FAIRYTALE ABOUT THE FORTH DIMENSION
Once upon a time, in a two-dimensional kingdom lived a King and as it was supposed there, he had a bunch of court wise men. And once, the chief adviser whispered in King’s ear a political plan and the King liked it. Next morning, public criers announced His Majesty’s order: if a man thrice enlarges the borders of the Kingdom, no matter how – declaring war, managing by ruse or through trading - the King will grant him a half of the kingdom.
Days passed, but there were no one who wished to try his luck. The advisor understood that he has to make excuses to the King – so he whispered in King’s ear again – that he should order to the court mechanician to fulfill the decree.
The mechanician was a specialist in tooth gearing (mechanisms didn’t work in some other way in the rwo-dimensional world), and moreover, he was in disgrace. The mechanician was taken to the His Majesty’s throne and was told to enlarge the kingdom no matter how. The mechanician was a specialist not only in different mechanisms, but also was skillful in pulling the long bow. He set his glasses straight, was silent for a couple of minutes and finally said:
- Your Flatness, I know one method using which you can enlarge your estate even five times - in no time.
The King nodded his head, meaning – go on. Nobles laughed up theirs sleeves – the man wouldn’t manage, but he said to the King: - Let’s imagine, that You are going downstairs, but on Your way You see a guard – how will You round him?
- That’s not a big deal, he will bow low and I’ll step over him, - the King answered.
- And if I say that there may be another staircase but not a floor up or down but at the side so you can round the guard using that staircase?
The King became angry: - There is no any “at the side”! You must move borders of my estate!
The mechanician answered: - But my point is that Your kingdom is larger than it seems.
- You haven’t convinced me, - laughed the King – and I forgot to say that everyone who will try but not manage to fulfill my decree will be executed, throw him into dungeon, and tomorrow he’ll be executed if doesn’t invent anything better!
No sooner said than done, the mechanician was thrown into a prison, and the scaffold was being prepared under the window. And the mechanician brooded – maybe he really could round the prison walls “at the side”? And he began scratching a draught on the wall – searching for the third dimension. It turned out, that three separate two-dimensional bodies form one three-dimensional. A good hour, feeling doom, had thought he about how it was possible to see a three-dimensional thing from the two-dimensional world. It seemed that he finally found the clue – the thing must be turned in some way in order to see one of its hidden sides, but unfortunately, all the other verges would disappear.
I wonder, he thought, how is it to live in a kingdom of three dimensions? Is it freer from kings and tsars or not? In an hour the forth figure was added to the three drawn on the wall – he had found also the forth dimension, proceeding from the third dimension it occurred that – let’s assume that a stone can be turned in such a way that you’ll see one of it’s sides that wasn’t a part of the three-dimensional world. And how does this side look like? How can we see hidden sides of, for instance, a gear-wheel, about which we know nothing?
The master remembered how he cast in mould these gear-wheels from metal and repaired them with file – and this was the solution- the form for casting, as far as the file, also has other sides, and it means that if you imagine the whole process of making you’ll understand their seizes. The mechanician spent twelve hours locked up and twelve figures were drawn on the wall when he was taken to the execution.
Executioner stroked his axe and stabbed. He stabbed three times but the head was still in its place, smiling.
The mechanician said: - My neck is so far from your axe that you can’t reach it even by an hours ride, executioner :) – and to the King he said – You, King, owe only one kingdom, but I owe twelve worlds, I’ve enlarged your kingdom but not for such flat people as you and your advisers are!
Foma Tuturov 2008