This was a long flat ribbon and ants used to live in it. In and not on, as these were flat ants and there was no space on either face of the strip for them to wander. In fact, there was not even room for space to be there: nothing existed outside of it, not even emptyness.
All these ants used to live in a small city surrounded by fields and sitting at nearly the same distance from the northern and the southern rims of the band. They would not leave it and explore their world…
“… Because” they would say, “this place is as good as any other, Science proved it.”
Here is how the mathematician Moescherit—an authority in topology—would put it in her famous writings: Let us assume, and this is the only reasonable hypothesis, that our ribbon Universe is infinite in both directions. Then every point lying at equal distance from both rims is a point around which the Universe is symmetric. All those points qualify equally to being the centre of the Universe. In particular, we live at the centre of the Universe, which is the best place to be. More precisely, let us consider the following equation on the differentiable fibre bundle […] This is usually the point where people would to close the book and feel an urge to think that the text was already convincing enough.
One day, an audacious physicist, Christophant Semicolon-Parens, claimed that the Universe was in fact closed on itself, like a ring, a bracelet or, say, the side of an enormous circular chocolate box.
“For example somebody walking towards the west for a long time shall end up to his starting point, arriving from the east.” He said.
“Fine, then please just do it, so as to prove your hypothesis.” Replied his fellow citizens.
“And,” They added between themselves, “we then get rid of you once for all.”
Hence our daring adventurer set off to the distant west with a handful of camp aids. One year later, from that same direction, they came back. Burdened by terrible news. They had to cancel his demonstration, for they discovered, very far in the west, another colony of ants. And these were a disgusting genus.
“At first they may seem to have reached the same level of civilization as we. From the distance we could see similar concrete houses and electric street lights.” Christophant started, “But then we went close and met them. They salute with their right antenna instead of the left one.” he said to the assembly.
Gasps. This was a sign of disdain here.
“They have no smell, which makes communication very hard.” He continued.
Pheromones is an essential part of ant communication even in that other universe.
“They drive on the other side of the road! Drinking their milk produce made us very sick. Oh and you won't believe that: their heart is on the right side of their body…”
“We thought it was our duty to come back and warn you.” He concluded when the noise settled.
“Did you declare war upon them?” Someone asked.
“Of course.” He replied.
“The situation is worse than you think, Christophant.” An important looking ant intervened. This was the mayor. “You were away when this happened, two seasons ago. A small delegation came from the east. A type of ants very similar to that evil spawn you just described. We declared war with them.”
It was clear then, that they were surrounded and that survival would be a matter of dire fighting.
An attack plan had to be devised. The idea came from Dextri Levo, a great chemist:
“We cannot drink their milk, we cannot smell their scent… I know why: their molecules are mirror images of ours. They carry in their bodies and fluids substances that our organism cannot recognize, cannot digest… and conversely. Now, there is this harmless compound, which we ingest on a daily basis but whose mirror image is toxic for us. The innocuous variant will certainly be toxic for them. Let us spray their city with it!”
Among the journalists present at the conference, one asked:
“What if they have the same idea?”
“This is why we shall start working right now.” Levo replied. “The course of victory may well depend on who arrives first.”
The two battalions loaded with their deadly gifts left on the same day. One headed west, to the city visited by Semicolonus-Parens; the other went to the east, looking for the land from where the other delegation came. It was chosen that the armies would both run along the northern side of the ribbon, for a surprise attack from the north.
The battle was ruthless.
Wandering in the ruins, one of the few survivor among her denizens, Moescherit, suddenly got her Eureka moment.
“Why have our enemies from the east and the west got the same idea as us, at the same time as we had? How comes they arrived simultaneously on us? This was just us! My model of the Universe was false, and Christophant's was almost correct. In reality we live in a Möbius strip; going around reverses the orientation. This would well match with the fact our city was swept down on from the south. Where are my notebooks?” She said to nobody, and went off dodging her dying fellow ants towards the remains of her university.
Morality: It is wiser to follow the advice of mathematicians, even when they are completely wrong.
Postface: To complete the Möbius band of this story, read it again but permute the words mathematician and physicist.
1997, Arnaud Chéritat (adapted to English by the author in 2016).