References for Bongard Problems and Related Topics

Note: this page is part of this set of pages on Bongard problems


  1. Bongard, Mikhail Moiseevitch. (1970). Pattern Recognition. Rochelle Park, N.J.: Hayden Book Co., Spartan Books.
    Original publication: Проблема Узнавания, Nauka Press, Moscow, 1967. Note: What later became known as “Bongard problems” appear in the Appendix of this book.
  2. Foundalis, Harry E. (2006). Phaeaco: A Cognitive Architecture Inspired by Bongard’s Problems. (Note: large PDF, 14 MB.) Doctoral dissertation, Indiana University, Center for Research on Concepts and Cognition (CRCC), Bloomington, Indiana.
  3. Hofstadter, Douglas R. (1977). “56 New Bongard Problems”. Unpublished manuscript. Available through CRCC. Note: These problems are now available through my index page, as problems #101–156.
  4. Hofstadter, Douglas R. (1979). Gödel, Escher, Bach: an Eternal Golden Braid. New York: Basic Books. See pp. 646-662. Note: This book introduced Bongard problems to a wide audience in the so-called “Western” world.
  5. Hofstadter, Douglas R. and the Fluid Analogies Research Group (1995). Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought. New York: Basic Books.
    Note: In particular, see pp. 212–216 for a description of the Slipnet, the long-term memory component of the FARG architecture, which is employed in Phaeaco, too.
  6. Hofstadter, Douglas R. (1995). On Seeing A’s and Seeing As. Stanford Humanities Review 4,2 pp. 109–121.
  7. Hofstadter, Douglas R. (1997). Le Ton beau de Marot. New York: Basic Books. See pp. 84-86.
  8. Linhares, Alexandre. (2000). A glimpse at the metaphysics of Bongard problems. Artificial Intelligence, Volume 121, Issue 1-2, August 2000. See pp. 251–270. Note: One of few publications that delve deep into the essence of Bongard problems. Part of this article includes Linhares’s critique of Saito & Nakano’s approach to solving BP’s.
  9. Maksimov, V. V. (1975). Система, обучающаяся классификации геометрических изображений (A system capable of learning to classify geometric images; PDF, 3 MB; translation from the Russian: Marina Eskina), in Моделирование Обучения и Поведения (Modeling of Learning and Behavior, in Russian), M.S. Smirnov, V.V. Maksimov (eds.), Nauka, Moskva. See pp. 29–120. Note: Maksimov was a colleague of Bongard’s.
  10. Montalvo, Fanya S. (1985). Diagram Understanding: the Intersection of Computer Vision and Graphics. M.I.T. Artificial Intelligence Laboratory, A. I. Memo 873, November 1985. Note: Tangential to Bongard problems, only. Montalvo proposes a set of graphics primitives for human-computer interaction, and uses Bongard problems proposing to infer such a set of primitives.
  11. Saito, K., and Nakano, R. (1993) A Concept Learning Algorithm with Adaptive Search. Proceedings of Machine Intelligence 14 Workshop. Oxford University Press. See pp. 347–363.
    Note: This is the RF4 algorithm, which claims to have solved “41 out of 100 Bongard problems”. But, see Alexandre Linhares’s formal critique of RF4, cited above. See also my informal critique.


Web links:

  1. A review paper by D. R. Hofstadter. (Also mentioned in the references, above.) Reviews DRH’s ideas on A.I., pattern recognition, Bongard problems, and other interesting topics, including the Letter Spirit project (developed by Gary E. McGraw [part 1], and John Rehling [part 2], at CRCC).
  2. Joseph A. L. Insana’s pages on Bongard problems, and his page on meta-BP’s.
  3. What used to be a Bongard problem generator, by Luis Alfonso von Ahn, but now appears as a dry page announcing a defunct direction of the “CAPTCHA project”.


BP-related games:

  1. The New Eleusis game: played with cards, where “scientists” try to guess the rule thought of by a “god”. Note: Have you ever wondered why web authors enjoy shuffling web pages and URLs around, killing links worldwide? Me too. I swear there used to be a neat New Eleusis page. Perhaps someone with superior web-search skills can find out and let me know.
  2. Zendo: played with actual 3D pyramid-shaped pieces, where a “Master” thinks of a rule, and “students” try to guess it by constructing configurations (called “koans”) with the pyramids (each “koan” corresponds to a Bongard box, in other words). Seems to be fun!

Last Update: 11/03/06

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