Gödel, Escher, Bach: a literary approach to minds and machines ~ Symbolic Systems 11si, a student-initiated course for Spring 2005 ~ Student Instructor: Brendan O'Connor - brendano@stanford.edu Faculty Sponsor: Maggie Johnson - johnson@cs.stanford.edu Fridays, 11:00-11:50 am, Building-Room 60-62C, 1 unit Credit/No Credit Can computer science have anything to do with art, music, or philosophy? Douglas Hofstadter's Pulitzer-winning Gödel, Escher, Bach freely integrates poetry, fugues, Zen, Platonic dialogues and metaphorical puns, all to pursue the thorny questions of artificial intelligence and the human mind. This class will take a playful approach to understand these ideas and literary technique through discussion, analysis, and performance. Will cover concepts in computational theory, mathematical logic, and philosophy of the mind. Students from all disciplines encouraged to join! We will read the book straight through with weekly discussions to clarify, understand, and explore the concepts and issues raised. Occasional speakers and events.

Questions about the course

Can you explain with any more detail, what the course is about?

The great bulk of the course is mostly just about reading through Gödel, Escher, Bach, which "delves, and not just superficially, into so many motley topics." Try taking a look at it in the bookstore.

What are the prerequisites?

None! Knowledge of some basic concepts in logic or computer science may be helpful, but we defintely will be covering these technical points of Hofstadter's argument during class. Much of the text is, however, devoted to explaining mathematical arguments. In many ways, the book functions as a literary introduction to logic and computational theory.

Kurt Gödel avec un paysan non identifié Taking a break from upending all mathematics.

The Syllabus! Also in .doc form.

Note that the reading schedule may later change from there; see the Schedule below.

The small Music library. Musical Offering #1 is what Hofstadter calls "Crab Canon" that we heard on the first day. "Bach's Strange Loop" is what the book calls the "Endlessly Rising Canon" -- done with Shepard tones, as described near the end of the book. The Musical Offering numbers are orignially from mp3.com. For all you Bach & musically inclined readers, please send me corrections or updates to what's here so far!

And also, some random images.

Schedule:

Week 1 (4/1): Course introduction

Week 2 (4/8): Formal Systems & Intro to Meaning

• Preface (only in 20^th anniversary edition) – just the first ~4 pages
• Introduction – A Musico-Logical Offering
• Chapter 1 – MU puzzle
• Chapter 2 – Meaning and Form
• Chapter 3 – Figure and Ground (metaphor from the visual arts, for mathematical knowledge)
• Chapter 4 – Consistency, Completeness, and Geometry
  • Highlight: Contracrostipunctus

Week 3 (4/15): Recursion, Meaning, and Music

• Chapter 5 – Recursive Structures
• Chapter 6 – Location of Meaning.

Week 4 (4/22): Logic, Numbers, and Zen

• Chapter 7 – The Propositional Calculus (introduction to propositional logic)
• Chapter 8 – Typographical Number Theory (Hofstadter’s formal system)
• Chapter 9 – Mumon and Gödel (a delightful almost-tangent on Buddhism and DNA)
• Can read ahead: Prelude… Ant Fugue, the joint dialogue for Chapters 10, 11

Week 5 (4/29): Holism, Reductionism, and Mind

• Chapter 10 – Levels of Description, and Computer Systems
• Chapter 11 – Brains and Thoughts
• Chapter 12 – Minds and Thoughts

Week 6 (5/6): Finally, Gödel’s Incompleteness Theorem

• Chapter 13 – BlooP, FlooP, GlooP (overview of computability)
• Chapter 14 – On Formerly Undecidable Propositions (the theorem, finally explained)

Week 7 (5/13): Implications of Incompleteness

• Chapter 15 – Jumping Out of the System
• Chapter 16 – Self-Ref and Self-Rep
• Chapter 17 – Church, Turing, Tarski, and Others

Week 8: (5/20): Artificial Intelligence

• Chapter 18 – AI: Retrospects
• Chapter 19 – AI: Prospects

Week 9 (5/27): Final discussion

• Chapter 20 – Strange Loops, or Tangled Hierarchies

Escher self-portrait & photo. This page's background, of course, is also by Escher.

Some Links

These have been borrowed from Sol Feferman's course website for Gödel's Theorem, Minds and Machines.

http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Godel.html
Mini-biography of Kurt Gödel.

http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Turing.html
Mini-biography of Alan Turing.

http://www.sm.luth.se/~torkel/eget/godel.html
Gödel on the net and a sketch of the incompleteness theorems, as presented by Torkel Franzén of Sweden.

http://plato.stanford.edu/entries/turing/
Extensive entry in the Stanford Encyclopedia of Philosophy on Turing's work and thought, by Andrew Hodges, author of Alan Turing: The Enigma.

http://www.turing.org.uk/turing
The Alan Turing Home Page, maintained by Andrew Hodges.

http://www-csli.stanford.edu/hp/Turing1.html
Introduction to Turing machines via state diagrams, taken from Turing's World by Jon Barwise and John Etchemendy.

http://users.ox.ac.uk/~jrlucas/index.html
Home page of J. R. Lucas, containing his paper "Minds, machines and Gödel" arguing that Gödel's incompleteness theorem indicates minds cannot be explained as (Turing) machines. This is the paper that Hosfstadter introduces in Chapter 7 of GEB. Lucas' home page also contains further papers and links on the ensuing controversy.

http://www.u.arizona.edu/~chalmers/online2.html#godel
This is on the home page of David Chalmers. He provides a truly extensive collection of useful links on the subject of consciousness, under the heading "Other philosophy of mind". Within that, one group of links is devoted to Godel's theorem and AI.