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Welcome to. Math 105 Gödel, Escher, and Bach. Question 1. What is the name of this song?. Question 2. NOW what’s the name of this song?. (Question 2). Musical shape can be stretched yet still retain its identity. (Question 2). Oh - say can you see. - PowerPoint PPT Presentation
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Welcome to
Math 105Gödel, Escher, and Bach
Question 1
What is the name of this song?
Question 2
NOW what’s the name of this song?
Musical shape can be stretched yet still retain its identity
(Question 2)
Musical objects often contain
internal symmetries
(Question 2)
Oh - say can you see
By the dawn’s ear- ly light
What so proud- ly we hailed
At the twi- light’s last glea- ming
Question 3
How many times does IT appear?
(Question 3)
Musical shape can be flipped yet still retain
its identity
J S BachBach visits the court of Frederick the Great of Prussia
• Improvises fugues on King’s complex theme
• Later composes canons on theme: WEIRD canons.
Crab canon
J S BachEndlessly rising canon
Strange loop
Gödel, Escher, and BachThe course
Lecture and careful note taking• DOING PROBLEMS
• DISCUSSING PROBLEMS
• DOING MORE PROBLEMS
If you can’t do it, you don’t know it
Gödel, Escher, and BachThe course web page
• How to get there: courses.richmond.edu (bookmark it!)
• How to log in: your net id (e.g. [email protected]) your password (must have at least 2 digits!)
• What to do when you’re there:
Problems vs Questions vs…???• Quiz questions (daily) - Rather mindless - A carrot - Feedback about Study Questions• Study questions (daily) - Active reading - Directly related to text• Problem set questions (weekly) - Integrative - Many answers possible - Approach more important than answer• Exam questions (quarterly) - Derived from Problem Sets
HELP!!!• Consider problems in groups in class
• Consider problems in review sessions
• Consider problems in groups outside of class
• Consider problems when you need it
Jeff Elhai Mike KerckhoveS-202 Gottwald 209 Jepsen289-8412 289-8774R&F 3:30-5:00 M&W 10:30-11:30
R 2:30-4:00
M.C. EscherAscending and Descending
Strange loop
Kurt GödelIncompleteness Theorem
Strange loop