Tuesday, October 30, 2007

I am a Strange Loop by Douglas Hofstadter.

Hofstatdter is the author of one of my favorite books: Godel, Esher, and Bach. published in 1979 and is a fascinating interplay between the works of the three men named in the title. Mostly, though, it is a long proof, and not and easy one, of Kurt Godel’s Incompleteness Theorem. In his current book, I am a Strange Loop, Hofstadter returns to the themes from GEB to better nail down how he thinks the loopiness described by Godel is responsible for our consciousness or our “I”. Heady stuff.

Before 1931 Bertrand Russel and Sir Alfred Whitehead thought they had totally nailed down the fundamentals of mathematics. They produced a system of axioms and rules to apply by which all the properties of mathematics could be systematically proved (or un true statemens disproved). In this system, and central to mathematics thinking, is that true statements are proveable and proveable statements are trure. The converse is equally correct, namely, unproveable statements are false and false statements are unproveable. The renegade Godel (only 25 at the time) produced a paper in 1931 which showed that not only this system but any logical system is doomed to failure. The essence of the theorem is the idea of self-referencing. Call the Russell/Whitehead system RW. Godel produced a theorem that basically said “This theorem is unprovable in RW”. Think about that. If you did prove it then it is true. . . but you already proved it! If it cannot be proved than it is false which means it should be provable.

Statements that contradict themselves have been an entertaining curiosity for eons but Godel’s theorem is actually deeper than that. Still, wacky sentences like that will give you the flavor of the problem. Here’s another example. There’s a game you can play (although not that fun) whereby you try to express numbers in english sentences in as few a number of syllables as possible. For example, 1024 could be expressed as ‘one thousand and twenty four’. 7 syllables. But you could also express it as ‘two to the tenth’. Only 4 syllables! So, I’ll make up a number, call it B. B is the first number that cannot be expressed in less than thirty syllables. Got that? But wait. I’ve now completely described this number in twenty syllables! But by it’s very definition it CANNOT be described in less than 30! Loopy.

It is this kind of self-referencing that Hofstadter is talking about. You can think of the operation of our brains in two ways. One way is at the basic level of atoms and synapses. At this level you will never come to any greater understanding of consciousness. Say you hear a song and it makes you remember a long lost girl friend. You’d be hard pressed to identify exactly which neurons (if any) are exactly responsible for either remembering the song or connecting it to the girl. Perhaps much more advantageous to work at the ‘symbol’ level of the brain. The brain retains an interconnected set of symbols for that song and that girl. The symbols are responsible for moving the atoms around and not the other way around! Now extend the idea of the symbols to being loopy and the loopiest of all in that it points to or references it’s own loop is the symbol that we call “I” - our consciousness or our soul. Hofstadter uses the word soul a lot but not in the Judeo-Christian sense. He uses it to mean that inner voice. That “I-ness”.

I should point out that these ideas are drawn out via a multitude of analogies and stories from his personal experience and I only offer a sketch of the big ideas.

The later part of the book goes into how the symbols of one person can be incorporated into another. Like when we adopt another’s mannerisms or shared memories. A jump is then made to perhaps even incorporating a grainy version of the other person’s “I-ness”. The question then comes up, if one person dies is that person or at least some of their brain symbols and perhaps even a crude “I-ness” still around in the other person’s brain?

Understand all of this is from a guy who is professor of Cognitive Sciences at Indiana University. While some of the ideas may sound mystical there is actually nothing in his writing to suggest that at all! This is an interesting but tough read and you don’t really have to read GEB as a prerequisite. He does a pretty good job of giving a shorter proof of Godel’s theorem in this book. You do need to read slowly and stop and reflect on occasion.

I have a few chapters to go and am interested to see how he wraps all of this up. In a strange loop I would guess!

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