Douglas R. Hofstadter

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Douglas Hofstadter (2006 in Stanford )

Douglas Richard Hofstadter (born February 15, 1945 in New York City ) is an American physicist , computer scientist and cognitive scientist .


Douglas Hofstadter is the son of the Nobel laureate in physics, Robert Hofstadter . He spent his youth in Geneva , studied at Stanford University until 1965 and at the University of Oregon until 1972 , where he received his doctorate in physics with Gregory Wannier in 1975 (dissertation: The energy levels of Bloch electrons in magnetic fields ). Hofstadter was a Predoctoral Fellow at the University of Regensburg in 1975 and later a visiting professor at MIT and is currently Professor of Cognitive Science at Indiana University .

He has two children. His first wife, whom he married in 1985, died in 1993. He has been married to Baofen Lin since 2012.

Hofstadter butterfly

In 1975 he examined the energetic spectrum of electrons in two-dimensional lattice structures with an external magnetic field that results in a self-similar fractal structure, the Hofstadter Butterfly (Hofstadter Butterfly). He carried out the first calculations with the help of an HP 9820A desktop computer at the University of Regensburg as a visiting scientist. It was also the subject of his dissertation. The results were later published in the Physical Review. This was also observed experimentally in 2013 in graphene superlattices independent of different groups (University of Manchester and a group around the high-field laboratory of the University of Florida). In his model, Hofstadter described Bloch electrons in magnetic fields, which force the electrons on orbits with the cyclotron frequencies determined by the magnetic field . The energy levels are quantized as a function of the ratio of the cyclotron frequency to the lattice parameters.

In order to be able to observe the effect, one had to use either very strong magnetic fields or grids with very large grid spacings (superlattices). In 2013 this was finally achieved through a combination of both. The superlattices were created with graphene on very smooth boron nitride surfaces - both had a hexagonal structure and their interaction created a kind of moiré lattice.

Hofstadter butterfly


Hofstadter became known to a large audience through his popular science book Gödel, Escher, Bach: an Endless Braided Band , for which he received the Pulitzer Prize in 1980 and the American Book Award in the Science Hardback category. The book refers to the mathematician Kurt Gödel , the draftsman MC Escher and the composer Johann Sebastian Bach in connection with various considerations, including Zen Buddhism and Artificial Intelligence.

Among other things, he presents several mathematical sequences of whole numbers with simple, recursive formation rules, which have since been referred to as Hofstadter sequences . The properties of the best-known of them, the Q-sequence , could not be proven in a strict mathematical sense until today. In particular, it is unknown whether the Q-sequence is well-defined at all points, that is, whether it breaks off somewhere. The representation of the Q sequence in Hofstadter's book is the first known mention of a meta- Fibonacci sequence in literature. The strange loop also comes from this work .

In 1981 he published The Mind's I together with the philosopher Daniel Dennett . In 1985 Metamagical Themas appeared , a collection of articles that he had published in the previous years as a permanent column in Scientific American (German as Metamagical in Spectrum of Science ). In this category he followed Martin Gardner with his Mathematical Games (German mathematical gimmicks ); Metamagical Themes is an anagram from Mathematical Games .

In 1995 Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought was published , which Hofstadter and colleagues from the Fluid Analogies Research Group (hence the word "FARGonauten" in the title of the German edition) from the Center for Research on Concepts and Cognition of Indiana University wrote. A copy of this work was the first book sold on Amazon .

In Le Ton beau de Marot : In Praise of the Music of Language from 1997, Hofstadter discusses the question of literary translation based on the poem À une Damoyselle malade by Clément Marot - various translations of the poem run through the book - and numerous other works. In particular, the beauty of the language, the problem of the translatability of the non-translatable and the question of how close one has to stay to the original play a major role.

In his book I Am a Strange Loop , published in 2007, Hofstadter combines his thought experiments and intellectual adventures with his own life story.

In 2009 he was elected to the American Academy of Arts and Sciences and the American Philosophical Society .

Be authored in 2013 together with Emmanuel Sander book Surfaces and Essences: Analogy as the Fuel and Fire of Thinking (dt .: The analogy: the heart of thought , 2014) is dedicated to the analogy as a basic principle of human thought and learning.

In 2018 Hofstadter took over the Albertus Magnus Professorship at the University of Cologne.


Hofstadter's main theme is the question of the nature of human intelligence , knowledge and the self . He approaches this predominantly from the direction of physics , computer science , formal mathematical logic and - to a limited extent - physiology . In the 1980s he was one of the representatives of the scientific direction that had great expectations of the field of artificial intelligence .

Hofstadter investigates how relatively simple, "stupid" components - such as the neurons of the human brain - can create intelligent systems with the ability to self- reflect. For this he coined the term sphexishness , after a certain behavior of a kind of digger wasps (lat. Sphex ). This is the leitmotif in his book Gödel, Escher, Bach . In this context, he warns against over-simplification and sheer reductionism and thinks that the solution must lie in the synthesis of holism and reductionism.

Hofstadter writes about Daryl Bem's psi experiments that there must be a “switch-off device for craziness” (also the title of his article on “A Cutoff for Craziness”). He opposes the publication in scientific journals of articles that would fundamentally change our understanding of the nature of the universe: “If any of his claims were true, then all of the bases underlying contemporary science would be toppled, and we would have to rethink everything about the nature of the universe. ... [W] e cannot lightly publish articles whose implications would necessarily send all of science as we know it crashing to the ground. Instead, we have to find out how those articles are wrong. Or perhaps we simply have to ignore them, because there are a million crazy ideas. "


Hofstadter has a passion for foreign languages. In addition to his native English, he speaks French and Italian fluently and quite good German. His book Onegin is a verse translation of the novel Eugene Onegin by Alexander Pushkin .

Individual evidence

  1. Douglas R. Hofstadter in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. Rumpelstiltskin spun gold . In: christian-forstner's website! October 17, 2017 ( [accessed October 20, 2017]).
  3. Rumpelstiltskin spun gold . In: christian-forstner's website! October 17, 2017 ( [accessed October 20, 2017]).
  4. Hofstadter Energy levels and wavefunctions of Bloch electrons in rational and irrational magnetic fields , Physical Review B 14, 1976, pp. 2239-2249.
  5. LA Ponomarenko, R. Gorbachev et al. a. Cloning of Dirac fermions in graphene superlattices , Nature, Volume 497, 2013, 594-597, abstract
  6. 40-year-old prediction confirmed: First direct proof of Hofstadter butterfly fractal observed in moire superlattices
  7. Dean et al. a. Hofstadter's butterfly in moire superlattices: A fractal quantum Hall effect, Arxiv Preprint , Nature, Volume 497, 2013, 598-602, abstract
  8. Hofstadter's butterfly spotted in Graphen , Physics World 2013
  9. a b Klaus Pinn: Order and Chaos in Hofstadter's Q (n) Sequence . In: Complexity . tape 4 , 1999, p. 42 , arxiv : chao-dyn / 9803012v2 .
  10. Klaus Pinn: A Chaotic Cousin of Conway's Recursive Sequence . In: Experimental Mathematics . tape 9 , no. 1 , 2000, pp. 57 , arxiv : cond-mat / 9808031 .
  11. a b B. Balamohan, A. Kuznetsov, Stephan M. Tanny : On the Behavior of a Variant of Hofstadter's Q-Sequence . In: Journal of Integer Sequences . tape 10 , no. 7 . University of Waterloo , 2007, ISSN  1530-7638 , pp. 2 ( [PDF]).
  12. ^ A b Nathanial D. Emerson : A Family of Meta- Fibonacci Sequences Defined by Variable-Order Recursions . In: Journal of Integer Sequences . tape 9 , no. 1 . University of Waterloo , March 17, 2006, ISSN  1530-7638 , pp. 7 ( [PDF]).
  13. ^ Nathanial D. Emerson : A Family of Meta- Fibonacci Sequences Defined by Variable-Order Recursions . In: Journal of Integer Sequences . tape 9 , no. 1 . University of Waterloo , March 17, 2006, ISSN  1530-7638 , pp. 1 ( [PDF]).
  14. History & Timeline.
  15. Member History: Douglas Hofstadter. American Philosophical Society, accessed October 2, 2018 .
  16. ^ Douglas Hofstadter: A Cutoff for Craziness. In: The New York Times Company, January 7, 2011, accessed May 12, 2013 .

Works (selection)

  • About the magic of the Rubik's Cube . Mathematical gimmicks. In: Spectrum of Science . Spektrum Akademischer Verlag, May 1981, ISSN  0170-2971 , p. 16 ff . (Contains, among other things, instructions for correct cube assembly, solution strategy, graphic patterns and variations. Original English : Scientific American , 1981).
  • Gödel, Escher, Bach: an endless braided ribbon . Klett-Cotta, Stuttgart 1985, ISBN 3-608-94338-2 (American English: Gödel, Escher, Bach: an Eternal Golden Braid . Original: 1979). ( Number 1 on the Spiegel bestseller list from April 29th to September 1st and from September 9th to 22nd, 1985 )
  • Insight into the self . Fantasies and reflections on self and soul. Klett-Cotta, Stuttgart 1986, ISBN 3-608-93038-8 (American English: The Mind's I. Original: 1981).
  • Metamagicum . Questions about the essence of mind and structure. Klett-Cotta, Stuttgart 1988, ISBN 3-608-95774-X (American English: Metamagical Themas . Original: 1985).
  • Douglas R. Hofstadter, The Fluid Analogies Research Group ( David Chalmers , Daniel Defays, Robert French, Gary McGraw, Melanie Mitchell) : The FARGonauts . About analogy and creativity. Klett-Cotta, Stuttgart 1996, ISBN 3-608-91758-6 (American English: Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought . Translated by Ulrich Enderwitz, Original: 1995).
  • Le Ton beau de Marot: In Praise of the Music of Language . 1997.
  • Eugene Onegin; A novel versification. Basic Books, New York 1999, ISBN 0-465-02094-1 .
  • I am a strange loop . Klett-Cotta, Stuttgart 2008, ISBN 978-3-608-94444-0 (American English: I Am a Strange Loop . Translated by Susanne Held, original: 2007).
  • The analogy: the heart of thought . Klett-Cotta, Stuttgart 2014, ISBN 978-3-608-94619-2 (American English: Surfaces and Essences: Analogy as the Fuel and Fire of Thinking . Translated by Susanne Held, original: April 2013 - first published in February 2013 under the original title L'Analogie. Cœur de la pensée ).

Web links

Commons : Douglas Hofstadter  - Collection of images, videos and audio files