D+iz+a+n+k+Meister's Journal: Godel, Escher, Bach: Some random thoughts on the book

Artificial Intelligence, and Intelligence in general, are not primarily concerned with "eneumerating truths" or "deciding propositions." If you think about it, in a very practical sense, one's intelligence is not a reflection of how many or how fast one eneumerates or decides the truth of a particular proposition. Especially when intelligence is used in the vernacular sense(or Turing Test sense).

However, there is, after a suitable explanation of Godel's Incompleteness Theorem, a nagging suspicion that the very idea of "Artifical Intelligence" is a contradiction. All programs are explicitly formal, definitely formal enough to fall prey to Godel's construction, so how could they possibly be intelligent with such an obvious and severely limiting property? Isn't it paradoxical to think that there could exist a formal system(program) that understood its own Godelian limitations?

Ultimately, it's no more a paradox than Zeno's paradox(es).

The knowledge that one can or cannot establish truth in the face of infinity is irrelevant IF there is any non-volatile level. Regarding Zeno's paradox and classical mechanics, the non-volatile level is the compact set that is any closed interval of the real line. Regarding AI. . .well that's the content of the ~750 pages of Hofstadter's book.

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The Location of Meaning
This was one of the more illuminating sections for me. It really sets up a nice argument against intentionality.

The question is: How does one know when any given "message" was "understood" "correctly"? What does it mean for a message to be understood?

Hofstadter outlines a 3 tiered structure for any message: The "outer" message, the "inner" message, and the meaning. The "outer" message serves the purpose of presenting "Hey, here's a message!" The "inner" message serves the purpose of presenting "Hey, here's how you decode me!" The meaning is the actual information contained in the message.

Regarding sending out LP's made of gold into space with the hope that they will be replayed by an alien race, the outer message has the form of a perfectly circular gold disc. A form so odd in nature, ANY intelligence will recognize that it must be more than just a shiny disc. The inner message is the grooves in the LP. Bumps and grooves that spiral from the outside towards the center. . .what to do with them. Again, just about ANY intelligence will recognize the isomorphism between this oddity on the surface of the disc, and the "information" this disc probably holds. Obviously then, the message is the audio stored in the grooves.

I think it's a fairly straight-forward way to explain general communication, especially when looked at from an informatin theory standpoint.

My question for people who believe in intentionality as a necessary condition for mental processes is: at what point did you intend to only decode messages from the visible light spectrum or the audible spectrum? The answer is it is programmed into you via your DNA. I don't believe that any human has existed that made the deliberate choice to only monitor those small parts of the spectrum for messages.

Thus, there exists a non-volatile level, our senses, that guide and limit our own mental activities, regardless of our intentions.

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misUnderstanding Zeno
Godel's Incompleteness Theorem, once properly understood, is a lot like Zeno's paradox(but on philosophical steroids).

Godel's Incompleteness Theorem applies to all formal systems with sufficient descriptive power. Those systems will either be inconsistent(unlikely by definition) or incomplete. But more importantly, if one adds those "missing" propositions in an effort to complete the system, the system remains incomplete. Much like Zeno's paradox, where one can never take a first step to even begin moving since one can never define a first step because of the infinite divisions.

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Koans

It seems that there is a very logical reason for teaching Zen through paradoxical koans. In order to fully grasp the paradox, one has to stop thinking in a decidable truth sense, and step outside the system to see the greater truth.

This is analogous to the sensation of looking at most Escher drawings. . .or constructing a Godel numbering. . .or playing an endlessly rising Cannon. . .or naming something without naming it.

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Godel's Incompleteness Theorem isn't a limit on what will be possible with computers. . .if anything it guarantees that what is possible with computer is at least capable of handling most decidable situations, and whatever emergent behavior comes along as a direct result of the program existing(running?) will obviously supplement those abilities.