Ralph Abraham

Ralph H. Abraham (b. July 4 1936, Burlington, Vermont) 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 Berkeley, Columbia, and Princeton. He has also held visiting positions in Amsterdam, Paris, Warwick, Barcelona, Basel, and Florence.

He founded the Visual Math Institute [ [http://www.vismath.org Visual Math Institute website] ] 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 research frontier and the development of dynamical systems theory in 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. [ [http://www.isss.org/conferences/sonoma2006/2006_ISSS_50thAnnualMeeting_Sonoma_Program-Body-Acrobat6-150dpi.pdf Complexity, Democracy and Sustainability] The 50th Anniversary Meeting of The International Society for the Systems Sciences. Sonoma State University, 2006. Retrieved 7 June 2008.]

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.

Publications

* 1978. "Foundations of Mechanics", 2nd edn. With J.E. Marsden
* 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 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". Wwith 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 roulette prediction.

References

External links

* [http://www.ralph-abraham.org/ Personal website] Ralph Abraham.
* [http://www.levity.com/mavericks/abr-int.htm An interview] with Ralph Abraham, 1989.
* [http://www.visual-chaos.org/jpx/ Chaos in Discrete Dynamical Systems]
* [http://www.blogs.targetx.com/wildriverreview/penworldvoices/2007/08/scenes_from_a_symposium_2.html Notes from the Lindisfarne Symposium]