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)
“When a paradox is widely believed, it is no longer recognized as a paradox.”
—Mason Cooley (b. 1927)