Math 195 GEB Class Notes Jan 16 Escher

Math 195: GEB Class Notes Jan 16 Escher and Strange Loops and Reality Linguistic Loops 2/21/2021 mkerckho@richmond. edu Jump to first page

Escher and Strange Loops n n http: //www. worldofescher. com/ gallery/Waterfall. Lg. html http: //www. worldofescher. com/ gallery/Drawing. Hands. Lg. html 2/21/2021 mkerckho@richmond. edu Jump to first page

Loops and Reality: The Periodic Table n n n 2/21/2021 Description and Prediction of Chemical Reactions http: //chemicool. com/ http: //chemlab. pc. maricopa. edu/pe riodic/spiraltable. html mkerckho@richmond. edu Jump to first page

"What portion of reality can be imitated in its behavior by a set of meaningless symbols governed by formal rules? " 2/21/2021 mkerckho@richmond. edu GEB, p 53. Jump to first page

Linguistic Loops n 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 2/21/2021 mkerckho@richmond. edu Jump to first page

Kinds of Statements 2/21/2021 n self-referential or not n well-formed or not n true or not n provable or not n meaningful or not mkerckho@richmond. edu Jump to first page

Which Do You Prefer? n This sentence has no punctuation; n This sentence has no punctuation. 2/21/2021 mkerckho@richmond. edu Jump to first page

n n n 2/21/2021 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. mkerckho@richmond. edu Jump to first page

Self-referencing and Selfdocumenting n 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. 2/21/2021 mkerckho@richmond. edu Jump to first page

n This sentence is false! 2/21/2021 mkerckho@richmond. edu Jump to first page