, are you coming back for lunch tomorrow?”
“Are you controlling me? Yes, I think so, and if you prepare something for lunch, it won’t disappoint me, anything you prepare.”
“Forget it! I’m busy tomorrow morning,” and he closed the line.
After that odd phone call, I asked myself what my son was planning for the evening. I hoped he wouldn’t organize an in-house rave party, destroying furniture and staining with coke or other unknown fluids every sofa in the living room, like two years before.
I shivered, regretting my excessive liberality. I couldn't even rely on the discrete surveillance of my daughter who was out of town, busy with exams at the university until the end of the week.
I finished arranging the test environment, and I pushed the run button. Then I remained in wait, while the number crunching evolved slowly, with minimal, ill-formatted reporting displaying on the screen. I would find a complete report in a file, at execution’s end.
The phone uttered an exotic fluttering sound: it was a message where Sonia said she couldn’t meet me that night. She had to go back home, and one of her colleagues would take her by car, as usual.
“Fuck!” I shouted, and slammed my fist on the table, risking damage to the whirling hard drive of my poor laptop, still struggling through the test procedure.
After the initial bout of rage, a stinging suspect went building up in my mind.
“Beep.”
The test procedure was complete.
I checked the report file, and I had the confirmation I expected. The results looked perfect, all well inside the allowed range of values.
My conjecture seemed right: the solutions overlapped near the boundaries of contiguous production regimes!
I jumped up and run outside in the garden, gesturing with tightened fists to the sky: “Yahooo!!! I did it!”
I had found the solution!
The warm wave of satisfaction flooded every corner of my body, but…
But I felt that this time, something had damped my excitement.
“Overlapping solutions… in the family?” I mumbled. “In my family!” I shouted.
The reality was taunting me.
Now, I wanted to make a personal test about another, personal conjecture.
It was six in the evening, and I was still in time to try a small experiment.
I called Aldo.
“Hello, dad?”
“Hello. I’m sorry, but I changed my mind. I have finished my work, and I will be back home this evening. I’ll take the last bus at seven. Sorry to jeopardize your plans.”
“Oh, I understand! Okay, don’t worry. We will organize for another time.” He sounded disappointed, but not too much. Perhaps they had a backup solution.
“Okay, later.”
It was a lie. I didn’t mean to move, there wasn’t any need to hurry back.
I remained in wait for some minutes; if I were lucky, something would happen.
After five minutes, still nothing: my phone kept silent.
Yet, this wasn’t meaningful. I had to make impossible for them any backup solution.
I wanted to know, and I made another, devious move.
I was sorry to concern my son, but it would be for the best.
“Hello, Aldo, Aldo?” - I said with a suffering voice.
“Yes, what’s the matter now, dad?!”
“I’m feeling sick, stomach sick. Are you already at home? You should come and pick me... Forget your plans for tonight. I’m sorry, but I need your help.”
“Sure! But, how are you?”
“Don’t worry. I must have eaten something wrong. Just come and take me home. Stay with me, I’ll get better.”
“I will be there in fifteen minutes!”
“Ok, thank you, and no need to run! Drive carefully.”
After this second, more dramatic call, I remained in wait again.
Under some conditions, I had created and applied what in logic is called a “necessity criterion.”
Now I just had to wait for the result.
This meant that,
If Sonia had a relationship with my son Aldo,
And
If Sonia was unaware that Aldo was my son –which was likely,
And
If Aldo was unaware that Sonia was my relationship–which was almost sure,
Then Sonia would soon call me back and confirm our date.
As with every necessity criterion, the implication acted in one way only. If Sonia had called, that would not be a definite proof of her relationship with Aldo but, given the concatenation of the events, it would have been a strong clue. Otherwise, if Sonia hadn’t called, I couldn’t draw any conclusion. I’d have to make further investigations.
The conditions to satisfy were many, but, yes, my intuition told me I had good chances to check if, at least, my doubt made sense.
Although, I couldn’t decide if solving it, would make me feel better or worse than remaining with it.
While I contemplated that dilemma, my phone rang.
“Hello, Sonia?”
“Hello! I solved my problem, and we can meet. I will be there by half-past eleven. Wait for me, and prepare a hot bath, please. I will be tired.”
At least I still was the second choice!
The best part of it was that, for the first time in my life, I felt proud of it.
“I’m sorry, but I have a terrible stomach ache. We can’t meet tonight, I apologize for the mishap, really!”
“Oh, I’m sorry for that! No need to apologize. Are you sure you don’t want me come and help you?”
“No, thank you. Don’t feel concerned for me. Somebody is already coming to help me.”
“What? Somebody... Who?”
She’d had the first doubt?
Aldo must have told her he had to reach his father, who was feeling sick. But I didn’t want to help her in that direction.
“My daughter is coming. Now I must close. I’ll call you back when I’m better.”
Now, I would question Aldo very well but seamlessly, and I would clear any residual doubt.
But, meanwhile, I asked myself, with all my pretenses of deep philosophical thinking, couldn’t I realize once and for all how ridiculous was I clambering after girls too younger than me?
Whatever information I could gather from Aldo, my final solution was already there, clear: to keep my mouth shut, and, with a full-throttle rear gear, speed quickly away from a domain where I couldn’t linger anymore.
