The Many Roots of Complexity Science

Post Your Favorite Roots in Chronological Order if you can [See explanation of project at end]

1937 - Landau published On the Theory of Phase Transitions... [Landau1937] The history of the theory of critical phenomena and phase transitions starts with Landau's works of 1937, where he introduced fundamental notions of spontaneous symmetry violation and the order parameter as a measure of this violation. It is impossible to exaggerate the impact which this idea had on practically all branches of physics and non-linear mechanics. Due to the concept of the order parameter, phase transition theory became a cross-disciplinary branch of science, much like the theory of oscillations. Landau gave simple prescriptions, how to describe order in terms of irreducible representations of the symmetry group. Around 1960 Landau formulated the general problem of fluctuation-driven phase transitions via a calculation of the path integral over all configurations of the order parameter. [Landau1937] L.D. Landau, ZhETF 7, 19 (1937); Phys. Zs. Sowjet. 11, 26 (1937).

1941 - Kolmogorov proposed a scaling approach for hydrodynamic turbulence. [Kolmogorov1941] A.N. Kolmogorov, DAN SSSR, 30, 299; Ib. 31, 99 (1941).

1944 - Onsager published an exact solution of the 2-d Ising model [Onsager1944], a truly exceptional (even singular) accomplishment. As of 2007, despite numerous attempts, 3D Ising model has eluded exact solution. It is even conjectured that the exact solution is in general not possible. [Onsager1944] L. Onsager, Phys, Rev. 65, 117 (1944);

1944 - Erwin Schrodinger published What is Life? I'm not the right person to speak to it's biological significance, but apparently it was a source of inspiration for Watson and Crick. It is an amazing read regarding both the nature of science, the relationships between statistics and laws, and transitions between cells as matter and cells as life (Contributed by Aaron Frank. What is Life?

1948 - Norbert Weiner published Cybernetics

He used the newly formed fields of statistical Information and Control Theory to establish the role of feedback and nonlinearity in engineering design and biology. [Cybernetics] (Contributed by J. DeRosa)

1950 - Norbert Weiner published The Human Use of Human Beings

In this companion book to Cybernetics, Weiner expounded on the principles of Cybernetics with no equations and warned of the dangers of scientific research that did not consider the social implications of the technology and research. [Cybernetics] (Contributed by J. DeRosa)

1959 - It is realized [Levanyuk1959],[Ginsburg1960] that mean field theory neglects fluctuations which grow rapidly near the phase transition point. Thus, mean field theory works well outside a small vicinity of the transition point and is invalidated by fluctuations within it. In this way the necessity to include fluctuations in phase transition theory was first recognized. Simultaneously Fisher [Fisher1959] approached the problem by attempting to generalize Onsager's results to non-exactly-solvable problems. By introducing critical exponents he made the decisive step to scaling. [Levanyuk1959] A.I. Levanyuk, ZhETF 36, 810 (1959); [Fisher1959] M.E. Fisher, Physica 25, 521 (1959); [Ginsburg1960] V.L. Ginsburg, Fizika Tverdogo Tela (Solid State Physics, in Russian) 2, 2034 (1960).

1958 - Norbert Weiner published Nonlinear Problems in Random Theory

This book is decidedly mathematical and lays out the framework for the general functional analysis of nonlinear systems. For a clear exposition of the mathematics see the book written by one of his students M. Schetzen The Volterra and Wiener Theory of Nonlinear Systems [System Theory] (Contributed by J. DeRosa)

1964 - Patashinskii and Pokrovskii in Russia formulated the field theory equations and conjectured correctly that the correlation functions of any order should obey scaling laws [Patashin1964]. Soon thereafter, they introduced the theory of scaling [Patashin1966], first presented at the International Symposium on Phase Transitions in Dubna, May 1965. The physical picture was that, for critical fluctuations the distribution of the order parameter remains invariant with temperature if the length scale and other observables are adjusted properly. The theory was physically equivalent to Kadanoff's formulation, which was published 4 months later[Kadanoff1966]. In addition, in his work Kadanoff first formulated a program of elimination of short-range degrees of freedom by decimation of spin blocks, an embryo of the Wilson Renormalization Group, though still not a practical tool for calculations. [Patashin1964] A.Z. Patashinskii and V.L. Pokrovskii, ZhETF, 50, 439 (1964) [Sov. Phys. JETP 19, 677 (1964)]; [Patashin1966] A.Z. Patashinskii and V.L. Pokrovskii, ZhETF 50, 439 (1966) [Sov. Phys. JETP 23, 292 (1966)]; [Kadanoff1966] L.P. Kadanoff, Physics 2, 263 (1966).

1968 - Polyakov and Migdal used such physical requirements as causality and unitarity, which permitted, in principle, numerical calculations of the critical exponents [Pol1968], [Mig1968]. Unfortunately, the equations were too complicated to solve using computers of that time. [Pol1968] A.M. Polyakov, ZhETF 55, 1026 (1968) [Sov. Phys. JETP 28, 533 (1969)]. [Mig1968] A.A. Migdal, ZhETF 55, 1964 (1968) [Sov. Phys. JETP 28, 1036 (1969)].

1971 - Kadanoff and Wegner proved the universality hypothesis. [Kadanoff1971] L.P. Kadanoff and F.J. Wegner, Phys. Rev. B4, 3989 (1971). According to this hypothesis, the critical behavior is determined by symmetry and how it is violated. All phase transitions may be divided into universality classes.

1972 - Wilson introduced renormalization group approach, which elucidated the structure of the theory to the extent that standard methods could be employed. This effectively marks the birth of the theory of phase transitions, scaling and renormalization group as we know it today. Kenneth Wilson went on to receive a Nobel Prize in Physics, 1982. [Wilson1972] K.G. Wilson, Phys, Rev. Lett. 28, 548 (1972).

1977 - Ilya Prigogine wins the Nobel Prize in Chemistry

For his groundbreaking work in non-equilibrium thermodynamics-especially non-dissipative structures. [Chemistry] (Contributed by J. DeRosa)

1978- Thomas Schelling publishes Micromotives and Macrobehavior Contains the seminal article on racial segregation which is now referred to as the Schelling Model. The book marks a notable departure from Schelling's previous work on military strategy and deterrence, but retains his emphasis on strategic interaction and emergence (Contributed by Aaron Frank). Micromotives and Macrobehavior

1984 - Ilya Prigogine and Isabelle Stengers publish Order out of Chaos: Man's New Dialogue with Nature

A brilliant account of the journey from Newtonian science to complex dynamical systems. An emphasis on thermodynamics and dissipative structures. One of the works that triggered the study of complexity science. [Chemistry] (Contributed by J. DeRosa)

1985 - Robert Axelrod publishes The Evolution of Cooperation. Probably the most famous analysis of the iterated Prisoner's Dilemma (IPD) game, conducted via a computational round-robin tournament (Contributed by Aaron Frank). The Evolution of Cooperation

1995 - Clifford Rogers publishes The Military Revolution Debate. This book is a collection of articles on military history. The articles review the definition and consequences of the Military Revolution in early modern Europe, a period of far reaching technological, social, economic, and political change - starting a process that ended feudalism in Europe, gave birth to the modern nation state, and European global exploration and colonization. Most importantly, it marks one of the first instances where Stephen Gould's concept of punctuated equilibrium is advanced as a hypothesis for explaining radical and rapid military and political change (Contributed by Aaron Frank). The Military Revolution Debate

1996 - Herbert Simon published the 3rd edition of The Sciences of the Artificial. A critical examination of systems design, development, and adaption. Simon advances a science of design beginning from the simplest of systems and works his way through the relationship between complexity and hierarchy. In the process he travels through psychology, computer science, economics, policy analysis and engineering, and even the departmental architecture of modern universities (Contributed by Aaron Frank). The Sciences of the Artificial

1999 - Gary William Flake published the The Computational Beauty of Nature. Computer explorations of fractals, chaos, complex systems and adaptation. (Contributed by --Luciano Oviedo 19:03, 24 June 2007 (MDT))

2003 - Robert Lempert, Steven Popper, and Steven Bankes publish Shaping the Next One Hundred Years: New Methods for Quantitative, long-Term policy Analysis. A powerful revisioning of policy analysis under the condition of "deep uncertainty." The authors work the history of and methodology of thinking about the future, and then develop a method of computational analysis for coping with inevitable and irresolvable uncertainties in order to develop strategies and polices that a designed to robust and adaptive (Contributed by Aaron Frank). Shaping the Next one Hundred Years

Use This Simple Template: (or refine it)

Date - Name(s) of Person(s) followed by Milestone

Description and significance (short text) [Source Discipline(s)] (Contributed by your name) [so we can backtrack to update]

== Team Members and Contributors== (Hopefully many will contribute)

1. Joe DeRosa

Explanation of Project

The Roots of Rock and Roll go deep into Gospel, Rythmn and Blues, Folk and Bluegrass - even the familiar I-IV-I-V-IV-I chord progressions can be found in Bach and Beethoven. When Elvis Presley and the Beatles appeared on the Ed Sullivan Show in 1956 and 1964, it was significant because huge audiences tuned in every Sunday night at 8:00. Rock and Roll became a legitimate part of the culture. When the Rolling stones hit the concert circuit in 1969, it was significant because they were billed as the greatest rock and roll band in the world, but also because they became drugs-sex-rock-and-roll cultural icons of the new social norms.

Here we all sit in the Rock and Roll of Complexity Science. Our roots are in physics, biology, sociology, etc. Collectively we know the “who, what and why” of the key milestones in our fields that led us here: The Roots of Complexity Science. This is a project for all those who wish to participate from the CSSS Class of 07. Who knows where the trajectory will lead?