Ralph H. Abraham (born July 4, 1936) is an American mathematician. He has been a member of the mathematics department at the University of California, Santa Cruz since 1968.
Life and work
Ralph Abraham earned his Ph.D. from the University of Michigan in 1960, and held positions at UC Santa Cruz, Berkeley, Columbia, and Princeton. He has also held visiting positions in Amsterdam, Paris, Warwick, Barcelona, Basel, and Florence.
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.
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.
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. 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".
- 1978. Foundations of Mechanics, 2nd edn. With Jerrold E. Marsden; 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.
- 1997. The Evolutionary Mind. With Terence McKenna and Rupert Sheldrake.
- 2000. The Chaos Avant-garde. With Yoshisuke Ueda.
- 1989. The Strange New Science of Chaos, as himself
- 2009. Cognition Factor 2009, as himself
- 2010. DMT: the Spirit Molecule, as himself
- ^ Visual Math Institute website, Vismath.org, retrieved
- ^ 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 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 (N.S.). 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