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Natural Computing

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01.06.2016

Classical, quantum and biological randomness as relative unpredictability

verfasst von: Cristian S. Calude, Giuseppe Longo

Erschienen in: Natural Computing | Ausgabe 2/2016

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Abstract

We propose the thesis that randomness is unpredictability with respect to an intended theory and measurement. From this point of view we briefly discuss various forms of randomness that physics, mathematics and computing science have proposed. Computing science allows to discuss unpredictability in an abstract, yet very expressive way, which yields useful hierarchies of randomness and may help to relate its various forms in natural sciences. Finally we discuss biological randomness—its peculiar nature and role in ontogenesis and in evolutionary dynamics (phylogenesis). Randomness in biology has a positive character as it contributes to the organisms’ and populations’ structural stability by adaptation and diversity.

Vorheriger Artikel Probability 1 computation with chemical reaction networks

Nächster Artikel Physarum in silicon: the Greek motorways study

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Such as the loan, in 1332, to the King of Britain Edward III who never returned it to the Bank of Bardi and Peruzzi—as all high school kids in Italy and our colleague Alberto Peruzzi in Florence know very well....

Non-analyticity is stronger than the presence of positive Lyapunov exponents in a non-linear function. These exponents may appear in the solution of a non-linear system or directly in a function describing a dynamics; they quantify how a minor difference in the initial conditions may be amplified along the trajectory. In this case, one has a form of “controlled” randomness, as the divergence of the trajectories starting within the same best interval of measurement will not exceed an exponentially increasing, yet pre-given value. In the absence of (analytic) solutions, bifurcations and homoclinic orbits may lead to sudden, “uncontrolled”, divergence.

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This was Borel’s definition of randomness (Borel 1909).

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It is not unreasonable to hypothesise that pseudo-randomness rather reflects its creators’ subjective “understanding” and “projection” of randomness. Psychologists have known for a long time that people tend to distrust streaks in a series of random bits, hence they imagine a coin flipping sequence alternates between heads and tails much too often for its own sake of “randomness.” As we said, the gambler’s fallacy is an example.

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Titel: Classical, quantum and biological randomness as relative unpredictability
verfasst von: Cristian S. Calude
Giuseppe Longo
Publikationsdatum: 01.06.2016
Verlag: Springer Netherlands
Erschienen in: Natural Computing / Ausgabe 2/2016
Print ISSN: 1567-7818
Elektronische ISSN: 1572-9796
DOI: https://doi.org/10.1007/s11047-015-9533-2

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