Ralph Abraham
Encyclopedia
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He has been a member of the mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
department at the University of California, Santa Cruz
University of California, Santa Cruz
The University of California, Santa Cruz, also known as UC Santa Cruz or UCSC, is a public, collegiate university; one of ten campuses in the University of California...
since 1968.
Life and work
Ralph Abraham earned his Ph.D.Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
from the University of Michigan
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...
in 1960, and held positions at UC Santa Cruz, Berkeley
University of California, Berkeley
The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...
, Columbia
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
, and Princeton
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
. He has also held visiting positions in Amsterdam
Amsterdam
Amsterdam is the largest city and the capital of the Netherlands. The current position of Amsterdam as capital city of the Kingdom of the Netherlands is governed by the constitution of August 24, 1815 and its successors. Amsterdam has a population of 783,364 within city limits, an urban population...
, Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
, Warwick, Barcelona
Barcelona
Barcelona is the second largest city in Spain after Madrid, and the capital of Catalonia, with a population of 1,621,537 within its administrative limits on a land area of...
, Basel
Basel
Basel or Basle In the national languages of Switzerland the city is also known as Bâle , Basilea and Basilea is Switzerland's third most populous city with about 166,000 inhabitants. Located where the Swiss, French and German borders meet, Basel also has suburbs in France and Germany...
, and Florence
Florence
Florence is the capital city of the Italian region of Tuscany and of the province of Florence. It is the most populous city in Tuscany, with approximately 370,000 inhabitants, expanding to over 1.5 million in the metropolitan area....
.
He founded the Visual Math Institute at UC 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
Lindisfarne Association
The Lindisfarne Association is a group of intellectuals of diverse interests organized by cultural historian William Irwin Thompson for the "study and realization of a new planetary culture"...
.
Abraham has been involved in the research frontier and the development of dynamical systems theory
Dynamical systems theory
Dynamical systems theory is an area of applied 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. When difference...
in the 1960s and 1970s. He has been a consultant on chaos theory
Chaos theory
Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...
and its applications in numerous fields, such as medical physiology, ecology, mathematical economics, psychotherapy, etc.
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
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
are combined into one presentation.
Abraham developed an interest in "Hip" activities in Santa Cruz in the 1960s and set up a web site gathering information on the topic (http://www.ralph-abraham.org/1960s/). He is featured in the documentary DMT: the Spirit Molecule, discussing his experiments with psilocybin
Psilocybin
Psilocybin is a naturally occurring psychedelic prodrug, with mind-altering effects similar to those of LSD and mescaline, after it is converted to psilocin. The effects can include altered thinking processes, perceptual distortions, an altered sense of time, and spiritual experiences, as well as...
, LSD
LSD
Lysergic acid diethylamide, abbreviated LSD or LSD-25, also known as lysergide and colloquially as acid, is a semisynthetic psychedelic drug of the ergoline family, well known for its psychological effects which can include altered thinking processes, closed and open eye visuals, synaesthesia, an...
and DMT
DMT
DMT may refer to:In chemical substances:* Dimethyltryptamine, a psychedelic tryptamine* Dimethyl terephthalate, a polyester precursor* Desoxymethyltestosterone, a designer anabolic steroid...
.
Publications
- 1978. Foundations of Mechanics, 2nd edn. With J.E. MarsdenJerrold E. MarsdenJerrold Eldon Marsden , was an applied 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.-Career:Marsden earned his B.Sc...
- 1982. Manifolds, Tensor Analysis, and Applications, 2nd edn. With J.E. Marsden and T. Ratiu.
- 1992. Dynamics, the Geometry of Behavior, 2nd edn. With C.D. Shaw.
- 1992. Trialogues on the Edge of the West. With Terence McKennaTerence McKennaTerence Kemp McKenna was an Irish-American philosopher, psychonaut, researcher, teacher, lecturer and writer on many subjects, such as human consciousness, language, psychedelic drugs, the evolution of civilizations, the origin and end of the universe, alchemy, and extraterrestrial beings.-Early...
and Rupert SheldrakeRupert SheldrakeRupert Sheldrake is an English scientist. He is known for having proposed an unorthodox account of morphogenesis and for his research into parapsychology. His books and papers stem from his theory of morphic resonance, and cover topics such as animal and plant development and behaviour, memory,...
), - 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.
- 1997. The Evolutionary Mind. With Terence McKenna and Rupert Sheldrake.
- 2000. The Chaos Avant-garde. With Yoshisuke Ueda.
Further reading:
- Thomas A. Bass. The Eudaemonic Pie: describes some early experimenting with rouletteRouletteRoulette is a casino game named after a French diminutive for little wheel. In the game, players may choose to place bets on either a single number or a range of numbers, the colors red or black, or whether the number is odd or even....
prediction.
External links
- Personal website Ralph Abraham.
- Chaos in Discrete Dynamical Systems
- Notes from the Lindisfarne Symposium
- Cognition Factor - Abraham expresses his personal ideas and philosophy in this smart movie