The Genetic Algorithm (GA) and Simulated Annealing (SA), two techniques for global optimization, were applied to a reduced (simplified) form of the phase problem (RPP) in computational crystallography. Results were compared with those of "enhanced pair flipping" (EPF), a more elaborate problem-specific algorithm incorporating local and global searches. Not surprisingly, EPF did better than the GA or SA approaches, but the existence of GA and SA techniques more advanced than those used in this study suggest that these techniques still hold (...) promise for phase problem applications. The RPP is, furthermore, an excellent test problem for such global optimization methods. (shrink)

This article explores aspects of Rosenzweig’s Star of Redemption from the perspective of systems theory. Mosès, Pollock, and others have noted the systematic character of the Star. While “systematic” does not mean “systems theoretic,” the philosophical theology of the Star encompasses ideas that are salient in systems theory. The Magen David star to which the title refers, and which deeply structures Rosenzweig’s thought, fits the classic definition of “system” – a set of elements (God, World, Human) and relations between the (...) elements (Creation, Revelation, Redemption). The Yes and No of the elements and their reversals illustrate the bridging of element and relation with the third category of “attribute,” a notion also central to the definition of “system.” In the diachronics of “the All,” the relations actualize what is only potential in the elements in their primordial state and thus remedy the incompleteness of these elements, fusing them into an integrated whole. Incompleteness is a major theme of systems theory, which also explicitly examines the relations between wholes and parts and offers a formal framework for expressing such fusions. In this article, the systems character of Parts I & II of the Star is explored through extensive use of diagrams; a systems exploration of Part III is left for future work. Remarkably, given its highly architectonic character, diagrams are absent in Rosenzweig’s book, except for the triangle of elements, the triangle of relations, and the hexadic star, which are presented on the opening page of each part of the book. While structures can be explicated entirely in words, diagrams are a visual medium of communication that supplements words and supports a nonverbal understanding that structures both thought and experience. (shrink)

The Catastrophe Theory of Rene Thom and E. C. Zeeman suggests a mathematical interpretation of certain aspects of Hegelian and Marxist dialectics. Specifically, the three 'classical' dialectical principles, (1) the transformation of quantity into quality, (2) the unity and struggle of opposites, and (3) the negation of negation, can be modeled with the seven 'elementary catastrophes' given by Thorn, especially the catastrophes known as the 'cusp' and the 'butterfly'. Far from being empty metaphysics or scholasticism, as critics have argued, the (...) dialectical principles embody genuine insights into a class of phenomena, insights which can now be expressed within a precise mathematical formalism. This fact does not, however, support the claim that these principles, possibly modified or supplemented, constitute the laws of motion for human thought and for natural and social processes or even just the last of these. (shrink)

partial review of Thomas Nagel’s book, Mind and Cosmos: Why the Materialist Neo-Darwinian Conception of Nature Is Almost Certainly False is used to articulate some systems-theoretic ideas about the challenge of understanding subjective experience. The article accepts Nagel’s view that reductionist materialism fails as an approach to this challenge, but argues that seeking an explanation of mind based on emergence is more plausible than seeking one based on pan-psychism, which Nagel favors. However, the article proposes something similar to Nagel’s neutral (...) monism by positing a hierarchy of information processes that spans the domains of matter, life, and mind. As depicted in this hierarchy, subjective experience is emergent, but also continuous with informational phenomena at lower levels. (shrink)

Reconstructability analysis (RA) decomposes wholes, namely data in the form either of set theoretic relations or multivariate probability distributions, into parts, namely relations or distributions involving subsets of variables. Data is modeled and compressed by variable-based decomposition, by more general state-based decomposition, or by the use of latent variables. Models, which specify the interdependencies among the variables, are selected to minimize error and complexity.

“Freedom” is a phenomenon in the natural world. This phenomenon—and indirectly the question of free will—is explored using a variety of systems-theoretic ideas. It is argued that freedom can emerge only in systems that are partially determined and partially random, and that freedom is a matter of degree. The paper considers types of freedom and their conditions of possibility in simple living systems and in complex living systems that have modeling subsystems. In simple living systems, types of freedom include independence (...) from fixed materiality, internal rather than external determination, activeness that is unblocked and holistic, and the capacity to choose or alter environmental constraint. In complex living systems, there is freedom in satisfaction of lower level needs that allows higher potentials to be realized. Several types of freedom also manifest in the modeling subsystems of these complex systems: in the transcending of automatism in subjective experience, in reason as instrument for passion yet also in reason ruling over passion, in independence from informational colonization by the environment, and in mobility of attention. Considering the wide range of freedoms in simple and complex living systems allows a panoramic view of this diverse and important natural phenomenon. (shrink)

Systems theory offers a language in which one might formulate a metaphysics (or more specifically an ontology) of problems. This proposal is based upon a conception of systems theory shared by vonBertalanffy, Wiener, Boulding, Rapoport, Ashby, Klir, and others,and expressed succinctly by Bunge, who considered game theory, information theory, feedback control theory, and the like to be attempts to construct an "exact and scientific metaphysics." Our prevailing conceptions of "problems" are concretized yet also fragmented, and in fact dissolved, by the (...) standard reductionist model of science, which cannot provide a general framework for analysis. The idea of a "systems theory," however, suggests the possibility of an abstract and coherent account of the origin and essence of problems. Such an account would constitute a secular theodicy. (shrink)

In this talk, I want to present a conception that I have been working on for a number of years (Zwick, 1983, 1995) about the use of systems ideas. I start from the negative and proceed to the positive. The negative assertion is that systems ideas by themselves , unsupplemented by more specific and concrete knowledge (e.g., from the various disciplines), are insufficient for practical application, either for obtaining knowledge about the world or for solving problems. The reason for (...) this is the inherent abstractness of these ideas. The positive assertion is that this metaphysics can be a rich source of insights needed to improve the human condition and a component of a new scientific world view. (shrink)

Spinoza distinguishes between causation that is external, as in A causing B where A is external to B, and causation that is internal, where C causes itself (causa sui), without any involvement of anything external to C. External causation is easy to understand, but self causation is not. This note explores an approach to self-causation based upon Gödelian undecidability and draws upon ideas from an earlier study of Gödel’s proof and the quantum measurement problem (Zwick, 1978).

This paper discusses similarities of both form and meaning between two symbolic structures: the Diagram of the Supreme Pole of Song Neo-Confucianism and the Kabbalistic Tree of medieval Jewish mysticism. These similarities are remarkable in the light of the many differences that exist between Chinese and Judaic thought, which also manifest in the two symbols. Intercultural influence might account for the similarities, but there is no historical evidence for such influence. An alternative explanation would attribute the similarities to the ubiquity (...) of religious-philosophical ideas about hierarchy, polarity, and macrocosm-microcosm parallelism, but this does not adequately account for the similar overall structure of the symbols. The question of how to understand these similarities remains open. (shrink)

This paper investigates how environmental structure, given the innate properties of a population, affects the degree to which this population can adapt to the environment. The model we explore involves simple agents in a 2-d world which can sense a local food distribution and, as specified by their genomes, move to a new location and ingest the food there. Adaptation in this model consists of improving the genomic sensorimotor mapping so as to maximally exploit the environmental resources. We vary environmental (...) structure to see its specific effect on adaptive success. In our investigation, two properties of environmental structure, conditioned by the sensorimotor capacities of the agents, have emerged as significant factors in determining adaptive success: (1) the information content of the environment which quantifies the diversity of conditions sensed, and (2) the expected utility for optimal action. These correspond to the syntactic and pragmatic aspects of environmental information, respectively. We find that the ratio of expected utility to information content predicts adaptive success measured by population gain and information content alone predicts the fraction of ideal utility achieved. These quantitative methods and specific conclusions should aid in understanding the effects of environmental structure on evolutionary adaptation in a wide range of evolving systems, both artificial and natural. (shrink)