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Natural Computing

, Volume 15, Issue 2, pp 263–278 | Cite as

Classical, quantum and biological randomness as relative unpredictability

  • Cristian S. Calude
  • Giuseppe Longo
Article

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.

Keywords

Randomness Quantum randomness Biological randomness 

Notes

Acknowledgments

The authors have been supported in part by Marie Curie FP7-PEOPLE-2010-IRSES Grant and 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.

References

  1. Abbott A, Calude CS, Svozil K (2015) A non-probabilistic model of relativised predictability in physics. Report CDMTCS-477, Centre for Discrete Mathematics and Theoretical Computer Science, University of Auckland, Auckland, New Zealand. http://www.cs.auckland.ac.nz/research/groups/CDMTCS/researchreports/?download&paper_file=545
  2. Abbott AA, Calude CS, Conder J, Svozil K (2012) Strong Kochen–Specker theorem and incomputability of quantum randomness. Phys Rev A 86:062,109. doi: 10.1103/PhysRevA.86.062109 CrossRefGoogle Scholar
  3. Abbott AA, Calude CS, Svozil K (2014) Value-indefinite observables are almost everywhere. Phys Rev A 89:032,109. doi: 10.1103/PhysRevA.89.032109 CrossRefGoogle Scholar
  4. Abbott AA, Calude CS, Svozil K (2014) Value indefiniteness is almost everywhere. Phys Rev A 89(3):032,109–032,116. doi: 10.1103/PhysRevA.89.032109. http://arxiv.org/abs/1309.7188
  5. Abbott AA, Calude CS, Svozil K (2015) On the unpredictability of individual quantum measurement outcomes. In: Beklemishev LD, Blass A, Dershowitz N, Finkbeiner B, Schulte W (eds) Fields of logic and computation II—essays dedicated to Yuri Gurevich on the occasion of his 75th birthday, Lecture notes in computer science, vol 9300, pp 69–86. Springer. doi: 10.1007/978-3-319-23534-9_4
  6. Anthes G (2011) The quest for randomness randomness. Commun ACM 54(4):13–15CrossRefGoogle Scholar
  7. Arjun R, van Oudenaarden R (2008) Stochastic gene expression and its consequences. Cell 135(2):216–226CrossRefGoogle Scholar
  8. Bailly F, Longo G (2009) Biological organization and anti-entropy. J Biol Syst 17(1):63–96. doi: 10.1142/S0218339009002715 MathSciNetCrossRefMATHGoogle Scholar
  9. Ball P (2011) The dawn of quantum biology. Nature 474:272–274CrossRefGoogle Scholar
  10. Barbara Bravi GL (2015) The unconventionality of nature: biology, from noise to functional randomness. In: Calude CS, Dinneen MJ (eds) Unconventional computation and natural computation conference, LNCS 9252, pp 3–34. Springer. http://www.di.ens.fr/users/longo/files/CIM/Unconventional-NatureUCNC2015
  11. Bell JS (1966) On the problem of hidden variables in quantum mechanics. Rev Mod Phys 38:447–452. doi: 10.1103/RevModPhys.38.447 MathSciNetCrossRefMATHGoogle Scholar
  12. Borel É (1909) Les probabilités dénombrables et leurs applications arithmétiques. Rend Circ Mat Palermo 1884–1940(27):247–271. doi: 10.1007/BF03019651 CrossRefMATHGoogle Scholar
  13. Bork P, Jensen LJ, von Mering C, Ramani AK, Lee I, Marcotte EM (2004) Protein interaction networks from yeast to human. Curr Opin Struct Biol 14:292–299CrossRefGoogle Scholar
  14. Born M (1926) Zur Quantenmechanik der Stoßvorgänge. Z Phys 37:863–867. doi: 10.1007/BF01397477 CrossRefMATHGoogle Scholar
  15. Born M (1969) Physics in my generation, 2nd edn. Springer, New YorkCrossRefMATHGoogle Scholar
  16. Bros J, Iagolnitzer D (1973) Causality and local mathematical analyticity: study. Ann Inst Henri Poincaré 18(2):147–184Google Scholar
  17. Buiatti M (2003) Functional dynamics of living systems and genetic engineering. Riv Biol 97(3):379–408Google Scholar
  18. Buiatti M, Longo G (2013) Randomness and multilevel interactions in biology. Theory Biosci 132:139–158CrossRefGoogle Scholar
  19. Calude C (2002) Information and randomness—an algorithmic perspective, 2nd edn. Springer, BerlinMATHGoogle Scholar
  20. Calude CS, Meyerstein W, Salomaa A (2012) The universe is lawless or “pantôn chrêmatôn metron anthrôpon einai”. In: Zenil H (ed) A computable universe: understanding computation & exploring nature as computation. World Scientific, Singapore, pp 539–547CrossRefGoogle Scholar
  21. Calude CS, Staiger L (2014) Liouville numbers, Borel normality and algorithmic randomness. University of Auckland. http://www.cs.auckland.ac.nz/CDMTCS/researchreports/448CS
  22. Calude CS, Svozil K (2008) Quantum randomness and value indefiniteness. Adv Sci Lett 1(2):165–168. doi: 10.1166/asl.2008.016. Eprint arXiv:quant-ph/0611029
  23. Champernowne DG (1933) The construction of decimals normal in the scale of ten. J Lond Math Soc 8:254–260MathSciNetCrossRefMATHGoogle Scholar
  24. Chang HH, Hemberg M, Barahona M, Ingber DE, Huang S (2008) Transcription wide noise control lineage choice in mammalian progenitor cells. Nature 453:544–548CrossRefGoogle Scholar
  25. Cooper SB (2004) Computability theory. Chapman Hall/CRC Mathematics Series, New YorkMATHGoogle Scholar
  26. Copeland AH, Erdös P (1946) Note on normal numbers. Bull Am Math Soc 52:857–860MathSciNetCrossRefMATHGoogle Scholar
  27. Cover TM, Thomas JA (1991) Elements of information theory. Wiley, New YorkCrossRefMATHGoogle Scholar
  28. del Giudice E (2015) http://www.i-sis.org.uk/Emilio_Del_Giudice.php. Accessed 25 Nov 2015
  29. Deutsch D (1985) Quantum theory, the Church–Turing principle and the universal quantum computer. In: Proceedings of the Royal Society of London. Series A, mathematical and physical sciences (1934–1990) 400(1818):97–117. doi: 10.1098/rspa.1985.0070
  30. Dietrich M (2003) Richard goldschmidt: hopeful monsters and other “heresies”. Nat Rev Genet 4:68–74MathSciNetCrossRefGoogle Scholar
  31. Downey R, Hirschfeldt D (2010) Algorithmic randomness and complexity. Springer, BerlinCrossRefMATHGoogle Scholar
  32. Eagle A (2005) Randomness is unpredictability. Br J Philos Sci 56(4):749–790. doi: 10.1093/bjps/axi138 MathSciNetCrossRefMATHGoogle Scholar
  33. Einstein A, Podolsky B, Rosen N (1935) Can quantum-mechanical description of physical reality be considered complete? Phys Rev 47(10):777–780. doi: 10.1103/PhysRev.47.777 CrossRefMATHGoogle Scholar
  34. Elowitz MB, Levine AJ, Siggia ED, Swain PS (2002) Stochastic gene expression in a single cell. Science 297(5584):1183–1186. doi: 10.1126/science.1070919. http://www.sciencemag.org/cgi/content/abstract/297/5584/1183
  35. Flajnik MF, Kasahara M (2010) Origin and evolution of the adaptive immune system: genetic events and selective pressures. Nat Rev Genet 11(1):47–59. doi: 10.1038/nrg2703 CrossRefGoogle Scholar
  36. Fleury V, Gordon R (2012) Coupling of growth, differentiation and morphogenesis: an integrated approach to design in embryogenesis. In: Swan L, Gordon R, Seckbach J (eds) Origin(s) of design in nature, cellular origin, life in extreme habitats and astrobiology, vol 23. Springer, Dordrecht, pp 385–428. doi: 10.1007/978-94-007-4156-0_22 Google Scholar
  37. Franklin JN, Towsner H (2014) Randomness and non-ergodic systems. arXiv:1206.2682
  38. Frigg R (2004) In what sense is the Kolmogorov–Sinai entropy a measure for chaotic behaviour? Bridging the gap between dynamical systems theory and communication theory. Br J Philos Sci 55:411–434MathSciNetCrossRefMATHGoogle Scholar
  39. Gács P, Hoyrup M, Rojas C (2011) Randomness on computable probability spaces—a dynamical point of view. Theory Comput Syst 48(3):465–485. doi: 10.1007/s00224-010-9263-x MathSciNetCrossRefMATHGoogle Scholar
  40. Galatolo S, Hoyrup M, Rojas C (2010) Effective symbolic dynamics, random points, statistical behavior, complexity and entropy. Inf Comput 208(1):23–41. doi: 10.1016/j.ic.2009.05.001. http://www.sciencedirect.com/science/article/pii/S0890540109001461
  41. Gould S (1989) Wonderful life. Norton, New YorkGoogle Scholar
  42. Gould S (1997) Full house: the spread of excellence from Plato to Darwin. Three Rivers Press, New YorkGoogle Scholar
  43. Graham R, Spencer JH (1990) Ramsey theory. Sci Am 262:112–117. doi: 10.2307/2275058 MathSciNetCrossRefGoogle Scholar
  44. Hilbert D (2014) Naturerkennen und logik naturerkennen und logik (230). http://www.jdm.uni-freiburg.de/JdM_files/Hilbert_Redetext. Accessed 18 Nov 2014
  45. Kochen SB, Specker E (1967) The problem of hidden variables in quantum mechanics. J Math Mech (now Indiana Univ Math J) 17(1):59–87. doi: 10.1512/iumj.1968.17.17004 MathSciNetCrossRefMATHGoogle Scholar
  46. Kupiec J (1983) A probabilistic theory of cell differentiation, embryonic mortality and dna c-value paradox. Specul Sci Techno 6:471–478Google Scholar
  47. Kupiec JJ (2010) On the lack of specificity of proteins and its consequences for a theory of biological organization. Prog Biophys Mol Biol 102:45–52CrossRefGoogle Scholar
  48. Kwon OH, Zewail AH (2007) Double proton transfer dynamics of model dna base pairs in the condensed phase. Proc Natl Acad Sci 104(21):8703–8708. doi: 10.1073/pnas.0702944104. http://www.pnas.org/content/104/21/8703.abstract
  49. Laloë F (2012) Do we really understand quantum mechanics? Cambridge University Press, Cambridge. www.cambridge.org/9781107025011
  50. Laplace PS philosophical essay on probabilities. Translated from the fifth French edition of 1825. Springer, Berlin, New York (1995, 1998). http://www.archive.org/details/philosophicaless00lapliala
  51. Laskar J (1994) Large scale chaos in the solar system. Astron Astrophys 287:L9–L12Google Scholar
  52. Longo G (2012) Incomputability in physics and biology. Math Struct Comput Sci 22(5):880–900. doi: 10.1017/S0960129511000569 MathSciNetCrossRefMATHGoogle Scholar
  53. Longo G (2015) How future depends on past histories in systems of life. to appear. http://www.di.ens.fr/users/longo/files/biolog-observ-history-future. Accessed 25 Nov 2015
  54. Longo G, Miquel PA, Sonnenschein C, Soto AM (2012) Is information a proper observable for biological organization? Prog Biophys Mol Biol 109(3):108–114. doi: 10.1016/j.pbiomolbio.2012.06.004 CrossRefGoogle Scholar
  55. Longo G, Montévil M (2014a) Perspectives on organisms: biological time. Symmetries and singularities. Springer, Berlin and HeidelbergCrossRefGoogle Scholar
  56. Longo G, Montévil M (2014b) Perspectives on organisms: biological time, symmetries and singularities. Lecture notes in morphogenesis. Springer, Dordrecht. doi: 10.1007/978-3-642-35938-5 CrossRefGoogle Scholar
  57. Longo G, Montévil M (2015) Models and simulations: a comparison by their theoretical symmetries. In: Dorato M, Magnani L, Bertolotti T (eds) Springer handbook of model-based science. Springer, HeidelbergGoogle Scholar
  58. Longo G, Montévil M, Kauffman S (2012) No entailing laws, but enablement in the evolution of the biosphere. In: Genetic and evolutionary computation conference. GECCO’12, ACM, New York, NY, USA. doi:DOIurl10.1145/2330784.2330946. (Invited paper)Google Scholar
  59. Longo G, Montévil M, Sonnenschein C, Soto AM (2015) In search of principles for a theory of organisms. (submitted)Google Scholar
  60. Luo ZX (2011) Developmental patterns in Mesozoic evolution of mammal ears. Annu Rev Ecol Evol Syst 42:355–380CrossRefGoogle Scholar
  61. Marinucci A (2011) Tra ordine e caos. Metodi e linguaggi tra fisica, matematica e filosofia. Aracne, RomaGoogle Scholar
  62. Monod J (1970) Le hasard et la nécessité. Seuil, ParisGoogle Scholar
  63. Munsky B, Trinh B, Khammash M (2009) Listening to the noise: random fluctuations reveal gene network parameters. Mol Syst Biol 5:318–325CrossRefGoogle Scholar
  64. Myrvold WC (2011) Statistical mechanics and thermodynamics: a Maxwellian view. Stud Hist Philos Sci Part B Stud Hist Philos Mod Phys 42(4):237–243. doi: 10.1016/j.shpsb.2011.07.001 MathSciNetCrossRefMATHGoogle Scholar
  65. Novick A, Weiner M (1957) Enzyme induction as an all-or-none phenomenon. Proc Natl Acad Sci 43(7):553–566. http://www.pnas.org/content/43/7/553.short
  66. O’Reilly EJ, Olaya-Castro A (2014) Non-classicality of the molecular vibrations assisting exciton energy transfer at room temperature. Nat Commun 5. doi: 10.1038/ncomms4012
  67. Pironio S, Acín A, Massar S, de la Giroday AB, Matsukevich DN, Maunz P, Olmschenk S, Hayes D, Luo L, Manning TA, Monroe C (2010) Random numbers certified by Bell’s theorem. Nature 464(7291):1021–1024. doi: 10.1038/nature09008 CrossRefGoogle Scholar
  68. Poincaré H (1902) La Science et l’hypothèseGoogle Scholar
  69. Richards EJ (2006) Inherited epigenetic variation revisiting soft inheritance. Nat Rev Genet 7(5):395–401MathSciNetCrossRefGoogle Scholar
  70. Shanahan T (2012) Evolutionary progress: conceptual issues. Wiley, Chichester. doi: 10.1002/9780470015902.a0003459.pub2 Google Scholar
  71. Shapiro JA (2011) Evolution: a view from the 21st century. FT Press, Upper Saddle RiverGoogle Scholar
  72. Soifer A (2011) Ramsey theory before Ramsey, prehistory and early history: an essay in 13 parts. In: Soifer A (ed) Ramsey theory, progress in mathematics, vol 285. Birkhäuser, Boston, pp 1–26. doi: 10.1007/978-0-8176-8092-31 CrossRefGoogle Scholar
  73. Turing AM (1950) Computing machinery and intelligence. Mind 59(236):433–460MathSciNetCrossRefGoogle Scholar
  74. Turing AM (1952) The chemical basis of morphogenesis. Philos Trans R Soc Lond Ser B Biol Sci 237(641):37–72. doi: 10.1098/rstb.1952.0012. http://rstb.royalsocietypublishing.org/content/237/641/37.abstract
  75. Weihs G, Jennewein T, Simon C, Weinfurter H, Zeilinger A (1998) Violation of Bell’s inequality under strict Einstein locality conditions. Phys Rev Lett 81:5039–5043. doi: 10.1103/PhysRevLett.81.5039 MathSciNetCrossRefMATHGoogle Scholar
  76. Wikipedia: stochastic gene regulation (2014a) http://q-bio.org/wiki/Stochastic_Gene_Regulation. Accessed 14 Nov 2014
  77. Wikipedia: stochastic process (2014b). http://en.wikipedia.org/wiki/Stochastic_process. Accessed 25 Nov 2015
  78. Zeilinger A (2005) The message of the quantum. Nature 438:743. doi: 10.1038/438743a CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of AucklandAucklandNew Zealand
  2. 2.Centre Cavaillès (République des Savoirs), CNRSCollège de France & École Normale SupérieureParisFrance
  3. 3.Department of Integrative Physiology and PathobiologyTufts University School of MedicineBostonUSA

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