Articles

A full listing (through 1998) may be found in the Vita.

A listing by SUBJECT may be found here HERE.

1988: MS#47

MS#47. Visual Musical Instruments and Chaos

High Frontiers, Fall, 1988. [PDF]

1991: MS#52, 58

MS#52. Order and Chaos in the Toral Logistic Lattice

with John B. Corliss and John E. Dorband

Int. J. Bifurcation and Chaos, 1(1), March 1991: pp. 227-234.

Subjects: Computational math, cellular dynamical systems, morphogenesis

Abstract. Cellular dynamical systems, alias lattice dynamical systems, emerged as a new mathematical structure and modeling strategy in the 1980's. Based, like cellular automata, on finite difference methods for partial differential equations, they provide challenging patterns of spatiotemporal organisation, in which chaos and order cooperate in novel ways. Here we present initial findings of our exploration of a two-dimensional logistic lattice with the Massively Parallel Processor (MPP) at NASA's Goddard Space Flight Center, a machine capable of 200 megaflops per second. A video-tape illustrating these findings is available.

MS#58. Visualization Techniques for Cellular Dynamata

In: Lui Lam, ed. Introduction to Noonlinear Physics,

New York: Springer, 1997; pp. 297-307.

Abstract. History and definition of reaction/diffusion equations and CDs (cellular dynamical systems). Methods of visualization for CDs with examples.

[PDF] 12 pp., 2.5 MB--

1992 - 1995: MS#67 -- 76, 78, 80 -- 83

MS#67. Dynamics and Time, 1992

In: Garland's Encyclopedia of Time, Sam Macey, ed.

Subjects: Philosophy, psychology

Abstract. Models for time from chaos theory and fractal geometry. [HTML] [PDF]

MS#68. North-South trade and the dynamics of the environment, 1994

with Graciela Chichilnisky and Ron Record

in: Sustainability: Dynamics and Uncertainty, eds. G. Chichilnisky, G.M.Heal and A. Vercelli,

Kluwer Academic Publishers, The Netherlands, 1998, pp. 77-108.

Subjects: Economics, environment

Abstract. We develop a discrete dynamical system for economic behavior of a North-South model of international trade. Capital stocks of the North and the South increase endogenously through time, defining an iterated dynamical system on the plane. Our simulations reveal the response diagram for this dynamic system with one of the coefficients of the model (a variable representing property rights on environmental resources) as control parameter. As property rights vary we establish the existence of oscillations, period doubling bifurcations, chaotic behavior, and multistability. We discuss the implications for business cycles, and the interaction of economic and environmental variables.

Full text: [PDF] ca 3 MB

MS#69. A Double Logistic Map (1992)

Subjects: Discrete dynamical systems, computational math

Abstract. Several endomorphisms of the plane have been constructed by coupling two logistic maps. Here we study the dynamics occurring in one of them, a twisted version due to J. Dorband, which (like the other models) is rich in global bifurcations. By use of critical curves, absorbing and invariant areas are determined, inside which global bifurcations of the attracting sets (fixed points, closed invariant curves, cycles or chaotic attractors) take place. The basins of attraction of the absorbing areas are determined together with their bifurcations. [PDF] 22.2 MB, 48 pages

MS#70. Book Review: Manfred Schroeder, Power Laws (1994) [PDF] 264 KB

MS#71. Experimental Mechanics: the First Forty Years (1992)

Subjects: Classical mechanics, computational math

Abstract. Since the first work of Fermi, Pasta, and Ulam in 1952, computation has played a small but stimulating role in the explosive development of conservative mechanics. Here is a brief survey of the highlights of the early experimental work in Hamiltonian mechanics, done by the pioneers of computational mathematics on digital computers. [PDF] 360 KB, 3 pages

MS#72. Cathedral Dreams, 1992

Subjects: Architecture, computer graphic art

Abstract. Fantasies for the Cathedral Church of Saint John the Divine, the largest Gothic cathedral in the world. [HTML] [PDF]

MS#73. Human Fractals: the Arabesque in Our Mind, 1993

Subjects: Psychology, psychotherapy

Abstract. The rise of fractal geometry as a new branch of mathematics is intertwined with paradigm shifts in the sciences. First, the physical sciences were impacted, then the biological, and now, the social sciences. What are we to think of the diffusion of fractals into cultural studies? Here, in response to Marilyn Strathern's important contribution to this volume, One-legged gender, we review the fractalization of anthropology since Donna Haraway's Cyborgs of 1985. [HTML] [PDF], 740 KB, 4 pages

MS#74. Endomorphisms and Visualization, 1998

Subjects: Discrete dynamics

Abstract. The emerging role of nonlinear dynamical systems theory in the sciences, both in model building and data analysis, is leading to a uniform working strategy in all fields of science. Thus, compatible models in these fields may be combined into massively complex models for whole systems, such as Gaian physiology (land, ocean, and atmosphere), human population growth and demographics, the world economy, or combinations of these. These massive models, though simpler than nature, may be too complex for our understanding. This problem is the basis for the new emphasis on scientific visualization in general, and dynamical visualization in particular. That is, given a continuous or discrete dynamical system of very high dimension, how can we visualize and understand its behavior? In this paper we will consider a special case of this problem, in which the massively complex dynamical system is a semi-cascade, that is, the iteration of non-invertible map, or endomorphism. The strategy of visualization of this system consists of projection of the trajectories onto a low-dimensional (especially, two- or three- dimensional) subspace. The new method of critical curves, discovered by Christian Mira in 1964 for the study of plane endomorphisms, provides tools to infer the behavior of the massive system from the simple observation of its projection onto a subspace.

[PDF], 388 KB, 3 pages

MS#75. MIMI and the Illuminati, 1994

Subjects: Visual math/music

Abstract. Upon the invitation of the Lindisfarne Association and the Cathedral Church of St. John the Divine in New York City, a concert of audiovisual mathematics/music took place in the Cathedral Church on 17 October, 1992, at about eight o'clock in the evening. Three computers and three persons cooperated in the performance. This is the story behind the event (and its video recording).

[PDF], 904 KB, 7 pages

MS#76. Erodynamics and the Dischaotic Personality, 1993

Subjects: Psychology, psychotherapy

Abstract. The binary dichotomy of chaos/dischaos is used in place of that of disorder/order in modeling the psyche in the style of Kurt Lewin. Application is made to several ideas of Gregory Bateson. [HTML] [PDF], 5.6 MB, 11 pages

MS#78. Peak Load Prediction in an Electrical Power System, 1996

Subjects: Electrical engineering

Abstract. In the operation and maintenance of an electric power system, it is very useful to know the load, especially the peak load, in advance. In this paper we consider the difficult problem of peak load prediction (PLP) in an electric power system. We propose a discrete, complex dynamical model for PLP, similar to those proposed recently for macroeconomic prediction, in the spirit of complex dynamical systems (CDS) theory. [PDF] 1.1 MB, 8 pages

MS#78A. Predicting Outage and Containing Chaos in a Power Grid, 1993

Subjects: Electrical engineering

Abstract. Chaotic fluctuations in the voltage available at different nodes in the electric power grid have been observed in connection with unwanted events, such as voltage collapse and power outage. The overall peak power in the grid also fluctuates unpredictably. In this report we consider techniques for controlling, or at least containing, the fluctuations after their appearance, as well as the problem of prediction of the peak load. In other reports, we will consider avoidance stretegies to prevent the appearance of these unwanted events. In all cases, the strategies we consider are based on the theory of complex dynamical systems: chaotic attractors and their bifurcations. [PDF] 463 KB, 4 pages

MS#80. The Electronic Rose Window, 1993

Subjects: Sacred art, environment

Abstract. Previously we have described a project to build an electronic stained glass window in the South Transept of the Cathedral Church of Saint John the Divine in New York City, the largest Gothic Cathedral in the world. Here, we sketch the historical background and motivation of this project. [HTML] [PDF]

MS#81. Educational Hypermedia and the World-Wide Web, 1994

Subjects: Education, web tech

Abstract. There are currently over 2 millions hosts and 20 million people on the Internet, and the numbers are growing rapidly. A large portion of this growth (estimated at 40%) is now attributed to the WWW, the World-Wide Web. In this article, we consider the use of the WWW to publish hypermedia in educational environments. (Many thanks to Will Russell of UC Santa Cruz for our graphics.) [HTML] [PDF]

MS#82. The Canon of Lespugue, 1994

Epigraphic Society Occasional Papers, Vol. 24, 2006; pp. 169-174.

Subjects: Math education, archeology

Abstract. Linear measurements taken from the Venus of Lespugue, a 25,000 year old sculpture, closely match the diatonic scale of the Vedic Aryans, also known as the Dorian mode of the ancient Greeks. [HTML], [PDF] 6 pages, 8.5 MB

MS#83. The Bifurcation of the !Kung, 1995

Subjects: Math education, archeology

Abstract. While the emergence of a planetary society unrolls, a backlash of neonationalism is raising global alarm. Here we combine earlier works on international synergy and social fractals into a model for the new world disorder, and apply it to the transformation of the !Kung as an example. [HTML] [PDF]

1996: MS#85 -- 90

MS#85. Webometry: measuring the compexity of the World Wide Web

World Futures 50 (1997): 785-791.

Also Ch. 39, in: Wolfang Hofkirchner, ed., The Quest for a Unified Theory of Information Amsterdam: Gordon and Breach, 1999, pp. 553-560.

Abstract. The explosive growth of the WWW may be viewed as the neurogenesis phase in the embryogenesis of a new planetary civilization. To empower this emergent phenomenon with self-reflection, we propose strategies for the visualization of the complexity of the WWW, seen as a neural net. The pointwise fractal dimension of a massive matrix is the basis of our strategy. [HTML] [PDF], 652 KB, 7 pages

MS#86. Vibrations: communication through a morphic field

Abstract. This is a progress report on the computer simulation of a mathematical model for a morphic field. The model is a two-dimensional lattice of oscillators derived from the d'Alembertian wave equation by spatial discretization. The communication is between two clamped objects inserted into the field. A change of shape in one of them sets off a transient wave which perturbs the boundary field of the other one after a brief delay. Unlike radio propagation, this is a static monopole transmission. [HTML] [PDF]

MS#86B. Vibrations: communication through a morphic field, Pt 2

Abstract. In this second simulation, we clamp the field at the edges of a rectangular region. This note is an explanation of the companion video, which is a record of the experiment. [TXT]

MS#87. Social interventions and the World Wide Web

Abstract. The World Wide Web is truly world-wide, providing essentially free access to tons of information, including up-to-date political, economic, and environmental data. What is more, with a very small budget, a relatively insignificant group of action-minded individuals, such as GERG, can publish the information it believes to be important for our future evolution. Here we present a brief history of GERG, its publishing program, and an exhortation to the WWW. [HTML] [PDF]

MS#88. Webometry: measuring the synergy of the World Wide Web

Abstract. This is the second progress report on the webometry project: acquisition of data regarding the density of links on the WWW. We illustrate the primary visualization strategy, the synergy matrix, in the case of a model subnet of nine nodes.

[HTML], [PDF], 4 pages, 1.9 MB

MS#89. Webometry: chronotopography of the World Wide Web

Written with Don Foresta (Paris)
Abstract. This is the third progress report on the webometry project: acquisition of data regarding the density of links on the WWW. Here we discuss the mapping from geography to chronotopography of the web as a basis for the complexity and simplexity of cyberspace. [HTML] [PDF]

MS#90. A bridge between Whitney's fold and cusp points and the critical curves LC-1 and LC in two-dimensional endomorphisms

Written with Laura Gardini and Gian-Italo Bischi (Urbino). Preprint [PDF] 17 pages, 1.1 MB

MS#91. Endosingularities

Abstract. We review the history and basic concepts of singularity theory, and contrast with the problems of iteration theory and the method of critical curves, in the two-dimensional case. We call the combination of these two theories endosingularity theory. [PDF] 8 pages, 104 KB

1997: MS#92, 93

MS#92. Chaos and the Millennium

Presentation to the National Collegiate Honors Council, Holloween, 1996. Transcript edited and posted July 1997.

Abstract.An explanation of the millennarian concept, and the role of the chaos revolution in our current bifurcation. [TEXT] 20 KB, [PDF] 16 pages, 5.2 MB

MS#93. The Geometry of Angels

Abstract. We analyze the mathematical vision behind the wings of the angel Gabriel, in a Renaissaance painting, the Cortona Annunciation of Fra Angelico. In the context of the Renaisance mathematics of perspective and conic sections, the flapping wings generate a family of toroids. We interpret this image as a painterly representation of the three-sphere of Dante. As such, this geometrical vision of Fra Angelico presaged seminal works of modern mathematics, such as the Hopf fibration. [PDF], 10 pages, 4.8 MB

1998: MS#94-101

MS#94. The Mathematics of Chaos and the Urban Revolution

Abstract. An earlier epoch of chaos came to an end with the urban revolution, millennia ago. And now, chaos reappears in a revolution of its own. Can chaos theory rectify the negative aspects of the urban revolution and help us create the future of Europe? I think so, and here's why. [PDF], 9 pages, 2.8 MB

MS#95. The Chaos Revolution: a Personal View

Abstract. Chaos theory began abruptly in 1889, in the prize work of Poincare, published in 1890. After a tangled history, it arrived in my life in Berkeley in 1960. It was then my luck to be an observer of the chaos revolution from fairly close-up. In this paper I try to recollect the main events of this story. [PDF], 8 pages, 1.0 MB

MS#96. The Origin of Algebra

Presentation to Homeokinetics 1998, July 25, 1998.

Partial draft [HTML]

Full text [TEXT]

MS#97. A Stairway to Chaos

Lecture on basic concepts of dynamical systems theory

to a hearing on general systems theory, Neuchatel, 9/4/98

Full text [PDF]

MS#98. Complex Dynamical Systems

Introduction to the basic concepts of CDS theory. [PDF]

MS#99. Thrice Upon a Time

Real, virtual, and simulation time. [PDF]

MS#100. Cyberspace and the Ecotopian Dream

The World Wide Web is indeed collective knowledge, but will not truly be collective intelligence in the sense of Pierre Levy until it combines hypermedia with the computer modeling and simulation of natural and social systems by means of complex dynamical systems techniques. [PDF]

MS#101. Nonlinear Resonance in Basin Portraits of Two Coupled Swings under Periodic Forcing

Joint work on electric power systems with Yoshisuke Ueda, Yoshinori Ueda, and Bruce Stewart [HTML]

1999: MS#102-103

MS#102. An old math program

A proposal for the a new math curriculum for schools, grades K to 12, based on world cultural history, multimedia presentation, integration, and of all things, Euclid. [RTF] [PDF] [HTML]

MS#102a. Perspectiva

Outline of a project on Perspective [RTF] [TXT]

MS#102b. Conics

Outline of a project on Conics [RTF] [TXT]

MS#103. Chaos and the monarch butterfly [HTML] [PDF]

The migration of the monarch butterfly is considered from the perspective of chaos theory, and compared to the evolution of human culture.

MS#103a. The chaos and fractals of Paris

Poincare, Kupka, and Satie [PDF]

2000: MS#104-107

MS#104. The Hexagrams of the Moon

Astrological chaos in the cycles of the moon [PDF]

MS#105. Vibrational Resonance and Cognitive Internalization

Abstract. Continuing in the spirit of earlier works, we propose a mathematical model for the process of internalization of ideas. This entire concept presupposes a paradigm of mind with internal and external regions, which we accept provisionally for the sake of discussion. In short, we envision a physical model comprising several excitable, continuous media in parallel planes, interconnected by a process of resonance of vibrations. The mathematical model for this physical analog is then discretised, and proposed verbatim as a computational model for the mental system. This model is typical of complex dynamical systems, as they have evolved during the last twenty years or so. [HTML] [PDF]

MS#106. A Two Worlds Model for Consciousness

Abstract. A model is proposed in which communication and action are extended both into the past and into the future. The chief feature of this model is its duality, manifest in a pair of parallel space-time worlds. Interaction between these worlds P consciousness P is effected through a moving window, through which influences pass by a process of resonance. [TXT] [PDF]

MS#107. Galileo's Leap into the Future

Abstract. Certainly one of the larger bifurcations of world cultural history must be the shift from medieval to modern science. According to many historians, the hinge point of that shift was Galileo's early works, beginning about 1611 CE: certainly an outstanding bolt from the blue. In this paper we dig up the roots of Galileo's leap into the future, and offer a theory of the yin-yang type, based on the ancient conflict between Plato and Aristotle. [PDF]

2002: MS#108-109

MS#108. The Genesis of Complexity

Abstract. The evolution of the theories of complexity, from three roots (cybernetics, general systems theory, and system dynamics) and brief descriptions of its many branches. [PDF] [HTML]

MS#109. Basin configuration of a six-dimensional model of an electric power system

With Y. Ueda, H. Amano, and H. Stewart

From the abstract: As part of an ongoing project on the stability of massively complex electrical power systems, we discuss the global geometric structure of contacts among the basins of attraction of a six-dimensional dynamical system. [HTML]

2003: MS#110-112

MS#110. Neural Networks for Economic Prediction

With L. Punzo [RTF]

MS#111. The Dynamics of Synchronization and Phase Regulation

With Alan Garfinkel [PDF]

MS#112. Attractor and Basin Portraits of a Double Swing Power System

With Yoshisuke Ueda, M. Hirano, and H. Ohta

IJBC 14(9), Sept. 2004, 3135-3152.

2004: MS#113-115

MS#113. Basic Sets and Attractors of a Double Swing Power System

With Yoshisuke Ueda and H. Ohta

To appear

MS#114. Landscape Dynamics and Conspicuous Consumption

With Dan Friedman [PDF], 1 MB

To appear, Proceedings of Intern. Symposium on Dynamic Games and Applications, Tucson, Dec. 2004.

MS#115. Landscape Dynamics, Complex Dynamics, and Agent Based Models

With Dan Friedman [PDF] 220 KB

To appear, Journal of the Calcutta Mathematical Society.

2005: MS#116-117

MS#116. The Death and Rebirth of the World Soul, 2500 BCE -- 2005 CE, A Concise Overview

In Ervin Laszlo, Science and the Reenchantment of the Cosmos:

The Rise of the Integral Vision of Reality, Inner Traditions, 2005; pp. 177-186.

[RTF] 28 KB; [PDF] 92 KB

MS#116a. The New Sacred Math

Longer version, World Futures, 62(1); pp. 6-16 (2006).

[RTF] 36 KB; [PDF] 11 pages, 1.5 MB

MS#117. The Broken Chain

The bifurcation from soul to force, Kepler, 1605 AD

[RTF] 48 KB; [PDF] 128 KB;

MS#117a. The Broken Chain

Shorter version, Elixir, #2 (2006); pp. 9-16.

[RTF] 32 KB, [PDF] 96 KB

2006: MS#118-120

MS#118. Vibrations and Forms

Submitted to Consciousness: A Deeper Scientific Search

Proceedings of the 3rd Int'l. Conf. on Science and Consciousness

Ramakrishna Mission Institute of Culture, Golpark, Kolkata, INDIA

[PDF] 14 pages with 2 figures, 220 KB

MS#119. Planck Scale and Agent Based Simulations of Quantum Spacetime

with Sisir Roy, ISI Calcutta

Intl Journal of Pure and Applied Math, to appear

Text and applets

MS#120. The Aesthetics and Fractal Dimension of Electric Sheep

with Scott Draves, Pablo Viotti, Fred Abraham, and Clint Sprott

Int'l. J. Bifurcations and Chaos, v.18, n.4, April 2008, to appear

[PDF] 20 pages with 6 figures, 6.7 MB

2007: MS#121-123

MS#121. Bubbles and Crashes: Escape Dynamics in Financial Markets

with Dan Friedman, UCSC, Santa Cruz, CA

[PDF] 37 pages, 352 KB

MS#122. A Digital Solution to the Mind/Body Problem

with Sisir Roy, ISI, Calcutta, India

[PDF] 8 pages, 88 KB

MS#123. Complex Dynamical Systems and the Social Sciences

with Dan Friedman and Paul Viotti, UC Santa Cruz,

[PDF] 13 pages with three figures, 264 KB

2008: MS#124---

MS#124. Mathematics and the Psychedelic Revolution

Submitted to MAPS

[PDF} 11 pages, 88 KB

MS#125. Bubbles and Crashes: a Simulation Approach

In: Vela Velupillai Festschrift, to appear

[PDF} 7 pages, 124 KB

MS#126. The Trouble with Math

In: Courtney Sale Ross Festschrift, to appear

[PDF} 18 pages, 168 KB

MS#127. The Misuse of Math

For Proceedings, MathKnow08, Springer Verlag

[PDF} 8 pages, 2.5 MB