My search for the origin of complexity and complex systems has taken me back to Herbert Spencer's 1857 essay, "Progress: Its Law and Cause." This essay later formed the basis of his 1862 book First Principles of a New System of Philosophy. In it Spencer expounded a theory of evolution which posits that all structures in the universe develop from a simple, undifferentiated, homogeneity to a complex, differentiated, heterogeneity while undergoing increasing integration of the differentiated parts. This evolutionary process can be observed, Spencer believed, throughout the cosmos. It is a universal law, applying to biological organisms, to human social organisation, and to the human mind.

The Oxford English Dictionary does not cite Spencer, but one of its earliest citations is Charles Darwin's 1859 Life and Letters, vII, p.219, where he writes "A tendency to advance in complexity of organization." It's very likely that Darwin's usage followed Spencer's, so from the beginning complexity was a key, perhaps a defining, attribute of living things.

In Herbert Simon's 1969 book The Sciences of the Artificial, he referenced his 1962 essay The Architecture of Complexity, where he traces the history back to the idea of a general systems theory, like that of Ludwig von Bertalanffy. Simon writes...

A NUMBER of proposals have been advanced in recent years for the development of "general systems theory" which, abstracting from properties peculiar to physical, biological, or social systems, would be applicable to all of them. We might well feel that, while the goal is laudable, systems of such diverse kinds could hardly be expected to have any nontrivial properties in common. Metaphor and analogy can be helpful, or they can be misleading. All depends on whether the similarities the metaphor captures are significant or superficial.

It may not be entirely vain, however, to search for common properties among diverse kinds of complex systems. The ideas that go by the name of cybernetics constitute, if not a theory, at least a point of view that has been proving fruitful over a wide range of application. It has been useful to look at the behavior of adaptive systems in terms of the concepts of feedback and homeostasis, and to analyze adaptiveness in terms of the theory of selective information. The ideas of feedback and information provide a frame of reference for viewing a wide range of situations, just as do the ideas of evolution, of relativism, of axiomatic method, and of operationalism.

In this paper I should like to report on some things we have been learning about particular kinds of complex systems encountered in the behavioral sciences.

In 1977 the Belgian physical chemist Ilya Prigogine won the Nobel prize for investigating the irreversibility of processes in complex physical systems far from equilibrium conditions.

These are physical or chemical systems far from equilibrium conditions that appear to develop "order out of chaos" and look to be "self-organizing." Like biological systems, matter and energy (of low entropy) flows through the "dissipative" structure. It is primarily free energy and negative entropy that is being "dissipated."

This similarity to biological systems (in just one very important thermodynamic respect) was exploited by Prigogine to say he had discovered "new laws of nature" that could connect the natural sciences to the human sciences. Dissipation also implies irreversibility, a very important characteristic of life.

Prigogine had no physical explanation for irreversibility - beyond the fact that his physical "dissipative structures" and biological systems - exhibited it. He generally attacked classical Newtonian dynamics as being time reversible and thus providing no understanding of time. His understanding of time was based on the work of Henri Bergson and the uneven flow of time Bergson called "duration."

The Nobel committee wrote...

The great contribution of Prigogine to thermodynamic theory in his successful extension of it to systems which are far from thermodynamic equilibrium. This is extremely interesting as large differences compared to conditions close to equilibrium had to be expected. Prigogine has demonstrated that a new form of ordered structures can exist under such conditions, and he has given them the name ''dissipative structures" to stress that they only exist in conjunction with their environment.

(Press Release on the 1977 Nobel Prize )

Prigogine is perhaps the most famous name in chaos theory and complexity theory. Although he made very few original contributions to these fields, he is famous for them, nevertheless. His work (especially his 1984 book written with Isabel Stengers, Order Out Of Chaos) is a major reference today for popular concepts like "self-organizing, "complex systems," "bifurcation points," "non-linearity,", "attractors," "symmetry breaking," "morphogenesis," "autocatalytic," "constraint," and of course "irreversibility," although none of these terms is originally Prigogine's. The name "dissipative structures" and perhaps the phrase "far from equilibrium" belong to Prigogine, but the thermodynamic concepts were already in Boltzmann, Bertalanffy, and Schrödinger, and perhaps many others.

In 1984 the Santa Fe Institute was founded by Los Alamos scientists George A Cowan, Murray Gell-Mann, and others. See this history.

Cowan also recounts the history in his 2010 book Manhattan Project to the Santa Fe Institute and this hour-long video interview

The Santa Fe Institute became famous for their studies of complexity and complex systems. Their mission is "Searching for Order in the Complexity of Evolving Worlds" and they write...

What is Complex Systems Science?

Complexity arises in any system in which many agents interact and adapt to one another and their environments. Examples of these complex systems include the nervous system, the Internet, ecosystems, economies, cities, and civilizations. As individual agents interact and adapt within these systems, evolutionary processes and often surprising "emergent" behaviors arise at the macro level. Complexity science attempts to find common mechanisms that lead to complexity in nominally distinct physical, biological, social, and technological systems

In 1989, a 5-day workshop on Complexity, Entropy, and the Physics of Information was attended by over 40 of the world's top scientists in those subjects (a key exception was Prigogine).. They published a manifesto in 1990...

COMPLEXITY, ENTROPY, AND THE PHYSICS OF INFORMATION - A MANIFESTO

■ A deep analogy between thermodynamic entropy and Shannon's infornation theoretic entropy. Since the introduction of Maxwell's Demon and, partiularly, since the celebrated paper of Szilard and even earlier discussions of Smolu chowski, the operation equivalence of the gain of information and the decrease of entropy has been widely appreciated. Yet, the notion that a subjective quantity such as infofmatton could influence "objective" thermodynamic properties of the system remains highly controversial.

It is, however, difficult to deny that the process of informalion can be directly tied to the ability to extract useful work. Thus, questions concerning thermodynamics, the second law, and the arrow of time have become intertwined with a half-century-old puzzle, that of the problem of measurements in quantum physics.

■ Quantum meanrements are usually analyzed in abstract terms or wave functions and hamiltonians. Only very few discussions of the measurement problem in quantum theory make an explicit effort to consider the crucial issue - the transfer of information. Yet obtaining knowledge is the very reason for making a measurement. Formulating quantum measurements and, more generally, quantum phenomena in terms of information should throw a new light on the problem of measurement, which has become difficult to ignore in light of new experiments on quantum behavior in macroscopic systems.

The distinction between what is and what is known to be, so clear in classical physics, is blurred, and perhaps does not exist at all on a quantum level. For instance, energetically insignificant interactions of an object with its quantum environment suffice to destroy its quantum nature. It is as if the "watchful eye" of the environment "monitoring" the state of the quantum system forced it to behave in an effectively classical manner. Yet, even phenomena involving gravity, which happen on the most macroscopic of all the scales, bear the imprint of quantum mechanics.

■ Black hole thermodynamics has established a deep and still largely mysterious connection between general relativity, quantum, and statistical mechanics. Related questions about the information capacity of physical systems, fundamental limits on the capacity of communication channels, the origin of entropy in the Universe, etc., are a subject of much recent research. The three subjects above lie largely in the domain of physics. The following issues forge connections between the natural sciences and the science of computation, or, rather, the subject of information processing regarded in the broadest sense of the word.

■ Physics of computation explores limitations imposed by the laws of physics on the processing of information. It is now established that both classical and quantum systems can be used to perform computations reversibly. That is, computation can be "undone" by running the computer backwards. It appears also conceivable that approximately reversible computer "chips" can be realized in practice. These results are of fundamental importance, as they demonstrate that, at least in principle, processing of information can be accomplished at no thermodynamic cost. Moreover, such considerations lead one to recognize that it is actually the erasure of the information which results in the increase of entropy.

The information which is being processed by the computer is a concrete "record," a definite sequence of symbols. Its information content cannot be represented adequately in terms of Shannon's probabilistic definition of information. One must instead quantify the information content of the specific, well-known "record" in the memory of the computer - and not its probability or frequency of occurrence, as Shannon's formalism would demand. Fortunately, a relatively new developmenta novel formulation of the information theory - has been already put forward.

■ Algorithmic randomness - an alternative definition of the information content of an object based on the theory of computation rather than on probabilities was introduced more then two decades ago by Solomonof. Kolmogorov, and Chaitin. It is equal to the size of the shortest message which describes this object. For instance, a string of 10⁵ 0's and 1 's:

01010101010101 ...

can be concisely described as "5 • 10⁴ 01 pairs." By contrast, no concise description can be found for a typical, equally long string of 0's and l's generated by flipping a coin. To make this definition more rigorous, the universal Turing Machine - a "generic" universal computer - is usually considered to be the "addressee" of the message. The size of the message is then equal to the length - in the number of bits - of the shortest program which can generate a sufficiently detailed description (for example, a plot) of the object in question.

It is tempting to suggest that physical entropy - the quantity which determines how much work can be extracted from a physical system - should take into account its algorithmic randomness. This suggestion can be substantiated by detailed discussions of examples of computer-operated engines as well as by results concerning the evolution of entropy and algorithmic randomness in the course of measurements. It provides a direct link between thermodynamics, measurements, and the theory of computation. Moreover, it is relevant to the definition of complexity.

■ Complerity, its meaning, its measures, its relation to entropy and information, and its role in physical, biological, computational, and other contexts have become an object of active research in the past few years.

Complexity, Entropy..., pp.vii-ix

The Santa Fe Institute took a turn toward theology (and teleology) at a 1999 conference at Santa Fe organized by Paul Davies, who had just four years earlier won a $1-million Templeton Prize. Significantly, Sir John Templeton attended the 1999 conference personally.

Presentations at the conference were reported in the 2003 book From Complexity to Life, edited by theologian Niels Hendrick Gregersen. It included papers by Davies, Charles Bennett, Gregory Chaitin, Stuart Kauffman, Werner Loewenstein, and Harold Morowitz. One paper was by William Dembski, the major proponent of Intelligent Design.

In 2010 Davies and Gregersen jointly edited the book Information and the Nature of Reality, which was a report on a 2006 conference in Copenhagen that included several important writers on complex systems, including Terrence Deacon, Jesper Hoffmeyer, Seth Lloyd, and Henry Stapp, as well as several prominent Christian theologians.

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