Incompleteness and Strange Loops :: Imaginify Community Network

People: Incompleteness and Strange Loops

Friday, May 18, 2007 - 05:08 PM

"Kurt Gödel's (1906-1978) monumental theorem of incompleteness demonstrated that in every formal system of arithmetic there are true statements that nevertheless cannot be proved. The result was an upheaval that spread far beyond mathematics, challenging conceptions of the nature of the mind."- Rebecca Goldstein, Radcliffe Institute for Advanced Study
Harvard University

"I am a Strange Loop" (2007), seeks to demonstrate
how the properties of self-referential systems,
demonstrated most famously in
Gödel's Incompleteness Theorem, can be
used to describe the unique properties of minds.
- Douglas_Hofstadter, Center for Research on Concepts and Cognition
Indiana University

"Douglas R. Hofstadter: Analogy as Core, Core as Analogy"
Glen Worthey, Humanities Digital Information Service (HDIS), Stanford University Libraries, 2006

"Is the core of cognition and animacy essentially only self-representation and self-reference (as in Bach, in our DNA and elsewhere)? Is it essential incompleteness (as in Gödel’s Theorem and elsewhere)? Is it strange loops and tangled hierarchies (as in Escher, in Hofstadter’s own book, I Am a Strange Loop, and elsewhere)? Is it in the patterns, puzzles, paradoxes, puns, poetry, and programming that we see throughout Hofstadter’s work? Or is it elsewhere?

Elsewhere.... Perhaps it is precisely in analogy that we find the common thread of all these cognitive and creative phenomena, and thus the common element in the endeavors that make us human, and thus the core of our humanity..."

"The Year of Mathemagical Thinking"
Lev Grossman, TIME Magazine, March 15, 2007

Review: "A Reflection on The Loopy Self"
Ben C. Burns, Harvard Crimson, April 27, 2007

“I Am a Strange Loop” sets out to probe the essence of the soul—in a philosophical, cognitive sense... Consciousness, soul, and “a light on inside” are all terms referring to the essential “I” which somehow composes an individual human self...

...is very self-referential, and that any explanation of the concept bends back onto the same concept again. The resulting loop, though, isn’t like most loops caused by self-reference, since there’s no feedback as in... an infinite corridor of TV screens on videotape. So consciousness isn’t a regular loop; it’s a strange loop.

..while presenting arguments of logic, clever bits of analogy here and there add up to reveal that the book itself is more than just a friendly essay: everywhere you turn, “Strange Loop” is drawing back on itself, too. For example, the book’s arguments are made almost entirely through symbols, analogies, and tales of personal experience. Appropriately, Hofstadter devotes much discussion to the reasons that symbols, analogies, and empathy (or, as he calls it, “Varying Degrees of Being Another”) actually work. This book is a work of art, unabashedly self-referential on every level..."

"Trying to Muse Rationally about the Singularity Scenario" [Quicktime] [MP3]
Singularity Summit, Stanford University, May 13, 2006

Abstract: "...And yet there are some basic ideas that we should not lose track of, and that should help to keep us from confusing wild speculation with grounded reality. In my talk, I will attempt to chart out a way of looking at the “singularity scenario” with one's feet on the ground, and I will try to give, using my moderate familiarity with a number of different scientific disciplines, a personal appraisal of what I see as the likelihood of our being eclipsed by (or absorbed into) a vast computational network of superminds, in the course of the next few decades."

"The So-called Singularity: An Onrushing Tsunami, or Another Y2K?" [MP3]
Artificial Life X: Tenth International Conference on the Simulation and Synthesis of Living Systems
Bloomington Campus, Indiana University, June 3-7, 2006

Abstract: "In the past few years, a number of futurologists, extrapolating on the basis of many interrelated exponential curves such as Moore's Law, have come to the conclusion that computer intelligence is rising so swiftly that quite soon, it will inevitably reach and then surpass human intelligence, and that at that monumental juncture in the history of this planet, humanity will be eclipsed and replaced by its own creations. Within a few decades, these cyberprophets proclaim, we humans will be living among superintelligent entities that are just as incomprehensible to us as we are incomprehensible to bacteria, and the upward spiral will continue from there on without limit, resulting in entities "who" are literally billions of times more intelligent than today's humans are, and "who" will soon commandeer stars and then whole galaxies, finally turning the entire universe into one single inconceivably intelligent self-reflective organism akin to the Omega Point of the mystic Jesuit philosopher Teilhard de Chardin..."

For more information:

"Gödel, Escher, Bach: an Eternal Golden Braid:
A metaphorical fugue on minds and machines
in the spirit of Lewis Carroll"
Douglas Hofstadter, 1980 Pulitzer Prize (1979, 1999)

People featured in GEB;
Alan Turing, Charles Babbage, Johann Sebastian Bach, Kurt Gödel, Lewis Carroll, M. C. Escher, Marvin Minsky, René Magritte

Fields of study covered in GEB;
Metamathematics, Symmetry, Artificial intelligence, Formal systems, computability, Paradoxes, Genetics, Molecular biology, Logic, number theory, Typography and syntax, Brain, mind, and cognition, Syntax vs. semantics, Free will vs. determinism, Holism vs. reductionism, The Lisp programming language, Fugue, counterpoint, and musical form, Isomorphisms and meaning, Juxtaposed layers of meaning, counterpoint, semiotics, codes, Self-reference, recursion, strange loops, Self-organizing, emergent sense of identity: consciousness ...