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Writer's picturejohn ordinary
May 23, 201811 min read

I Am a Strange Loop


Douglas Hofstadter


Early life and education

Hofstadter was born in New York City, the son of Nobel Prize-winning physicist Robert Hofstadter and Nancy Givan 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, and received his Ph.D. in Physics from the University of Oregon in 1975, where his study of the energy levels of Bloch electrons in a magnetic field led to his discovery of the fractal known as the Hofstadter butterfly.


Academic career

Since 1988, Hofstadter has been the College of Arts and Sciences Distinguished Professor of Cognitive Science and Comparative Literature 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. He was also appointed adjunct professor of history and philosophy of science, philosophy, comparative literature, and psychology, but has said that his involvement with most of those departments is nominal. In 1988 Hofstadter received the In Praise of Reason award, the Committee for Skeptical Inquiry's highest honor. In April 2009 he was elected a Fellow of the American Academy of Arts and Sciences and a member of the American Philosophical Society. In 2010 he was elected a member of the Royal Society of Sciences in Uppsala, Sweden. Hofstadter's many interests include music, visual art, the mind, creativity, consciousness, self-reference, translation and mathematics. 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 M. French. Hofstadter's doctoral student James Marshall subsequently extended the Copycat project under the name "Metacat". 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 include 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. The pursuit of beauty has driven Hofstadter both inside and outside his professional work. He seeks beautiful mathematical patterns, beautiful explanations, beautiful typefaces, beautiful sonic patterns in poetry, etc. 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 figureof Joseph Jastrow), and his "Whirly Art" (music-inspired visual patterns realized using shapes based on various alphabets from India). (Hofstadter invented the term "ambigram" in 1984; many ambigrammists all over the world have since taken up the concept.) 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, including:

  • 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 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 feature 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. 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. Hofstadter has translated many other poems too (always respecting their formal constraints), and two 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.


Hofstadter's Law

Hofstadter's LawHofstadter's Law states that "It always takes longer than you expect, even when you take into account Hofstadter's Law." The Law is outlined in his work Gödel, Escher, Bach: An Eternal Golden Braid.


Students

Hofstadter's former Ph.D. students include (with dissertation title):

  • Don Byrd—Music Notation by Computer

  • David Chalmers—Toward a Theory of Consciousness

  • Gray A. Clossman—A Model of Categorization and Learning in a Connectionist Broadcast System

  • Hamid Ekbia—AI Dreams and Discourse: Science and Engineering in Tension

  • Harry Foundalis—Phaeaco: A Cognitive Architecture Inspired by Bongard's Problems

  • Bob French—Tabletop: An Emergent, Stochastic Model of Analogy-Making

  • Francisco Lara-Dammer—Modeling Human Discoverativity in Geometry

  • Abhijit Mahabal—SeqSee: A Concept-centered Architecture for Sequence Perception

  • Jim Marshall—Metacat: A Self-Watching Cognitive Architecture for Analogy-making and High level Perception

  • Gary McGraw—Letter Spirit (Part One): Emergent High-level Perception of Letters Using Fluid Concepts

  • Marsha Meredith—Seek-Whence: A Model of Pattern Perception

  • Eric Nichols—Musicat: A Computer Model of Musical Listening and Analogy-Making

  • Melanie Mitchell—Copycat: A Computer Model of High-Level Perception and Conceptual Slippage in Analogy-making

  • John Rehling—Letter Spirit (Part Two): Modeling Creativity in a Visual Domain

  • Wang Pei (Pei Wang)—Non-Axiomatic Reasoning System: Exploring the Essence of Intelligence

  • William York—Aesthetics and the Scope and Limits of Cognitive Science


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 Garry 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 (a hypothetical moment in the future of humanity when a self-reinforcing, runaway development of artificial intelligence causes a radical change in technology and culture), 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 and 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 1988 Dutch director Piet Hoenderdos created a docudrama about Hofstadter and his ideas, Victim of the Brain, based on The Mind's I. It includes interviews with Hofstadter about his work.


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" (1985), 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; Hofstadter published it under the pseudonym William Satire, an allusion to William Safire. 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 Frédéric 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 until her death. 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".In the fall of 2010, Hofstadter met Baofen Lin in a chacha class, and the two were married in Bloomington in September 2012. 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.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. As a consequence of his attitudes about consciousness and empathy, Hofstadter has been a vegetarian for roughly half his life.


In popular culture

In the 1982 novel 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". The movie uses the term "H. Möbius loop".On April 3, 1995, Hofstadter's book Fluid Concepts & Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought was the first book ever sold by Amazon.com.


Published works

Books

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

Papers

Hofstadter has written, among many others, the following papers:

Hofstadter has also written over 50 papers that were published through the Center for Research on Concepts and Cognition.

Involvement in other books

Hofstadter has written forewords for or edited the following books:

From Wikipedia, the free encyclopedia.

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