AIT be of any help to meet this challenge? From a highly epistemic perspective, one may say that the phenotypes cannot be described before they appear. Thus, they form an incompressible list of described/describable phenotypes, at each moment of the evolutionary process. It seems hard to turn such a contingent/linguistic statement into an objective scientific analysis.
In contrast to AIT, in which randomness is developed for infinite sequences of numbers, in a measurement independent way, any study of randomness in a specific context, physical or biological, for example, depends on the intended theory which includes its main assumptions (see, for example, section 1.3 for the “principles” used in the analysis of quantum randomness and for the theory-and-measurement-dependent notion of the predictor).
As a consequence, our focus on unpredictability and randomness in natural sciences, where access to knowledge crucially requires physical or biological measurement, cannot and should not be interpreted as an argument that “the world is random” and even less that it is “computable” – we, historical and linguistic humans, effectively write our theories and compute them in order to predict (see Calude et al. 2012 for a discussion on the hypothesis of a lawless (physical) Universe).
We used (strong forms of) relative unpredictability as a tool to compare different forms of determination and stability in natural sciences, sometimes by a conceptual or mathematical duality (showing the “relevance of negative results”), other times by stressing the role of randomness in the robustness or resilience of phenomena. The ways we acquire knowledge may be enlightened by this approach, also in view of the role of symmetries and invariance in mathematical modeling and of the strong connections between spontaneous symmetry breaking and random events discussed in Longo and Montévil (2015).
1.8. Acknowledgments
The authors have been supported in part by Marie Curie FP7-PEOPLE-2010-IRSES Grant and have benefitted from discussions and collaboration with A. Abbott, S. Galatolo, M. Hoyrup, T. Paul and K. Svozil. We also thank the referees for their excellent comments and suggestions. We also warmly thank Springer Editions for authorizing the translation of the original article (Classical, Quantum and Biological Randomness as Relative Unpredictability. Invited Paper, special issue of Natural Computing, Volume 15, Issue 2, pp. 263–278, Springer, March 2016) and Louis Ter Ovanessian who provided the translation.
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Champernowne, D.G.
