- - Friday, April 6, 2012

By Jan Westerhoff
Oxford University Press, $11.95, 144 pages

”We’re living in Escher’s world it seems / we’re wide awake within our dreams.” The couplet comes from a CD by the 1990s band Chagall Guevara. The “Escher” they sing about is Maurits Cornelis “M.C.” Escher, the 20th-century Dutch artist of impossible visions that appear possible because of their mathematical exactitude.

The band describes images from some of Escher’s more memorable woodcuts thus: “Up’s down, down is out, out is in / stairways circle back to where you’ve been / time falls, water crawls, are you listening?” If you were listening, certain images very likely just cycled through your brain. The artist’s work remains popular and is easily available in books, in wall calendars and on the Internet.

Escher puts in a key appearance in philosopher Jan Westerhoff’s “Reality: A Very Short Introduction.” We see the whole of Escher’s “Print Gallery” reproduced in the first chapter, a visual puzzle that “depicts a young man in a picture gallery, looking at a print with a harbor and a city behind it. As we enter the picture and examine the city, we see a woman sitting at a window above a picture gallery, in which the very same young man is looking at the picture we are currently in!”

Question: According to the logic of the picture, is the man “real?” Mr. Westerhoff says this is “impossible to determine” because we cannot judge “whether the man is outside the picture, and therefore real, or part of the picture itself, and therefore unreal.”

In fact, there remain “equally good reasons for either view,” depending on how we look at the picture. If our starting point is the man, “we see that he stands in front of the picture.” Yet if we draw back and start with the picture, “we see that the man is clearly in it.” The puzzle is ultimately unsolvable because “there is no additional information to be gained, no further facts to appeal to that would settle how matters really are.”

The author uses this illusion to help prod us further on a number of fronts, including the ultimate question: How can you, the knower, know that you are real? The philosopher Rene Descartes thought this a bedrock truth. “Cogito ergo sum,” he said, which is usually translated “I think, therefore I am.” (Leading to the obvious joke: Descartes’ wife informed him that they would be going to the theater that night. “I think not,” he exclaimed and - poof - he disappeared.)

Philosophical solipsism, which Descartes did not quite fully embrace, has been “the femme fatale and bete noire of philosophical theorizing for centuries, seductive because it appears irrefutable, frightening because such a world would strike most people as claustrophobic,” Mr. Westerhoff writes.

Yet many philosophers have interrogated solipsism’s claim, asking: What is this “I” you speak of? How does it know things? And if you are the only irreducible truth, what happens when you are no more? For that matter, how can you know that you are, if you admit no other measures as valid?

Most of us, even the philosophers, are not quite that self-centered. Yet many of the things we think of as “real” - time, numbers, concepts - can be pretty slippery fish. (Two plus two equals four of what?)

Mr. Westerhoff does a competent job surveying the philosophical challenges to various pieces of reality while maintaining the appropriate skepticism of ultimate skepticism. He begins the introduction by saying that you, the reader “probably believe that th[is] book, the paper it’s printed on, and the letters printed on the page are real.” “This,” he reassures us, “reflects a healthy psychological attitude.” Yet he would like to stretch our “philosophical imagination” a little bit.

Toward that end, the author asks how can you be so sure that you aren’t dreaming right this minute? He explains that during the REM phase of sleep, which we experience every night, our consciousness is almost indistinguishable from waking consciousness. During this time, you experience and consider serious questions just like when you are awake, which is why some people can go to bed with a puzzle and wake up with the solution.

Or not. People can also “awaken” from dreams only to find that they’re still sleeping, and repeat this Russian doll-like process several times. This terrifying phenomenon was well captured by the 2010 Christopher Nolan-directed heist film “Inception.” You might try pinching yourself to confirm your waking consciousness, dear reader, but no guarantees that will work.

 • Jeremy Lott is.

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