Screen LibraryThe lure of modern science : fractal thinking /
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 ra...
Saved in:
| Main Authors: | |
|---|---|
| Corporate Authors: | |
| Group Author: | |
| Published: |
World Scientific Pub. Co.,
|
| Publisher Address: | Singapore : |
| Publication Dates: | 1995. |
| Literature type: | eBook |
| Language: | English |
| Series: |
Studies of nonlinear phenomena in life sciences ;
v. 3 |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/2689#t=toc |
| Summary: |
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. |
| Carrier Form: | 1 online resource (viii,421pages) : illustrations. |
| Bibliography: | Includes bibliographical references (pages 401-414) and index. |
| ISBN: | 9789812813022 |
| CLC: | O411 |
| Contents: | 1. Lure of modern science. 1.1. Setting the stage. 1.2. How science has changed. 1.3. The stages of model building. 1.4. Previews -- 2. Linear spaces and geometry in natural philosophy. 2.1. Spaces. 2.2. Physics; a linear world view. 2.3. Irreversibility, equipartition and solitons. 2.4. Distribution of errors. 2.5. Spaces of unusual dimensions. 2.6. Looking back -- 3. Noise in natural philosophy. 3.1. Power spectrum. 3.2. Inverse power laws. 3.3. Normal to lognormal distributions. 3.4. From lognormal to 1/f. 3.5. Noise and music. 3.6. Noise in general. 3.7. Distribution functions. 3.8. Recapitulation -- 4. Self-similarity, fractals and measurements. 4.1. Self-similarity. 4.2. Fractal curves. 4.3. Fractal physiology. 4.4. Fractal physics -- 5. Maps and dynamics. 5.1. Discrete dynamical equations. 5.2. One-humped maps. 5.3. Higher-dimensional maps. 5.4. Probability density -- 6. Dynamics in fractal dimensions. 6.1. A brief history of unpredictability. 6.2. The fractal heart. 6.3. Strange attractors and nerves. 6.4. Electoencephalogram data and ART. 6.5. Overcoming the limitations of GPA. 6.6. Chaos and chemistry. |