Irreducibility and Computational Equivalence

Volume 2 of the series Emergence, Complexity and Computation pp 79-88

More Complex Complexity: Exploring the Nature of Computational Irreducibility across Physical, Biological, and Human Social Systems

  • Brian BeckageAffiliated withDepartment of Plant Biology, University of Vermont
  • , Stuart KauffmanAffiliated withDepartment of Mathematics, Department of Biochemistry, and Complexity Group, University of Vermont
  • , Louis J. GrossAffiliated withNational Institute for Mathematical and Biological Synthesis, University of Tennessee
  • , Asim ZiaAffiliated withDepartment of Community Development and Applied Economics, University of Vermont
  • , Christopher KolibaAffiliated withDepartment of Community Development and Applied Economics, University of Vermont

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The predictability of many complex systems is limited by computational irreducibility, but we argue that the nature of computational irreducibility varies across physical, biological and human social systems. We suggest that the computational irreducibility of biological and social systems is distinguished from physical systems by functional contingency, biological evolution, and individual variation. In physical systems, computationally irreducibility is driven by the interactions, sometimes nonlinear, of many different system components (e.g., particles, atoms, planets). Biological systems can also be computationally irreducible because of nonlinear interactions of a large number of system components (e.g., gene networks, cells, individuals). Biological systems additionally create the probability space into which the system moves: Biological evolution creates new biological attributes, stores this accumulated information in an organism’s genetic code, allows for individual genetic and phenotypic variation among interacting agents, and selects for the functionality of these biological attributes in a contextually dependent manner. Human social systems are biological systems that include these same processes, but whose computational irreducibility arises as well from sentience, i.e., the conscious perception of the adjacent possible, that drives social evolution of culture, governance, and technology. Human social systems create their own adjacent possible through the creativity of sentience, and accumulate and store this information culturally, as reflected in the emergence and evolution of, for example, technology. The changing nature of computational irreducibility results in a loss of predictability as one moves from physical to biological to human social systems, but also creates a rich and enchanting range of dynamics.


computational irreducibility complexity evolution