Tuesday, September 06, 2005


I wsa introduced to the world of Bongard problems by Douglas R. Hofstadter's book Godel, Escher, Bach: an Eternal Golden Braid. Bongard problems are studies in pattern recognition and are, thus, useful to such researchers as neurologists and psychologists as well as those studying artificial intelligence.

A Bongard problem is a set of twelve squares — six on the left, six on the right — with figures in them. The left group of figures have some property that links them while the right group lacks that property. The challenge is to identify the property. In the example below, the property is three sidedness. The potential properties cover a wide range, including color, size, curvatures, angles, and so forth. Many of the problems are exceptionally subtle and can be a real challenged to figure out.

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Harry Foundalis has put together an index of 263 (as of this writing) problems, which constitute today's link. Be warned, these are Bongard problems. No solutions are provided; you will need to work those out on your own. The nice thing abount these, though, is that once you've found a solution, it's usually self-evident that you have the correct answer.

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