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Conway and Kochen, The Strong Free Will Theorem, published in Notices of the AMS. Volume 56, Number 2, February 2009. Rehmeyer, Julie (August 15, 2008). "Do Subatomic Particles Have Free Will?". Science News. Introduction to the Free Will Theorem, videos of six lectures given by J. H. Conway, Mar. 2009. Wüthrich, Christian (September 2011).
A linear group is not amenable if and only if it contains a non-abelian free group (thus the von Neumann conjecture, while not true in general, holds for linear groups). The Tits alternative is an important ingredient [2] in the proof of Gromov's theorem on groups of polynomial growth. In fact the alternative essentially establishes the result ...
Because the sum of the reciprocals of the primes diverges, the Green–Tao theorem on arithmetic progressions is a special case of the conjecture. The weaker claim that A must contain infinitely many arithmetic progressions of length 3 is a consequence of an improved bound in Roth's theorem. A 2016 paper by Bloom [4] proved that if {,..
On that basis "...free will cannot be squeezed into time frames of 150–350 ms; free will is a longer term phenomenon" and free will is a higher level activity that "cannot be captured in a description of neural activity or of muscle activation..." [185] The bearing of timing experiments upon free will is still under discussion.
In the 1980s, John Stewart Bell discussed superdeterminism in a BBC interview: [7] [8] There is a way to escape the inference of superluminal speeds and spooky action at a distance. But it involves absolute determinism in the universe, the complete absence of free will. Suppose the world is super-deterministic, with not just inanimate nature ...
The theorem of Du Bois-Reymond asserts that this weak form implies the strong form. If L {\displaystyle L} has continuous first and second derivatives with respect to all of its arguments, and if ∂ 2 L ∂ f ′ 2 ≠ 0 , {\displaystyle {\frac {\partial ^{2}L}{\partial f'^{2}}}\neq 0,} then f {\displaystyle f} has two continuous derivatives ...
The modern proof of the strong law is more complex than that of the weak law, and relies on passing to an appropriate subsequence. [17] The strong law of large numbers can itself be seen as a special case of the pointwise ergodic theorem. This view justifies the intuitive interpretation of the expected value (for Lebesgue integration only) of a ...
The strong cosmic censorship hypothesis asserts that, generically, general relativity is a deterministic theory, in the same sense that classical mechanics is a deterministic theory. In other words, the classical fate of all observers should be predictable from the initial data.