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Surfaces and Essences: Analogy as The Fuel and Fire of Thinking by Douglas Hofstadter and Emmanuel Sander, Basic Books, 530 pages ($35).

Should anyone go through life under the delusion that he or she is already smart enough – or, for that matter, always capable of being smart enough, given the right instruction – we sometimes have new books by Douglas Hofstadter to disabuse us of our folly.

Of Hofstadter’s daunting brilliance there has never been any doubt. If a Pulitzer Prize for his book “Godel, Escher and Bach” fooled large hordes of book buyers into believing they had the tenacity and intellectual wherewithal to negotiate all the stops and turns and careening straightaways of his mind, there was the book itself, not to mention his next book “I Am a Strange Loop” to cast serious doubt.

Reading a Hofstadter book from beginning to end is so intellectually bracing that it resembles an entire graduate school – rather than a graduate school course – all to itself.

Here is his newest book, a collaboration with a professor of psychology at the University of Paris whose simple premise is that – as the title says – “analogy” is “the fuel and fire of thinking.”

A tiny sample of what Hofstadter does. Imagine, as he does, that “Paul and Tom are attending a conference. They are having a lively conversation in the bar of their hotel. An hour passes and Paul says ‘I’m going to pay for my beer.’ Tom replies ‘Me Too.’ ”

Unlike us, Douglas Hofstadter thinks “Tom’s tiny remark … turned out to be surprisingly complex, and indeed in the ‘geometry’ of situations there are seldom if ever parallel lines.” To Hofstadter, Tom’s “casual ‘me too’ really means ‘if one looks closely’ I understand the intention you just described concerning the situation you’re currently in, and it’s my intention to do the analogous thing in the corresponding situation that I find myself in.”

Understand, then, how you understand what you do, what you think about what you do and do what you do. Unless, of course, it’s too hard, in which case understanding that may be the most profound thought you have all month.

– Jeff Simon