Ralph Abraham | |
---|---|

Born | Ralph Herman Abraham July 4, 1936 |

Nationality | American |

Alma mater | University of Michigan |

Scientific career | |

Fields | Mathematics |

Institutions | University of California, Santa Cruz |

Thesis | Discontinuities in General Relativity (1960) |

Doctoral advisor | Nathan Coburn |

**Ralph Herman Abraham** (born July 4, 1936) is an American mathematician. He has been a member of the faculty of the University of California, Santa Cruz (where he is currently professor emeritus of mathematics) since 1968.

Abraham earned his B.S.E. (1956), M.S. (1958) and Ph.D. (1960) from the University of Michigan. Prior to joining Santa Cruz, he held positions at the University of California, Berkeley (research lecturer in mathematics; 1960-1962), Columbia University (postdoctoral fellow and assistant professor of mathematics; 1962-1964) and Princeton University (assistant professor of mathematics; 1964-1968). He has also held visiting positions in Amsterdam, Paris, Warwick, Barcelona, Basel, and Florence.

He founded the Visual Math Institute^{ [1] } at Santa Cruz in 1975; at that time, it was called the "Visual Mathematics Project". He is editor of *World Futures* and for the *International Journal of Bifurcations and Chaos*. Abraham is a member of cultural historian William Irwin Thompson's Lindisfarne Association.

Abraham has been involved in the development of dynamical systems theory since the 1960s and 1970s. He has been a consultant on chaos theory and its applications in numerous fields, such as medical physiology, ecology, mathematical economics, psychotherapy, etc.^{ [2] }

Another interest of Abraham's concerns alternative ways of expressing mathematics, for example visually or aurally. He has staged performances in which mathematics, visual arts and music are combined into one presentation.

Abraham developed an interest in "Hip" activities in Santa Cruz in the 1960s and has a website gathering information on the topic.^{ [3] } He credits his use of the psychedelic drug DMT for "swerv[ing his] career toward a search for the connections between mathematics and the experience of the Logos".^{ [4] }

- Publications

- 1978.
*Foundations of Mechanics*, 2nd edn. With Jerrold E. Marsden;^{ [5] }1st edition 1967. - 1982.
*Manifolds, Tensor Analysis, and Applications*, 2nd edn. With Jerrold E. Marsden and Tudor Ratiu. - 1992.
*Dynamics, the Geometry of Behavior*, 2nd edn. With C. D. Shaw. - 1992.
*Trialogues on the Edge of the West*. With Terence McKenna and Rupert Sheldrake), - 1992.
*Chaos, Gaia, Eros*. - 1995.
*The Web Empowerment Book*. With Frank Jas and Will Russell. - 1995.
*Chaos in Discrete Dynamical Systems*. With Laura Gardini and Christian Mira.^{ [6] } - 1997.
*The Evolutionary Mind*. With Terence McKenna and Rupert Sheldrake. - 2000.
*The Chaos Avant-garde*. With Yoshisuke Ueda.

- Film

- 1989.
*The Strange New Science of Chaos*, as himself - 2009.
*Cognition Factor 2009*^{[ permanent dead link ]}, as himself - 2010.
*DMT: The Spirit Molecule*, as himself^{ [7] }

**Ayahuasca** is a South American psychoactive brew used as a traditional spiritual medicine in ceremonies among the indigenous peoples of the Amazon basin. It is an entheogenic brew commonly made out of the *Banisteriopsis caapi* vine, and the *Psychotria viridis* shrub or a substitute, and possibly other ingredients; although, a chemically similar preparation, sometimes called "pharmahuasca", can be prepared using *N*,*N*-Dimethyltryptamine (DMT) and a pharmaceutical monoamine oxidase inhibitor (MAOI) such as isocarboxazid. *B. caapi* contains several alkaloids that act as MAOIs, which are required for DMT to be orally active. The other required ingredient is a plant that contains the primary psychoactive, DMT. This is usually the shrub *P. viridis*, but *Diplopterys cabrerana* may be used as a substitute. Other plant ingredients often or occasionally used in the production of ayahuasca include *Justicia pectoralis*, one of the *Brugmansia* or *Datura* species, and *mapacho*.

** N,N-Dimethyltryptamine** is a chemical substance that occurs in many plants and animals and which is both a derivative and a structural analog of tryptamine. It is used as a recreational psychedelic drug and prepared by various cultures for ritual purposes as an entheogen.

**Alfred Rupert Sheldrake** is an English author, and researcher in the field of parapsychology, who proposed the concept of morphic resonance, a conjecture which lacks mainstream acceptance and has been characterised as pseudoscience. He worked as a biochemist at Cambridge University from 1967 to 1973 and as principal plant physiologist at the International Crops Research Institute for the Semi-Arid Tropics in India until 1978.

**Mathematical physics** refers to the development of mathematical methods for application to problems in physics. The *Journal of Mathematical Physics* defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories".

**Terence Kemp McKenna** was an American ethnobotanist and mystic who advocated for the responsible use of naturally occurring psychedelic plants. He spoke and wrote about a variety of subjects, including psychedelic drugs, plant-based entheogens, shamanism, metaphysics, alchemy, language, philosophy, culture, technology, environmentalism, and the theoretical origins of human consciousness. He was called the "Timothy Leary of the '90s", "one of the leading authorities on the ontological foundations of shamanism", and the "intellectual voice of rave culture".

**Dynamical systems theory** is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called *continuous dynamical systems*. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle. When difference equations are employed, the theory is called *discrete dynamical systems*. When the time variable runs over a set that is discrete over some intervals and continuous over other intervals or is any arbitrary time-set such as a Cantor set, one gets dynamic equations on time scales. Some situations may also be modeled by mixed operators, such as differential-difference equations.

**Dennis Jon McKenna** is an American ethnopharmacologist, research pharmacognosist, lecturer and author. He is the brother of well-known psychedelics proponent Terence McKenna and is a founding board member and the director of ethnopharmacology at the Heffter Research Institute, a non-profit organization concerned with the investigation of the potential therapeutic uses of psychedelic medicines.

**Rick Strassman** is an American clinical associate professor of psychiatry at the University of New Mexico School of Medicine. He has held a fellowship in clinical psychopharmacology research at the University of California San Diego and was Professor of Psychiatry for eleven years at the University of New Mexico. After 20 years of intermission, Strassman was the first person in the United States to undertake human research with psychedelic, hallucinogenic, or entheogenic substances with his research on *N,N*-dimethyltryptamine, also known as DMT. He is also the author of *DMT: The Spirit Molecule*, which summarizes his academic research into DMT and other experimental studies of it, and includes his own reflections and conclusions based on this research.

**Jerrold Eldon Marsden** was a Canadian mathematician. He was the Carl F. Braun Professor of Engineering and Control & Dynamical Systems at the California Institute of Technology. Marsden is listed as an ISI highly cited researcher.

**Alan David Weinstein** is a professor of mathematics at the University of California, Berkeley who works in symplectic geometry, Poisson geometry, and mathematical physics.

**Jerrold Jacob Katz** was an American philosopher and linguist.

**Robert Stetson Shaw** is an American physicist who was part of Eudaemonic Enterprises in Santa Cruz in the late 1970s and early 1980s. In 1988 he was awarded a MacArthur Fellowship for his work in chaos theory.

**David Jay Brown** is an American writer, interviewer and consciousness researcher. Brown has studied parapsychology, and the effects of psychoactive drugs. With parapsychologist Rupert Sheldrake, he studied pets and people who apparently anticipate events. Brown has served as a guest editor for the Multidisciplinary Association for Psychedelic Studies (MAPS), and he has published many interviews of prominent thinkers.

**Alejandro** "**Alex**" **Kacelnik**, FRS is an Argentine-British zoologist, professor of behavioural ecology at Oxford University and E.P. Abraham Fellow of Pembroke College, Oxford. Kacelnik heads the Behavioural Ecology Research Group at Oxford. The author of more than 200 peer reviewed publications, his research focuses on the evolution of behaviour and mathematical modelling. His work uses an interdisciplinary approach, combining data and methods from zoology, psychology and economic theory. In 2011 Kacelnik was honoured by the Comparative Cognition Society for his contributions to the field of animal cognition. He has also received the Cogito Prize for interdisciplinary research linking the natural and social sciences, shared with Professor Ernst Fehr of the University of Zurich, the de Robertis Medal of the Argentinian Society of Neurosciences, and the Raíces ("Roots") Prize for contributions to international collaborations between Argentinian and other scientists.

**Geometric mechanics** is a branch of mathematics applying particular geometric methods to many areas of mechanics, from mechanics of particles and rigid bodies to fluid mechanics to control theory.

**Gerald Lee Alexanderson** (1933–2020) was an American mathematician. He was the Michael & Elizabeth Valeriote Professor of Science at Santa Clara University, and in 1997–1998 was president of the Mathematical Association of America. He was also president of The Fibonacci Association from 1980 to 1984.

**Tudor Stefan Rațiu** is a Romanian-American mathematician who has made contributions to geometric mechanics and dynamical systems theory.

**David Gregory Ebin** is an American mathematician, specializing in differential geometry.

**Anthony Joseph Tromba** is an American mathematician, specializing in partial differential equations, differential geometry, and the calculus of variations.

- ↑
*Visual Math Institute website*, Vismath.org, retrieved 2012-12-25 - ↑ Complexity, Democracy and Sustainability The 50th Anniversary Meeting of The International Society for the Systems Sciences. Sonoma State University, 2006. Retrieved 7 June 2008.
- ↑ "S Cruz 1960s".
*www.ralph-abraham.org*. - ↑ Sheldrake, Rupert; McKenna, Terence; Abraham, Ralph (2013-08-20).
*The Evolutionary Mind: Conversations on Science, Imagination & Spirit*. Monkfish Book Publishing. pp. 63–. ISBN 9781939681102 . Retrieved 12 April 2014. - ↑ Sternberg, Shlomo (1980). "Review:
*Foundations of mechanics*, 2nd edition, revised and enlarged, by Ralph Abraham and Jerrold E. Marsden" (PDF).*Bulletin of the American Mathematical Society*. New Series.**2**(2): 378–387. doi: 10.1090/S0273-0979-1980-14771-0 . - ↑ companion CD-ROM by Ronald Joe Record and Ralph Abraham
- ↑ "Full cast and crew",
*DMT: The Spirit Molecule*, IMDb, 2010

- Personal website Ralph Abraham.
- Ralph Abraham at the Mathematics Genealogy Project
- Cognition Factor – 2009 film participant.

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Images, videos and audio are available under their respective licenses.