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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).
However, if the generalized Riemann hypothesis is true, there exists a quadratic nonresidue < , [7] making it possible to check every up to that limit and find a suitable within polynomial time. Keep in mind, however, that this is a worst-case scenario; in general, z {\displaystyle z} is found in on average 2 trials as stated above.
In probability theory, a Chernoff bound is an exponentially decreasing upper bound on the tail of a random variable based on its moment generating function.The minimum of all such exponential bounds forms the Chernoff or Chernoff-Cramér bound, which may decay faster than exponential (e.g. sub-Gaussian).
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.
Marston Morse applied calculus of variations in what is now called Morse theory. [6] Lev Pontryagin, Ralph Rockafellar and F. H. Clarke developed new mathematical tools for the calculus of variations in optimal control theory. [6] The dynamic programming of Richard Bellman is an alternative to the calculus of variations. [7] [8] [9] [c]
Renewal theory is the branch of probability theory that generalizes the Poisson process for arbitrary holding times. Instead of exponentially distributed holding times, a renewal process may have any independent and identically distributed (IID) holding times that have finite mean. A renewal-reward process additionally has a random sequence of ...
The free will theorem says that if we have free will, then particles must have free will. This presumably is counterintuitive. It makes no claim about a world in which we don't have free will (a deterministic world). There's no way to argue for free will on the basis of this theorem - and yet, this is what the section claims, without any ...
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 ...