The Fractal Self

The Fractal Self

Author: John L. Culliney

Publisher: University of Hawaii Press

Published: 2017-07-31

Total Pages: 257

ISBN-13: 0824866649

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Our universe, science reveals, began in utter simplicity, then evolved into burgeoning complexity. Starting with subatomic particles, dissimilar entities formed associations—binding, bonding, growing, branching, catalyzing, cooperating—as “self” joined “other” following universal laws with names such as gravity, chemical attraction, and natural selection. Ultimately life arose in a world of dynamic organic chemistry, and complexity exploded with wondrous new potential. Fast forward to human evolution, and a tension that had existed for billions of years now played out in an unprecedented arena of conscious calculation and cultural diversity. Cooperation interleaving with competition; intimacy oscillating with integrity—we dwell in a world where yin meets yang in human affairs on many levels. In The Fractal Self, John Culliney and David Jones uncover surprising intersections between science and philosophy. Connecting evidence from evolutionary science with early insights of Daoist and Buddhist thinkers, among others, they maintain that sagely behavior, envisioned in these ancient traditions, represents a pinnacle of human achievement emerging out of our evolutionary heritage. They identify an archetype, “the fractal self,” a person in any walk of life who cultivates a cooperative spirit. A fractal self is a sage in training, who joins others in common cause, leads from within, and achieves personal satisfaction in coordinating smooth performance of the group, team, or institution in which he or she is embedded. Fractal selves commonly operate with dedication and compassionate practice in the service of human society or in conserving our planet. But the competitive side of human nature is susceptible to greed and aggression. Self-aggrandizement, dictatorial power, and ego-driven enforcement of will are the goals of those following a self-serving path—individuals the authors identify as antisages. Terrorist leaders are an especially murderous breed, but aggrandizers can be found throughout business, religion, educational institutions, and governments. Humanity has reached an existential tipping point: will the horizon already in view expand with cooperative progress toward godlike emergent opportunities or contract in the thrall of corrupt oligarchs and tribal animosities? We have brought ourselves to a chaotic edge between immense promise and existential danger and are even now making our greatest choice.


Book Synopsis The Fractal Self by : John L. Culliney

Download or read book The Fractal Self written by John L. Culliney and published by University of Hawaii Press. This book was released on 2017-07-31 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our universe, science reveals, began in utter simplicity, then evolved into burgeoning complexity. Starting with subatomic particles, dissimilar entities formed associations—binding, bonding, growing, branching, catalyzing, cooperating—as “self” joined “other” following universal laws with names such as gravity, chemical attraction, and natural selection. Ultimately life arose in a world of dynamic organic chemistry, and complexity exploded with wondrous new potential. Fast forward to human evolution, and a tension that had existed for billions of years now played out in an unprecedented arena of conscious calculation and cultural diversity. Cooperation interleaving with competition; intimacy oscillating with integrity—we dwell in a world where yin meets yang in human affairs on many levels. In The Fractal Self, John Culliney and David Jones uncover surprising intersections between science and philosophy. Connecting evidence from evolutionary science with early insights of Daoist and Buddhist thinkers, among others, they maintain that sagely behavior, envisioned in these ancient traditions, represents a pinnacle of human achievement emerging out of our evolutionary heritage. They identify an archetype, “the fractal self,” a person in any walk of life who cultivates a cooperative spirit. A fractal self is a sage in training, who joins others in common cause, leads from within, and achieves personal satisfaction in coordinating smooth performance of the group, team, or institution in which he or she is embedded. Fractal selves commonly operate with dedication and compassionate practice in the service of human society or in conserving our planet. But the competitive side of human nature is susceptible to greed and aggression. Self-aggrandizement, dictatorial power, and ego-driven enforcement of will are the goals of those following a self-serving path—individuals the authors identify as antisages. Terrorist leaders are an especially murderous breed, but aggrandizers can be found throughout business, religion, educational institutions, and governments. Humanity has reached an existential tipping point: will the horizon already in view expand with cooperative progress toward godlike emergent opportunities or contract in the thrall of corrupt oligarchs and tribal animosities? We have brought ourselves to a chaotic edge between immense promise and existential danger and are even now making our greatest choice.


Gaussian Self-Affinity and Fractals

Gaussian Self-Affinity and Fractals

Author: Benoit Mandelbrot

Publisher: Springer Science & Business Media

Published: 2002

Total Pages: 672

ISBN-13: 9780387989938

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This third volume of the Selected Works focusses on a detailed study of fraction Brownian motions. The fractal themes of "self-affinity" and "globality" are presented, while extensive introductory material, written especially for this book, precedes the papers and presents a number of striking new observations and conjectures. The mathematical tools so discussed will be valuable to diverse scientific communities.


Book Synopsis Gaussian Self-Affinity and Fractals by : Benoit Mandelbrot

Download or read book Gaussian Self-Affinity and Fractals written by Benoit Mandelbrot and published by Springer Science & Business Media. This book was released on 2002 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third volume of the Selected Works focusses on a detailed study of fraction Brownian motions. The fractal themes of "self-affinity" and "globality" are presented, while extensive introductory material, written especially for this book, precedes the papers and presents a number of striking new observations and conjectures. The mathematical tools so discussed will be valuable to diverse scientific communities.


The Fractal Self

The Fractal Self

Author: John L. Culliney

Publisher:

Published: 2017

Total Pages:

ISBN-13: 9780824875763

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In 'The Fractal Self', John Culliney and David Jones uncover surprising intersections between science and philosophy. Connecting evidence from evolutionary science with early insights of Daoist and Buddhist thinkers, among others, they maintain that sagely behaviour, envisioned in these ancient traditions, represents a pinnacle of human achievement emerging out of our evolutionary heritage.


Book Synopsis The Fractal Self by : John L. Culliney

Download or read book The Fractal Self written by John L. Culliney and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In 'The Fractal Self', John Culliney and David Jones uncover surprising intersections between science and philosophy. Connecting evidence from evolutionary science with early insights of Daoist and Buddhist thinkers, among others, they maintain that sagely behaviour, envisioned in these ancient traditions, represents a pinnacle of human achievement emerging out of our evolutionary heritage.


Fractal River Basins

Fractal River Basins

Author: Ignacio Rodríguez-Iturbe

Publisher: Cambridge University Press

Published: 1997

Total Pages: 574

ISBN-13: 9780521004053

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This book provides a theoretical basis to the arrangement of river basins and networks.


Book Synopsis Fractal River Basins by : Ignacio Rodríguez-Iturbe

Download or read book Fractal River Basins written by Ignacio Rodríguez-Iturbe and published by Cambridge University Press. This book was released on 1997 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a theoretical basis to the arrangement of river basins and networks.


Fractured Fractals and Broken Dreams

Fractured Fractals and Broken Dreams

Author: Guy David

Publisher: Oxford University Press

Published: 1997

Total Pages: 226

ISBN-13: 9780198501664

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This book proposes new notions of coherent geometric structure. Fractal patterns have emerged in many contexts, but what exactly is a "pattern" and what is not? How can one make precise the structures lying within objects and the relationships between them? The foundations laid herein provide a fresh approach to a familiar field. From this emerges a wide range of open problems, large and small, and a variety of examples with diverse connections to other parts of mathematics. One of the main features of the present text is that the basic framework is completely new. This makes it easier for people to get into the field. There are many open problems, with plenty of opportunities that are likely to be close at hand, particularly as concerns the exploration of examples. On the other hand the general framework is quite broad and provides the possibility for future discoveries of some magnitude. Fractual geometries can arise in many different ways mathematically, but there is not so much general language for making comparisons. This book provides some tools for doing this, and a place where researchers in different areas can find common ground and basic information.


Book Synopsis Fractured Fractals and Broken Dreams by : Guy David

Download or read book Fractured Fractals and Broken Dreams written by Guy David and published by Oxford University Press. This book was released on 1997 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book proposes new notions of coherent geometric structure. Fractal patterns have emerged in many contexts, but what exactly is a "pattern" and what is not? How can one make precise the structures lying within objects and the relationships between them? The foundations laid herein provide a fresh approach to a familiar field. From this emerges a wide range of open problems, large and small, and a variety of examples with diverse connections to other parts of mathematics. One of the main features of the present text is that the basic framework is completely new. This makes it easier for people to get into the field. There are many open problems, with plenty of opportunities that are likely to be close at hand, particularly as concerns the exploration of examples. On the other hand the general framework is quite broad and provides the possibility for future discoveries of some magnitude. Fractual geometries can arise in many different ways mathematically, but there is not so much general language for making comparisons. This book provides some tools for doing this, and a place where researchers in different areas can find common ground and basic information.


Fractal Dimension for Fractal Structures

Fractal Dimension for Fractal Structures

Author: Manuel Fernández-Martínez

Publisher: Springer

Published: 2019-04-23

Total Pages: 204

ISBN-13: 3030166457

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This book provides a generalised approach to fractal dimension theory from the standpoint of asymmetric topology by employing the concept of a fractal structure. The fractal dimension is the main invariant of a fractal set, and provides useful information regarding the irregularities it presents when examined at a suitable level of detail. New theoretical models for calculating the fractal dimension of any subset with respect to a fractal structure are posed to generalise both the Hausdorff and box-counting dimensions. Some specific results for self-similar sets are also proved. Unlike classical fractal dimensions, these new models can be used with empirical applications of fractal dimension including non-Euclidean contexts. In addition, the book applies these fractal dimensions to explore long-memory in financial markets. In particular, novel results linking both fractal dimension and the Hurst exponent are provided. As such, the book provides a number of algorithms for properly calculating the self-similarity exponent of a wide range of processes, including (fractional) Brownian motion and Lévy stable processes. The algorithms also make it possible to analyse long-memory in real stocks and international indexes. This book is addressed to those researchers interested in fractal geometry, self-similarity patterns, and computational applications involving fractal dimension and Hurst exponent.


Book Synopsis Fractal Dimension for Fractal Structures by : Manuel Fernández-Martínez

Download or read book Fractal Dimension for Fractal Structures written by Manuel Fernández-Martínez and published by Springer. This book was released on 2019-04-23 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a generalised approach to fractal dimension theory from the standpoint of asymmetric topology by employing the concept of a fractal structure. The fractal dimension is the main invariant of a fractal set, and provides useful information regarding the irregularities it presents when examined at a suitable level of detail. New theoretical models for calculating the fractal dimension of any subset with respect to a fractal structure are posed to generalise both the Hausdorff and box-counting dimensions. Some specific results for self-similar sets are also proved. Unlike classical fractal dimensions, these new models can be used with empirical applications of fractal dimension including non-Euclidean contexts. In addition, the book applies these fractal dimensions to explore long-memory in financial markets. In particular, novel results linking both fractal dimension and the Hurst exponent are provided. As such, the book provides a number of algorithms for properly calculating the self-similarity exponent of a wide range of processes, including (fractional) Brownian motion and Lévy stable processes. The algorithms also make it possible to analyse long-memory in real stocks and international indexes. This book is addressed to those researchers interested in fractal geometry, self-similarity patterns, and computational applications involving fractal dimension and Hurst exponent.


The Fractal Brain Theory

The Fractal Brain Theory

Author: Wai Tsang

Publisher: Lulu.com

Published: 2016-08-02

Total Pages: 532

ISBN-13: 1326753223

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The Fractal Brain Theory, or the Symmetry, Self Similarity and Recursivity Theory of Brain and Mind, is a Revolutionary new way of looking at the nature of intelligence and also genomics. It is the key to a powerful and new kind of Recursively Self Modifying Artificial Intelligence. Wai H. Tsang presents an exciting new synthesis of all things psychological, linguistic, neuroscientific, genomic, evolutionary, informatic, computational, complex and fractal. Dealing with the most central puzzles of mind science and AI, and weaving in some of the most fundamental concepts in mathematics such as symmetry, geometry, functions, discrete maths and formal axiomatic systems. This book presents nothing less than a seamless unified theory of Brain, Mind, Artificial Intelligence, Functional Genomics, Ontogenesis and Evolution. Also covering topics such as the quest for the Perfect & Universal Language, Recursively Self Modifying Algorithms, Super Intelligence & Technological Singularity.


Book Synopsis The Fractal Brain Theory by : Wai Tsang

Download or read book The Fractal Brain Theory written by Wai Tsang and published by Lulu.com. This book was released on 2016-08-02 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fractal Brain Theory, or the Symmetry, Self Similarity and Recursivity Theory of Brain and Mind, is a Revolutionary new way of looking at the nature of intelligence and also genomics. It is the key to a powerful and new kind of Recursively Self Modifying Artificial Intelligence. Wai H. Tsang presents an exciting new synthesis of all things psychological, linguistic, neuroscientific, genomic, evolutionary, informatic, computational, complex and fractal. Dealing with the most central puzzles of mind science and AI, and weaving in some of the most fundamental concepts in mathematics such as symmetry, geometry, functions, discrete maths and formal axiomatic systems. This book presents nothing less than a seamless unified theory of Brain, Mind, Artificial Intelligence, Functional Genomics, Ontogenesis and Evolution. Also covering topics such as the quest for the Perfect & Universal Language, Recursively Self Modifying Algorithms, Super Intelligence & Technological Singularity.


Fractals: A Very Short Introduction

Fractals: A Very Short Introduction

Author: Kenneth Falconer

Publisher: OUP Oxford

Published: 2013-09-26

Total Pages: 153

ISBN-13: 0191663441

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Many are familiar with the beauty and ubiquity of fractal forms within nature. Unlike the study of smooth forms such as spheres, fractal geometry describes more familiar shapes and patterns, such as the complex contours of coastlines, the outlines of clouds, and the branching of trees. In this Very Short Introduction, Kenneth Falconer looks at the roots of the 'fractal revolution' that occurred in mathematics in the 20th century, presents the 'new geometry' of fractals, explains the basic concepts, and explores the wide range of applications in science, and in aspects of economics. This is essential introductory reading for students of mathematics and science, and those interested in popular science and mathematics. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.


Book Synopsis Fractals: A Very Short Introduction by : Kenneth Falconer

Download or read book Fractals: A Very Short Introduction written by Kenneth Falconer and published by OUP Oxford. This book was released on 2013-09-26 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many are familiar with the beauty and ubiquity of fractal forms within nature. Unlike the study of smooth forms such as spheres, fractal geometry describes more familiar shapes and patterns, such as the complex contours of coastlines, the outlines of clouds, and the branching of trees. In this Very Short Introduction, Kenneth Falconer looks at the roots of the 'fractal revolution' that occurred in mathematics in the 20th century, presents the 'new geometry' of fractals, explains the basic concepts, and explores the wide range of applications in science, and in aspects of economics. This is essential introductory reading for students of mathematics and science, and those interested in popular science and mathematics. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.


Fractal Geometry and Number Theory

Fractal Geometry and Number Theory

Author: Michel L. Lapidus

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 277

ISBN-13: 1461253144

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A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. We refer the reader to [Berrl-2, Lapl-4, LapPol-3, LapMal-2, HeLapl-2] and the ref erences therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7. 1, 10. 3 and 10. 4, along with Ap pendix B.) In Chapter 1, we introduce the basic object of our research, fractal strings (see [Lapl-3, LapPol-3, LapMal-2, HeLapl-2]). A 'standard fractal string' is a bounded open subset of the real line. Such a set is a disjoint union of open intervals, the lengths of which form a sequence which we assume to be infinite. Important information about the geometry of . c is contained in its geometric zeta function (c(8) = L lj. j=l 2 Introduction We assume throughout that this function has a suitable meromorphic ex tension. The central notion of this book, the complex dimensions of a fractal string . c, is defined as the poles of the meromorphic extension of (c.


Book Synopsis Fractal Geometry and Number Theory by : Michel L. Lapidus

Download or read book Fractal Geometry and Number Theory written by Michel L. Lapidus and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. We refer the reader to [Berrl-2, Lapl-4, LapPol-3, LapMal-2, HeLapl-2] and the ref erences therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7. 1, 10. 3 and 10. 4, along with Ap pendix B.) In Chapter 1, we introduce the basic object of our research, fractal strings (see [Lapl-3, LapPol-3, LapMal-2, HeLapl-2]). A 'standard fractal string' is a bounded open subset of the real line. Such a set is a disjoint union of open intervals, the lengths of which form a sequence which we assume to be infinite. Important information about the geometry of . c is contained in its geometric zeta function (c(8) = L lj. j=l 2 Introduction We assume throughout that this function has a suitable meromorphic ex tension. The central notion of this book, the complex dimensions of a fractal string . c, is defined as the poles of the meromorphic extension of (c.


Ergodic Theory and Fractal Geometry

Ergodic Theory and Fractal Geometry

Author: Hillel Furstenberg

Publisher: American Mathematical Society

Published: 2014-08-08

Total Pages: 82

ISBN-13: 1470410346

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Fractal geometry represents a radical departure from classical geometry, which focuses on smooth objects that "straighten out" under magnification. Fractals, which take their name from the shape of fractured objects, can be characterized as retaining their lack of smoothness under magnification. The properties of fractals come to light under repeated magnification, which we refer to informally as "zooming in". This zooming-in process has its parallels in dynamics, and the varying "scenery" corresponds to the evolution of dynamical variables. The present monograph focuses on applications of one branch of dynamics--ergodic theory--to the geometry of fractals. Much attention is given to the all-important notion of fractal dimension, which is shown to be intimately related to the study of ergodic averages. It has been long known that dynamical systems serve as a rich source of fractal examples. The primary goal in this monograph is to demonstrate how the minute structure of fractals is unfolded when seen in the light of related dynamics. A co-publication of the AMS and CBMS.


Book Synopsis Ergodic Theory and Fractal Geometry by : Hillel Furstenberg

Download or read book Ergodic Theory and Fractal Geometry written by Hillel Furstenberg and published by American Mathematical Society. This book was released on 2014-08-08 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal geometry represents a radical departure from classical geometry, which focuses on smooth objects that "straighten out" under magnification. Fractals, which take their name from the shape of fractured objects, can be characterized as retaining their lack of smoothness under magnification. The properties of fractals come to light under repeated magnification, which we refer to informally as "zooming in". This zooming-in process has its parallels in dynamics, and the varying "scenery" corresponds to the evolution of dynamical variables. The present monograph focuses on applications of one branch of dynamics--ergodic theory--to the geometry of fractals. Much attention is given to the all-important notion of fractal dimension, which is shown to be intimately related to the study of ergodic averages. It has been long known that dynamical systems serve as a rich source of fractal examples. The primary goal in this monograph is to demonstrate how the minute structure of fractals is unfolded when seen in the light of related dynamics. A co-publication of the AMS and CBMS.