An Essay on the Importance of Being Nonlinear PDF Download
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Author: Bruce J. West
Publisher: Springer Science & Business Media
ISBN: 3642933068
Category : Mathematics
Languages : en
Pages : 215
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Book Description
One of my favorite quotes is from a letter of Charles Darwin (1887): "I have long discovered that geologists never read each other's works, and that the only object in writing a book is proof of earnestness, and that you do not form your opinions without undergoing labour of some kind. " It is not clear if this private opinion of Darwin was one that he held to be absolutely true, or was one of those opinions that, as with most of us, coincides with our "bad days," but is replaced with a more optimistic view on our "good days. " I hold the sense of the statement to be true in general, but not with regard to scientists never reading each other's work. Even if that were true however, the present essay. would still have been written as a proof of earnestness. This essay outlines my personal view of how nonlinear mathematics may be of value in formulating models outside the physical sciences. This perspective has developed over a number of years during which time I have repeatedly been amazed at how an "accepted" model would fail to faithfully characterize the full range of avail able data because of its implicit or explicit dependence on linear concepts. This essay is intended to demonstrate how linear ideas have come to dominate and therefore limit a scientist's ability to understand any given class of phenomena.
Author: Bruce J. West
Publisher: Springer Science & Business Media
ISBN: 3642933068
Category : Mathematics
Languages : en
Pages : 215
Get Book Here
Book Description
One of my favorite quotes is from a letter of Charles Darwin (1887): "I have long discovered that geologists never read each other's works, and that the only object in writing a book is proof of earnestness, and that you do not form your opinions without undergoing labour of some kind. " It is not clear if this private opinion of Darwin was one that he held to be absolutely true, or was one of those opinions that, as with most of us, coincides with our "bad days," but is replaced with a more optimistic view on our "good days. " I hold the sense of the statement to be true in general, but not with regard to scientists never reading each other's work. Even if that were true however, the present essay. would still have been written as a proof of earnestness. This essay outlines my personal view of how nonlinear mathematics may be of value in formulating models outside the physical sciences. This perspective has developed over a number of years during which time I have repeatedly been amazed at how an "accepted" model would fail to faithfully characterize the full range of avail able data because of its implicit or explicit dependence on linear concepts. This essay is intended to demonstrate how linear ideas have come to dominate and therefore limit a scientist's ability to understand any given class of phenomena.
Author: Bruce J West
Publisher:
ISBN: 9783642933073
Category :
Languages : en
Pages : 220
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Book Description
Author: Bruce J. West
Publisher: World Scientific
ISBN: 9789810221973
Category : Science
Languages : en
Pages : 444
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Book Description
The authors describe mostly in non-technical language the development of a new scientific paradigm based on nonlinear deterministic dynamics and fractal geometry. The concepts from these two mathematical disciplines are interwoven with data from the physical, social and life sciences. In this way rather sophisticated mathematical concepts are made accessible through experimental data from various disciplines, and the formalism is relegated to appendices. It is shown that the complexity of natural and social phenomena invariably lead to inverse power law distributions, both in terms of probabilities and spectra. This book tries to show how to think differently about familiar phenomena, such as why the bell-shape curve ought not to be used in teaching or in the characterization of such complex phenomena as intelligence.
Author: Tamotsu Onozaki
Publisher: Springer
ISBN: 4431549714
Category : Business & Economics
Languages : en
Pages : 227
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Book Description
This book pursues a nonlinear approach in considering both chaotic dynamical models and agent-based simulation models of economics, as well as their dynamical behaviors. Three key concepts arising in this context are “nonlinearity,” “bounded rationality” and “heterogeneity,” which also make up the title of the book. Nonlinearity is the warp that runs throughout all models because systems that exhibit chaotic or other complex behavior in the absence of any exogenous disturbances are absolutely nonlinear. Bounded rationality constitutes the woof, because economic systems do not exhibit complex behavior if all agents are perfectly rational, as is usually assumed in neoclassical economics. Agents who are boundedly rational have to struggle to do their best with limited information and tend to adapt to their economic environment without knowing what is the best. Furthermore, the heterogeneity of firms or consumers dyes the fabric of complex dynamics woven from the warp and woof.
Author: Frank Kessel
Publisher: Routledge
ISBN: 1000308499
Category : Psychology
Languages : en
Pages : 428
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Book Description
These original essays, written by prominent scholars, pay tribute to the work of William Bevan. In the course of his distinguished career, Bevan has exhibited an almost unique capacity to focus a clear-eyed, critical gaze on operating assumptions and actions—his own and those of others—and to initiate consequential, constructive steps forward, both
Author: Bruce J West
Publisher: World Scientific
ISBN: 9811234116
Category : Science
Languages : en
Pages : 372
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Book Description
A nonsimple (complex) system indicates a mix of crucial and non-crucial events, with very different statistical properties. It is the crucial events that determine the efficiency of information exchange between complex networks. For a large class of nonsimple systems, crucial events determine catastrophic failures - from heart attacks to stock market crashes.This interesting book outlines a data processing technique that separates the effects of the crucial from those of the non-crucial events in nonsimple time series extracted from physical, social and living systems. Adopting an informal conversational style, without sacrificing the clarity necessary to explain, the contents will lead the reader through concepts such as fractals, complexity and randomness, self-organized criticality, fractional-order differential equations of motion, and crucial events, always with an eye to helping to interpret what mathematics usually does in the development of new scientific knowledge.Both researchers and novitiate will find Crucial Events useful in learning more about the science of nonsimplicity.
Author: John Casti
Publisher: John Wiley & Sons
ISBN: 9780471594871
Category : Mathematics
Languages : en
Pages : 464
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Book Description
Sponsored by the Swedish Council for Planning and Coordination of Research, these internationally renowned scholars discussed and debated the complementary effects of individual self-interest and collective group interests. The twelve chapters in this volume, representing a wide range of perspectives, are the fruit of this meeting.
Author: I. Ethem Gonenc
Publisher: CRC Press
ISBN: 020349332X
Category : Technology & Engineering
Languages : en
Pages : 523
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Book Description
Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development describes the concepts, models, and data needed to design and implement management programs for long-term sustainability of coastal lagoons. Based on a project conducted under the auspices of NATO-CCMS, the book provides information and methodologies essential for
Author: Ronald E Mickens
Publisher: World Scientific
ISBN: 9814531928
Category : Mathematics
Languages : en
Pages : 354
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Book Description
The purpose of this review volume is to present the opinions of a number of distinguished individuals who have given careful thought as to why mathematics is so “unreasonably effective” when applied to the analysis of the natural sciences.
Author: Michael A. Arbib
Publisher: MIT Press
ISBN: 9780262011594
Category : Medical
Languages : en
Pages : 442
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Book Description
In Neural Organization, Arbib, Erdi, and Szentagothai integrate structural, functional, and dynamical approaches to the interaction of brain models and neurobiologcal experiments. Both structure-based "bottom-up" and function- based "top-down" models offer coherent concepts by which to evaluate the experimental data. The goal of this book is to point out the advantages of a multidisciplinary, multistrategied approach to the brain.Part I of Neural Organization provides a detailed introduction to each of the three areas of structure, function, and dynamics. Structure refers to the anatomical aspects of the brain and the relations between different brain regions. Function refers to skills and behaviors, which are explained by means of functional schemas and biologically based neural networks. Dynamics refers to the use of a mathematical framework to analyze the temporal change of neural activities and synaptic connectivities that underlie brain development and plasticity--in terms of both detailed single-cell models and large-scale network models.In part II, the authors show how their systematic approach can be used to analyze specific parts of the nervous system--the olfactory system, hippocampus, thalamus, cerebral cortex, cerebellum, and basal ganglia--as well as to integrate data from the study of brain regions, functional models, and the dynamics of neural networks. In conclusion, they offer a plan for the use of their methods in the development of cognitive neuroscience."
