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Abbott, A.A., Calude, C.S., Conder, J., Svozil, K. (2012). Strong Kochen-Specker theorem and incomputability of quantum randomness. Physical Review A, 86, 062109 [Online]. Available at: http://dx.doi.org/10.1103/PhysRevA.86.062109 [Accessed January 2021].

Abbott, A.A., Calude, C.S., Svozil, K. (2014a). Value-indefinite observables are almost everywhere. Physical Review A, 89, 032109 [Online]. Available at: http://dx.doi.org/10.1103/PhysRevA.89.032109 [Accessed January 2021].

Abbott, A.A., Calude, C.S., Svozil, K. (2014b). Value indefiniteness is almost everywhere. Physical Review A, 89(3), 032109 [Online]. Available at: http://arxiv.org/abs/1309.7188 [Accessed January 2021].

Abbott, A.A., Calude, C.S., Svozil, K. (2015a). A non-probabilistic model of relativised predictability in physics. Information, 6, 773–789.

Abbott, A.A., Calude, C.S., Svozil, K. (2015b). On the unpredictability of individual quantum measurement outcomes. In Fields of Logic and Computation II – Essays Dedicated to Yuri Gurevich on the Occasion of His 75th Birthday, Lecture Notes in Computer Science, Beklemishev, L.D., Blass, A., Dershowitz, N., Finkbeiner, B., Schulte, W. (eds). Springer, 9300, 69–86 [Online]. Available at: http://dx.doi.org/10.1007/978-3-319-23534-9_4 [Accessed January 2021].

Anthes, G. (2011). The quest for randomness. Communications of the ACM, 54(4), 13–15. Arjun, R. and van Oudenaarden, R. (2008). Stochastic gene expression and its consequences. Cell, 135(2), 216–226.

Bailly, F. and Longo, G. (2009). Biological organization and anti-entropy. Journal of Biological Systems, 17(1), 63–96.

Ball, P. (2011). The dawn of quantum biology. Nature, 474, 272–274.

Barbara Bravi, G.L. (2015). The unconventionality of nature: Biology, from noise to functional randomness. In Unconventional Computation and Natural Computation Conference, Calude, C.S., Dinneen, M.J. (eds). Springer, LNCS 9252 [Online]. Available at: http://www.di.ens.fr/users/longo/files/CIM/Unconventional-NatureUCNC2015.pdf [Accessed January 2021].

Bell, J.S. (1966). On the problem of hidden variables in quantum mechanics. Reviews of Modern Physics, 38, 447–452 [Online]. Available at: http://dx.doi.org/10.1103/RevModPhys.38.447.

Borel, E. (1909). Les probabilités dénombrables et leurs applications arithmétiques. Rendiconti del Circolo Matematico di Palermo (1884–1940), 27, 247–271 [Online]. Available at: http://dx.doi.org/10.1007/BF03019651 [Accessed January 2021].

Bork, P., Jensen, L.J., von Mering, C., Ramani, A.K., Lee, I., Marcotte, E.M. (2004). Protein interaction networks from yeast tohuman. Current Opinion in Structural Biology, 14, 292–299.

Born, M. (1926). Zur Quantenmechanik der Stoßvorg änge. Zeitschrift für Physik, 37, 863–867 [Online]. Available at: http://dx.doi.org/10.1007/BF01397477 [Accessed January 2021].

Born, M. (1969). Physics in my Generation, 2nd edition. Springer, New York.

Bros, J. and Iagolnitzer, D. (1973). Causality and local mathematical analyticity: Study. Ann. Inst. Henri Poincaré, 18(2), 147–184.

Buiatti, M. (2003). Functional dynamics of living systems and genetic engineering. Rivista di biologia, 97(3), 379–408.

Buiatti, M. and Longo, G. (2013). Randomness and multilevel interactions in biology. Theory Bioscience, 132, 139–158.

Calude, C. (2002). Information and Randomness – An Algorithmic Perspective, 2nd edition. Springer, Berlin.

Calude, C.S. and Staiger, L. (2018). Liouville numbers, Borel normality and algorithmic randomness. Theory of Computing Systems, 62(7), 1573–1585.

Calude, C.S. and Svozil, K. (2008). Quantum randomness and value indefiniteness. Advanced Science Letters, 1(2), 165–168 [Online]. Available at: http://dx.doi.org/10.1166/asl.2008.016.EprintarXiv:quant-ph/0611029 [Accessed January 2021].

Calude, C.S., Meyerstein, W., Salomaa, A. (2012). The universe is lawless or “pantôn chrêmatôn metron anthrôpon einai”. A Computable Universe: Understanding Computation & Exploring Nature as Computation, Zenil, H. (ed.). World Scientific, Singapore.

Champernowne, D.G. (1933). The construction of decimals normal in the scale of ten. The Journal of London Mathematical Society, 8, 254–260.

Chang, H.H., Hemberg, M., Barahona, M., Ingber, D.E., Huang, S. (2008). Transcription wide noise control lineage choice in mammalian progenitor cells. Nature, 453, 544–548.

Cooper, S.B. (2004). Computability Theory. Chapman Hall/CRC Mathematics Series, Boca Raton.

Copeland, A.H. and Erdös, P. (1946). Note on normal numbers. Bull. Amer. Math. Soc., 52, 857–860.

Cover, T.M. and Thomas, J.A. (1991). Elements of Information Theory. John Wiley & Sons, New York.

Deutsch, D. (1985). Quantum theory, the Church-Turing principle and the universal quantum computer. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences (1934–1990), 400(1818), 97–117 [Online]. Available at: http://dx.doi.org/10.1098/rspa.1985.0070 [Accessed January 2021].

Dietrich, M. (2003). Richard Goldschmidt: Hopeful monsters and other “heresies”. Nature Reviews Genetics: Historical Article Journal Article Portraits, 4, 68–74.

Downey, R. and Hirschfeldt, D. (2010). Algorithmic Randomness and Complexity. Springer, Berlin.

Eagle, A. (2005). Randomness is unpredictability. British Journal for the Philosophy of Science, 56(4), 749–790 [Accessed January 2021].

Einstein, A., Podolsky, B., Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete? Physical Review, 47(10), 777–780 [Online]. Available at: http://dx.doi.org/10.1103/PhysRev.47.777 [Accessed January 2021].

Elowitz, M.B., Levine, A.J., Siggia, E.D., Swain, P.S. (2002). Stochastic gene expression in a single cell. Science, 297(5584), 1183–1186 [Online]. Available at: http://www.sciencemag.org/cgi/content/abstract/297/5584/1183 [Accessed January 2021].

Flajnik, M.F. and Kasahara, M. (2010). Origin and evolution of the adaptive immune system: Genetic events and selective pressures. NatRev. Genet., 11(1), 47–59 [Online]. Available at: http://dx.doi.org/10.1038/nrg2703 [Accessed January 2021].

Fleury, V. and Gordon, R. (2012). Coupling of growth, differentiation and morphogenesis: An integrated approach to design in embryogenesis. In Origin(s) of Design in Nature, Cellular Origin, Life in Extreme Habitats and Astrobiology, Volume 23, Swan, L., Gordon, R., Seckbach, J. (eds). Springer, Netherlands [Online]. Available at: http://dx.doi.org/10.1007/978-94-007-4156-0_22 [Accessed January 2021].

Franklin, J.N. and Towsner, H. (2014). Randomness and Non-ergodic Systems [Online]. Available at: http://arxiv.org/abs/1206.2682.ArXiv:1206.2682 [Accessed January 2021].

Frigg, R. (2004). In what sense is the Kolmogorov-Sinai entropy a measure for chaotic behavior? Bridging the gap between dynamical systems theory and communication theory. British Journal for the Philosophy of Science, 55, 411–434.

Gàcs, P., Hoyrup, M., Rojas, C. (2011). Randomness on computable probability spaces – A dynamical point of view. Theory Comput. Syst., 48(3), 465–485 [Online]. Available at: http://dx.doi.org/10.1007/s00224-010-9263-x [Accessed January 2021].

Galatolo, S., Hoyrup, M., Rojas, C. (2010). Effective symbolic dynamics, random points, statistical behavior, complexity and entropy. Information and Computation, 208(1), 23–41 [Online]. Available at: http://www.sciencedirect.com/science/article/pii/S0890540109001461 [Accessed January 2021].

del Giudice, E. (2007). Old and new views on the structure of matter and the special case of living matter. Journal of Physics: Conference Series, 67, 012006.n [Online]. Available at: http://www.i-sis.org.uk/Emilio_Del_Giudice.php [Accessed January 2021].

Gould, S. (1989). Wonderful Life. Norton, New York, USA.

Gould, S. (1997). Full House: The Spread of Excellence from Plato to Darwin. Three Rivers Press, New York, USA.

Graham, R. and Spencer, J.H. (1990). Ramsey theory. Scientific American, 262, 112–117 [Online]. Available at: http://dx.doi.org/10.2307/2275058 [Accessed January 2021].

Hilbert, D. (1930). Naturerkennen und logik naturerkennen und logik, 230 [Online]. Available at: http://www.jdm.uni-freiburg.de/JdM_files/Hilbert_Redetext.pdf [Accessed January 2021].

Kochen, S.B. and Specker, E. (1967). The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics (now Indiana University Mathematics Journal), 17(1), 59–87 [Online]. Available at: http://dx.doi.org/10.1512/iumj.1968.17.17004 [Accessed January 2021].

Kupiec, J. (1983). A probabilistic theory of cell differentiation, embryonic mortality and DNA c-value paradox. Specul. Sci. Techno., 6, 471–478.

Kupiec, J.J. (2010). On the lack of specificity of proteins and its consequences for a theory of biological organization. Progress in Biophysics and Molecular Biology, 102, 45–52.

Kwon, O.H. and Zewail, A.H. (2007). Double proton transfer dynamics of model DNA base pairs in the condensed phase. Proceedings of the National Academy of Sciences, 104(21), 8703–8708 [Online]. Available at: http://www.pnas.org/content/104/21/8703 [Accessed January 2021].

Laloë, F. (2012). Do We Really Understand Quantum Mechanics? Cambridge University

Press, Cambridge [Online]. Available at: www.cambridge.org/9781107025011 [Accessed January 2021].

Laplace, P.S. (1998). Philosophical Essay on Probabilities. Translated from the 5th French edition of 1825. Springer, Berlin, New York [Online]. Available at: http://www.archive.org/details/philosophicaless00lapliala [Accessed January 2021].

Laskar J. (1994). Large scale chaos in the solar system. Astron. Astrophys., 287, L-L12.

Longo, G. (2012). Incomputability in physics and biology. Mathematical. Structures in Comp. Sci., 22(5), 880–900 [Online]. Available at: http://dx.doi.org/10.1017/S0960129511000569 [Accessed January 2021].

Longo, G. (2017). How future depends on past histories in systems of life. Foundations of Science, 1–32 [Online]. Available at: http://www.di.ens.fr/users/longo/files/biolog-observ-history-future.pdf [Accessed January 2021].

Longo, G. (2018). Interfaces of incompleteness. In Systemics of Incompleteness and Quasi-systems, Minati, G., Abram, M., Pessa, E. (eds). Springer, New York.

Longo, G. and Montévil, M. (2014a). Perspectives on Organisms: Biological Time, Symmetries and Singularities. Springer, Berlin and Heidelberg.

Longo, G. and Montévil, M. (2014b) Perspectives on Organisms: Biological Time, Symmetries and Singularities. Lecture Notes in Morpho-genesis. Springer, Dordrecht.

Longo, G. and Montévil, M. (2015). Models and simulations: A comparison by their theoretical symmetries. In Springer Handbook of Model-Based Science, Dorato, M., Magnani, L., Bertolotti, T. (eds). Springer, Heidelberg [to appear].

Longo, G., Montévil, M., Kaufman, S. (2012a). No entailing laws, but enablement in the evolution of the biosphere. In Genetic and Evolutionary Computation Conference, GECCO’12. ACM, New York [Invited Paper].

Longo, G., Miquel, P.A., Sonnenschein, C., Soto, A.M. (2012b). Is information a proper observable for biological organization? Progress in Biophysics and Molecular Biology, 109(3), 108–114.

Longo, G., Montévil, M., Sonnenschein, C., Soto, A.M. (2015). In Search of Principles for a Theory of Organisms. Journal of Biosciences, Springer, 40(5), 955–968.

Luo, Z.X. (2011). Developmental patterns in mesozoic evolution of mammal ears. Annual Review of Ecology, Evolution, and Systematics, 42, 355–380.

Marinucci, A. (2011). Tra ordine e caos. Metodi e linguaggi tra fisica, matematica e filosofia. Aracne, Rome.

Monod, J. (1970). Le hasard et la nécessité. Le Seuil, Paris.

Munsky, B., Trinh, B., Khammash, M. (2009). Listening to the noise: Random fluctuations reveal gene network parameters. Molecular Systems Biology, 5, 318–325.

Myrvold, W.C. (2011). Statistical mechanics and thermodynamics: A Maxwellian view. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 42(4), 237–243 [Online]. Available at: http://dx.doi.org/10.1016/j.shpsb.2011.07.00 [Accessed January 2021].

Novick, A. and Weiner, M. (1957). Enzyme induction as an all-or-none phenomenon. Proceedings of the National Academy of Sciences, 43(7), 553–566 [Online]. Available at: http://www.pnas.org/content/43/7/553.shor.

O’Reilly, E.J. and Olaya-Castro, A. (2014). Non-classicality of the molecular vibrations assisting exciton energy transfer at room temperature. Nat. Common., 5 [Online]. Available at: http://dx.doi.org/10.1038/ncomms4012 [Accessed January 2021].

Pironio, S., Acin, A., Massar, S., de la Giroday, A.B., Matsukevich, D.N., Maunz, P., Olmschenk, S., Hayes, D., Luo, L., Manning, T.A., Monroe, C. (2010). Random numbers certified by Bell’s theorem. Nature, 464(7291), 1021–1024 [Online]. Available at: http://dx.doi.org/10.1038/nature09008 [Accessed January 2021].

Poincaré, H. (1902). La Science et l’hypothèse.

Richards, E.J. (2006). Inherited epigenetic variation revisiting soft inheritance. Nature Reviews Genetics, 7(5), 395–401.

Shanahan, T. (2012). Evolutionary Progress: Conceptual Issues. John Wiley & Sons Ltd, Chichester.

Shapiro, J.A. (2011). Evolution: A View from the 21st Century. FT Press, Upper Saddle River, New Jersey.

Soifer, A. (2011). Ramsey theory before Ramsey, prehistory and early history: An essay in 13 parts. In Ramsey Theory, Progress in Mathematics, Vol. 285, Soifer, A. (ed.). Birkhäuser, Boston [Online]. Available at: http://dx.doi.org/10.1007/978-0-8176-8092-3_1 [Accessed January 2021].

Turing, A.M. (1950). Computing machinery and intelligence. Mind, 59(236), 433–460. Turing, A.M. (1952). The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 237(641), 37–72 [Online]. Available at: http://rstb.royalsocietypublishing.org/content/237/641/37 [Accessed January 2021].

Weihs, G., Jennewein, T., Simon, C., Weinfurter, H., Zeilinger, A. (1998). Violation of Bell’s inequality under strict Einstein locality conditions. Physical Review Letters, 81, 5039–5043 [Online]. Available at: http://dx.doi.org/10.1103/PhysRevLett.81.5039 [Accessed January 2021].

Zeilinger, A. (2005). The message of the quantum. Nature, 438, 743 [Online]. Available at: http://dx.doi.org/10.1038/438743a [Accessed January 2021].

1 1 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.

2 2 The non-analyticity is stronger than the presence of positive Lyapunov exponents for a nonlinear function. These exponents can appear in the solution of a nonlinear system or directly in a function describing a dynamic. They quantify how a minor difference in initial conditions can be magnified along a trajectory. In this case, we can have a form of “controlled” randomness because the divergence of the trajectories starting within the same best measurement interval will never exceed a pre-assumed, exponentially increasing value. In the absence of (analytical) solutions, bifurcations and homoclinic orbits can lead to sudden and “uncontrolled” divergence.

3 3 A macroscopic cause cannot have more elements of symmetry than the effects it produces. Its informational equivalent, called data processing inequality, asserts that no manipulation of information can improve the conclusions drawn from such data (Cover and Thomas 1991).

4 4 Laplace was also aware of this, but Lagrange, Laplace and Fourier firmly believed that any system of Cauchy equations possessed a linear approximation (Marinucci 2011).

5 5 A correlation between random events and symmetry breakings is discussed in Longo et al. (2015). In this case, measurement produces a value (up or down), which breaks the in-determined or in-differentiated (thus, symmetric) situation before measurement.

6 6 The model does not assess the ability to make statistical predictions – as probabilistic models might – but rather the ability to predict precise measurement outcomes.

7 7 Eagle argued that a physical process is random if it is “maximally unpredictable” (Eagle 2005).

8 8 Some molecular types are present in a few tenths or hundreds of molecules. Brownian motion may suffice to split them in slightly but non-irrelevantly different numbers.

9 9 An organism is an ecosystem inhabited by about 1014 bacteria, for example, and by an immune system, which in itself is an ecosystem (Flajnik and Kasahara 2010). Yet an ecosystem is not an organism: it has no relative metric stability (distance from its constituents), nor general organs of regulation and action, such as the nervous system found in animals.

10 10 Some may prefer to consider viruses as the least form of life. The issue is controversial, but it would not change Gould’s and our perspective at all: we only need a minimum biological complexity which differs from inert matter.

11 11 This was the definition of chance informally proposed by Borel (1909): the proportion of times that a finite sequence is in an infinite (even very long) sequence corresponds (approximately) to the probability that such a sequence occurs during a particular test.

12 12 The British mathematician and logician Frank P. Ramsey studied conditions under which order must appear.

13 13 The adjective “large” has precise definitions for both finite and infinite sets.

14 14 Consider a gas particle and its momentum: the average value of the momentum over time (the time integral) is asymptotically assumed to coincide with the average momenta of all particles in the given, sufficiently large, volume (the space integral).

15 15 It is not unreasonable to hypothesize that pseudo-randomness 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.

16 16 Incidentally, the same conference at which Gödel presented his famous incompleteness theorem.

Chapter written by Cristian S. CALUDE and Giuseppe LONGO.