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1986 | Buch

Allowing, Forbidding, but not Requiring: A Mathematic for a Human World Kapitel lesen Erstes Kapitel lesen

Complexity, Language, and Life: Mathematical Approaches

herausgegeben von: John L. Casti, Anders Karlqvist

Verlag: Springer Berlin Heidelberg

Buchreihe : Biomathematics

Enthalten in: Professional Book Archive

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Über dieses Buch

In May 1984 the Swedish Council for Scientific Research convened a small group of investigators at the scientific research station at Abisko, Sweden, for the purpose of examining various conceptual and mathematical views of the evolution of complex systems. The stated theme of the meeting was deliberately kept vague, with only the purpose of discussing alternative mathematically based approaches to the modeling of evolving processes being given as a guideline to the participants. In order to limit the scope to some degree, it was decided to emphasize living rather than nonliving processes and to invite participants from a range of disciplinary specialities spanning the spectrum from pure and applied mathematics to geography and analytic philosophy. The results of the meeting were quite extraordinary; while there was no intent to focus the papers and discussion into predefined channels, an immediate self-organizing effect took place and the deliberations quickly oriented themselves into three main streams: conceptual and formal structures for characterizing sys­ tem complexity; evolutionary processes in biology and ecology; the emergence of complexity through evolution in natural lan­ guages. The chapters presented in this volume are not the proceed­ ings of the meeting. Following the meeting, the organizers felt that the ideas and spirit of the gathering should be preserved in some written form, so the participants were each requested to produce a chapter, explicating the views they presented at Abisko, written specifically for this volume. The results of this exercise form the volume you hold in your hand.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Allowing, Forbidding, but not Requiring: A Mathematic for a Human World
Abstract
In Morris Kline’s extraordinarily thoughtful Mathematics: The Loss of Certainty (Kline, 1980), one aspect emerges clearly: over by far the greatest part of its history, mathematics has been driven by the need to describe the physical world of things. The distinction between pure and applied mathematics did not emerge until comparatively recently; no sharp distinction was made between mathematics and science in the seventeenth and eighteenth centuries, and all the great names contributed to the vast overlapping area between the two. In brief “there was some pure mathematics but no pure mathematicians” (Kline, 1980, p 281). It is unfortunate that, just as the biological and human sciences started to hive off from philosophy as separate fields of inquiry, so mathematics began to detach itself from the physical sciences. First, this means that few mathematicians today have ever been truly challenged by the biological and human sciences, with the result that old and inappropriate forms of mathemetics have been borrowed from the realm of the physical world to distort descriptions of the biological and human worlds. Second, the possibilities for creating new and appropriate qualitative mathematics have been diminished as mathematicians look increasingly to mathematics itself, rather than to the challenges beyond their distressingly private realm of discourse.
Peter Gould
Chapter 2. A Theory of Stars in Complex Systems
Abstract
A complex system such as a company, an institution, or a nation, can be thought of as being made up of very many interrelated parts experiencing local or global change through time. The practical need to control social institutions through planning, management, and government underlies the need to find scientific methods to describe and understand complex social systems, in the same way that the requirements of engineering underlie the need to find scientific methods to describe complex physical systems.
Jeffrey Johnson
Chapter 3. Pictures as Complex Systems
Abstract
When we try to process images — restore, analyze, or understand them — we can approach the problem by viewing the image as a complex system of units, combined by certain rules of regularity. The choice of units is by no means straightforward. Initially, it may appear that a natural choice would be the picture elements (pixels), say black and white, or gray scale, or color, etc. A closer scrutiny, however, reveals this approach to be too superficial and that we must use more intrinsic, more informative, units that lead to the construction of random geometries, several instances of which we study herein.
Ulf Grenander
Chapter 4. A Survey of Replicator Equations
Abstract
What are the units of natural selection? This question has aroused considerable debate in theoretical biology. Suggestions range from pieces of polynucleotides, genes, or gene complexes to individuals, groups, or species. It could be, however, that different answers are correct in different contexts, depending on the scale on which selection acts most decisively. This is somewhat analogous to physics, where the dominant force may be gravitational, electromagnetic, or strong or weak interparticle attractions, depending on the problem.
Karl Sigmund
Chapter 5. Darwinian Evolution in Ecosystems: A Survey of Some Ideas and Difficulties Together with Some Possible Solutions
Abstract
Ecology, the biological science of environment, has not produced a synthesis of environment from its broad technical knowledge of influence of external parameters on organisms. Before Darwin (1859), environment was considered an organic whole. Everything in it made some contribution and has some meaning with respect to everything else. Darwin subscribed to this view, but his emphasis, and that of his followers, on the evolving organism struggling to survive, suppressed the exploration of holistic aspects of the origin of species that might have been developed. After Darwin, the organism came into great focus, first as a comparative anatomical entity, then later with physiological, cellular, molecular, behavioural, and genetic detail. In contrast, the organism’s environment blurred through relative inattention into a fuzzy generality. The result was two distinct things (dualism), organism and environment, supplanting the original unified organism—environment whole (synergism). (Patten, 1982).
Nils Chr. Stenseth
Chapter 6. On System Complexity: Identification, Measurement, and Management
Abstract
The notion of system complexity is much like St. Augustine’s description of time: “What then is time [complexity]? If no one asks me, I know; if I wish to explain it to one that asks, I know not.” There seem to be fairly well-developed, intuitive ideas about what constitutes a complex system, but attempts to axiomatize and formalize this sense of the complex all leave a vague, uneasy feeling of basic incompleteness, and a sense of failure to grasp important aspects of the essential nature of the problem. In this chapter we examine some of the root causes of these failures and outline a framework for the consideration of complexity that provides a starting point for the development of operational procedures in the identification, characterization, and management of complex processes. In the process of developing this framework for speculation, it is necessary to consider a variety of system-theoretic concepts closely allied to the notion of complexity: hierarchies, adaptation, bifurcation, self-organization, and reductionism, to name but a few. The picture that emerges is that of complexity as a latent or implicate property of a system, a property made explicit only through the interaction of the given system with another. Just as in baseball where some pitches are balls and some are strikes, but “they ain’t nothin” until the umpire calls them, complexity cannot be thought of as an intrinsic property of an isolated (closed) system; it is only made manifest by the interaction of the system with another, usually in the process of measurement and/or control.
John L. Casti
Chapter 7. On Information and Complexity
Abstract
We introduce the rather wide-ranging considerations which follow with a discussion of the concept of information and its role in scientific discourse. Ever since Shannon began to talk of information theory (by which he meant a probabilistic analysis of the deleterious effects of propagating signals through channels; cf. Shannon and Weaver, 1949), the concept has been relentlessly analyzed and reanalyzed. The time and effort expended on these analyses must surely rank as one of the most unprofitable investments in modern scientific history; not only has there been no profit, but also the currency itself has been debased to worth- lessness. Yet, in biology, for example, the terminology of information intrudes itself insistently at every level; code, signal, computation, recognition. It may be that these informational terms are simply not scientific at all; that they are a temporary anthropomorphic expedient; a facon de parler which merely reflects the immaturity of biology as a science, to be replaced at the earliest opportunity by the more rigorous terminology of force, energy, and potential which are the province of more mature sciences (i.e. physics), in which information is never mentioned. Or, it may be that the informational terminology which seems to force itself upon us bespeaks something fundamental; something that is missing from physics as we now understand it. We take this latter viewpoint, and see where it leads us.
Robert Rosen
Chapter 8. Organs and Tools: A Common Theory of Morphogenesis
Abstract
At the beginning of the sixteenth century, people began to anatomize dead bodies and discovered organs for which the putative function had to be found. The simplest method of establishing this was to associate the organ with a tool, which apparently naive procedure led, nevertheless, to striking successes. Within that century, Harvey showed the heart to be a pump that sent blood through natural pipes, the blood vessels. The skeleton (bones, joints, and muscles) provided obvious mechanical interpretations (a member acting as a lever, for instance); and the lungs were compared to a pair of bellows (with the obvious omission of the fundamental physiological function of gas exchange between air and blood). All these mechanical analogies led to Descartes’ theory of the animal machine. It was only with our noblest organ, the brain (the seat of the soul), that these analogical explanations met with difficulties: How could consciousness and thinking be generated inside this apparently amorphous gray or white substance? But the mechanical imagery was to achieve, around 1950, its most notable success. The almost simultaneous appearance, in the middle of the twentieth century, of computers and molecular biology developed the idea that the genetic material, DNA, was the analogue of a computer program for the development of an adult organism from an egg. This interpretation offered a new, important breakthrough: previously the mechanical analogy had constantly raised the problem of biological finality.
René Thom
Chapter 9. The Language of Life
Abstract
In the spring of 1984, I delivered two lectures at IIASA under the title The Language of Life. Dianne Goodwin was kind enough to prepare a verbatim transcript of my talks; I have used the months since then to purge the written record of what I said of its incoherence, vagrant inaccuracies, and general slovenliness.
David Berlinski
Chapter 10. Universal Principles of Measurement and Language Functions in Evolving Systems
Abstract
The ability to construct measuring devices and to predict the results of measurements using models expressed in formal mathematical language is now generally accepted as the minimum requirement for any form of scientific theory. The modern cultural development of these skills is usually credited to the Newtonian epoch, although traces go back at least 2000 years to the Milesian philosophers. In any case, from the enormously broader evolutionary perspective, covering well over three billion years, the inventions of measurement and language are commonly regarded as only the most recent and elaborate form of intelligent activity of the most recent and elaborate species.
H. H. Pattee
Metadaten
Titel
Complexity, Language, and Life: Mathematical Approaches
herausgegeben von
John L. Casti
Anders Karlqvist
Copyright-Jahr
1986
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-70953-1
Print ISBN
978-3-642-70955-5
DOI
https://doi.org/10.1007/978-3-642-70953-1