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. KGodel@Richmond.Edu) 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