I finally started digging into “Godel, Escher, Bach” by Douglas Hofstadter. This is a big book; over 700 pages. And it’s mostly about math. Well, really it’s about “meta-math”: the bigger ideas behind math. But in order to get to the bigger ideas, the reader has to wade thru a lot of stuff about ordinary math, the kind of stuff that you sat thru in high school and freshman year in college, bored out of your skull. Mr. Hofstadter tries to make it as un-boring as possible by telling entertaining stories and presenting little ‘brain-tickler’ puzzles and hosting a fairly wide sample of artistic works by Escher (those crazy drawings that defy the normal rules of dimensionality and gravity). And he wants to convince you that math is the foundation of human consciousness.

I’m only at page 110, but so far I can’t see how a group of conventions regarding sets and axioms and theorems are going to explain why I think there is a ‘me’ inside of me. But that’s just it, Hofstadter would say. Consciousness is all about chasing your tail, about looping around without any starting or ending points. And that’s just what a lot of mathematicians have been thinking about over the past 100 years or so. Well, all this recursive math stuff is pretty interesting, but I’m still not sure that it’s going to bring me any closer to the mystery of subjective mental experience than the various neuroscientists, psychologists and philosophers, whose books about the mind and consciousness line some of my shelves. (Or sit on my floor – I don’t exactly have a nice, neat library here in my dinky apartment).

Hofstadter is enthralled with Bach’s musical works, because of the complex relationships between the various musical patterns that interweave cleverly through many of his compositions. I can’t say that I’m a big classical music fan; and even the Bach that I have heard . . . . well, let’s just say that I’ve thus far failed to appreciate the genius behind it.

The best song that I know of which deftly intermixes a group of wandering musical elements is a guitar instrumental by The Ventures, from their Live in Japan ’65 album. The song in question is a 3 and ½ minute medley of three Ventures hit songs from the early 60’s: Walk, Don’t Run; Perfedia; and Lullaby of the Leaves. It uses the standard 4-man pop tune setup typical of the mid-60’s: drums, lead guitar, rhythm guitar and base, i.e. the same line-up that the Beatles and their imitators made famous. But I’ve never heard a song where each musical element is so distinctive and independent, and yet plays off the other three so well. When listening to Medley, you can easily pick out one instrument and follow it all the way through. Even rhythm guitar, something that you hardly notice on most “fab four” songs, is a distinctive contributor to Medley. Each player gets his moment in the spotlight (even Bob Bogle on bass fills in the weak spots with some fantastic rides). But at just about every point in the record, each player is present, working away. I’m not sure about the math behind the notes on Medley. But my conscious mind tells me that there was some real genius at work in putting it together.

One more thing about the Ventures versus Bach: most classical work is quite complex but rather slow tempoed. Medley moves along at a lively clip. There isn’t much room for error. It’s kind-of like a race car ballet, moving along at 150, everyone hoping that everyone else gets the moves right and doesn’t crash. Maybe that’s not a bad way to think about how our minds work – at least when they work right. Every now and then they go crash, and all the notes in life are off-key. At least three-fifths of my typical work-week goes like that! And not like Godel, Escher, Bach, and The Ventures.

I’ve been reading some interesting articles lately by Ed Fredkin and Lee Smolin which imply that reality — matter, energy, and even empty space — is ultimately made up of little boxes. According to these theories, even time is not continuous; it proceeds in spurts. The boxes and spurts are extremely tiny, so we never notice them. Everything seems smooth to us. But at some point of extreme magnification, reality may well become “granular”. We could never directly “see” this granularity. It’s so tiny that even the smallest blips of energy (photons, electrons, gravitons, whatever) are relatively huge. And the only way we see anything is by bouncing these blips of energy off the thing. The little grains of reality are too small to make any difference in the way that photons (light particles) bounce.

Don’t ask what lies within the boxes in space and spurts of time. That is where reality, as far as we are concerned, ends. We can never know if there’s a creamy cupcake filling deep inside all of those little thing-a-ma-jiggies that make up space and time. All we would know is that Picasso and the other Cubist painters ultimately had the right idea.

Smolin is a main-line physicist, extremely bona fide. His work is a rigorous (though yet still unproven) extension of both Einstein’s theories of relativity and quantum theory. Fredkins’ work is deeply rooted in science, but veers off into metaphysics (via the fascinating field of “complexity” and “emergence”, where high-powered mathematics and modern computer science interact). Fredkin has said (more or less) that a digital universe actually looks and acts something like a computer. Some people take him to say that as a computer, the universe is actually computing something. If that were to be true, then perhaps the answer to what life means IS truly blowing in the wind. But Fredkin cuts you off before you can accuse him of believing in God. He won’t go so far as the 18th century theologians who argued that just as a watch requires a watchmaker, an orderly universe requires an intelligent and godly creator.

If you want to continue along the digital reality spectrum into the realm of New Age speculation, the next guy to see after Fredkin would be Australian philosopher David Chalmers. Chalmers hasn’t said too much yet about digital reality, but he has put out a theory of generic consciousness that takes up from Fredkin. Fredkin talks a lot about the fundamental nature of information, and so does Chalmers. Fredkin sets up the picture of a digital universe mediating information on many different levels, from tiny, super-fast micro-events within the atom to huge, billion-year macro events between galaxies. Chalmers equates information with consciousness, and posits that different flavors of consciousness may exist on both tiny and huge scales; the human brain might not have a monopoly on consciousness according to Chalmers.

These other forms of consciousness, if they do exist, would seem very strange to us. But then again, during the last 500 years when cultures from different corners of the globe first laid eyes on each other, the feelings were quite similar (e.g., when European explorers first saw African pigmies, they had a hard time thinking they were really human; it took a lot of reflection to accept that in spite of the many differences, Englishmen and pigmies share all of the salient features of the human race).

Well, in a previous essay I said that I couldn’t dig the Chalmers view. It seemed to me that consciousness is a human brain thing. I’m still not ready to accept Chalmers’ speculation about thermostats having a form of consciousness just because they process information about their environment. But the grand arc that sweeps from the digital nature of Smolins’ “loop quantum gravity” theories (which stand a decent chance of being proved right), through Fredkins’ computerized universe ideas, proceeding across Chalmers’ bridge between information and consciousness, does inspire some huge thoughts. Perhaps the Universe is somehow conscious? And that consciousness is somehow related to our individual human consciousness? And once the techno-theologians jump in to this, does God make a comeback (in spite of Fredkin and Chalmers’ atheism)? Or maybe — are those little unbreakable, unknowable granules of space and time — are they God?

Folks, this could get very, very interesting.

PS, after I wrote this essay, I went out running. In the dark eastern sky I could see beams of light shooting up from lower Manhattan. Yea, it’s been five years since nine-eleven. Definitely a reality check.