Math 195: GEB

1
Math 195 GEB

• Class Notes Jan 16
• Escher and Strange Loops
• Strange Loops and Reality
• Linguistic Loops

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Escher and Strange Loops

• http//www.worldofescher.com/gallery/WaterfallLg.
  html
• http//www.worldofescher.com/gallery/DrawingHands
  Lg.html

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Loops and Reality The Periodic Table

• Description and Prediction of Chemical Reactions
• http//chemicool.com/
• http//chemlab.pc.maricopa.edu/periodic/spiraltabl
  e.html

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"What portion of reality can be imitated in its
behavior bya set of meaningless symbols
governed by formal rules?" GEB, p53.
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Linguistic Loops

• This is the song that has no end It just goes on
  and on my friend Some people started singing it
  not knowing what it was Now they'll
  continue singing it forever just because
• Song from the Sheri Lewis and Lambchop Hour

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Kinds of Statements

• self-referential or not
• well-formed or not
• true or not
• provable or not
• meaningful or not

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Which Do You Prefer?

• This sentence has no punctuation
• This sentence has no punctuation
• This sentence has no punctuation.

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• This sentence, though not interrogative,
  nevertheless ends in a question mark?
• This sentence offers its reader(s) various
  alternatives/options that he or she (or they) is
  (are) free to accept and/or reject?!.
• This sentence has you in its power you cannot
  stop reading until you reach the period at the
  end.

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Self-referencing and Self-documenting

• In this sentence, the number of occurrences of 0
  is 1, of 1 is 11, of 2 is 2, of 3 is 1, of 4 is
  1, of 5 is 1, of 6 is 1, of 7 is 1, of 8 is
  1, and of 9 is 1.

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• This sentence is false!