|A pocketbook contains a gateway to another universe, and a group of unlikely heroes tries to save ours from the aliens there by reaching in and grabbing it.
This is a cute short story, with a not-particularly-sound gateway into another dimension. However, the mathematical discussion of which surfaces can be inverted through pinholes is well-done.
i read this years ago and it stuck with me as a disturbing little story. I have often wondered what the other end intended.
Note that at least some of the story is available for free at the moment as part of a Google Book. Unfortunately, the part Sarah-Marie Belcastro mentions is on a page that is missing from that free version. Here is an excerpt for your convenience:
|(quoted from Tiger by the Tail)|
Collins dropped an aluminum button into the purse. It went through the aluminum circle and vanished. "Say," he asked suddenly, scowling, "what do you mean you can't turn this thing inside out?"
"It's a second-order geometric form." Evanson lit a cigarette carefully. "You can turn a first-order form, like a sphere or rubber ball, inside out through a small hole in the surface. But, you can't turn an inner tube inside out, no matter what you do."
"Because it's got a hole in it. And you can't pull a hole through a hole, not even an infinitesimal hole."
Originally published in Galaxy in 1951, reprinted in 1961 in an anthology of the same name and in the book 50 Short Science Fiction Tales edited by Asimov and Conklin in 1997.
Important Mathematical Note: Chris Chiesa has written to point out that the claim of this story is incorrect. In fact, it is possible to invert an "innertube" through a hole. Moreover, it is an interesting inversion, because doing so reverses the role of the two directions on the surface. Or, as Wikipedia (currently) puts it, "If a torus is punctured and turned inside out then another torus results, with lines of latitude and longitude interchanged." Thank you, Chris, for bringing that to our attention!