This story (available in "The Black Mirror and Other Stories"
and first published in the anthology, "Ways to Impossibility", 1983) is an interesting twist on the idea of one-sided surfaces. Based on Gustav Meyrink's "The Black Sphere" ("Die Schwarze Kugel"), the story tells us how the human race might be a little immature to handle some gifts from aliens. The "Riddhans", a technologically advanced race of humanoids 12 lights years from earth have established communication with us and one of their spaceship is now bearing a precious cargo for us. As it goes, "There were rumors that the gift was of mathematical nature. There was also a mention of a one-sided surface - which made people think of a Mobius strip - but at the same time some kind of mirror".
Turns out that one side of the disk-shaped object is a perfect mirror which reflects everything with 100% efficiency. The other side is the exact opposite - it absorbs everything and in some senses, does not exist. It is a mathematical boundary; Objects which pass through this abstract boundary on the disk disappear complete ("in the negative dimension"). The exchange in the auditorium where the object is presented is quite tongue-in-cheek and Seinfeldian:
|(quoted from The Black Mirror)|
"Truly an ideal nothing"
"It is not 'a nothing'. It is *nothing*. It is not a nothing, nor is it ideal, it is nothing at all"
"Strictly speaking, it is not even nothing at all. It's the other side of something that has only one side"
"A realized abstraction - and therefore not present in reality"
"A mathematical surface, which is ideally permeable and yet lets nothing through, since that which goes through ceases to exist."
"And what does not exist cannot go through"
"The audience understood nothing - that is, precisely the topic in question."
So what happens now? As the Riddhans put it after seeing how humans plan to use it:
|(quoted from The Black Mirror)|
"I think we should never have come. Bit by bit, they will throw the whole universe into the black hole empty half. That's the curse of our visit to the Earth, Brother."
The story is also reviewed by Adam Robert in "Strange Horizons".
Since Vijay mentions The Black Sphere in the comments above, but I am not inclined to give that story its own separate entry, here is what he had to say about it:
Gustav Meyrink's "The Black Sphere" ("Die Schwarze Kugel")
Originally in his German anthology "The Magic Horn of the German Philistine", 1913.
The story in German is available for google-translation at:
(The machine translation is actually quite poor so if some German=speaking reader can translate this, that would be fantastic!)
In this tale, a group of Brahmins from India show a device which can materialize human thoughts to the Germans. An army lieutenant ends up thinking about "absolute, mathematical nothingness", which is conjured up in the form of the perfect, one-sided hole in space (like a black-hole but without the mass or gravity). The hole is now slated to devour all of Reality into nothingness. The Brahmins call this the curse of their visit to the West.
The idea of one-sided disk also appears in Borges's very short, fabulist story, "The Disk", which describes mattter-of-factly how a woodcutter murders a visitor to get hold of a magical object - a disk which has a single side. As described:
“It is the disk of Odin,” the old man said in a patient voice, as though he were speaking to a child. “It had but one side. There is not another thing on earth that has but one side. So long as I hold it in my hand I shall be king.”
“Is it gold?” I said.
“I know not. It is the disk of Odin and it has but one side.”