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)
“The paradox of education is precisely this—that as one begins to become conscious one begins to examine the society in which he is being educated.”
—James Baldwin (1924–1987)