GEB

//Godel, Escher, Bach: The Golden Eternal Braid// //by Douglas Hofstadter//
 * Book Club **


 * Topic: Strange Loops**
 * **Godel** || **Escher** || **Bach** ||
 * * "All Cretans are liars."

paper by Craig S. Kaplan || * The Musical Offering - A Musical Pedagogical Workshop by J.S. Bach (The Musical Geometry of Bach's Puzzle Cannons http://schillerinstitut.dk/moweb/musical_offering.htm
 * The following statement is false.
 * The previous statement is true. || [[image:metamorfosis.jpg width="188" height="235" align="center" caption="matamorfosis"]]
 * [|Bach ric3.pdf]
 * [|Bach Ric3.mp3] ||

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**Tools for Thinking**
 * 1) Isomorphisms
 * 2) Recursion
 * 3) Paradox
 * 4) Infinity
 * 5) Formal Systems


 * Topic: Isomorphism**

The word “isomorphism” applies when two complex structures can be mapped onto each other, in such a way that to each part of one structure there is a corresponding part in the other structure, where “corresponding” means that the two parts play similar roles in their respective structures. (G ̈odel, Escher, Bach, p. 49)

A list of instructions that you follow and repeat until you reach a final case. Example: Fibonacci Series: 1,1,2,3,5,8,13,21,... f(n) = f(n-2) + f(n-1) "define the 'thing' in terms of itself" Example: Fractals
 * Topic: Recursion**


 * Topic: Infinity**

**Topic: Paradoxes** http://en.wikipedia.org/wiki/Paradox The Barber's Paradox: The barber only shaves people who don't shave themselves. Does the barber shave himself?
 * Veridical - Zeno and the inability to move (half the distance)
 * Falsidical: 1-1+1-1+1-1 ... = 0, 1-1+1-1+1-1+1 ... = 0
 * Antinomy: This sentence is not true.
 * Help: Having trouble with the idea of a set that contains "sets of things that don't contain themselves." **


 * Topic: Systems**

Of course, there are cases where only a rare individual will have the vision to perceive a system which governs many people’ lives, a system which had never before even been recognized as a system; then such people often devote their lives to convincing other people that the system really is there, and that it ought to be exited from! (pp. 37)
 * [|MU-system.pdf]: Excerpt from the text
 * [|The_MU_system.pdf]: My condensed version for high school math students
 * [|The_MU_system.docx]

**Definitions** ** Note: GEB dialogues refer to Bach's music. How? ** little fugue in G minor
 * Axiom - a starting point for reasoning
 * String - ordered sequence
 * Theorem - derivation of ideas
 * Rules of Inference -

Web Resources:
 * http://ocw.mit.edu/high-school/courses/godel-escher-bach/