Of Naturalness and Complexity

  • Sauro SucciEmail author
Regular Article


It is argued that the occurrence of disproportionately (“un-natural”) large (or small) numbers, as well as deep cancellations, are comparatively natural traits of the way Nature is geared to operate in most complex systems. The idea is illustrated by means of two outstanding and over-resilient problems in theoretical physics: fluid turbulence and the computation of ground states of quantum many-body fermion systems. Potential connections with the issue of Naturalness, or lack thereof, in high-energy physics are sketched out.


  1. 1.
    G.F. Giudice, The dawn of post-naturalness era, arXiv:1710.07663 [physics.hist-ph] (2017)Google Scholar
  2. 2.
    S. Succi, The Lattice Boltzmann Equation for Complex States of Flowing Matter (Oxford University Press, 2018) (More than Universality itself, the book discusses the notion of “Weakly Broken Universality”, namely the subtle and problem-dependent coexistence of Universality and Individualism which characterises foams, emulsions, gels, polymers melts and many other complex states of soft-flowing matter.)Google Scholar
  3. 3.
    P. Williams, Stud. Hist. Philos. Sci. B 51, 82 (2015)CrossRefGoogle Scholar
  4. 4.
    J. Maldacena, Int. J. Theor. Phys. 38, 1113 (1999)CrossRefGoogle Scholar
  5. 5.
    U. Frisch, Turbulence (Cambridge University Press, 1995)Google Scholar
  6. 6.
    J. Ambjorn, J. Jurkiewicz, R. Loll, Phys. Rev. Lett. 95, 171301 (2005) (These quantum gravity simulations based on causal dynamic triangulations, seem to indicate that smooth spacetime may emerge already two decades above the Planck scale, incidentally the same two decades which separate classical fluids from molecules. However, this by no means implies that the coherence scale should also be located two decades above the Planck scale, because matter and spacetime are likely to interact very non-linearly in that regime.)CrossRefGoogle Scholar
  7. 7.
    D. Frenkel, B. Smit, Understanding Molecular Simulation: From Algorithms to Applications (Elsevier, 2002) p. 24Google Scholar
  8. 8.
    J.D. Wells, Finetuned Cancellations and Improbable Theories, arXiv:1809.03374v1 [physics.hist-ph] (2018)Google Scholar
  9. 9.
    S. Hossenfelder, Screams for Explanation: Fine-tuning and Naturalness in the Foundations of Physics, arXiv:1801.02176 [physics.hist-ph] (2018)Google Scholar
  10. 10.
    H.C. Levinson, Chance, Luck and Statistics (1963) p. 29, reprinted by Dover (2001). (I owe this reference to Daan Frenkel, while the blame for invoking preferential attachment is all on me)Google Scholar
  11. 11.
    J. Preskill, M. Wise, F. Wilczek, Phys. Lett. B 120, 127 (1983)CrossRefGoogle Scholar
  12. 12.
    H. Chen, S. Kandasamy. S. Orszag, R. Shock, S. Succi, V. Yakhot, Science 301, 633 (2003)CrossRefGoogle Scholar
  13. 13.
    Ken A. Dill, J.L. MacCallum, Science 338, 1042 (2012)CrossRefGoogle Scholar
  14. 14.
    R. Barbieri, G.F. Giudice, Nucl. Phys. B 306, 63 (1988)CrossRefGoogle Scholar
  15. 15.
    P.G. Wolynes, J.N. Onuchic, D. Thirumalai, Science 267, 1619 (1995)CrossRefGoogle Scholar
  16. 16.
    M. Troyer, U.J. Wiese, Phys. Rev. Lett. 94, 170201 (2005) (I am very grateful to Matthias Troyer for elucidating to me the issue of exponential cancellations in quantum-many body fermion simulations and for clarifying to me the topological nature of the sign problem.)CrossRefGoogle Scholar
  17. 17.
    D. Ceperley, Rev. Mod. Phys. 67, 279 (1995)CrossRefGoogle Scholar
  18. 18.
    E. Kaxiras, private communicationGoogle Scholar
  19. 19.
    R. Feynman, Int. J. Theor. Phys. 21, 467 (1982)CrossRefGoogle Scholar
  20. 20.
    Q.M. Troyer, private communication (The sign problem is an artifact of not working in the eigenbasis. In the eigenbasis the Hamiltonian would be diagonal and all weights thus positive. However, we have no way of storing or calculating eigenstates on classical computers. It would need exponential memory. Quantum computers, on the other hand, have no problems storing quantum states. The wave function of the quantum system can directly be encoded in the wave function of the qubits.)Google Scholar
  21. 21.
    H. Risken, The Fokker-Planck Equation, in Springer Series in Synergetics (Springer, 1996)Google Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Center for Life Nano Sciences at La SapienzaIstituto Italiano di TecnologiaRomaItaly
  2. 2.Institute for Applied Computational Science, J. Paulson School of Engineering and Applied SciencesHarvard UniversityCambridgeUSA

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