Schedule

Jan-12 - Jan-18

• Assignments:
  • Discussion leader sign-up: Assigned on Wed, Jan 14 | Assignment
• Wed, Jan 14 Lecture: Intro; Three-Part Invention; Ch 1 MU-Puzzle
  • Topics:
    • Course framing; GEB overview; MU rules; invariant idea; two Day 1 quizzes
  • Preparation:
    • 📖 GEB Intro; Three-Part Invention; Ch 1 (pp. 3–42)
  • Extra Resources:
    • An etymological joke by autological word

Jan-19 - Jan-25

• Assignments:
• Mon, Jan 19 Lecture: No class (MLK Day)
• Wed, Jan 21 Lecture: Two-Part Invention; Ch 2 Meaning & Form
  • Topics:
    • pq-system; isomorphism; truth vs provability (preview)
  • Preparation:
    • 📖 GEB: Two-Part Invention; Ch 2
  • Extra Resources:
    • Another multiplication algorithm and how it works (vi hart)
    • Machine recognize itself in a loop

Jan-26 - Feb-01

• Assignments:
  • Formal systems office viva (MU, pq, tq, or DND): Assigned on Mon, Jan 26 | Assignment
• Mon, Jan 26 Lecture: Sonata (Unaccompanied); Ch 3 Figure & Ground
  • Topics:
    • Figure/ground; RE vs R (recognition vs generation)
  • Preparation:
    • 📖 GEB: Sonata for Unaccompanied Achilles; Ch 3
  • Extra Resources:
    • Visual Proof of the Pythagorean Theorem (1:17-2:02)
• Wed, Jan 28 Lecture: Contracrostipunctus; Ch 4 Consistency/Completeness/Geometry
  • Topics:
    • Self-reference paraphrases; undefined terms; rival geometries
  • Preparation:
    • 📖 GEB: Contracrostipunctus; Ch 4
  • Extra Resources:
    • Political Acrostic Obscenity
    • What was Euclid really doing? (3Blue1Brown video)
    • Paraconsistent logic (SEP)

Feb-02 - Feb-08

• Assignments:
• Mon, Feb 02 Lecture: Little Harmonic Labyrinth; Ch 5 Recursion
  • Topics:
    • Nested structures; recursion across domains
  • Preparation:
    • 📖 GEB: Little Harmonic Labyrinth; Ch 5
  • Extra Resources:
    • Extending Factorial!
• Wed, Feb 04 Lecture: Canon by Intervallic Augmentation; Ch 6 Location of Meaning
  • Topics:
    • Where meaning resides; code/decoder/receiver
  • Preparation:
    • 📖 GEB: Canon by Intervallic Augmentation; Ch 6

Feb-09 - Feb-15

• Assignments:
• Mon, Feb 09 Lecture: Chromatic Fantasy; Ch 7 Propositional Calculus
  • Topics:
    • Rules that preserve truth; zen-tences
  • Preparation:
    • 📖 GEB: Chromatic Fantasy; Ch 7
• Wed, Feb 11 Lecture: Crab Canon; Ch 8 TNT
  • Topics:
    • Typographical Number Theory; formal arithmetic
  • Preparation:
    • 📖 GEB: Crab Canon; Ch 8

Feb-16 - Feb-22

• Assignments:
• Mon, Feb 16 Lecture: A Mu Offering; Ch 9 Mumon & Godel
  • Topics:
    • Zen metaphors; Godel numbering; first pass at incompleteness
  • Preparation:
    • 📖 GEB: A Mu Offering; Ch 9
  • Extra Resources:
    • Which is better, closures or objects?
• Wed, Feb 18 Lecture: Nagel & Newman chs 1–3 (history; arithmetization; fixed points)
  • Topics:
    • Scaffold for formal proof day; coding syntax; diagonal idea
  • Preparation:
    • 📖 Nagel & Newman: chs 1–3
  • Extra Resources:
    • Really nice Godel numbering programs
    • Mating with two knights

Feb-23 - Mar-01

• Assignments:
• Mon, Feb 23 Lecture: Prelude ... ; Ch 10 Levels & Computer Systems
  • Topics:
    • Levels of description; machine/assembly/compiler/OS
  • Preparation:
    • 📖 GEB: Prelude; Ch 10
  • Extra Resources:
    • Summary of Fermat's last theorem (archive.org link)
    • Link to related Dr.Math Archive Background (links require archive.org spelunking)
    • Perlis: Epigrams on Programming
    • A thing that does suck dust (What math grad students do today)
    • Compiled Languages vs Interpreted Languages
• Wed, Feb 25 Lecture: ... Ant Fugue; Ch 11 Brains & Thoughts
  • Topics:
    • Holism vs reductionism; ant colony mind
  • Preparation:
    • 📖 GEB: Ant Fugue; Ch 11
  • Extra Resources:
    • Platonic Representation Hypothesis
    • The most complex model we understand
    • The supervenience argument against non-reductive physicalism (Andrew Russo)

Mar-02 - Mar-08

• Assignments:
• Mon, Mar 02 Lecture: No class (Spring Break)
• Wed, Mar 04 Lecture: No class (Spring Break)

Mar-09 - Mar-15

• Assignments:
• Mon, Mar 09 Lecture: English-French-German Suite; Ch 12 Minds & Thoughts
  • Topics:
    • Mapping languages/minds; communication across brains
  • Preparation:
    • 📖 GEB: English-French-German Suite; Ch 12
• Wed, Mar 11 Lecture: Aria w/ Diverse Variations; Ch 13 Bloop/Floop/Gloop
  • Topics:
    • Primitive vs general recursion; predictable vs unbounded search
  • Preparation:
    • 📖 GEB: Aria with Diverse Variations; Ch 13
  • Extra Resources:
    • Collatz Conjecture Hailstone Sequences
    • Prime Spirals (Cf)

Mar-16 - Mar-22

• Assignments:
  • Assigned paper reading for Wednesday: Assigned on Mon, Mar 16 | Assignment
• Mon, Mar 16 Lecture: Air on G's String; Ch 14 Undecidable Propositions (Godel I proof day)
  • Topics:
    • Diagonal lemma; true-but-unprovable; TNT completeness vs truth
  • Preparation:
    • 📖 GEB: Air on G's String; Ch 14
• Wed, Mar 18 Lecture: Nagel & Newman chs 6–7; Boolos
  • Topics:
    • Godel II in plain language; Con(T) unprovable inside T
  • Preparation:
    • 📖 Nagel & Newman: chs 6–7
    • 📖 Boolos: Godel II in words of one syllable
  • Extra Resources:
    • Godel from an historical perspective

Mar-23 - Mar-29

• Assignments:
• Mon, Mar 23 Lecture: Birthday Cantatatata; Ch 15 Jumping Out; Lucas
  • Topics:
    • Essential incompleteness; Lucas argument (critique setup)
  • Preparation:
    • 📖 GEB: Birthday Cantatatata; Ch 15
• Wed, Mar 25 Lecture: Chalmers on Godel vs Mechanism/AI
  • Topics:
    • Reply to Lucas; what Godel does/does not imply for AI
  • Preparation:
    • 📖 Chalmers: minds, machines, and mathematics (excerpt)
    • 📖 Penrose reply
  • Extra Resources:
    • Chinese room video 1
    • Chinese room video 2
    • Internet Encyclopedia of Philosophy entry on Lucas's argument
    • Searle on the Chinese Room argument (@ Google)

Mar-30 - Apr-05

• Assignments:
  • Small 1# assignment (pre-class demo): Assigned on Mon, Mar 30
  • UTM project (universal 1#) assigned: Assigned on Wed, Apr 01
• Mon, Mar 30 Lecture: Edifying Thoughts; Ch 16 Self-Ref & Self-Rep
  • Topics:
    • Self-reference and self-reproduction; quines; replication
  • Preparation:
    • 📖 GEB: Edifying Thoughts of a Tobacco Smoker; Ch 16
  • Extra Resources:
    • Smoke Rings (Cf "Edifying Thoughts")
    • Smoke Rings (alt: Mills Brothers)
    • Limerick_(poetry) on Wiki (there are some good ones!)
    • Henkin's Method and the Completeness Theorem (gently)
    • 128-language quine relay
    • From Turing machines to computer viruses
• Wed, Apr 01 Lecture: 1# / TRM (assign UTM)
  • Topics:
    • 1# model; live quine demo; names and descriptions; assign UTM project
  • Preparation:
    • 📖 1#: a Text Register Machine Introduction to Computability Theory
    • 📖 Getting Started with 1#
    • 📖 Programs for Arithmetic
    • 📖 Programs for Programs
    • 📖 Self-replicating Programs
    • 📖 Recursion Theorems
    • 📖 Universal Programs
  • Extra Resources:
    • Recursion Theorems and Self-Replication Via Text Register Machine Programs
    • Chiang: Seventy-Two Letters
    • (Audiobook version of the above)

Apr-06 - Apr-12

• Assignments:
• Mon, Apr 06 Lecture: No class (Easter)
  • Extra Resources:
    • The Computer Scientist Training AI to Think With Analogies
• Wed, Apr 08 Lecture: The Magnificrab, Indeed; Ch 17 Church–Turing–Tarski; Pullum
  • Topics:
    • CT-thesis variants; Halting; Tarski; assign Pullum poem
  • Preparation:
    • 📖 GEB: The Magnificrab, Indeed; Ch 17
    • 📖 Pullum: Scooping the Loop Snooper
  • Extra Resources:
    • Gödel, Escher, Bach, and AI, by Douglas Hofstadter
    • Generative AI Should Not Replace Thinking at My University, by Douglas Hofstadter
    • "The Man Who Knew Infinity" (IMDB)

Apr-13 - Apr-19

• Assignments:
  • Medium 1# assignment (out): Assigned on Sun, Apr 12
  • UTM demo (graded): Assigned on Sun, Apr 12
• Mon, Apr 13 Lecture: SHRDLU; Ch 18 AI Retrospects
  • Topics:
    • Turing Test; early AI; NLP in blocks world
  • Preparation:
    • 📖 GEB: SHRDLU; Ch 18
  • Extra Resources:
    • The Thrilling Adventures of Lovelace and Babbage (Padua)
    • Sutton: The Bitter Lesson
    • Stillwell: Emil Post and His Anticipation of Gödel and Turing
    • Open copy of Stillwell article
    • Davis: Why Gödel didn't have Church's thesis
    • Rapaport, PhiCS draft (archived): Ch. 19 Philosophy of AI
    • An AI Model Has Officially Passed the Turing Test
• Wed, Apr 15 Lecture: 1# reinforcement (programs for programs; self-reference; UTM prep)
  • Topics:
    • φ_p and program-as-data
    • write and s₁¹
    • diag and self
    • UTM setup
  • Preparation:
    • 📖 (Reread) Programs for Programs
    • 📖 (Reread) Self-replicating Programs
    • 📖 (Reread) Recursion Theorems
    • 📖 (Reread) Universal Programs

Apr-20 - Apr-26

• Assignments:
• Mon, Apr 20 Lecture: Contrafactus; Ch 19 AI Prospects
  • Topics:
    • Knowledge representation; frames; concept interaction
  • Preparation:
    • 📖 GEB: Contrafactus; Ch 19
  • Extra Resources:
    • Dehaene et al.: What is consciousness, and could machines have it?
    • Rapaport, PhiCS draft (archived): Ch. 20 Computer Ethics II: AI
• Wed, Apr 22 Lecture: Rapaport PoCS grab-bag (halting, CT-thesis, implementation)
  • Topics:
    • Halting, CT-thesis, and implementation as semantic interpretation
  • Preparation:
    • 📖 Rapaport, PhiCS draft (archived): Ch. 7.6.7-end (WITS pp. 280–308)
    • 📖 Rapaport, PhiCS draft (archived): Ch. 14-14.3 (pp. 549–567)

Apr-27 - May-03

• Assignments:
• Mon, Apr 27 Lecture: Sloth Canon; Ch 20 Strange Loops
  • Topics:
    • Tangled hierarchies; free will questions
  • Preparation:
    • 📖 GEB: Sloth Canon; Ch 20
    • 🎥 Assigned Video (3B1BR)
• Wed, Apr 29 Lecture: Aaronson 'Who Can Name the Bigger Number?' + Busy Beaver
  • Topics:
    • Naming power; Busy Beaver after Halting; growth beyond computable
  • Preparation:
    • 📖 Aaronson: Who Can Name the Bigger Number?
  • Extra Resources:
    • Busy Beaver Hunters Bag #5
    • What is a strange loop, and what is it like to be one?

May-04 - May-10

• Assignments:
• Mon, May 04 Lecture: Six-Part Ricercar (closing dialogue)
  • Topics:
    • Capstone seminar; synthesis; optional final TRM check-offs
  • Preparation:
    • 📖 GEB: Six-Part Ricercar
  • Extra Resources:
    • Limits of Logic: The Godel Legacy