A polymath (, '''', "having learned much") is a person whose expertise spans a significant number of different subject areas. In less formal terms, a polymath (or polymathic person) may simply be someone who is very knowledgeable. Most ancient scientists were polymaths by today's standards.

The common term ''Renaissance man'' is used to describe a person who is well educated or who excels in a wide variety of subjects or fields. The concept emerged from the numerous great thinkers of that era which excelled in multiple fields of the arts in science, including Leonardo da Vinci, Michelangelo, Copernicus and Francis Bacon; the emergence of these thinkers were likewise attributed to the then rising notion in Renaissance Italy expressed by one of its most accomplished representatives, Leon Battista Alberti (1404–1472): that "a man can do all things if he will." It embodied the basic tenets of Renaissance humanism, which considered humans empowered, limitless in their capacities for development, and led to the notion that people should embrace all knowledge and develop their capacities as fully as possible. Thus the gifted people of the Renaissance sought to develop skills in all areas of knowledge, in physical development, in social accomplishments, and in the arts. The term has since expanded from original usage and has been applied to other great thinkers before and after the Renaissance such as Aristotle, Johann Goethe, and Isaac Newton.

Related terms

A different term for the secondary meaning of polymath is ''Renaissance man'' or woman. (a term first recorded in written English in the early 20th century). Other similar terms also in use are ''Homo Universalis'' (Latin) and ''Uomo Universale'' (Italian), which translate to "universal person" or "universal man". These expressions derived from the ideal in Renaissance Humanism that it was possible to acquire a universal learning in order to develop one's potential, (covering both the arts and the sciences and without necessarily restricting this learning to the academic fields). When someone is called a Renaissance man or woman today, it is meant that they do not have only broad interests or a superficial knowledge of several fields, but rather that their knowledge is profound and often that they also have proficiency or accomplishments in at least some of these fields and in some cases even at a level comparable to the proficiency or the accomplishments of an expert. The related term ''Generalist'' is used to contrast this general approach to knowledge to that of the specialist. The expression Renaissance person today commonly implies only intellectual or scholastic proficiency and knowledge and not necessarily the more universal sense of "learning" implied by Renaissance humanism. Note, however, that some dictionaries use the term "Renaissance man" as roughly synonymous with polymath in the first meaning, to describe someone versatile with many interests or talents, while others recognize a meaning restricted to the Renaissance era and more closely related to Renaissance ideals.

A more colloquial term for such a person would be a jack of all trades, though this often refers to skill and not necessarily knowledge. The term "jack of all trades" also occasionally has negative connotation (see, for instance, jack of all trades, master of none); such a person may be labeled as a dilettante, while "polymath" typically has a positive connotation.

The term ''Universal Genius'' is also used, taking Leonardo da Vinci as a prime example again. The term seems to be used especially when a Renaissance man has made historical or lasting contributions in at least one of the fields in which he was actively involved, and when he had a universality of approach. Despite the existence of this term, a polymath may not necessarily be classed as a genius; and certainly a genius may not display the breadth of knowledge to qualify as a polymath. Isaac Newton, Albert Einstein, and Marie Curie are examples of people widely viewed as geniuses, but who are not generally considered to be polymaths.

Renaissance ideal

Many notable polymaths lived during the Renaissance period, a cultural movement that spanned roughly the 14th through the 17th century, beginning in Italy in the late Middle Ages and later spreading to the rest of Europe. They had a rounded approach to education that was typical of the ideals of the humanists of the time. A gentleman or courtier of that era was expected to speak several languages, play a musical instrument, write poetry, and so on, thus fulfilling the Renaissance ideal. The idea of a universal education was pivotal to achieving polymath ability, hence the word university was used to describe a seat of learning. At this time universities did not specialize in specific areas, but rather trained their students in a broad array of science, philosophy and theology. This universal education, as such, gave them a grounding from which they could continue into apprenticeship to a Master of a specific field. It is important to note that a university education was highly regarded. A person was not considered to need this broad knowledge to apprentice as a carpenter, but to apprentice in the sciences or philosophy it contributed hugely to their being able to comprehend the universe as it was understood at the time. During the Renaissance, Baldassare Castiglione, in his ''The Book of the Courtier'', wrote a guide on becoming a polymath.

Castiglione's guide stressed the kind of attitude that should accompany the many talents of a polymath, an attitude he called "sprezzatura". A courtier should have a detached, cool, nonchalant attitude, and speak well, sing, recite poetry, have proper bearing, be athletic, know the humanities and classics, paint and draw and possess many other skills, always without showy or boastful behavior, in short, with "sprezzatura". The many talents of the polymath should appear to others to be performed without effort, in an unstrained way, almost without thought. In some ways, the gentlemanly requirements of Castiglione recall the Chinese sage, Confucius, who far earlier depicted the courtly behavior, piety and obligations of service required of a gentleman. The easy facility in difficult tasks also resembles the effortlessness inculcated by Zen, such as in archery where no conscious attention, but pure spontaneity, produces better and more noble skill. For Castiglione, the attitude of apparent effortlessness should accompany great skill in many separate fields. In word or deed the courtier should "avoid affectation ... (and) ... practice ... a certain sprezzatura ... conceal all art and make whatever is done or said appear to be without effort and almost without any thought about it".

This Renaissance ideal differed slightly from the "polymath" in that it involved more than just intellectual advancement. Historically (roughly 1450–1600) it represented a person who endeavored to "develop his capacities as fully as possible" (''Britannica'', "Renaissance Man") both mentally and physically, and, as Castiglione suggests, without "affectation". For example, being an accomplished athlete was considered integral and not separate from education and learning of the highest order. Leon Battista Alberti, who was a Roman Catholic priest, architect, painter, poet, scientist, mathematician, inventor, and sculptor, was in addition a skilled horseman and archer.

Renaissance men

The above list provides examples of notable polymaths (in the secondary meaning only, that is, Renaissance men). Caution is necessary when interpreting the word polymath (in the second meaning or any of its synonyms) in a source, since there's always ambiguity of what the word denotes. Also, when a list of subjects in relation to the polymath is given, such lists often seem to imply that the notable polymath was reputable in all fields, but the most common case is that the polymath made his reputation in one or two main fields where he had widely recognized achievements, and that he was merely proficient or actively involved in other fields, but, once again, not necessarily with achievements comparable to those of renowned experts of his time in these fields. The list does not attempt to be comprehensive or authoritative in any way. The list also includes the ''Hakeem'' of the Islamic Golden Age (also known as the "Islamic Renaissance"), and other polymaths from other parts of the world.

Polymath and polyhistor compared

Many dictionaries of word origins list these words as synonyms or, as words with very similar meanings. Thomas Moore took the words as corresponding to similarly erudite "polys" in one of his poems titled The Devil Among Scholars:

''Off I fly, careering far'' ''In chase of Pollys, prettier far'' ''Than any of their namesakes are'' ''—The Polymaths and Polyhistors,'' ''Polyglots and all their sisters.''

According to the ''Oxford English Dictionary'', the words mean practically the same; "the classical Latin word ''polyhistor'' was used exclusively, and the Greek word frequently, of Alexander Polyhistor", but ''polymathist'' appeared later, and then ''polymath''. Thus today, regardless of any differentiation they may have had when originally coined, they are often taken to mean the same thing.

The root terms ''histor'' and ''math'' have similar meanings in their etymological antecedents (to learn, learned, knowledge), though with some initial and ancillarily added differing qualities. Innate in ''historíā'' (Greek and Latin) is that the learning takes place via inquiry and narrative. ''Hístōr'' also implies that the polyhistor displays erudition and wisdom. From Proto-Indo-European it shares a root with the word "''wit''". Inquiry and narrative are specific sets of pedagogical and research heuristics.

Polyhistoric is the corresponding adjective. The word polyhistory (meaning varied learning), when used, is often derogatory.

Notable polymaths

A number of people have been described as "polymaths" by reliable sources, fulfilling the ''primary definition'' of the term, although there may not be expert consensus that each is a ''prime example'' in the ''secondary'' meaning, as "Renaissance men" and "universal geniuses" (see the list of renaissance men above for prime examples of "renaissance men" or "universal geniuses").

Other uses of "polymath"

In Britain, phrases such as "polymath sportsman", "sporting polymath", or simply "polymath" are occasionally used in a restricted sense to refer to athletes that have performed at a high level in several very different sports. (One whose accomplishments are limited to athletics would not be considered to be a "polymath" in the usual sense of the word). Examples would include: Howard Baker – "Similar claims to the title of sporting polymath could be made for Howard Baker" (who won high jump titles, and played cricket, football, and water polo): Maxwell Woosnam – "Sporting polymath is a full-time post..."

The term can also be used loosely in other ways, for example, Rolf Harris (whose fame has come as a popular artist, television presenter and singer) has also been described by the ''Daily Mail'' as "the People's Polymath".

See also

Philomath

Polyglot (disambiguation)

Polymath (novel)

Competent man

Opsimath

References and notes

Further reading

Frost, Martin, "Polymath: A Renaissance Man"

Mirchandani, Vinnie, ''The New Polymath: Profiles in Compound-Technology Innovations", John Wiley & Sons, 2010

Category:Giftedness Category:Greek loanwords Category:The Enlightenment Category:Renaissance Category:Thought

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name	Douglas R. Hofstadter
birth date	February 15, 1945
birth place	New York, New York
occupation	Professor of cognitive science
nationality	United States
alma mater	Stanford University (B.S.), University of Oregon (Ph.D)
period	1979–present
subject	Cognitive science, philosophy of mind, translation, analogy-making }}

Douglas Richard Hofstadter (born February 15, 1945) is an American academic whose research focuses on consciousness, analogy-making, artistic creation, literary translation, and discovery in mathematics and physics. He is best known for his book ''Gödel, Escher, Bach: an Eternal Golden Braid'', first published in 1979, for which he was awarded the 1980 Pulitzer Prize for general non-fiction.

Early life and education

Hofstadter was born in New York, New York, the son of Nobel Prize-winning physicist Robert Hofstadter. He grew up on the campus of Stanford University, where his father was a professor, and he attended the International School of Geneva in 1958–1959. He graduated with Distinction in Mathematics from Stanford University in 1965. He continued his education and received his Ph.D. in Physics from the University of Oregon in 1975.

Academic career

Hofstadter is College of Arts and Sciences Distinguished Professor of Cognitive Science at Indiana University in Bloomington, where he directs the Center for Research on Concepts and Cognition which consists of himself and his graduate students, forming the "Fluid Analogies Research Group" (FARG). He was initially appointed to the Indiana University's Computer Science Department faculty in 1977, and at that time he launched his research program in computer modeling of mental processes (which at that time he called "artificial intelligence research", a label that he has since dropped in favor of "cognitive science research"). In 1984, he moved to the University of Michigan in Ann Arbor, where he was hired as a professor of psychology and was also appointed to the Walgreen Chair for the Study of Human Understanding. In 1988 he returned to Bloomington as "College of Arts and Sciences Professor" in both Cognitive Science and Computer Science, and also was appointed Adjunct Professor of History and Philosophy of Science, Philosophy, Comparative Literature, and Psychology, but he states that his involvement with most of these departments is nominal. In April 2009 Hofstadter was elected a Fellow of the American Academy of Arts and Sciences and a Member of the American Philosophical Society.

Hofstadter's many interests include music, visual art, the mind, creativity, consciousness, self-reference, translation and mathematics. Several recursive number-theoretical sequences and concepts in triangle geometry have been named after him.

At the University of Michigan and Indiana University, he co-authored, with Melanie Mitchell, a computational model of "high-level perception" – Copycat – and several other models of analogy-making and cognition, including the Tabletop project, co-developed with Robert French. The Copycat project was subsequently extended under the name "Metacat" by Hofstadter's doctoral student James Marshall. The Letter Spirit project, implemented by Gary McGraw and John Rehling, aims to model the act of artistic creativity by designing stylistically uniform "gridfonts" (typefaces limited to a grid). Other more recent models are Phaeaco (implemented by Harry Foundalis) and SeqSee (Abhijit Mahabal), which model high-level perception and analogy-making in the microdomains of Bongard problems and number sequences, respectively, as well as George (Francisco Lara-Dammer), which models the processes of perception and discovery in triangle geometry.

Both inside and outside his professional work, Hofstadter is driven by a pursuit of beauty. He seeks beautiful mathematical patterns, beautiful explanations, beautiful typefaces, beautiful sonic patterns in poetry, and so forth. Hofstadter has said of himself, "I'm someone who has one foot in the world of humanities and arts, and the other foot in the world of science." He has had several exhibitions of his artworks in various university art galleries. These shows have featured large collections of his gridfonts, his ambigrams (pieces of calligraphy created with two readings, either of which is usually obtained from the other by rotating or reflecting the ambigram, but sometimes simply by "oscillation", like the Necker Cube or the rabbit/duck figure of Joseph Jastrow), and his "Whirly Art" (music-inspired visual patterns realized using shapes based on various alphabets from India). (The term "ambigram" was invented by Hofstadter in 1984 and has since been taken up by many ambigrammists all over the world.)

Hofstadter collects and studies cognitive errors (largely, but not solely, speech errors), "bon mots" (spontaneous humorous quips), and analogies of all sorts, and his long-time observation of these diverse products of cognition, and his theories about the mechanisms that underlie them, have exerted a powerful influence on the architectures of the computational models developed by himself and FARG members.

All FARG computational models share certain key principles, among which are: that human thinking is carried out by thousands of independent small actions in parallel, biased by the concepts that are currently activated; that activation spreads from activated concepts to less activated "neighbor concepts"; that there is a "mental temperature" that regulates the degree of randomness in the parallel activity; that promising avenues tend to be explored more rapidly than unpromising ones. FARG models also have an overarching philosophy that all cognition is built from the making of analogies. The computational architectures that share these precepts are called "active symbols" architectures.

Hofstadter's thesis about consciousness, first expressed in ''Gödel, Escher, Bach (GEB)'' but also present in several of his later books, is that it is an emergent consequence of seething lower-level activity in the brain. In ''GEB'' he draws an analogy between the social organization of a colony of ants and the mind seen as a coherent "colony" of neurons. In particular, Hofstadter claims that our sense of having (or being) an "I" comes from the abstract pattern he terms a "strange loop", which is an abstract cousin of such concrete phenomena as audio and video feedback, and which Hofstadter has defined as "a level-crossing feedback loop". The prototypical example of this abstract notion is the self-referential structure at the core of Gödel's incompleteness theorems. Hofstadter's 2007 book ''I Am a Strange Loop'' carries his vision of consciousness considerably further, including the idea that each human "I" is distributed over numerous brains, rather than being limited to precisely one brain.

Hofstadter's writing is characterized by an intense interaction between form and content, as is exemplified by the 20 dialogues in ''GEB'', many of which simultaneously talk about and imitate strict musical forms used by Bach, such as canons and fugues. Most of Hofstadter's books are characterized by some kind of structural alternation: in ''GEB'' between dialogues and chapters, in ''The Mind's I'' between selections and reflections, in ''Metamagical Themas'' between Chapters and Postscripts, and so forth. Both in his writing and in his teaching, Hofstadter stresses the concrete, constantly using examples and analogies, and avoids the abstract. Typical of the courses he teaches is his seminar "Group Theory and Galois Theory Visualized", in which abstract mathematical ideas are rendered as concretely as possible. He puts great effort into making ideas clear and visual, and asserts that when he teaches, if his students do not understand something, it is never their fault but always his own.

Hofstadter is passionate about languages. He has studied many of them, and speaks them to varying degrees. In addition to English, his mother tongue, he speaks French and Italian fluently (the language spoken at home with his children is Italian). At various times in his life, he has studied (in descending order of level of fluency reached) German, Russian, Spanish, Swedish, Mandarin, Dutch, Polish, and Hindi. His love of sounds pushes him to strive to minimize, and ideally get rid of, any foreign accent.

''Le Ton beau de Marot: In Praise of the Music of Language'' is a long book devoted to language and translation, especially poetry translation, and one of its leitmotifs is a set of some 88 translations of "Ma Mignonne", a highly constrained poem by 16th-century French poet Clément Marot. In this book, Hofstadter jokingly describes himself as "pilingual" (meaning that the sum total of the varying degrees of mastery of all the languages that he's studied comes to 3.14159...), as well as an "oligoglot" (someone who speaks "a few" languages).

In 1999, the bicentennial year of Russian poet and writer Alexander Pushkin, Hofstadter published a verse translation of Pushkin's classic novel-in-verse ''Eugene Onegin''. It is highly constrained and filled with many types of sonic pattern. Aside from ''Eugene Onegin'', Hofstadter has translated many other poems (always respecting their formal constraints), and two other novels (in prose): ''La Chamade'' (''That Mad Ache'') by French writer Françoise Sagan, and ''La Scoperta dell'Alba'' (''The Discovery of Dawn'') by Walter Veltroni, the then head of the Partito Democratico in Italy. ''The Discovery of Dawn'' was published in 2007, and ''That Mad Ache'' was published in 2009, bound together with Hofstadter's essay ''Translator, Trader: An Essay on the Pleasantly Pervasive Paradoxes of Translation.''

Public image

Hofstadter has said that he feels "uncomfortable with the nerd culture that centers on computers". He admits that "a large fraction [of his audience] seems to be those who are fascinated by technology", but when it was suggested that his work "has inspired many students to begin careers in computing and artificial intelligence" he replied that he was pleased about that, but that he himself has "no interest in computers." In that interview he also mentioned a course he has twice given at Indiana University, in which he took a "skeptical look at a number of highly-touted AI projects and overall approaches." For example, upon the defeat of Kasparov by Deep Blue, he commented that "It was a watershed event, but it doesn't have to do with computers becoming intelligent".

Provoked by predictions of a technological singularity (the hypothetical moment at which artificial intelligence will surpass human intelligence), Hofstadter has both organized and participated in several public discussions of the topic. At Indiana University in 1999 he organized such a symposium, and in April 2000, he organized a larger symposium entitled "Spiritual Robots" at Stanford University, in which he moderated a panel consisting of Ray Kurzweil, Hans Moravec, Kevin Kelly, Ralph Merkle, Bill Joy, Frank Drake, John Holland, John Koza. Hofstadter was also an invited panelist at the first Singularity Summit, held at Stanford in May 2006. Hofstadter expressed doubt about the likelihood of the singularity coming to pass in the foreseeable future.

In April 2009, when told about his Wikipedia article, he commented, "[It] is filled with inaccuracies, and it kind of depresses me." When asked why he didn't correct it, he replied, "The next day someone will fix it back." (In Aug. 2011 Hofstadter said he is happy with the article and the only inaccurate part of his Wikipedia entry was the previous sentence because the inaccuracies were subsequently fixed. ) (See http://en.wikipedia.org/wiki/Talk:Douglas_Hofstadter#Citation

In 1988 Dutch director Piet Hoenderdos created a docudrama about Hofstadter and his ideas entitled Victim of the Brain based on ''The Mind's I''. It includes interviews with Hofstadter about his work.

In ''2010: Odyssey Two'', Arthur C. Clarke's first sequel to ''2001: A Space Odyssey'', HAL 9000 is described by Dr. Chandra as being caught in a "Hofstadter-Möbius loop".

Hofstadter's book ''Fluid Concepts & Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought'' was the first book ever sold by Amazon.com.

Columnist

When Martin Gardner retired from writing his "Mathematical Games" column for ''Scientific American'' magazine, Hofstadter succeeded him in 1981–1983 with a column entitled ''Metamagical Themas'' (an anagram of "Mathematical Games"). An idea he introduced in one of these columns was the concept of "Reviews of This Book", a book containing nothing but cross-referenced reviews of itself which has an online implementation. One of Hofstadter's columns in ''Scientific American'' concerned the damaging effects of sexist language, and two chapters of his book ''Metamagical Themas'' are devoted to that topic, one of which is a biting analogy-based satire entitled "A Person Paper on Purity in Language", in which the reader's presumed revulsion at racism and racist language is used as a lever to motivate an analogous revulsion at sexism and sexist language. Another column reported on the discoveries made by University of Michigan professor Robert Axelrod in his computer tournament pitting many iterated Prisoner's Dilemma strategies against each other, and a follow-up column discussed a similar tournament that Hofstadter and his graduate student Marek Lugowski organized. The "Metamagical Themas" columns ranged over many themes, and included, to name just three, one on patterns in Frederic Chopin's piano music (particularly the études), another on the concept of superrationality (choosing to cooperate when the other party/adversary is assumed to be equally intelligent as oneself), and one on the self-modifying game of Nomic, based on the way in which the legal system modifies itself, and developed by philosopher Peter Suber.

Personal life

Hofstadter was married to Carol Ann Brush. They met in Bloomington, and married in Ann Arbor in 1985. They had two children, Danny and Monica. Carol died in 1993 from the sudden onset of a brain tumor – glioblastoma multiforme – when their children were five and two. The Carol Ann Brush Hofstadter Memorial Scholarship for Bologna-bound Indiana University students was established in 1996 in her name. Hofstadter's book ''Le Ton beau de Marot'' is dedicated to their two children and its dedication reads "To M. & D., living sparks of their Mommy's soul".

Hofstadter has composed numerous pieces for piano, and a few for piano and voice. He created an audio CD with the title ''DRH/JJ'', which includes all these compositions performed primarily by pianist Jane Jackson, but with a few performed by Brian Jones, Dafna Barenboim, Gitanjali Mathur and himself.

Hofstadter is related by marriage to the evolutionary theorist Stephen Jay Gould: Hofstadter's paternal aunt was married to Gould's maternal uncle.

The dedication for ''I Am A Strange Loop'' is: "To my sister Laura, who can understand, and to our sister Molly, who cannot." Hofstadter explains in the preface that his younger sister Molly never developed the ability to speak or understand language.

Published works

Books

The books published by Hofstadter are (the ISBNs refer to paperback editions, where available):

''Gödel, Escher, Bach: an Eternal Golden Braid'' (ISBN 0-465-02656-7) (1979)

''Metamagical Themas'' (ISBN 0-465-04566-9) (collection of ''Scientific American'' columns and other essays, all with postscripts)

''Ambigrammi: un microcosmo ideale per lo studio della creatività'' (in Italian only) ISBN 88-7757-006-7

''Fluid Concepts and Creative Analogies'' (ISBN 0-465-02475-0)

''Rhapsody on a Theme by Clement Marot. The Grace A. Tanner Lecture in Human Values, 1995.'' (Published 1996)

''Le Ton beau de Marot: In Praise of the Music of Language'' (ISBN 0-465-08645-4)

''Eugene Onegin: A Novel Versification'' (ISBN 0-465-02094-1)

''I Am a Strange Loop'' (ISBN 0-465-03078-5) (2007)

''The Discovery of Dawn'' (ISBN 9780847831098) (2007) (a translation of a novel by Walter Veltroni)

''That Mad Ache'', co-bound with ''Translator, Trader: An Essay on the Pleasantly Pervasive Paradoxes of Translation'' (ISBN 9780465010981) (2009)

''Surfaces and Essences'', co-authored with Emmanuel Sander (ISBN 0465018475). Expected in November 2011.

Papers

Hofstadter wrote, among many others, the following papers:

"Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields", Rev. B'' 14 (1976) 2239.

*Written while he was at the University of Oregon, this paper soon became well-known because, extending the ideas of Russian (now Israeli) physicist Mark Ya. Azbel', it pointed the way to an understanding of a famous unsolved problem in quantum mechanics, by showing that the allowed energy-level values of an electron in a crystal lattice in a magnetic field form a graph (energy versus magnetic field) that is a self-similar (fractal) shape. This fractal structure is generally known as "Hofstadter's butterfly", which was the first fractal ever found in physics, and it has recently been confirmed in transport measurements in two-dimensional electron systems with a superimposed nano-fabricated lattice.

"A non-deterministic approach to analogy, involving the Ising model of ferromagnetism", in E. Caianiello (ed.), ''The Physics of Cognitive Processes''. Teaneck, NJ: World Scientific, 1987.

"Speechstuff and thoughtstuff: Musings on the resonances created by words and phrases via the subliminal perception of their buried parts", in Sture Allen (ed.), ''Of Thoughts and Words: The Relation between Language and Mind. Proceedings of the Nobel Symposium 92'', London/New Jersey: World Scientific Publ., 1995, 217-267.

"On seeing A's and seeing As.", ''Stanford Humanities Review'' 4,2 (1995) pp. 109–121.

"''Analogy as the Core of Cognition''", in Dedre Gentner, Keith Holyoak, and Boicho Kokinov (eds.) ''The Analogical Mind: Perspectives from Cognitive Science'', Cambridge, MA: The MIT Press/Bradford Book, 2001, pp. 499–538.

"To Err is Human; To Study Error-making is Cognitive Science" (co-authored by David J. Moser), Michigan Quarterly Review, Vol. XXVIII, No. 2, 1989, pp. 185-­215.

Hofstadter wrote over 50 papers that were published through the Center for Research on Concepts and Cognition

Involvement in other books

Hofstadter wrote forewords for or edited the following books:

''Sparse Distributed Memory'' by Pentti Kanerva (Bradford Books/MIT Press, 1988). (ISBN 0262111322)

''The Mind's I: Fantasies and Reflections on Self and Soul'' (co-edited with Daniel Dennett) (ISBN 0-465-03091-2 and ISBN 0-553-01412-9) (ISBN 0-553-34584-2) 1981

''Alan Turing: The Enigma'' by Andrew Hodges. (Preface)

''Gödel's Proof'' (2002 revised edition) by Ernest Nagel and James R. Newman, edited by Hofstadter (ISBN 0-8147-5816-9). In the foreword, Hofstadter explains that the book (originally published in 1958) exerted a profound influence on him when he was young.

''Who invented the computer? The legal battle that changed computing history.'' (2003) by Alice Rowe Burks.

''Alan Turing: Life and Legacy of a Great Thinker'' by Christof Teuscher (Editor)

''Jason Salavon: Brainstem Still Life'' (ISBN 981-05-1662-2) 2004 (Introduction)

''Masters of Deception: Escher, Dali & the Artists of Optical Illusion'' 2004 by Al Seckel. Hofstadter wrote the foreword.

''King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry'' by Siobhan Roberts, Walker and Company, 2006. Hofstadter wrote the foreword.

''Are Quanta Real? A Galilean Dialogue'' by J.M. Jauch (ISBN 0-253-20545-X) 1989 Indiana University Press; Hofstadter wrote the foreword.

Students

Some of Hofstadter's former students include:

David Chalmers - philosopher of mind

Melanie Mitchell - computer scientist and complexity theorist

Robert M. French - cognitive scientist

Scott A. Jones - inventor of voicemail

Harry Foundalis - creator of Phaeaco, an architecture to solve Bongard Problems

See also

Platonia dilemma

Egbert B. Gebstadter

BlooP and FlooP

Hofstadter's law

Superrationality

American philosophy

List of American philosophers

References

External links

Stanford University Presidential Lecture - site dedicated to Hofstadter and his work

Profile at c2.com

Profile at Resonance Publications

NF Reviews - bibliographic page with reviews of several of Hofstadter's books

Radio interview on Philosophy Talk

Category:1945 births Category:20th-century philosophers Category:21st-century philosophers Category:American science writers Category:American vegetarians Category:Cognitive scientists Category:Indiana University faculty Category:Members of the Board of Visitors of Ralston College Category:Guggenheim Fellows Category:Living people Category:Fellows of the American Academy of Arts and Sciences Category:Philosophers of mind Category:Pulitzer Prize for General Non-Fiction winners Category:Stanford University alumni Category:University of Oregon alumni Category:Translators of Alexander Pushkin

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name	Susan Sontag
birth date	January 16, 1933
birth place	New York City, New York
death date	December 28, 2004
death place	New York City
occupation	Novelist, Essayist
nationality	American
genre	Fiction, essays, nonfiction
website	}}

Susan Sontag (; January 16, 1933 – December 28, 2004) was an American author, literary theorist, feminist, public intellectual and political activist; her published works include ''On Photography'' and ''Against Interpretation''.

Life

Sontag, born Susan Rosenblatt, was born in New York City to Jack Rosenblatt and Mildred Jacobsen, both Jewish. Her father managed a fur trading business in China, where he died of tuberculosis when Susan was five years old. Seven years later, her mother married Nathan Sontag. Susan and her sister, Judith, were given their stepfather's surname, although he never adopted them formally. Sontag did not have a religious upbringing. She claimed not to have entered a synagogue until her mid-twenties.

Sontag grew up in Tucson, Arizona, and, later, in Los Angeles, where she graduated from North Hollywood High School at the age of 15. She began her undergraduate studies at Berkeley but transferred to the University of Chicago in admiration of its famed core curriculum. At Chicago, she undertook studies in philosophy, ancient history and literature alongside her other requirements (Leo Strauss, Richard McKeon, Peter von Blanckenhagen and Kenneth Burke were among her lecturers) and graduated with an A.B. She did graduate work in philosophy, literature, and theology at Harvard with Paul Tillich, Jacob Taubes and Morton White et al. After completing her Master of Arts in philosophy and beginning doctoral research into metaphysics, ethics, Greek philosophy and Continental philosophy and theology at Harvard, Sontag was awarded an American Association of University Women's fellowship for the 1957-1958 academic year to St Anne's College, Oxford, where she had classes with Iris Murdoch, J. L. Austin, Alfred Jules Ayer, Stuart Hampshire and others. Oxford did not appeal to her, however, and she transferred after Michaelmas term of 1957 to the University of Paris. It was in Paris that Sontag socialised with expatriate artists and academics including Allan Bloom, Jean Wahl, Alfred Chester, Harriet Sohmers and Maria Irene Fornes. Sontag remarked that her time in Paris was, perhaps, the most important period of her life. It certainly provided the basis of her long intellectual and artistic association with the culture of France.

At 17, while at Chicago, Sontag married Philip Rieff after a ten-day courtship. The philosopher Herbert Marcuse lived with Sontag and Rieff for a year while working on his book ''Eros and Civilization''. Sontag and Rieff were married for eight years throughout which they worked jointly on the study ''Freud: The Mind of the Moralist'' that would be attributed solely to Philip Rieff as a stipulation of the couple's divorce in 1958. The couple had a son, David Rieff, who later became his mother's editor at Farrar, Straus and Giroux, as well as a writer in his own right.

The publication of ''Against Interpretation'' (1966), accompanied by a striking dust-jacket photo by Peter Hujar, helped establish Sontag's reputation as "the Dark Lady of American Letters." Movie stars like Woody Allen, philosophers like Arthur Danto, and politicians like Mayor John Lindsay met her.

Like Jane Fonda, Sontag went to Hanoi, and wrote of the North Vietnamese society with much sympathy and appreciation (see "Trip to Hanoi" in ''Styles of Radical Will''). She maintained a distinction, however, between North Vietnam and Maoist China and the Soviet Union, as well as East-European communism, which she all later criticized as "fascism with a human face."

Sontag died in New York City on 28 December 2004, aged 71, from complications of myelodysplastic syndrome which had evolved into acute myelogenous leukemia. Sontag is buried in Montparnasse Cemetery, in Paris. Her final illness has been chronicled by her son, David Rieff.

Work

Sontag's literary career began and ended with works of fiction. After teaching philosophy and theology at Sarah Lawrence College, City University of New York and Columbia University under Jacob Taubes from 1960 to 1964, Sontag ended her relationship with academia and devoted herself to full-time writing. At age 30, she published an experimental novel called ''The Benefactor'' (1963), following it four years later with ''Death Kit'' (1967). Despite a relatively small output, Sontag thought of herself principally as a novelist and writer of fiction. Her short story "The Way We Live Now" was published to great acclaim on 26 November 1986 in ''The New Yorker''. Written in an experimental narrative style, it remains a significant text on the AIDS epidemic. She achieved late popular success as a best-selling novelist with ''The Volcano Lover'' (1992). At age 67, Sontag published her final novel ''In America'' (2000). The last two novels were set during the past, which Sontag said gave her greater freedom to write in the polyphonic voice.

It was as an essayist, however, that Sontag gained early fame and notoriety. Sontag wrote frequently about the intersection of high and low art and the form/content dichotomy across the arts. Her celebrated and widely-read 1964 essay "Notes on 'Camp'" was epoch-defining, examining an alternative sensibility to that which considers the best art in terms of its seriousness. It gestured towards and expounded the "so bad it's good" concept of popular culture for the first time. During 1977, Sontag wrote the essay ''On Photography''. The essay is an exploration of photographs as a collection of the world, mainly by travelers or tourists, and the way we therefore experience it. She outlines the concept of her theory of taking pictures as you travel:

The method especially appeals to people handicapped by a ruthless work ethic – Germans, Japanese and Americans. Using a camera appeases the anxiety which the work driven feel about not working when they are on vacation and supposed to be having fun. They have something to do that is like a friendly imitation of work: they can take pictures.

Sontag suggested photographic "evidence" be used as a presumption that "something exists, or did exist", regardless of distortion. For her, the art of photography is "as much an interpretation of the world as paintings and drawings are", for cameras are produced rapidly as a "mass art form" and are available to all of those with the means to attain them. Focusing also on the effect of the camera and photograph on the wedding and modern family life, Sontag reflects that these are a "rite of family life" in industrialized areas such as Europe and America.

To Sontag "picture-taking is an event in itself, and one with ever more peremptory rights - to interfere with, to invade, or to ignore whatever is going on". She considers the camera a phallus, comparable to ray guns and cars, which are "fantasy-machines whose use is addictive". For Sontag the camera can be linked to murder and a promotion of nostalgia while evoking "the sense of the unattainable" in the industrialized world. The photograph familiarizes the wealthy with "the oppressed, the exploited, the starving, and the massacred" but removes the shock of these images because they are available widely and have ceased to be novel.

Sontag championed European writers such as Walter Benjamin, Roland Barthes, Antonin Artaud, E. M. Cioran, and W. G. Sebald, along with some Americans such as María Irene Fornés. During several decades she would study attention to novels, film, and photography. In more than one book, Sontag wrote about cultural attitudes toward illness. Her final nonfiction work, ''Regarding the Pain of Others'', re-examined art and photography from a moral consideration. It concerned how the media affects culture's ideas of conflict.

A new visual code

In her Essay ''On Photography'' Sontag says that the evolution of modern technology has changed the viewer in three key ways. She calls this the emergence of a new visual code.

Firstly, Sontag suggests that modern photography, with its convenience and ease, has created an overabundance of visual material. As photographing is now a practice of the masses, due to a drastic decrease of camera size and increase of ease in developing photographs, we are left in a position where “just about everything has been photographed” (Sontag, Susan, (1977), On Photography 3). We now have so many images available to us of: things, places, events and people from all over the world, and of not immediate relevance to our own existence, that our expectations of what we have the right to view, want to view or should view has been drastically affected. Arguably, gone are the days that we felt entitled to view only those things in our immediate presence or that affected our micro world; we now seem to feel entitled to gain access to any existing images. “In teaching us a new visual code, photographs alter and enlarge our notion of what is worth looking at and what we have the right to observe” (3). This is what Sontag calls a change in the “ethics of seeing” (3).

Secondly, Sontag comments on the effect of modern photography on our education, claiming that photographs “now provide most of the knowledge people have about the look of the past and the reach of the present”(4). Without photography only those few people who had been there would know what the Egyptian pyramids or the Parthenon look like, yet most of us have a good idea of the appearance of these places. Photography teaches us about those parts of the world that are beyond our touch in ways that literature can not.

Thirdly, Sontag also talked about the way in which photography desensitizes its audience. Sontag introduced this discussion by telling her own story of the first time she saw images of horrific human experience. At twelve years old, Sontag found images of holocaust camps and was so distressed by them she says “When I looked at those photographs something broke... something went dead, something is still crying” (20). Sontag argues that there was no good to come from her seeing these images as a young girl, before she fully understood what the holocaust was. For Sontag the viewing of these images has left her a degree more numb to any following horrific image she viewed, as she had been desensitized. According to this argument, “Images anesthetize” and the open accessibility to them is a negative result of photography (20).

Sontag examines the relationship between photography and reality. Photographs are depicted as a representation of realism. Sontag claimed that “such images are indeed able to usurp reality because first of all a photograph is not only an image, an interpretation of the real; it is also a trace, something directly stenciled off the real (Sontag, Susan (1982), The Image World 350). It is a resemblance of the real as the photograph becomes an extension of the subject. However, the role of the photograph has changed, as copies destroy the idea of an experience. The image has altered to convey information and become an act of classification. Sontag highlights the notion that photographs are a way of imprisoning reality- making the memory stand still. Ultimately images are surveillance of events that trigger the memory. In modern society, photographs are a form of recycling the real. When a moment is captured it is assigned a new meaning as people interpret the image in their own manner. Sontag claims that images desensitize the reality, as people's perceptions are distorted by the construction of the photograph. However this has not stopped people from consuming images; there is still a demand for more photographs.

Sontag observed some uses of photography, “Photography has become one of the principal devices for experiencing something, for giving an appearance of participation” (Sontag,1977 10), such as memorizing and providing evidence. She also states that “to collect photographs is to collect the world.” (Sontag,1997 3)

Sontag believes that photography implies that we know about the world if we accept it as the camera records it. She states that photography has ‘become one of the principal devices for experiencing something, for giving an appearance of participation’. She refers to photographs as memento mori, where to take a photograph is to participate in another person’s mortality, vulnerability and mutability. The progression from written word to an image shifts the interpretation from the author to the receiver. Sontag believes however that ‘photographed images do not seem to be statements about the world so much as pieces of it, miniatures of reality that anyone can make or acquire’. It is a slice in time and in effect, is more memorable than moving images for example, videos. It fills the gaps in our mind of the past and present. Even though photography has such effect, there are limits to photographic knowledge of the world. The limitations are that it can never be interpreted ethical or political knowledge. It will always be some kind of sentimentalism, whether cynical or humanist.

Activism

In 1968, Sontag signed the “Writers and Editors War Tax Protest” pledge, vowing to refuse tax payments in protest against the Vietnam War.

During 1989 Sontag was the President of PEN American Center, the main U.S. branch of the International PEN writers' organization. This was the year when Iranian leader Ayatollah Khomeini issued a ''fatwa'' death sentence against writer Salman Rushdie after the publication of his novel ''The Satanic Verses''. Khomeini and some other Islamic fundamentalists claimed the novel was blasphemous. Sontag's uncompromising support of Rushdie was critical in rallying American writers to his cause.

A few years later, Sontag gained attention for directing Samuel Beckett's ''Waiting for Godot'' during the nearly four-year Siege of Sarajevo. Early in that conflict, Sontag referred to the War in Bosnia and Herzegovina as the "Spanish Civil War of our time". She started controversy among U.S. leftists for advocating U.S. and European military intervention. Sontag lived in Sarajevo for many months of the Sarajevo siege.

Sontag continued to theorize about the role of photography in real life in her essay "Looking at War: Photography's View of Devastation and Death" which appeared in the December 9th, 2002 issue of ''The New Yorker''. In it she acknowledges that the problem of our reliance on images and especially photographic images is not that "people remember through photographs but that they remember only the photographs, .... that the photographic image eclipses other forms of understanding--and remembering. .... To remember is, more and more, not to recall a story but to be able to call up a picture" (94). She re-examines the arguments she posed in ''On Photography.''

Controversies

Sontag drew fire for writing (in the Partisan Review, 1967) that:

"Mozart, Pascal, Boolean algebra, Shakespeare, parliamentary government, baroque churches, Newton, the emancipation of women, Kant, Balanchine ballets, ''et al.'' don't redeem what this particular civilization has wrought upon the world. The white race is the cancer of human history."

According to journalist Christopher Hitchens, Sontag later recanted this statement, saying that "it slandered cancer patients".

In "Sontag, Bloody Sontag," an essay in her book ''Vamps and Tramps'', Camille Paglia describes her initial admiration for Sontag and her subsequent disillusionment. Paglia writes,

Sontag's cool exile was a disaster for the American women's movement. Only a woman of her prestige could have performed the necessary critique and debunking of the first instant-canon feminist screeds, such as those of Kate Millett or Sandra Gilbert and Susan Gubar, whose middlebrow mediocrity crippled women's studies from the start. No patriarchal villains held Sontag back; her failures are her own.

Paglia mentions several criticisms of Sontag, including Harold Bloom's comment on Paglia's doctoral dissertation, of "Mere Sontagisme!" This "had become synonymous with a shallow kind of hip posturing." Paglia also describes Sontag as a "sanctimonious moralist of the old-guard literary world", and tells of a visit by Sontag to Bennington College, in which she arrived hours late, ignored the agreed-upon topic of the event, and made an incessant series of ridiculous demands.

Ellen Lee accused Sontag of plagiarism when Lee discovered at least twelve passages in ''In America'' that were similar to passages in four other books about Helena Modjeska. Those books included a novel by Willa Cather. (Cather wrote: "When Oswald asked her to propose a toast, she put out her long arm, lifted her glass, and looking into the blur of the candlelight with a grave face, said: 'To my coun-n-try!'" Sontag wrote, "When asked to propose a toast, she put out her long arm, lifted her glass, and looking into the blur of the candlelight, crooned, 'To my new country!'" "Country," muttered Miss Collingridge. "Not 'coun-n-try.'") The quotations were presented without credit or attribution.

Sontag said about using the passages, "All of us who deal with real characters in history transcribe and adopt original sources in the original domain. I've used these sources and I've completely transformed them. I have these books. I've looked at these books. There's a larger argument to be made that all of literature is a series of references and allusions."

"Fascism with a human face"

At a New York pro-Solidarity rally during 1982, Sontag stated that "people on the left", like herself, "have willingly or unwillingly told a lot of lies". She added that they

Sontag's speech "drew boos and shouts from the audience". ''The Nation'' published her speech, excluding the passage comparing the magazine with ''Reader's Digest'', and reactions to the speech from fellow intellectuals. Responses varied, with some claiming that she had betrayed her ideals.

Personal life

Sontag became aware of her homosexuality during her early teens and at 15 wrote in her diary, "so now I feel I have lesbian tendencies (how reluctantly I write this)." At 16, she had her first sexual encounter with a woman: "Perhaps I was drunk, after all, because it was so beautiful when H began making love to me .... It had been 4:00 before we had gotten to bed ... I became fully conscious that I desired her, she knew it, too...."

During the early 1970s, Sontag was involved romantically with Nicole Stéphane (1923–2007), a Rothschild banking heiress turned movie actress. Sontag later engaged in a committed relationship with photographer Annie Leibovitz, with whom she was close during her last years; choreographer Lucinda Childs, writers María Irene Fornés and Harriet Sohmers Zwerling, and other women.

In an interview in ''The Guardian'' during 2000, Sontag was quite open about her bisexuality:

:"Shall I tell you about getting older?", she says, and she is laughing. "When you get older, 45 plus, men stop fancying you. Or put it another way, the men I fancy don't fancy me. I want a young man. I love beauty. So what's new?" She says she has been in love seven times in her life, which seems quite a lot. "No, hang on," she says. "Actually, it's nine. Five women, four men."

Many of Sontag's obituaries failed to mention her significant same-sex relationships, most notably that with Leibovitz. In response to this criticism, ''The New York Times''' Public Editor, Daniel Okrent, defended the newspaper's obituary, stating that at the time of Sontag's death, a reporter could make no independent verification of her romantic relationship with Leibovitz (despite attempts to do so). After Sontag's death, ''Newsweek'' published an article about Leibovitz that made clear reference to her decade-plus relationship with Sontag, stating: "The two first met in the late '80s, when Leibovitz photographed her for a book jacket. They never lived together, though they each had an apartment within view of the other's." Susan Sontag's son, David Rieff, the executor of her estate, has said that only sentimental items were bequeathed to Leibovitz.

Sontag was quoted by Editor-in-Chief Brendan Lemon of ''Out'' magazine as saying "I grew up in a time when the modus operandi was the 'open secret'. I'm used to that, and quite OK with it. Intellectually, I know why I haven't spoken more about my sexuality, but I do wonder if I haven't repressed something there to my detriment. Maybe I could have given comfort to some people if I had dealt with the subject of my private sexuality more, but it's never been my prime mission to give comfort, unless somebody's in drastic need. I'd rather give pleasure, or shake things up."

Cultural references

In the film ''Bull Durham'', Kevin Costner as "Crash" Davis declares that "the novels of Susan Sontag are self-indulgent, overrated crap."

In the musical "Bloody Bloody Andrew Jackson", the song "Illness as a Metaphor" makes reference to Susan Sontag's cancer.

Works

Fiction

(1963) ''The Benefactor'' ISBN 0-385-26710-X

(1967) ''Death Kit'' ISBN 0-312-42011-0

(1977) ''I, etcetera'' (Collection of short stories) ISBN 0-374-17402-4

(1991) ''The Way We Live Now'' (short story) ISBN 0-374-52305-3

(1992) ''The Volcano Lover'' ISBN 1-55800-818-7

(1999) ''In America '' ISBN 1-56895-898-6 (National Book Award for fiction in 2000)

Plays

(1991) "A Parsifal" [one-act play, first published in _Antaeus_ 67 (1991): 180-185.]

(1993) ''Alice in Bed'' Library of Congress catalog card number 93-71280

(1999) "Lady from the Sea" [adaptation of Henrik Ibsen's play of the same name; first published in _Theater_ 29.1 (1999): 89-91.]

Nonfiction

Collections of essays

(1966) ''Against Interpretation'' ISBN 0-385-26708-8 (includes Notes on "Camp")

(1969) ''Styles of Radical Will'' ISBN 0-312-42021-8

(1980) ''Under the Sign of Saturn'' ISBN 0-374-28076-2

(2001) ''Where the Stress Falls'' ISBN 0-374-28917-4

(2002) ''Regarding the Pain of Others'' ISBN 0-374-248583

(2007) ''At the Same Time: Essays & Speeches'' ISBN 0-374-10072-1 (edited by Paolo Dilonardo and Anne Jump, with a foreword by David Rieff)

Sontag also published nonfiction essays in ''The New Yorker'', ''The New York Review of Books'', ''Times Literary Supplement'', ''The Nation'', ''Granta'', ''Partisan Review'' and the ''London Review of Books''.

Monographs

(1977) ''On Photography'' ISBN 0-374-22626-1

(1978) ''Illness as Metaphor'' ISBN 0-394-72844-0

(1988) ''AIDS and Its Metaphors'' (a continuation of ''Illness as Metaphor'') ISBN 0-374-10257-0

(2003) ''Regarding the Pain of Others'' ISBN 0-374-24858-3

Films

(1969) Duett för kannibaler ''(Duet for Cannibals)''

(1971) Broder Carl ''(Brother Carl)''

(1974) Promised Lands

(1983) Unguided Tour ''AKA Letter from Venice''

Other

(2004) Contribution of phrases to Fischerspooner's third album "Odyssey."

(2002) Liner notes for Patti Smith album ''Land''.

(2008) ''Reborn: Journals and Notebooks 1947-1963''

Books and articles on Susan Sontag

''Sontag and Kael'' by Craig Seligman ISBN 1-58243-311-9.

''The Din in the Head.'' Essays by Cynthia Ozick ISBN 978-0-618-47050-1 See Forward: On Discord and Desire.

''Conversations with Susan Sontag.'' Edited by Leland Poague ISBN 0-87805-833-8 Susan Sontag in her own words.

''Susan Sontag: The Elegiac Modernist'' by Sohnya Sayres ISBN 0-415-90031-X

''Swimming in a Sea of Death'' by David Rieff A memoir about Susan Sontag's death by her son.

''Notes on Sontag'' by Phillip Lopate

''Sempre Susan: A Memoir of Susan Sontag'' by Sigrid Nunez

Awards and honors

1978: National Book Critics Circle Award for ''On Photography''

1990: MacArthur Fellowship

1992: Malaparte Prize, Italy

1999: Commandeur de l'Ordre des Arts et des Lettres, France

2000: National Book Award for ''In America''

2001: Was awarded the Jerusalem Prize, which is awarded every two years to a writer whose work explores the freedom of the individual in society.

2002: Received her second George Polk Award, for Cultural Criticism for "Looking at War," in The New Yorker

2003: Received the ''Peace Prize of the German Book Trade (Friedenspreis des deutschen Buchhandels)'' during the Frankfurt Book Fair (Frankfurter Buchmesse).

2003: Won the Prince of Asturias Award on Literature.

2004: Two days after her death, the mayor of Sarajevo announced the city would name a street after her, calling her an "author and a humanist who actively participated in the creation of the history of Sarajevo and Bosnia." An initiative by Sarajevo Mayor Muhidin Hamamdzic to pay tribute to Susan Sontag, who has died recently, by renaming Theatre Square outside the National Theatre Susan Sontag Theatre Square, was accepted on Thursday (27 January) at a session of the Sarajevo City Council. It took long 5 years for that to become official, since nationalist political parties ignored that promise. On March 30, 2009. it was officially announced that Theater Square in front of National Theater in Sarajevo will get the name of Susan Sontag. 2010: On 13. January 2010 City of Sarajevo post a plate with a new street name for Theater Square - Theater Square of Susan Sontag.

References

External links

"with Ramona Koval", ''Books and Writing,'' ABC Radio National, 30/1/2005

Susan Sontag, official website

Susan Sontag – Photos by Mathieu Bourgois.

The ''Friedenspreis'' acceptance speech (2003-10-12)

''Fascinating Fascism'' illustrated text of Sontag's seminal 1974 article on Nazi filmmaker Leni Riefenstahl's aesthetics, from ''Under the Sign of Saturn''

Sontag's comments in the New Yorker, September 24, 2001 about the September 11th attack on the United States

Terry Castle, ''Desperately Seeking Susan'', London Review of Books, March 2005

Sheelah Kolhatkar, "Notes on camp Sontag" ''New York Observer'', January 8, 2005

'Susan Sontag: The Collector', by Daniel Mendelsohn, ''The New Republic''

A review of "Reborn" - by James Patrick

Category:1933 births Category:2004 deaths Category:Alumni of St Anne's College, Oxford Category:American activists Category:American anti–Vietnam War activists Category:American dissidents Category:American feminist writers Category:American historical novelists Category:American tax resisters Category:American women writers Category:Bisexual writers Category:Cancer deaths in New York Category:Deaths from leukemia Category:Guggenheim Fellows Category:Harvard Centennial Medal recipients Category:University of California, Berkeley alumni Category:University of Paris alumni Category:Jewish American writers Category:Jewish feminists Category:Jewish women writers Category:LGBT feminists Category:LGBT Jews Category:LGBT writers from the United States Category:LGBT parents Category:MacArthur Fellows Category:Recipients of the Peace Prize of the German Book Trade Category:People from New York City Category:Photography critics Category:Sarah Lawrence College faculty Category:University of Chicago alumni Category:Burials at Montparnasse Cemetery

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Name	Omar Khayyám عمر خیام
Birth date	18 May 1048
Death date	1131
Madhhab	Shi'a Muslim
school tradition	Persian mathematics, Persian poetry, Persian philosophy
main interests	Poetry, Mathematics, Philosophy, Astronomy
influences	Abū Rayhān al-Bīrūnī, Avicenna
pronunciation	}}

Omar Khayyám (; 1048–1131) was a Persian mathematician, astronomer, philosopher and poet. He also wrote treatises on mechanics, geography, and music.

Born in Nishapur, at a young age he moved to Samarkand and obtained his education there, afterwards he moved to Bukhara and became established as one of the major mathematicians and astronomers of the medieval period. He is the author of one of the most important treatises on algebra written before modern times, the ''Treatise on Demonstration of Problems of Algebra,'' which includes a geometric method for solving cubic equations by intersecting a hyperbola with a circle. He contributed to a calendar reform.

His significance as a philosopher and teacher, and his few remaining philosophical works, have not received the same attention as his scientific and poetic writings. Zamakhshari referred to him as “the philosopher of the world”. Many sources have testified that he taught for decades the philosophy of Ibn Sina in Nishapur where Khayyám was born and buried and where his mausoleum today remains a masterpiece of Iranian architecture visited by many people every year.

Outside Iran and Persian speaking countries, Khayyám has had an impact on literature and societies through the translation of his works and popularization by other scholars. The greatest such impact was in English-speaking countries; the English scholar Thomas Hyde (1636–1703) was the first non-Persian to study him. The most influential of all was Edward FitzGerald (1809–83), who made Khayyám the most famous poet of the East in the West through his celebrated translation and adaptations of Khayyám's rather small number of quatrains (''rubaiyaa''s) in ''Rubáiyát of Omar Khayyám''.

Early life

Khayyám's full name was Ghiyath al-Din Abu'l-Fath Umar ibn Ibrahim Al-Nishapuri al-Khayyami (). He was born in Nishapur, Iran, then a Seljuk capital in Khorasan (present Northeast Iran), which rivaled Cairo or Baghdad in cultural prominence in that era. He is thought to have been born into a family of tent makers (''al-khayyami'', lit. in Arabic "tent-maker"), which he would make this into a play on words later in life:

He spent part of his childhood in the town of Balkh (present northern Afghanistan), studying under the well-known scholar Sheikh Muhammad Mansuri. He later studied under Imam Mowaffaq Nishapuri, who was considered one of the greatest teachers of the Khorassan region.

Mathematician

Khayyám was famous during his times as a mathematician. He wrote the influential ''Treatise on Demonstration of Problems of Algebra'' (1070), which laid down the principles of algebra, part of the body of Persian Mathematics that was eventually transmitted to Europe. In particular, he derived general methods for solving cubic equations and even some higher orders. In the ''Treatise'' he wrote on the triangular array of binomial coefficients known as Pascal's triangle. In 1077, Khayyám wrote ''Sharh ma ashkala min musadarat kitab Uqlidis'' (Explanations of the Difficulties in the Postulates of Euclid) published in English as "On the Difficulties of Euclid's Definitions". An important part of the book is concerned with Euclid's famous parallel postulate, which attracted the interest of Thabit ibn Qurra. Al-Haytham had previously attempted a demonstration of the postulate; Khayyám's attempt was a distinct advance, and his criticisms made their way to Europe, and may have contributed to the eventual development of non-Euclidean geometry.

Khayyám had notable works in geometry, specifically on the theory of proportions.

Theory of parallels

Khayyám wrote a book entitled ''Explanations of the difficulties in the postulates in Euclid's Elements''. The book consists of several sections on the parallel postulate (Book I), on the Euclidean definition of ratios and the Anthyphairetic ratio (modern continued fractions) (Book II), and on the multiplication of ratios (Book III).

The first section is a treatise containing some propositions and lemmas concerning the parallel postulate. It has reached the Western world from a reproduction in a manuscript written in 1387-88 AD by the Persian mathematician Tusi. Tusi mentions explicitly that he re-writes the treatise "in Khayyám's own words" and quotes Khayyám, saying that "they are worth adding to Euclid's Elements (first book) after Proposition 28." This proposition states a condition enough for having two lines in plane parallel to one another. After this proposition follows another, numbered 29, which is converse to the previous one. The proof of Euclid uses the so-called parallel postulate (numbered 5). Objection to the use of parallel postulate and alternative view of proposition 29 have been a major problem in foundation of what is now called non-Euclidean geometry.

The treatise of Khayyám can be considered as the first treatment of parallels axiom which is not based on petitio principii but on more intuitive postulate. Khayyám refutes the previous attempts by other Greek and Persian mathematicians to ''prove'' the proposition. And he, as Aristotle, refuses the use of motion in geometry and therefore dismisses the different attempt by Ibn Haytham too. In a sense he made the first attempt at formulating a non-Euclidean postulate as an alternative to the parallel postulate,

Geometric algebra

This philosophical view of mathematics (see below) has had a significant impact on Khayyám's celebrated approach and method in geometric algebra and in particular in solving cubic equations. In that his solution is not a direct path to a numerical solution and in fact his solutions are not numbers but rather line segments. In this regard Khayyám's work can be considered the first systematic study and the first exact method of solving cubic equations.

In an untitled writing on cubic equations by Khayyám discovered in 20th century, where the above quote appears, Khayyám works on problems of geometric algebra. First is the problem of "finding a point on a quadrant of a circle such that when a normal is dropped from the point to one of the bounding radii, the ratio of the normal's length to that of the radius equals the ratio of the segments determined by the foot of the normal." Again in solving this problem, he reduces it to another geometric problem: "find a right triangle having the property that the hypotenuse equals the sum of one leg (i.e. side) plus the altitude on the hypotenuse. To solve this geometric problem, he specializes a parameter and reaches the cubic equation $x^3+200x=20x^2+2000$. Indeed, he finds a positive root for this equation by intersecting a hyperbola with a circle.

This particular geometric solution of cubic equations has been further investigated and extended to degree four equations.

Regarding more general equations he states that the solution of cubic equations requires the use of conic sections and that it cannot be solved by ruler and compass methods. A proof of this impossibility was plausible only 750 years after Khayyám died. In this paper Khayyám mentions his will to prepare a paper giving full solution to cubic equations: "If the opportunity arises and I can succeed, I shall give all these fourteen forms with all their branches and cases, and how to distinguish whatever is possible or impossible so that a paper, containing elements which are greatly useful in this art will be prepared."

This refers to the book ''Treatise on Demonstrations of Problems of Algebra'' (1070), which laid down the principles of algebra, part of the body of Persian Mathematics that was eventually transmitted to Europe. In particular, he derived general methods for solving cubic equations and even some higher orders.

Binomial theorem and extraction of roots

This particular remark of Khayyám and certain propositions found in his Algebra book has made some historians of mathematics believe that Khayyám had indeed a binomial theorem up to any power. The case of power 2 is explicitly stated in Euclid's elements and the case of at most power 3 had been established by Indian mathematicians. Khayyám was the mathematician who noticed the importance of a general binomial theorem. The argument supporting the claim that Khayyám had a general binomial theorem is based on his ability to extract roots.

Khayyám-Saccheri quadrilateral

The Saccheri quadrilateral was first considered by Khayyám in the late 11th century in Book I of ''Explanations of the Difficulties in the Postulates of Euclid''. Unlike many commentators on Euclid before and after him (including of course Saccheri), Khayyám was not trying to prove the parallel postulate as such but to derive it from an equivalent postulate he formulated from "the principles of the Philosopher" (Aristotle):

:Two convergent straight lines intersect and it is impossible for two convergent straight lines to diverge in the direction in which they converge.

Khayyám then considered the three cases (right, obtuse, and acute) that the summit angles of a Saccheri quadrilateral can take and after proving a number of theorems about them, he (correctly) refuted the obtuse and acute cases based on his postulate and hence derived the classic postulate of Euclid.

It wasn't until 600 years later that Giordano Vitale made an advance on Khayyám in his book ''Euclide restituo'' (1680, 1686), when he used the quadrilateral to prove that if three points are equidistant on the base AB and the summit CD, then AB and CD are everywhere equidistant. Saccheri himself based the whole of his long, heroic, and ultimately flawed proof of the parallel postulate around the quadrilateral and its three cases, proving many theorems about its properties along the way.

Astronomer

Like most Persian mathematicians of the period, Khayyám was famous as an astronomer. In 1073, the Seljuk Sultan Sultan Jalal al-Din Malekshah Saljuqi (Malik-Shah I, 1072–92), invited Khayyám to build an observatory, along with various other distinguished scientists. According to some accounts, the version of the medieval Iranian calendar in which 2,820 solar years together contain 1,029,983 days (or 683 leap years, for an average year length of 365.24219858156 days) was based on the measurements of Khayyám and his colleagues. Another proposal is that Khayyám's calendar simply contained eight leap years every thirty-three years (for a year length of 365.2424 days). In either case, his calendar was more accurate to the mean tropical year than the Gregorian calendar of 500 years later. The modern Iranian calendar is based on his calculations.

Calendar reform

Khayyám is claimed to be a member of a panel that introduced several reforms to the Persian calendar. On March 15, 1079, Sultan Malik Shah I accepted this corrected calendar as the official Persian calendar.

This calendar was known as Jalali calendar after the Sultan, and was in force across Greater Iran from the 11th to the 20th centuries. It is the basis of the Iranian calendar which is followed today in Iran and Afghanistan. While the Jalali calendar is more accurate than the Gregorian, it is based on actual solar transit, (similar to Hindu calendars), and requires an Ephemeris for calculating dates. The lengths of the months can vary between 29 and 31 days depending on the moment when the sun crossed into a new zodiacal area (an attribute common to most Hindu calendars). This meant that seasonal errors were lower than in the Gregorian calendar.

The modern-day Iranian calendar standardizes the month lengths based on a reform from 1925, thus minimizing the effect of solar transits. Seasonal errors are somewhat higher than in the Jalali version, but leap years are calculated as before.

Khayyám built a star map (now lost), which was famous in the Persian and Islamic world.

Poet

Khayyám's poetic work has eclipsed his fame as a mathematician and scientist.

He is believed to have written about a thousand four-line verses or rubaiyat (quatrains). In the English-speaking world, he was introduced through the ''Rubáiyát of Omar Khayyám'' which are rather free-wheeling English translations by Edward FitzGerald (1809–1883). Other English translations of parts of the rubáiyát (''rubáiyát'' meaning "quatrains") exist, but FitzGerald's are the most well known.

Ironically, FitzGerald's translations reintroduced Khayyám to Iranians "who had long ignored the Neishapouri poet." A 1934 book by one of Iran's most prominent writers, Sadeq Hedayat, ''Songs of Khayyam'', (Taranehha-ye Khayyam) is said to have "shaped the way a generation of Iranians viewed" the poet.

Khayyam's poetry is translated to many languages.

Khayyám's personal beliefs are not known with certainty, but much is discernible from his poetic oeuvre.

Poetry

And, as the Cock crew, those who stood before   The Tavern shouted - "Open then the Door! You know how little time we have to stay,   And once departed, may return no more."

Alike for those who for TO-DAY prepare,   And that after a TO-MORROW stare, A Muezzin from the Tower of Darkness cries   "Fools! your reward is neither Here nor There!"

Why, all the Saints and Sages who discuss'd   Of the Two Worlds so learnedly, are thrust Like foolish Prophets forth; their Words to Scorn   Are scatter'd, and their mouths are stopt with Dust.

Oh, come with old Khayyam, and leave the Wise   To talk; one thing is certain, that Life flies; One thing is certain, and the Rest is Lies;   The Flower that once has blown for ever dies.

Myself when young did eagerly frequent   Doctor and Saint, and heard great Argument About it and about: but evermore   Came out of the same Door as in I went.

With them the Seed of Wisdom did I sow,   And with my own hand labour'd it to grow: And this was all the Harvest that I reap'd -   "I came like Water, and like Wind I go."

Into this Universe, and why not knowing,   Nor whence, like Water willy-nilly flowing: And out of it, as Wind along the Waste,   I know not whither, willy-nilly blowing.

The Moving Finger writes; and, having writ,   Moves on: nor all thy Piety nor Wit Shall lure it back to cancel half a Line,   Nor all thy Tears wash out a Word of it.

And that inverted Bowl we call The Sky,   Whereunder crawling coop't we live and die, Lift not thy hands to It for help - for It   Rolls impotently on as Thou or I.

Views on religion

In his own writings, Khayyám rejects strict religious structure and a literalist conception of the afterlife.

There have been widely divergent views on Khayyám. According to Seyyed Hossein Nasr no other Iranian writer/scholar is viewed in such extremely differing ways. At one end of the spectrum there are nightclubs named after Khayyám, and he is seen as an agnostic hedonist. On the other end of the spectrum, he is seen as a mystical Sufi poet influenced by platonic traditions.

Robertson (1914) believes that Khayyám was not devout and had no sympathy for popular religion,

The following two quatrains are representative of numerous others that serve to reject many tenets of religious dogma:

:خيام اگر ز باده مستى خوش باش :با ماه رخى اگر نشستى خوش باش :چون عاقبت كار جهان نيستى است :انگار كه نيستى، چو هستى خوش باش

which translates in FitzGerald's work as:

:And if the Wine you drink, the Lip you press, :End in the Nothing all Things end in — Yes — :Then fancy while Thou art, Thou art but what :Thou shalt be — Nothing — Thou shalt not be less.

A more literal translation could read:

:If with wine you are drunk be happy, :If seated with a moon-faced (beautiful), be happy, :Since the end purpose of the universe is nothing-ness; :Hence picture your nothing-ness, then while you are, be happy!

:آنانكه ز پيش رفته‌اند اى ساقى :درخاك غرور خفته‌اند اى ساقى :رو باده خور و حقيقت از من بشنو :باد است هرآنچه گفته‌اند اى ساقى

which FitzGerald has boldy interpreted as:

:Why, all the Saints and Sages who discuss’d :Of the Two Worlds so learnedly — are thrust :Like foolish Prophets forth; their Words to Scorn :Are scatter’d, and their Mouths are stopt with Dust.

A literal translation, in an ironic echo of "all is vanity", could read:

:Those who have gone forth, thou cup-bearer, :Have fallen upon the dust of pride, thou cup-bearer, :Drink wine and hear from me the truth: :(Hot) air is all that they have said, thou cup-bearer.

But some specialists, like Seyyed Hossein Nasr who looks at the available philosophical works of Khayyám, maintain that it is really reductive to just look at the poems (which are sometimes doubtful) to establish his personal views about God or religion; in fact, he even wrote a treatise entitled "al-Khutbat al-gharrå˘" (The Splendid Sermon) on the praise of God, where he holds orthodox views, agreeing with Avicenna on Divine Unity. In fact, this treatise is not an exception, and S.H. Nasr gives an example where he identified himself as a Sufi, after criticizing different methods of knowing God, preferring the intuition over the rational (opting for the so-called "kashf", or unveiling, method):

The same author goes on by giving other philosophical writings which are totally compatible with the religion of Islam, as the "al-Risålah fil-wujud" (Treatise on Being), written in Arabic, which begin with Quranic verses and asserting that all things come from God, and there is an order in these things. In another work, "Risålah jawåban li-thalåth maså˘il" (Treatise of Response to Three Questions), he gives a response to question on, for instance, the becoming of the soul post-mortem. S.H. Nasr even gives some poetry where he is perfectly in favor of Islamic orthodoxy, but expressing mystical views (God's goodness, the ephemerical state of this life, ...):

:Thou hast said that Thou wilt torment me, :But I shall fear not such a warning. :For where Thou art, there can be no torment, :And where Thou art not, how can such a place exist?

:The rotating wheel of heaven within which we wonder, :Is an imaginal lamp of which we have knowledge by similitude. :The sun is the candle and the world the lamp, :We are like forms revolving within it.

:A drop of water falls in an ocean wide, :A grain of dust becomes with earth allied; :What doth thy coming, going here denote? :A fly appeared a while, then invisible he became.

Considering misunderstandings about Khayyám in the West and elsewhere, S.H. Nasr concludes by saying that if a correct study of the authentic rubaiyat is done, but along with the philosophical works, or even the spiritual biography entitled ''Sayr wa sulak'' (Spiritual Wayfaring), we can no longer view the man as a simple hedonistic wine-lover, or even an early skeptic, but a profound mystical thinker and scientist whose works are more important than some verses. C.H.A. Bjerregaard earlier summarised the situation:

Abdullah Dougan, a modern Naqshbandi Sufi, provides commentary on the role and contribution of Omar Khayyam to Sufi thought. Dougan says that while Omar is a minor Sufi teacher compared to the giants – Rumi, Attar and Sana’i – one aspect that makes Omar’s work so relevant and accessible is its very human scale as we can feel for him and understand his approach. The argument over the quality of Fitzgerald’s translation of the Rubaiyat has, according to Dougan, diverted attention from a fuller understanding of the deeply esoteric message contained in Omar’s actual material – ''"Every line of the Rubaiyat has more meaning than almost anything you could read in Sufi literature"''.

Philosopher

Khayyám himself rejects to be associated with the title ''falsafi-'' (''lit.'' philosopher) in the sense of Aristotelian one and stressed he wishes "to know who I am". In the context of philosophers he was labeled by some of his contemporaries as "detached from divine blessings".

It is now established that Khayyám taught for decades the philosophy of Avicena, especially "the Book of Healing", in his home town Nishapur, till his death. In an incident he had been requested to comment on a disagreement between Avicena and a philosopher called Abu'l-Barakat (known also as Nathanel) who had criticized Avicena strongly. Khayyám is said to have answered "[he] does not even understand the sense of the words of Avicenna, how can he oppose what he does not know?"

Khayyám the philosopher could be understood from two rather distinct sources. One is through his Rubaiyat and the other through his own works in light of the intellectual and social conditions of his time. The latter could be informed by the evaluations of Khayyám's works by scholars and philosophers such as Bayhaqi, Nezami Aruzi, and Zamakhshari and Sufi poets and writers Attar Nishapuri and Najmeddin Razi.

As a mathematician, Khayyám has made fundamental contributions to the Philosophy of mathematics especially in the context of Persian Mathematics and Persian philosophy with which most of the other Persian scientists and philosophers such as Avicenna, Biruni, and Tusi are associated. There are at least three basic mathematical ideas of strong philosophical dimensions that can be associated with Khayyám.

# Mathematical order: From where does this order issue, and why does it correspond to the world of nature? His answer is in one of his philosophical "treatises on being". Khayyám's answer is that "the Divine Origin of all existence not only emanates wojud or being, by virtue of which all things gain reality, but It is the source of order that is inseparable from the very act of existence." # The significance of postulates (i.e. axiom) in geometry and the necessity for the mathematician to rely upon philosophy and hence the importance of the relation of any particular science to prime philosophy. This is the philosophical background to Khayyám's total rejection of any attempt to "prove" the parallel postulate, and in turn his refusal to bring motion into the attempt to prove this postulate, as had Ibn al-Haytham, because Khayyám associated motion with the world of matter, and wanted to keep it away from the purely intelligible and immaterial world of geometry. # Clear distinction made by Khayyám, on the basis of the work of earlier Persian philosophers such as Avicenna, between natural bodies and mathematical bodies. The first is defined as a body that is in the category of substance and that stands by itself, and hence a subject of natural sciences, while the second, called "volume", is of the category of accidents (attributes) that do not subsist by themselves in the external world and hence is the concern of mathematics. Khayyám was very careful to respect the boundaries of each discipline, and criticized Ibn al-Haytham in his proof of the parallel postulate precisely because he had broken this rule and had brought a subject belonging to natural philosophy, that is, motion, which belongs to natural bodies, into the domain of geometry, which deals with mathematical bodies.

Legacy

A lunar crater ''Omar Khayyam'' was named after him in 1970.

A minor planet called ''3095 Omarkhayyam'', discovered by Soviet astronomer Lyudmila Zhuravlyova in 1980, is named after him.

See also

Nozhat al-Majales

''The Keeper: The Legend of Omar Khayyam''

''Omar Khayyam'' (film)

Mathematics in medieval Islam

Astronomy in medieval Islam

Xayyam Project

Notes

References

External links

Khayyam's works in original Persian at Ganjoor Persian Library

Khayyam in Tarikhema.ir

Omer Khayyam Rubaiyat

Listen to The Rubáiyát of Omar Khayyám audiobook at LibriVox

The illustrated Rubáiyát of Omar Khayyám at Internet Archive.

Omar Khayyam's Rubaiyat as translated by Edward Fitzgerald – 1st edition

The Rubaiyat by Omar Khayyam – The Internet Classics Archive

Illustrations to the Rubaiyat by Adelaide Hanscom

Category:1048 births Category:1122 deaths Category:People from Nishapur Category:Persian poets Category:Medieval Persian astronomers Category:Medieval Persian mathematicians Category:Persian philosophers Category:Persian spiritual writers Category:11th-century mathematicians Category:12th-century mathematicians Category:Medieval writers Category:Astronomers of medieval Islam Category:Mathematicians of medieval Islam

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