An analogy seems an appropriate way to begin a review of a book whose central theme is creative analogies: This review is to Douglas Hofstadter’s book as a musician’s improvisations are to the melody upon which he or she is improvising. For Hofstadter, this and other analogies grow out of the human ability, which lies at the core of creativity, to see similarities in things that appear otherwise dissimilar. Book reviewing, improvising a jazz solo, and discovering computer analogues to human thinking involve, respectively, new and preconceived ideas, musical phrases, and computer structures that are creative responses to a particular task, situation, or problem. Creativity is a very complex process, and over the centuries, different people have studied it in astonishingly different ways. One of the most difficult things for creative people to do is to choose a path through what at first seems a chaos of experiences and ideas, because in choosing a single theme to organize their thinking, they are forced to ignore many other facets of an inexhaustible subject. The risk that Hofstadter takes in Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought is awesome, since he is gambling that his study of concepts and analogy making will capture really big game—the essence of human cognition.
Douglas Hofstadter, the son of a Nobel Prize-winning physicist, has been interested in science, mathematics, music, and art from childhood. He became known to the public with his Pulitzer Prize-winning bookGödel, Escher, Bach: An Eternal Golden Braid (1979), a fascinating interdisciplinary study of how ideas of pattern recognition in the aesthetically driven work of a mathematician, an artist, and a musician could illuminate one another and also shed light on human creativity. Since 1977, when Hofstadter became an assistant professor of computer science at Indiana University, he and his graduate students have been developing computer models of how humans create concepts and discover new analogies. Fluid Concepts and Creative Analogies is the product of this research.
For almost as long as humans have thought about what it means to be human, mental activity—the ability to form concepts and to solve problems of increasing complexity—has been considered a unique attribute of the species. Hofstadter and other cognitive scientists believe, however, that a machine—the computer—will be able to model human thinking, and thus the chief tool of Hofstadter’s research has been the computer program. The greater part of his book consists of chapters describing specific computer programs that explore how to solve number sequences, anagrams, letter analogies, pointing analogies, and the recognition and creation of artistic typefaces. Though some of these programs succeeded in solving their targeted problems, this was not their principal purpose. Hofstadter used these programs to gain insight into analogy making, which he believes is the heart and soul of intelligence. The human mind is also adept at using fluid concepts that stretch to adapt to unanticipated situations. According to Hofstadter, the mental mechanism that enables humans to use fluid concepts and develop creative analogies is a system of many independent and parallel “subcognitive” agents that collectively construct coherent mental structures.
The fluid properties of thought suggested the name of Hofstadter’s group, the Fluid Analogies Research Group (FARG), but his book seems less like a work of group authorship than the product of the synthesizing intelligence of Hofstadter himself. He wrote four chapters, ten prefaces, and the prologue and epilogue, and he shared authorship of six other chapters, leaving only one with a sole other author. Therefore Hofstadter’s theme of pattern finding as the key to human consciousness, intelligence, and creativity dominates the book and undergirds all the computer programs designed to imitate human thinking.
An early program that enabled Hofstadter to begin this process was called Seek-Whence because the program would seek whence a sequence of numbers originated. For example, it would investigate the sequence 1, 3, 6, 10, 15, 21, and so on. These are called “triangular numbers,” because the Pythagoreans classified the numbers according to the shapes made by arranging dots in sand, and these numbers correspond to triangularly arranged dots. This number sequence of triangular numbers thus constitutes a puzzle, and the computer program had to find its underlying rule. In this case the rule is that the nth number is the sum of the first n integers; for example, the fifth triangular number is 15, since 1 + 2 + 3 + 4 + 5 = 15. This may seem simple, but to get a machine to do it (and other number sequences) proved to be very difficult, since guessing a pattern from a short sequence is like trying to predict what sort of adult a child will eventually become. For both number sequences and children, a prodigious number of possibilities exist, so the program is designed to make guesses, but such risks sometimes result in failure.
Because the initial program resisted moving off the beaten track, he developed another that used such “aesthetic pressures” as simplicity, consistency, symmetry, and elegance to make sense of number-sequence patterns. In formal terms, the program solved number sequences by parallel processing with probabilistic biases. Though the developed Seek-Whence program was able to find patterns in some number sequences, it was unable to succeed in many others, since the ability to perceive a theme in novel sequences required the generation of unforeseen concepts.
Seek-Whence acquainted Hofstadter with the difficulties of artificially simulating basic cognitive processes, and in his next program, Jumbo, he carefully designed a restricted domain where only certain salient characteristics of human understanding would be modeled. The Jumbo program tried to imitate the particular human skills used in solving anagrams; that is, it attempted to construct potential English words out of a group of letters by putting them into plausible combinations. The program had no English dictionary; it was a construction program. It started with isolated units (the letters), gradually constructed chunks of letters, and then combined these chunks into various clusters, syllables, and words. The process is analogous to how complex molecules are constructed inside living cells. Hofstadter also compares Jumbo’s strategy to the way bonds of human friendship are formed in the social world. Random selection characterizes the artificial microworld of Jumbo just as it characterizes the natural macroworld of human life. Some letters are strongly attracted to each other (as with...
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