Ralph Abraham

The Legacies of David Loye: The General Evolution Research Group, Partnership, Chaos, Darwin, and Action Research

Interdisciplinary Journal of Partnership Studies

Mathematician Ralph Abraham recounts memories of Dave Loye, Riane Eisler, Ervin Laszlo, the Gener... more

format_quoteThe initial meeting in Santa Cruz sparked a collaborative project aimed at addressing world problems through multidisciplinary scholarship.format_quote

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Manifolds, Tensor Analysis, and Applications (Ralph Abraham, Jerrold E. Marsden and Tudor Ratiu)

SIAM Review, 1984

ABSTRACT

Predicting Outage and Containing Chaos in a Power Grid

Chaotic fluctuations in the voltage available at different nodes in the electric power grid have ... more 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.

The Emergence of Spacetime from the Akasha

In our recent book (Abraham and Roy, 2010) we have proposed a mathematical model for the quantum ... more In our recent book (Abraham and Roy, 2010) we have proposed a mathematical model for the quantum vacuum as a model of consciousness. We emphasized that the quantum vacuum is not identical to cosmic consciousness. The word akasha is translated in English as space or ether. In the Eastern tradition ether has two phases, subtle and gross. In our model, the nodes of a network correspond to subtle ether, while the physical space created in temporal slices by condensation corresponds to gross ether. In essence, the akasha is a subtle background against which everything in the material universe becomes perceptible. In this essay we expand on the self-organization of the gross ether from a subtle (submicroscopic) cellular network, with special emphasis on the illusion of time, and the apparent paradoxes such as precognition, retro-causation, and entanglement.

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The Electronic Rose Window

The Chaos and Fractals of Paris

Kupka and Satie foresaw the homoclinic tangle of Poincare.

Geometry of the Early Neolithic

Following a visit in the Winter of 2007 to the Alhambra — a Moorish palace built around 1350 CE i... more Following a visit in the Winter of 2007 to the Alhambra — a Moorish palace built around 1350 CE in southern Spain — I have been digging up the roots of the Alhambra Theorem, which says that Moorish craftsmen in the Middle Ages knew that there were exactly 17 crystallographic groups in two dimensions. This fundamental result of modern group theory emerged into the mathematical literature only in 1891. Digging back from the Alhambra, we found an Ur source for the motifs of the Alhambra in the earliest wall-paintings of Çatal Hüyük, around 10 KYA (thousand years ago). Digging deeper led to the cave paintings of Upper Paleolithic Europe, beginning around 35 KYA. There appears to be a straight line of development from the Upper Paleolithic caves to the Neolithic villages of Anatolia, and on to the Alhambra. In this article we tell the story of the geometric patterns found in the Neolithic village of Çatal Hüyük.

Entheogens in the Himalayan Foothills

Reporting a miraculous week of entheogens and sadhus in a temple in the montane jungle of the Him... more

Shamanism and Noh

The Paleolithic Birth of Geometric Thinking

Following a visit in the Winter of 2007 to the Alhambra — a Moorish palace built around 1300 CE i... more Following a visit in the Winter of 2007 to the Alhambra — a Moorish palace built around 1300 CE in the South of Spain — I have been digging up the roots of the Alhambra Theorem, which says that Moorish craftsmen in the Middle Ages knew that there were exactly 17 crystallographic groups. This fundamental result of modern group theory emerged into the mathematical literature only in 1891. Digging back from the Alhambra, we found an Ur source for the motifs of the Alhambra in the earliest Turkish carpets of Catal Hüyük, around 10 KYA (thousand years ago). Digging deeper led to the cave paintings of Upper Paleolithic Europe, beginning around 35 KYA. In this article we tell the story of the earliest geometric motifs we have found. This reveals the birth of geometric thinking in the ambiance of psychedelic shamanism -- religion, art, and mathematics were born together in the youth of our species.

Vibrations: communication through a morphic field, Pt 2

This is a further progress report on the computer simulation of a mathematical model for a morphi... more This is a further 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&#39;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. 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.

Chaos Theory and the Tragedy of the Commons

Complex dynamical systems models have been used (and misused) in service of the sustainability (o... more Complex dynamical systems models have been used (and misused) in service of the sustainability (or tragedy) of a commons. Their misuse results from the widespread ignorance of chaos theory. Here we consider this problem in general, and study the special case of the tragedy of the oceans in detail. We go on then to relate the mathematical model for sheries, due to Beverton and Holt in the 1940s, to the chaos revolution that followed. Finally, a potential role of education in commons management is proposed, in which participative simulation using NetLogo might be an integral part.

The Mathematics of Chaos and the Urban Revolution

... Third Vienna Architecture Congress, November 3,1995: Conventional Thoughts on the Chaos of Eu... more

Webometry: chronotopography of the World Wide Web

... RH Abraham, MS#89, Webometry #3, Preprint 1. Introduction. ... today permit a full exploratio... more

An Old Math Program

Galileo's Leap into the Future

... Dedicated to Courtney Sale Ross and Anders Holst Abstract. Certainly one of the larger bifurc... more ... Dedicated to Courtney Sale Ross and Anders Holst 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 Gali-leo&amp;#x27;s early works, beginning about ...

Chaos and the Monarch Butterfly

The migration of the monarch butterfly is considered from the perspective of chaos theory, and co... more

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The emergence of geometric thinking

Complex Dynamical Systems Theory: Historical Origins, Contemporary Applications

The New Evolutionary Paradigm, 2019

Complex dynamical systems theory is an evolution of nonlinear dynamics, developed for modeling an... more Complex dynamical systems theory is an evolution of nonlinear dynamics, developed for modeling and simulation of biological systems. Here, we speculate on the potential of this strategy for the emerging theory of social systems, for general evolution theory, and the implications for the future of our own planetary society.

Complex Dynamical Systems

Complex dynamical systems theory and system dynamics diverged at some point in the recent past, a... more

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