- Dear children! What are you doing here? - Beta and Bit saw an older man standing in front of them. It was very cold, icy cold. Bit knew that feeling from books: they were cold during the teleportation; sometimes they felt pain; it seemed to them that some void was sucking them in. But this wasn’t like that. Bit was cold all the time, not only for a moment when he was travelling in time. There was no void either. The world was absolutely real and his body was suffering real freezing cold. Bit looked around. – We must’ve got back in time – he muttered looking at the soldiers standing close to a tank.
- My dears! Get inside or you will end up with pneumonia or something even worse – the older man warned them. He was wearing a sheepskin coat with a fur collar. Beta and Bit were dressed in the light summer clothes they’d been wearing when they entered Pietraszko’s study.
Two soldiers were marching in step in their direction. The man quickly put his arms around the teenagers and he pushed them lightly in the direction of the gate leading to a tenement house they were standing next to. - Citizen! – they heard one of the soldiers cry after them. The older man turned around. – They’re my grandchildren – he explained. – They went out with me.
- Take better care of them then – the soldier grunted.
The older man only nodded his head and hugging the teenagers again he led them out of that place. The soldiers turned back. – Come, I’ll make you a hot tea. You’ll warm up a bit – he invited them.
His flat was gloomy grayish and dark. Its big windows didn’t let much light in.
In the living room there was a small sofa covered with a brown coverlet, a round table with four chairs and a little cupboard on legs. It caught Beta’s attention. She had seen a similar cupboard at her grandpa’s place, only it was bigger. This one was a little higher than Bit and just like the grandpa’s piece it had a lockable drink cabinet. On the left-hand side of the drink cabinet there was a cupboard with glass door. There was also a narrow shelf shielded by similar glass door hanging above both cupboards.
- Sit down on the sofa bed – said the host. – Go ahead – he encouraged them pointing to the sofa. – I’ll put the kettle on. And you, child– the older man turned to Beta who was still staring at the cupboard – can you take out the glasses?
The cupboard with glass door was filled with small and big glasses, metal cases, brown cups with painted flowers and one white cup with rose pattern. It differed considerably from other cups. It was fragile and dignified. Beta thought that this was the only real china cup in the service. The upper shelf was a place for some crystal bowls, jugs and an ashtray. The girl took out the glasses in yellow apples – she liked these best. She put them on the table and sat next to her brother.
- Ok, so this is a sofa bed, not a sofa –Bit said.
Their host returned with a little red teakettle in his hands. He threw a glance at the table and he smiled benevolently. – My grandchildren, the real ones, also like these glasses best. Children are partial to them, it seems. Unfortunately, they cannot be used for tea – he said and he took from the cupboard three other glasses and three metal cases. Beta stood up to put the glasses into cases and the older man poured tea into them. „That’s it?” - Beta thought when she saw that the tea barely covered the bottom of the glass. The older man disappeared and after a while he returned with another kettle. – And now we add boiling water – he said to himself. – After my wife died I had to learn everything, even how to make tea – he started to explain.- This teakettle was her idea. She used to put dry tea inside the kettle filling it almost to the lid and then she poured some boiling water. She poured a little of that essence into glasses and filled them to the top with boiling water. I do it now in the same way.
He took a silver sugar bowl from the cupboard. –Oh, yes, and the spoons – he remembered and he went to the kitchen again.
- You have to forgive me, I don’t have visitors often – he said as he came back to the living room. Beta and Bit were familiar with such monologues. Their grandpa behaved in the same way during their visits. He was talking all the time; he wanted to discuss everything. – Have you got any names? – the host asked jokingly.
- Great. I’m Jan – he introduced himself. – You must be still cold, I bet. There are blankets in my son’s room. I’ll bring them in a second– the older man left for a moment.
- We’re in the period of war again – Bit said. He knew they had little time to talk. – We must’ve moved back in time.
- I think you’re wrong. Look around – Beta pointed to a small table standing in the corner under the window. – There’s a radio. And besides, the soldier was speaking Polish.
- True. But what he said was weird. ‘Citizen’ - who’s talking like that? – Bit asked.
- I’m back – their host came back suddenly. – It took a while but I found two blankets. Here you are – he said as he gave the blankets to the teenagers. – Wrap yourselves and sit at the table.
Beta and Bit obediently sat on the chairs and picked up the cups by their metal handles. They were really cold. They first froze outside and then inside the flat of their host which was rather cold as well. The teenagers were slowly sipping at their tea. It tasted like paper but they didn’t mind that. It made them warm and that was enough.
- Next time you want to get outside –the older man started – put on some coats. Although it would be better if you don’t go outside at all. At least not without your parents.
Their host took a sip of tea.
- What’s been going on these two days... – the man stopped and lowered his head sadly. – Civil war. Brothers against brothers. Poles against Poles.
Another sip of tea and silence again. Beta started to look around the room. There were pictures on the wall: a smiling woman, a young couple, a little boy sitting grandly on the armchair. And a very characteristic picture of the Mother of God with a silver moon underneath.
Suddenly they heard a sound of a key in a lock. A young man jumped into the room. He couldn’t have been more than thirty years old although his moustache suggested otherwise.
- Hi, dad! – he said. – You’ve got visitors?
- Neighbors’ kids – the host explained.
- I haven’t seen them before – the man with mustache was surprised. - Anyway. I came to take a few things –he said and he went to the other room.
- That’s my son, Krzysztof –the older man said to Beta and Bit.
- Bye, then! I’m off. Take care.
- Do you... –Mr Jan didn’t finish. The man slammed the door and locked them. Krzysztof disappeared as suddenly as he came. - ... also - Beta and Bit barely heard that word.
- My grandchildren are much younger than you – he said finally after a longer pause. – They are little children actually. Peter is five and Anna’s three. They are the best part of my son’s life. Mine too, in fact. Unfortunately, he believes that he is a member of the next generation of Polish insurgents. He wants to fight for a better Poland and he jeopardizes the safety of his family for some vague ideals and fancied purposes. And he is as stubborn as a donkey; he doesn’t listen to his father’s arguments and advice. He should listen because I know what I’m saying. I have seen occupation and insurrection; I had to run away from my native city; I was cast out of the destroyed capital and I returned to the ruins.
So we’re still in Warsaw. These are different times but we’re still in the capital – Beta thought.
The host stopped. They sank into silence. Beta and Bit were still silent.
- I’ve been afraid for these two days again –the man continued. –I’m scared for my family and for myself.
He stopped and after a moment he continued but this time his voice was completely different. – Come on – Mr. Jan stood up from his chair and went to the window. – I’ll show you something.
Beta and Bit rose up. Still wrapped up in the blankets they went up to a dirty window to look at equally dirty world. The cloudy sky was grey like the filthy snow covering everything all around. They saw the same tank they’d seen before and several soldiers.
- The tank is still there –Beta said.
- Yes, it is. Only it’s not a tank, it’s a transporter. But look where it is standing. What a meaningful coincidence.
Beta and Bit only then noticed that the tank was parked in front of a high building. At the top of the building hanged a huge word ‘Moscow’. On the building below there was also another word ‘cinema’. Lower still, above the very entrance, there was a big white poster with the title ‘Czas Apokalipsy’ (Apocalypse Now).
- Sometimes I stand by that window and look at all of that and I wonder how is that possible that none of them hasn’t noticed it yet. And then I smile to myself because it means that they are not as omnipotent as they’d like to think. Not everything depends on them. Would you like to drink some more tea? – the man asked suddenly.
- Yes, I’d love to– Bit looked as if he’d just woken up. – My sister would like more tea too –he added although Beta shook her head. The older man went to the kitchen.
- What are you doing? – she asked nervously.
- What do you mean? I’ve sent that man to the kitchen so we could discuss how to get home –the boy explained. –Let us gather the dates again.
Bit took a pencil and a newspaper he’d earlier noticed on the table with the radio and he sat by the big table.
- 1876 and 1885 are the first pair – Beta said as she sat next to her brother. - 1876 was on Pietraszko’s gadget and 1885 was the year of publication of the newspaper that we read then.
- Then I entered 2015 and we were thrown into 1945 as you claimed – Bit added.
- I still think it was 1945; I don’t have any better idea. The city looked as if the war’d just ended. And later on I don’t know where we were because you entered some year yourself, just for kicks.
- Not for kicks, I wanted to make it easier for us to get home. I wrote 2098. We only need to find out where we are now and calculate somehow what date we have to enter to get back to Pietraszko’s shelter. Maybe we’ll just ask our host what’s the year now?
- No way –Beta answered quickly. – What if he shows us the door? Do you want to calculate that out in the cold? I think that we are not very far from our times. The soldier said ‘citizen’ just like in the comedies dad likes to watch.
- The ones only he finds funny –Bit reminded.
-They are not funny for you because you don’t understand them; you don’t know the context. But dad is laughing when he watches them because they show the times when he was a child. I think that we’re in that period now. 1970s or 1980s, I don’t know exactly.
- Wow, you really limited our room for maneuvers – Bit couldn’t leave that without remark
- I’m back – said their host. He was holding a red teakettle in one hand and a kettle with boiling water in the other. –Some puzzle? –he asked looking at their notes in the newspaper which Bit inefficiently tried to hide from him. – I like puzzles, especially the mathematical ones. I used to work in the CSO for years – their host went to the kitchen and he quickly returned –this time without the teakettle or the kettle.
- CSO, that is, the Central Statistical Office – he explained – I’ve cut my teeth on number crunching. Show me what you’ve got –he said standing next to Bit.
According to Beta everything was going in the wrong direction. She was sure that in a moment they would return to the cold street and pressed by the circumstances once again they would enter some random year in that strange watch.
Bit, on the other hand, loved unexpected situations. He coped with them much better than his sister. He quickly showed the notes to their host.
- We’re trying to find a relationship between several points –he started to explain. – They are dates. We have three pairs: 1876 – 1885, 2015 – 1945 and 2098 and the current year.
- Then write 1981. What are you waiting for? – Mr. Jan said.
Beta didn’t expect that it would be so simple. Bit grinned widely and wrote down 1981.
-We also have the second element of the fourth pair: 2015. We want to find its first element – he continued.
- Have you tried to draw it? – the man asked. – From your expressions I can tell that you haven’t – he said kind-heartedly. –Let us start then. Boy, draw the coordinates. – He said taking a notebook, ruler and a pencil out of his desk. He found a blank page in the notebook and gave it to Bit.
Bit competently drew the three points describing their adventures.
- Look, these points are almost ideally placed along a straight line. You can use a ruler to draw a straight line running through these points and then you may check where that line crosses the line corresponding to 2015 – Mr. Jan said drawing a line going straight through all the points with an expert hand. – Look, you can find an approximate solution to this puzzle with nothing more than a ruler and pencil.
- But can we find an exact, not approximate result?– Beta asked. She preferred to avoid approximate results and time travels which would result from them.
- Of course, you only need to draw the best fit line of the linear regression, that is, the function with equation y = a x + b. The value of y and x are the coordinates of your points, and the values of a and b are the unknown values that need to be calculated.
- But how to it? – Beta urged him.
- This is really an interesting problem. Generally, you have to minimize the distance between the points and the line. You can do it in many ways– Mr. Jan started a lecture. – The very name of the problem – regression- comes from the expression ,,regression toward the mean’’, used by Sir Francis Galton, when he started to examine relationship between height of parents and their sons. He noticed that the height of the sons is closer to the average height of the whole population than the height of their parents...
- But how to solve this particular problem? – Beta burst out although in any other situation she would listen to a lecture on data analysis with interest. This time, however, she was frozen to the marrow, tired, scared and she wanted to go home finally.
- In this particular case – Mr. Jan’s regret was almost audible as he continued – notice that when the values from the horizontal axis changed from 1876 to 2098, that is, they changed by 222 units, the values of the vertical axis changed from 1885 to 1981, that is, by 96 units. If we divide it – Mr. Jan divided three- digit numbers with ease - 96 / 222 is around 0.43, then a one-unit move on the horizontal axis gives us a 0.43-unit increase on the vertical axis. You want to move vertically from 1981 to 2015, that is, by 34 units. By how many units do you think you have to move horizontally?
- Ooooo –Bit started a little dimwittedly. I could do with a laptop or at least a calculator.
- That would be 34 divided by 0.43 so almost 340 divided by 4, which is 170 by 2, so around 85… - Beta calculated out loud.
- And even more around it will be 79 –Mr. Jan smiled. Mental calculations were much easier for him.
- So we need to move on the horizontal axis from 2098 to 2098 plus 79, that is, 2177 – Bit wanted to obliterate the memory of his not too smart reaction.
- Exactly, that is the solution to your puzzle! See how easy it was? – Mr. Jan looked very pleased. – Now you know what linear regression is. Maybe you’ll make use of that knowledge some day.
Beta and Bit smiled widely. They’ll be able to go home finally. They chose not to think for the time being about Pietraszko’s reaction to their intrusion and discovery of his secret cavern. Was it possible that he didn’t notice anything? Maybe he hasn’t even returned with Jacek to his study yet? No, that would be too good to be true although they stood a ghost of chance.
- I haven’t had such an interesting day for some time. I forgot about the martial law for a moment. I’m really happy that I could help you. Although maybe it was you who helped me – Mr. Jan said.
- Without you we wouldn’t be able to get home –Beta said suddenly.
- That’s an exaggeration. I just lied a bit to the soldiers, that’s it – their host smiled. – You haven’t drunk your tea because of all that mathematics – he observed. – Now it’s completely cold.
- We don’t mind – the siblings said almost simultaneously. They drank their tea down in one draught. It tasted like paper even when cold.
- So maybe we’ll just go now – Bit said as he got up from the table. – Thank you for tea and your help – he thanked heading for the door. Beta followed him.
Mr. Jan opened the door for them. – Good buy – they said to their host. When he closed the door Bit grabbed his sister by her hand and pushed her up the stair to the next floor.
- So let’s check it – he said entering 2177 in the watch.