Delving into multiple aspects of drawing analogies, this book targets a broader class of readers than just those scientifically interested in the most recent developments in understanding analogical thinking.

With its broad scope and abundance of examples, its stated avoidance of technical jargon and emphasis on accessibility, Mental leaps should be at least leafed through by all those serious amateurs who have enjoyed such books as Gödel,  Escher,  Bach [1]. That does not mean that Holyoak and Thagard have Hofstadter’s writing prowess, charm, and ability to build surprising new analogies. I just want to suggest that a reader of Gödel, Escher, Bach should enjoy the journey through many domains, including the evolution of thinking in animals, decision making in politics, education, and the role of intelligent machines, that Holyoak and Thagard propose.

Early in their book, the authors introduce three basic kinds of constraints that they use for every example. First, analogies are guided by direct similarity of the elements involved. The need to identify structural similarities between the source and the target is the second restriction. Third, there is always a purpose, hidden or not, for considering an analogy. Analogical thinking works by trying to satisfy these sometimes discordant constraints. Holyoak and Thagard avoid building a rigid mechanism. On the contrary, they emphasize that the restrictions do not necessarily operate sequentially, and that one should imagine them as a set of “light pressures” that push forward the task of achieving a certain goal.

Devoting most of their work to showing how the human mind uses these restrictions in the process of thinking by analogy, Holyoak and Thagard consider evolutionary changes in a special chapter, “The Analogical Ape.” Although all the vertebrates have the capability to go beyond direct similarities between objects, only primates can perform simple attribute mappings between representations of objects, and only chimpanzees and humans are able to explicitly think about sameness of relations. In chimps, these results are achieved after years of special training, and research has not proven their ability to rationalize about higher-order relations such as cause.

The following chapter, “The Analogical Child,” focuses on child psychology. There is no doubt that preschool children can learn general schemas and strategies from experience. Evidence suggests that relational mapping capability emerges at around age 3 or 4. A five-year-old child begins making analogical inferences based on causal relations. Holyoak and Thagard point out that lower-level techniques are often used in conjunction with higher-level ones. A three-year-old, capable of building analogies based on first-order relations, is still using similarity of objects or similarity based on explicit attributes, methods he or she discovered in infancy. Furthermore, an adult who has the potential for uncommon creative mental leaps will still use simple similarities. As Holyoak and Thagard phrase this interesting point, “the analogical child continues to be part of the analogical adult.”

After revisiting the aforementioned constraints and the role they play in various stages of analogy use--selection, mapping, evaluation, and learning--Holyoak and Thagard devote the next few chapters to analyzing major domains of human activity where use of analogy is the most successful. They discuss decision making, scientific discoveries, metaphorical thinking, and education, using a plethora of examples. The Nazi threat as a justification for the war in Kuwait, Plato’s comparison between cosmic and social order in his dialogues, Darwin’s evolutionary theory, and the Japanese tea ceremony are just a few of them.

Eventually, Holyoak and Thagard add a computational dimension to their psychological, philosophical, and linguistic investigation of analogy. They review the importance of the analogy between computers and minds for cognitive science. Without elaborating too much, they discuss how their own theory of analogy has its roots in the connection between parallel constraint satisfaction in visual perception and in human thinking. Readers are offered a superficial overview of several computer programs implementing their ideas, and those interested are referred to papers where details can be found.

The last couple of pages are devoted to the future of analogy. While retrieval and mapping have been modeled with relative success, not much is known about selection’s operating algorithm. More than that, if we are presented with multiple source analogs, how do we pick the most useful one and how do we combine relevant information pertaining to each of them? What are the mechanisms driving analogy in the human brain? Holyoak and Thagard admit that, not surprisingly, as some answers seem to have been found, more questions arise. Finding out more about analogy is similar to any other scientific work, and, by analogy, as painful.