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It was an hour after Neo passed out. Astrid asked me if I would sleep over at her house. I replied no, that I would go in search of Selene at the merchants' guild. She did not insist. She told me that, if I couldn't find her, I could come back and she would leave me a guest room. She would wait for Durman, who would be a while longer.
There was no need to go back. The lights of the guild were on. There were Selene and her sister Sena, accompanied by several members of the guild, surrounded by documents, scrolls and half-empty cups. Selene greeted me with a tired smile.
— Selene — Please wait a little while. We have a problem to solve before we go. — she said as she pointed to a pile of papers and numbers on a large table.
They were trying to predict how many merchants would arrive in the city in the next month. Sena, with her straight posture and calm authority, nodded as Selene looked at me with a raised eyebrow, as if asking for permission.
— Sena — Go ahead, I'm sure you have something to contribute, Hunt —
— Adjutant (1) — Sena Who is this man? —
— Adjutant (2) — Excuse me Sena, Selene, but we can't let this individual, brought by Mrs. Astrid look at these documents. —
— Sena — Calm down, this man will help us. —
I approached. I went through all the documents in silence. It was like coming home. Numbers. Patterns. I asked for paper. Selene handed it to me without saying anything. I pushed the messy papers aside a bit. First I took the figures from previous years, number of traders arriving month by month, their variations, the annual cycles. I organized everything mentally like a Markov system. Each state represented a range of traders in a month, and the transition to the next month depended on previous patterns.
So I put together a K-order, square, transition matrix. Each cell represented the probability of moving from state j to state i.
(If I can diagonalize this matrix, everything will be easier.) I looked for the eigenvalues. I formed the matrix P with the eigenvectors, and the diagonal matrix D . I tried to calculate M = PDP^-1 . Nothing fit. The result did not preserve the correct transitions. I forgot to check if the matrix is diagonalizable. Everyone looked at me, some curiously, some impatiently. Sena crossed her arms. I took a deep breath and checked everything from scratch. This time I checked to see if the matrix was faulty. It didn't have enough eigenvectors. It was not diagonalizable. (Never mind, Plan B.) I opted to take the matrix to its Jordan form, with triangular blocks with eigenvalues on the diagonal and ones on the immediate superdiagonal. With that, I formed an upper triangular matrix. Now yes M^k = P T^k P^-1. I raised the matrix to the desired power (a projection to the next few months).
But that was not enough. The estimates had to incorporate uncertainty. Human behavior is not governed by linear systems alone.
I used a normal distribution, i.e. a Gaussian Curve. Centered on the mean of the projected data, and with a standard deviation constructed from the historical dispersion of the records. The extremes did not interest me. I concentrated on the central 68% ( most likely and most stable, I think.)
After a few more minutes of calculations, I closed the paper and slid it on the table.
■— 1342,6. With a tolerance of about 30 to the downside and 45 to the upside. That's the most reliable range.
— Adjutant (3) — That...that can't be. We project over 2000. — he mumbled, puzzled.
— Assistant (3) — That... that can't be. We projected more than 2000 — he muttered, puzzled.
— Adjutant (4) — Even considering the increase in trade due to the festival.... how can it be so low? — asked another, checking his notes at full speed.
Sena frowned. Selene watched me carefully, though it was clear she didn't quite understand what I had done.
— Sena — And are you sure about that result? — she asked, crossing her arms, trying to hide her bewilderment.
■— As sure as I can be with this level of data. You overestimated because you took a raw mean and projected it without filtering out trends or anomalies. This is a common mistake if you don't know queuing theory or probabilistic modeling - I said without raising my voice.
The assistants began to whisper among themselves, some clearly disgruntled.
— Selene — That's enough for today. You're all tired, aren't you? Besides, it's already late. Go home, get some sleep. I'll check the calculations myself tomorrow - she said, cutting off the discussions calmly but firmly.
One by one, the guild members began to leave, collecting papers, still exchanging incredulous glances.
When only Selene, Sena and I were left in the office, Sena sat back in her desk chair slightly, and stared at me, though it was clear to me that she hadn't understood a word about matrices, eigenvalues or Gaussian curves.
— Sena — Since I know you come from another world, one more developed than ours... how I would have loved to see what the traders of your world were capable of. —
■— There the markets were like living creatures. Companies were valued every second, and their performance was reflected in charts that changed in real time. Each company had shares, small parts that were bought and sold like chips. And those tokens, their price, depended on how many people trusted that company to perform well in the future. If confidence went up, so did the value. If it fell... the whole system could shake. —
I drew you several charts, one of the most representative was the Japanese candlestick chart. Vertical rectangles, some filled and some empty, that showed the behavior of a stock in a time interval. The top and bottom of the rectangle indicated the opening and closing prices, while thin lines, like wicks, marked the extremes of the price reached. By observing the sequence of these candlesticks, the mood of the market could be read, as if it were a coded language.
Selene and Sena were almost asleep. Their eyelids were heavy as wet parchments and the words came out slowly.
— Selene — We'd better go to sleep, it's already too late — she mumbled, getting up with a yawn.
— Sena — Yes, there's no point in staying awake — she added as she picked up a couple of papers scattered on the table.
The three of us left the guild and walked through the quiet streets of the city, barely illuminated by street lamps and the pale reflection of the moon. Arriving at the sisters' house, I stopped for a moment to look at the facade.
■— This house looks a lot like Astrid and Durman's — I commented, curious.
— Sena — The houses of guild masters are almost identical. Institutional architecture, they call it. — she replied with a complicit smile.
Selene took my arm as they opened the door. Just before climbing the stairs, Sena turned to us.
— Sena — Don't make too much noise — she said with a mischievous smile, and then disappeared behind the door of her room.
Already in the room, while I lit the fire in the fireplace, Selene started to change. Wearing only a large white nightgown, she lay down on the bed while I took off my shirt and lay down beside her. The atmosphere was soft, intimate, filled with a warmth that needed no candles or grandiloquent words.
■— Is it normal in your town to form couples so quickly? —
Selene looked at me surprised, but not uncomfortable. Her expression was a mixture of tenderness and curiosity.
— Selene — Yes, it is normal. —
■— Don't you think Neo and Dalia go too fast? And let's not even talk about us. —
— Selene — I guess you and I have been going faster than usual... but, after all, it's the custom here. —
■— Custom? —
— Selene — Sure. You come from another world, in this world couples are usually formed in spring. It's a trial period, you try to sleep together and if you get to winter... there you already try to conceive a child. —
■— And why wait until winter to conceive? —
— Selene — Obviously, because only in winter we can conceive children. —
■— How —
— Selene — In your world women could have children whenever they wanted, or what? —
■— I don't have a lot of data on how women's bodies work, but I understand that in my world women are fertile almost all month long, except for a few days. —
— Selene — Lucky you. In this world, we women are only fertile once a year, during the middle two months of winter. It is so that the children are born in spring or summer, when there are more resources and less diseases —
I noticed that the subject was more serious than I expected. The mood had become contemplative, almost melancholic. But I didn't want to leave her thinking about biology and fertility.
■— So... does that mean it's safe to "play" with you now? — I asked with a raised eyebrow and mischievous grin.
And without warning, I started tickling her. Selene let out an involuntary giggle, soft and clean.
— Selene: Wait, wait... I can't breathe! — she said between laughs, pushing me gently.
— Selene — Stop... we can't do this here, my sister might hear us...—
■— How can we not? — I said before kissing her, as my fingers slowly moved down from her neck, outlining her abdomen. —
Her laughter turned into a sigh, and the room filled with a different warmth.