Excerpt

Mid-twentieth-century science pivoted to new, almost unseen issues following Warren Weaver’s brilliant lead in this vital essay, which broaches six topics. In statements below and the adjoined commentaries, I ask where we are seventy-six years after Weaver’s pivot.

I. The Sciences of Simplicity

Weaver rightly explains that the sciences of simplicity start with Newton in the seventeenth century and the invention of classical physics. This is the Newtonian paradigm:

1. Identify the relevant variables, for example, position and momentum.

2. Write laws of motion in differential form among these variables, for example, Newton’s three laws of motion and gravitation.

3. Identify the boundary conditions which thereby determine all possible combined values of the relevant variables, hence the phase space of the system.

4. Specify the initial state of the system.

5. Integrate the differential equations of motion to determine the entailed trajectory of the system within its phase space.

Over the next two centuries classical physics gave rise to further laws such as Maxwell’s equations, general relativity, and a myriad of novel technologies impacting modern mid-twentieth-century civilization, airplanes, cars, radios, and telephones.

Bibliography

Barabási, A.-L. 2009. “Scale-Free Networks: A Decade and Beyond.” Science 325 (5939): 412–413. https :

//doi.org/10.1126/science.117329.

Beggs, J. 2008. “The Criticality Hypothesis: How Local Cortical Networks Might Optimize Information

Processing.” Philosophical Transactions of the Royal Society A 366:329–343. https : / / doi . org / 10 .

1098/rsta.2007.2092.

Bischi, G. I., C. Chiarella, and L. Gardini. 2009. Nonlinear Dynamics in Economics, Finance, and the Social

Sciences. Berlin, Germany: Springer.

Bohm, D. 1989. Quantum Theory. New York, NY: Dover.

Bornholdt, S., and S. A. Kauffman. 2019. “Ensembles, Dynamics, and Cell Types: Revisiting the Statistical

Mechanics Perspective on Cell Regulation.” Journal of Theoretical Biology 467:15–22.

Brush, S. G. 1965. Kinetic Theory. Vol. 1 and 2. Oxford, UK: Pergamon. https://doi.org/10.1016/C2013-

0-07974-1.

Buckner, C., and J. Garson. 2019. “Connectionism.” In The Stanford Encyclopedia of Philosophy (Fall 2019),

edited by E. N. Zalta. https://plato.stanford.edu/archives/fall2019/entries/connectionism/.

Daniels, B. C., H. Kim, D. Moore, S. Zhou, H. B. Smith, B. Karas, S. A. Kauffman, and S. I. Walker. 2018.

“Criticality Distinguishes the Ensemble of Biological Regulatory Networks.” Physical Review Letters

121:138102.

277

F O U N D A T I O N A L P A P E R S I N C O M P L E X I T Y S C I E N C E

Devereaux, A., R. Koppl, S. A. Kauffman, and A. Roli. 2021. “An Incompleteness Result Regarding Within-

System Modeling.” SSRN, https://doi.org/10.2139/ssrn.3968077.

Edwards, S. F., and P. W. Anderson. 1975. “Theory of Spin Glasses.” Journal of Physics F: Metal Physics 5 (5):

965–974. https://doi.org/10.1088/0305-4608/5/5/017.

Epstein, I. R., and J. A. Pojman. 1998. An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves,

Patterns, and Chaos. Oxford, UK: Oxford University Press.

Everett, III, H., J. A. Wheeler, B. S. DeWitt, L. N. Cooper, D. van Vechten, N. B. D. Graham, and

R. N. Graham, eds. 1973. The Many-Worlds Interpretation of Quantum Mechanics. Princeton, NJ:

Princeton University Press.

Frankena, W. K. 1939. “The Naturalistic Fallacy.” Mind 48 (192): 464–477. https : / / doi . org / 10 . 1093 /

mind/XLVIII.192.464.

Gleick, J. 1987. Chaos: The Making of a New Science. London, UK: Penguin.

Gödel, K. 1986. “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme,

I.” In Kurt Gödel: Collected Works, Volume I: Publications 1929–1936, edited by S. Feferman, J. W.

Dawson, Jr., S. C. Kleene, G. H. Moore, R. M. Solovay, and J. v. Heijenoort, I:144–195. Oxford, UK:

Oxford University Press.

Kauffman, S. A. 1969. “Metabolic Stability and Epigenesis in Randomly Constructed Genetic Nets.” Journal

of Theoretic Biology 22:437–467. https://doi.org/10.1016/0022-5193(69)90015-0.

. 1993. Origins of Order. Oxford, UK: Oxford University Press.

. 2019. A World Beyond Physics. Oxford, UK: Oxford University Press.

Kauffman, S. A., and W. S. McCulloch. 1967. Random Nets of Formal Genes. Technical report. Quarterly

Progress Report 34, Research Laboratory of Electronics, Massachusetts Institute of Technology.

Kauffman, S. A., and A. Roli. 2021a. “Beyond the Newtonian Paradigm: A Statistical Mechanics of

Emergence.” OSF preprint, https://osf.io/m9kpz/.

. 2021b. “The World Is Not a Theorem.” Entropy 23 (11): 1467. https : / / doi . org / 10 . 3390 /

e23111467.

. 2021c. “What is Consciousness?” arXiv, https://arxiv.org/abs/2106.15515.

Langton, C. G. 1990. “Computation at the Edge of Chaos: Phase Transitions and Emergent Computation.”

Physica D 42:12–37.

Longo, G., M. Montévil, and S. A. Kauffman. 2012. “No Entailing Laws, but Enablement in the Evolution of

the Biosphere.” In Proceedings of the Fourteenth International Conference on Genetic and Evolutionary

Computation, 1379–1392. https://doi.org/10.1145/2330784/2330946.

May, R. M. 1976. “Simple Mathematical Models with Very Complicated Dynamics.” Nature 261 (5560):

459–467. https://doi.org/10.1038/261459a0.

McCulloch, W., and W. Pitts. 1943. “A Logical Calculus of Ideas Immanent in Nervous Activity (1943).” Bulletin of Mathematical Biology 52 (1–2): 99–115. https://doi.org/10.1007/BF02459570.

Mitchell, M. 2019. Artificial Intelligence: A Guide for Thinking Humans. New York, NY.

Nagel, T. 2012. Mind and Cosmos: Why the Materialist Neo-Darwinian Conception of Nature is Almost Certainly False. Oxford, UK: Oxford University Press.

Penrose, R. 1989. The Emperor’s New Mind. Oxford, UK: Oxford University Press.

Poincaré, J. H. 2017. The Three-Body Problem and the Equations of Dynamics: Poincaré's Foundational Work on Dynamical Systems Theory. Translated by B. D. Popp. Cham, Switzerland: Springer International Publishing.

Roli, A., Y. Jaeger, and S. A. Kauffman. 2022. “How Organisms Come to Know their World: Fundamental Limits on Artificial General Intelligence.” Frontiers in Ecology and Evolution, https://doi.org/10.3389/fevo.2021.806283.

Russell, B. 1912. The Problems of Philosophy. New York, NY: Henry Holt & Company.

Schwab, J. D., S. D. Kühlwein, N. Ikonomi, M. Kühl, and H. A. Kestler. 2020. “Concepts in Boolean Network Modeling: What Do They All Mean?” Computational and Structural Biotechnology Journal 18:571–582. https://doi.org/10.1016/j.csbj.2020.03.001.

Searle, J. 1990. “Is the Brain’s Mind a Computer Program?” Scientific American 262 (1): 26–31.

Strogatz, S. H. 1994. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Boca Raton, FL: CRC Press.

Tisza, L. 1963. “The Conceptual Structure of Physics.” Reviews of Modern Physics 35 (1).

Turing, A. M. 1937. “On Computable Numbers, with an Application to the Entscheidungsproblem.” Proceedings of the London Mathematical Society s2-42 (1): 230–265. https://doi.org/10.1112/plms/s2-42.1.230.

Vandermeer, J. 2020. “Confronting Complexity in Agroecology: Simple Models from Turing to Simon.” Frontiers in Sustainable Food Systems 07. https://doi.org/10.3389/fsufs.2020.00095.

Villani, M., L. La Rocca, S. A. Kauffman, and R. Serra. 2018. “Dynamical Criticality in Gene Regulatory Networks.” Complexity 2018. https://doi.org/10.1155/2018/5980636.

von Neumann, John. 1927. “Mathematische Begründung der Quantenmechanik.” Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 1–57. http://eudml.org/doc/59215.

Wittgenstein, L. 1922. Tractatus Logico-Philosophicus. London, UK: Kegan Paul.

—. 1953. Philosophical Investigations. Edited by G. E. M. Anscombe and R. Rhees. Translated by G. E. M. Anscombe. Oxford, UK: Blackwell.

BACK TO Foundational Papers in Complexity Science