Mathematical Formalism-or-Kurt Gödel's To Infinity...and Beyond

"To infinity... and beyond!". Buzz Lightyear Toy Story

As a University student, I had become very interested in Karl Pribram's ideas about the "holographic theory" of brain function. In the early 1980's, I had gone to psychology workshops in places like Spain, Germany and Switzerland which featured the likes of Pribram, Fritjof Capra and Ronald D. Laing. This was about the time that I also began a conversation with a Swiss physicist, which remains ongoing. During that time, I read such works as Capra's "Tao of Physics", Pirzig's "Zen and the Art of Motorcycle Maintenance", Zukav's "Dancing Wu Li Masters" and Rudy Ducker's "Infinity and the Mind". This "Field Note" is about a dream found in the latter book. 

Infinity and the Mind -or- Dreaming of Kurt Gödel 

The Western philosophy of mathematics dates back to the ancient Greeks. Rene Descartes Cartesian coordinate system revolutionized mathematics in the 17th century, and is still be seen operating in our everyday life. In the 20th century, another mathematical revolution would take place. David Hilbert had set out to create the rational basis for a complete formal mathematical system. 

Hilbert's enterprise would be forever defeated by another man by the name of Kurt Gödel who created the "incompleteness theorem", which mathematically proves that no mathematical system will ever be complete. While fatal to Hilbert's rational program of mathematical formalism, I actually believe that Gödel's theorem is liberating, creative and mystical. Gödel proved that there never is a fixed mathematical method to determine the truth (nor will there ever be one), and it is in this rational sense that mathematics will always have to depend on creativity to make progress. 

Ironically, David Deutsch "The Fabric of Reality" informs us that; "David Hilbert, the great German mathematician who provided much of the mathematical infrastructure of both the general theory of relativity and quantum theory, remarked that ‘the literature of mathematics is glutted with inanities and absurdities which have had their source in the infinite'." Is it surprising that the creator of "Alice in Wonderland" was a mathematician? 

Drucker "Infinity and the Mind" (p 184, Bantam paperback) recounts a dream he had; "I wanted to visit Gödel again, but he told me that he was too ill. In the middle of January 1978, I dreamed I was at his bedside. There was a chessboard on the covers in front of him. Gödel reached his hand out and knocked the board over, tipping the men on the floor. The chessboard expanded to an infinite mathematical plane. And then that, too, vanished. There was a brief play of symbols, and then emptiness-an emptiness flooded with even white light. The next day I learned that Kurt Gödel was dead." 

If Drucker does not interpret his dream vision, then I will. The dream illustrates the great mathematical beauty that can be found in our dreams. The obvious idea that we can read in this dream, is when Gödel knocks the chess board over, he is saying that for himself, it is "game over". We can see, like in many other dreams, perhaps all dream interpretations posted at the International Institute for Dream Research website, that all dreams can be viewed from a game theory perspective. 

Like something out of Alice in Wonderland, "the chessboard expanded to an infinite mathematical plane", ironically the concept of "infinity" is the topic of Drucker's book. The board then reached the visual "vanishing point", and disappears. After the brief play of symbols, "emptiness" which was part of yesterday's dream interpretation "Ontopoetics of Emptiness"  floods the dream with even white light. Is this a representation of a final mathematical dream's fireworks to celebrate one man's game of life well played? 

On a few final notes, Drucker asks; "Does a dream which you never remember really exist?" Drucker also refers to the "Mindscape", which is nothing less than what is known in some esoteric forms of knowledge as a "mental plane" (or world of thought). From a more traditional perspective, I see our dreams influenced by the cultural "marketplace of thought" we live in. From my own more literary perspective, our everyday dream visions create a phantasmagoria of dream worlds. Much like Dante's "Divine Comedy", "1001 Nights in the Global Village" will provide you the reader with a poetic post-modern guide to navigate the human historical marketplace of thought and the phantasmagoria of dream worlds found in dream vision. 

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All material Copyright 2006 International Institute for Dream Research. All rights reserved.