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unusual facts about Smale's paradox


Homotopy principle

Smale's paradox can be done using C^1 isometric embedding of S^2.


Blum–Shub–Smale machine

In computation theory, the Blum–Shub–Smale machine, or BSS machine, is a model of computation introduced by Lenore Blum, Michael Shub and Stephen Smale, intended to describe computations over the real numbers.

Braess's paradox

In 2012, scientists at the Max Planck Institute for Dynamics and Self-Organization demonstrated through computational modeling the potential for this phenomenon to occur in power transmission networks where power generation is decentralized.

Denny's paradox

Writing in the Journal of Fluid Mechanics, David Hu and John Bush state that Denny's paradox "rested on two flawed assumptions.

Fenno's paradox

It is named after Richard Fenno who discussed this in his 1978 book Home Style: House Members in Their Districts.

G. E. Moore

Moore is also remembered for drawing attention to the peculiar inconsistency involved in uttering a sentence such as "It is raining but I do not believe it is raining."—a puzzle which is now commonly called "Moore's paradox."

Gray's paradox

In 2009, researchers from the National Chung Hsing University in Taiwan introduced new concepts of “kidnapped airfoils” and “circulating horsepower” to explain the swimming capabilities of the swordfish.

Handlebody

The expression is non-unique: the manipulation of handlebody decompositions is an essential ingredient of the proof of the Smale h-cobordism theorem, and its generalization to the s-cobordism theorem.

Heegaard splitting

Assuming smoothness the existence of a Heegaard splitting also follows from the work of Smale about handle decompositions from Morse theory.

Lover's paradox

Francesco Alberoni, Falling in love, New York, Random House, 1983.

Low-dimensional topology

The solution by Smale, in 1961, of the Poincaré conjecture in higher dimensions made dimensions three and four seem the hardest; and indeed they required new methods, while the freedom of higher dimensions meant that questions could be reduced to computational methods available in surgery theory.

Philip Jourdain

He corresponded with Georg Cantor and Gottlob Frege, and took a close interest in the paradoxes related to Russell's paradox, formulating the card paradox version of the liar paradox.

Schrödinger's paradox

Schrödinger's cat, a thought experiment relating to quantum physics

Stephen Smale

Since 2002 Smale is a Professor at the Toyota Technological Institute at Chicago; starting August 1, 2009, he is also a Distinguished University Professor at the City University of Hong Kong.

The Orbital

With integration high up on the agenda, the now 18-month-old website was updated by Jack Smale and Julian Farmer with even greater core presence on Facebook and Twitter.

Use–mention distinction

Self-referential statements mention themselves or their components, often producing logical paradoxes, such as Quine's paradox.

William Newcomb

William Newcomb (died 1999), a professor and theoretical physicist at the University of California's Lawrence Livermore Laboratory, is best known as the creator of Newcomb's paradox, devised in 1960.


see also