The Year of Mathemagical Thinking

Thursday, Mar. 15, 2007 By LEV GROSSMAN

Carol and Douglas Hofstadler in a mutual nose touching, forming a (metaphorical) "strange loop" in July of 1987 in the Wallowa Mountains in Eastern Oregon.

When I was growing up, there was a book in our house that my brother and sister and I all read. It was a very odd book, a rattlebag of art, mathematics, music, philosophy, symbolic logic, computers, genetics, paradoxes, palindromes and Zen koans among many, many other things. Most of it went way over my head--my precocious older sister, who later became a mathematician, and even later a sculptor, was the real target audience--but it was playfully written and deeply weird and off-the-charts smart and generally just the thing for a household of pretentious, alienated adolescents to chew on. My siblings and I weren't especially close, but we always had that book in common: it was our secret shared nerd bible. 

The book was called Gödel, Escher, Bach: An Eternal Golden Braid--Gödel being the Austrian mathematician Kurt Gödel; Escher, the fantastical Dutch artist M.C. Escher; and Bach, the Baroque composer Johann Sebastian Bach. The extraordinary mind that braided these three figures together in one book belonged to one Douglas Hofstadter, a physics Ph.D. who was only 34 years old at the time. He won the Pulitzer Prize in 1980 for Gödel, Escher, Bach, and it went on to become a cult classic that influenced a generation of thinkers. Since then Hofstadter has published on numerous subjects, but he never went back at length to the themes of his first book. 

Until now. Later this month Hofstadter will publish I Am a Strange Loop (Basic Books; 412 pages), in which he expands and builds on the groundwork he laid in his earlier work. But Hofstadter has been through a lot in the past 28 years, including the tragic death of his wife, and I Am a Strange Loop goes to far darker and more personal places than the playful book I read as a teenager.

Hofstadter's unique intellectual makeup is rooted in his childhood. His father was Robert Hofstadter, who won the Nobel Prize for Physics in 1961. As a boy, Hofstadter was fascinated by visual and conceptual loops: feedback, self-reference, recursiveness, anything that curved back on itself in an unexpected way. He provides several examples in I Am a Strange Loop (which is, among many other things, an intellectual autobiography). In the comic strip Nancy, Sluggo has a dream about a dreaming Sluggo, who is also dreaming of Sluggo, and so on in an infinite chain. The girl on the Morton's Salt box holds a Morton's Salt box that has her own image on it, which in turn has a tiny salt box with another girl on it--the series would regress endlessly if her arm didn't get in the way. Goofing around with a video camera, Hofstadter pointed it straight at the TV screen to create an infinite receding tunnel of video feedback. 

Hofstadter might have grown up to be a straight-up physicist like his dad if it hadn't been for his younger sister Molly. When Hofstadter was 12, it became clear that she had grave neurological problems--she never learned to speak or understand language. "I was very interested already in how things in my mind worked," Hofstadter says. (He speaks very gently and deliberately, as if Mr. Rogers had been a super-intelligent rocket scientist instead of a Presbyterian minister.) "When Molly's unfortunate plight became apparent, it all started getting connected to the physical world. It really made you think about the brain and the self, and how the brain determines who the person is." 

Those themes--recursive loops and the physical origins of consciousness--get braided together in I Am a Strange Loop in unexpected ways. The book returns to a theme that Hofstadter first sounded in Gödel, Escher, Bach: exploring the nature of the human mind through the work of Gödel, who demonstrated in 1931 that conventional mathematics, which we think of as a supremely logical and consistent system, is actually capable of making all sorts of strange, paradoxical, self-referential statements about itself. For example, Gödel discovered there are mathematical statements that, while true, can never be proved. How can something be both true and unprovable? This idea, loosely known as "incompleteness," came as a logical bombshell to all right-thinking mathematical philosophers--you could compare it in its impact (a little glibly) to Heisenberg's famous uncertainty principle. It turns out that mathematics isn't a neat straight line; it's a loop, and a deeply strange one at that. 

Hofstadter sees in Gödel's work a structural parallel to the mystery that is the human mind. The brain, which is merely a squishy agglomeration of madly firing neurons, shouldn't by rights be able to think--it shouldn't be able to wake up, twist around, become aware of itself, and in doing so become an "I," but it does. Just like Gödel's mathematics, the mind is a strange, self-referential loop--it's a mirage, Hofstadter writes, but "a very peculiar kind of mirage ... a mirage that perceived itself, and of course it didn't believe that it was perceiving a mirage, but no matter--it still was a mirage." 

Hofstadter's model of the self occupies a middle ground, hard won via logico-philosophical reasoning: it's neither spiritual--he's not a religious man--nor is it locked into the cold neurological materialism of cellular mechanics. To Hofstadter, the human mind is a bright, shimmering, self-sustaining miracle of philosophical bootstrappery: "vague, metaphorical, ambiguous, and sometimes exceedingly beautiful." 

I Am a Strange Loop scales some lofty conceptual heights, but it remains very personal, and it's deeply colored by the facts of Hofstadter's later life. In 1993 Hofstadter's beloved wife Carol died suddenly of a brain tumor at only 42, leaving him with two young children to care for. Hofstadter was overwhelmed by grief, and much of I Am a Strange Loop flows from his sense that Carol lives on in him - that the strange loop of her mind persists in his, a faint but real copy of her software running on his neural hardware, her tune played on his instrument. "It was that sense that the same thing was being felt inside her and inside me--that it wasn't two different feelings, it was the same feeling," Hofstadter says. "If you believe that what makes for consciousness is some kind of abstract pattern, then it's sort of a self-evident fact that whatever pattern exists in my brain could exist in other physical structures in the world." I Am a Strange Loop is a work of rigorous thinking, but it's also an extraordinary tribute to the memory of romantic love: The Year of Magical Thinking for mathematicians.

Just before the epilogue of I Am a Strange Loop, there's a photograph of a sculpture, an in-curving, interlaced metal knot that could almost be a three-dimensional map of one of those recursive, self-referential arguments Hofstadter is so fond of. When I saw it, I was struck not just by how beautiful it was but also by the fact that I'd seen it before: it was made by my sister, who was so deeply inspired by Gödel, Escher, Bach 28 years ago. Purely by chance, it was given to Hofstadter for Christmas one year, and he photographed it and put the picture in his book. I told Hofstadter, who loves this kind of spectacular oddity--it's evidence, maybe, that something of his mental pattern made its way into his writing, then into my sister, on into her art and finally back to its original source, Hofstadter himself, thus closing the circle. "That is hilarious," he says. "It is really a strange loop."