Self-organized criticality: An explanation of the 1/f noise.

(Litho, The American Physical Society), 1987. Royal8vo. In the original blue printed wrappers. In "Physical Review Letters" Vol. 59, Number 4, July 27, 1987. A few traces are having been bend to extremities. Small label with subscriber's name printed on to back wrapper. Otherwise a fine and clean copy. Pp. 381-84. [Entire volume: 381-519, (5) pp.].

First printing of Bak, Tang and Wiesenfeld landmark paper in which they proposed their self-organized criticality (SOC) theory or the Abelian sandpile model: the mechanisms by which complexity arises in nature. It is one of the very few evolutionary models to challenge Darwinism. It is regarded as one of the most profound and fundamental theories put forth in the later part of the 20th century and the paper is one of the most frequently-cited papers in the last few decades.
Its concepts have been applied across fields as diverse as geophysics, physical cosmology, evolutionary biology and ecology, bio-inspired computing and optimization (mathematics), economics, quantum gravity, sociology, solar physics, plasma physics, neurobiology and many others.

SOC is typically observed in slowly driven non-equilibrium systems with extended degrees of freedom and a high level of nonlinearity.
"The nonlinear dynamics approach encapsulated in GCT envisions self-organization as an asymptotic process of approaching stability through a series of intermediate states (also known as evolution). There exists, however, a fundamentally different process known as self-organized criticality (SOC) in which an avalanche-like transformation rapidly moves the system into a self-organized mode. A popular metaphor for SOC is the sandpile paradigm. If additional sand grains are randomly added on top of a sand pile then inevitably an instance will occur when local steepness of the slope surpasses a certain critical threshold thus causing local failure of structural stability. The excess of material will cascade into adjacent areas of the pile causing their failures as well. Thus an avalanche will occur, shifting the entire sandpile into a new stable state. What is fundamentally important in this process is that a random local event quickly propagates through the entire system, thus establishing longrange correlations within the system" (Rosenfeld, Global Consensus Theorem and Self-Organized Criticality).

"Ask the average person, What is the theory of evolution? and you are likely to get answers like "natural selection", or "survival of the fittest", or "Darwin's theory". Because these ideas are systematically taught in classrooms, they may represent the only evolutionary theory people know. But, ask, What is the theory of Earth evolution? you will likely get a blank stare, or at best a superficial discussion of the fossil record. The Earth as a multi-faceted evolutionary system that undergoes continuous change through time was incorporated in the National Science Education Standards, even if it is absent from many contemporary curricula and common perceptions. Darwinism, however, is not the only mechanism of evolution. If we define evolutionary change as any process that leads to increases in complexity, diversity, order, and/or interconnectedness then there are at least three distinct mechanisms, or theories of evolution: elaboration, self-organization, and fractionation." (Journal of Geoscience Education, v. 58, n. 2, March, 2010, p. 58-64).

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