Who's Counting: Hofstadter's Strange Loops -- as Well as Colbert and Borat Book says our own reality is complicated and multilayered.

June 3, 2007  -- Who are you? Douglas Hofstadter, the Pulitzer Prize-winning author of "Godel, Escher, Bach: An Eternal Golden Braid," has just written a sequel to that much-acclaimed book in which he focuses on the nature of consciousness and self.

What does it mean to be conscious, to be self-aware? What is a self? What is an "I"? One reason it is so difficult to get a scientific handle on these questions is that we're too close to them. We can't employ the usual scientific technique of stripping away the subjective elements of a phenomenon to arrive at an objective account of it since it is the subjective elements we want to understand.

The gist of Hofstadter's answer to these questions in "I Am a Strange Loop" is that the self and awareness are best understood by looking at higher-level patterns and structures made possible by the underlying biochemistry of our brains. These patterns and structures are self-referential and emerge over time from complex neuronal activity.

What does this mean? One of the joys of Hofstadter's book is that it is full of suggestive metaphors. To hint at the unexpected consequences of even the simplest self-reference, for example, he considers a video camera aimed at a television monitor that shows its own output resulting, especially when the camera is moving, in a variety of hall-of-mirrors effects, some familiar, some not.

Careeniums and Simmballs

Another illuminating metaphor helps elucidate how symbolic thought emerges from lower-level neuronal buzz. Hofstadter asks us to imagine a billiard table with countless small interacting magnetic marbles, or simms. These simms careen around the table, leading Hofstadter to term it the careenium.

Sometimes these simms clump together magnetically and form spherical clusters of simms or simmballs. The simms move around randomly, but these larger simmballs have trajectories that are partially determined by external forces to the careenium, and their movement thus begins to model conditions outside the careenium.

Substituting cranium for careenium, individual neurons for simms, and symbols for simmballs, we understand that these symbols and structures gradually reflect a more and more refined representation of the outside world. Note that this awareness does not inhere in individual nerve cells but in the large-scale structures, the symbols, within the brain.

Symbols develop for all manner of entities including, at a sufficiently complex level of development, a symbol for an "I," that is, a symbol that represents itself. This symbol is aware of itself and of other objects, people, ideas, desires, fears, motivations, et cetera, but not of the neurons of which it's composed. The stories of our "I" symbols are the stories of our lives.

Strange Loops and Godel

This self-referential emergent loop that is the "I" symbol is indeed strange and abstract. Hofstadter argues that neuronal commotion can give rise to high-level symbolic thought in something like the way that dry statements about numbers can be interpreted, via appropriately clever codings and other techniques, as high-level statements about provability, consistency and the like.

As Kurt Godel showed, statements about numbers have coded within them higher-level statements that "talk" about themselves and the arithmetic system of which they're a part. Likewise, a long developmental process has resulted in neuronal movements having coded within them higher-level symbolic patterns that "talk" about the world and themselves.

This self-reference and criss-crossing of levels is why we're all strange loops, or, as Hofstadter also puts it, "hallucinations hallucinated by hallucinations."

That's the almost criminally abbreviated gist of this wonderful book, but there's much more in "I Am a Strange Loop." Included are discussions of why these high-level mind patterns are not necessarily dependent on the particular physical stuff of the brain, of how identities can be distributed throughout several brains, of gradual self-construction and degrees of self-awareness, and of ways we model others in our minds and thus give them a pale sort of life within us.

Reflections in Humor and Popular Culture

This all may seem quite esoteric, but questions like these lie near the surface of popular culture from the virtual world of "Second Life" to the surreal world of television news. I just read of a panel discussion held in Colorado, for example, whose subject was the number of levels of reality present if Stephen Colbert, anchor of the faux news "Colbert Report," were to interview Sacha Baron Cohen, creator of the characters Borat and Ali G.

Colbert is, one senses, a very nice guy, but he is also a comedian who pretends to be a self-centered, overbearing blowhard of a television pundit. Cohen is intelligent and thoughtful, but he is also a comedian pretending to be an ignorant, anti-Semitic homophobe. We sit at home watching the interview and forming little ancillary "I" symbols in our minds for each of these men as well as for their ancillary sub "I" 's.

This self-referential tangle, being indefinitely extensible and recursive, leads to strange psychological effects, one being that the characters played by Colbert and Cohen can be more truthful in disguise than they can if they present themselves straight.

That we can understand these various levels and personas, their interaction, and analogies to other situations is testament to how natural are some of the seemingly abstract ideas in "I Am a Strange Loop." Humor, in particular, calls on our ability to model others' personalities, understand their points of view, and stand outside ourselves.

Even the verbal and nonverbal cues (raising an eyebrow, changing one's tone of voice, winking) that are present in joke-telling are somewhat paradoxical. They say, in effect, "This is unreal," and they are more or less equivalent to the classic "I am lying," or, "This statement is false," which is true if and only if it's false.

Strange and loopy are we.

John Allen Paulos, a professor of mathematics at Temple University, has written such best-sellers as "Innumeracy" and "A Mathematician Plays the Stock Market." His "Who's Counting?" column on ABCNEWS.com appears the first weekend of every month.