In differential topology, Smale's paradox states that it is possible to turn a sphere inside out in a three-dimensional space with possible self-intersections but without creating any crease, a process often called sphere eversion (eversion means "to turn inside out"). This is surprising, and is hence deemed a veridical paradox. More precisely, let
be the standard embedding; then there is a regular homotopy of immersions
such that ƒ0 = ƒ and ƒ1 = −ƒ.
Famous quotes containing the words smale and/or paradox:
“Of smale houndes hadde she that she fedde
With rosted flessh, or milk and wastel-breed.
But soore wepte she if oon of hem were deed,
Or if men smoot it with a yerde smerte—
And al was conscience and tendre herte.”
—Geoffrey Chaucer (1340?–1400)
“A good aphorism is too hard for the teeth of time and is not eaten up by all the centuries, even though it serves as food for every age: hence it is the greatest paradox in literature, the imperishable in the midst of change, the nourishment which—like salt—is always prized, but which never loses its savor as salt does.”
—Friedrich Nietzsche (1844–1900)