# Video Lectures

Special software is required to use some of the files in this section: .rm.

During the summer of 2007, Gödel, Escher, Bach was recorded especially for OpenCourseWare. Below are links to the videos, along with breakdowns of the video content.

## Lecture 1 Video: (RM - 220k)

Video lecture table.
SEG # SEGMENT TITLES SEGMENT TOPICS STARTS AT (HR:MIN:SEC)
1 Introduction Short bio of teacher, Justin Curry. Question of what is 'I'? How does consciousness arise out of unconscious components? 0:00:00
2 Tools for Thinking Themes that will run through the course: isomorphism, recursion, paradox, infinity, and formal systems. Fractal dimensions (non integer). Examples of paradoxes 0:06:23
3 MU Puzzle Explanation of the puzzle, and a challenge to students 0:27:58
4 Meta-thinking The ability of humans to step outside of formal systems - meta thinking. 0:37:42
5 PQ- Exploration of a very simple formal system 0:42:53
6 Reality: A Formal System? Is reality just the most complex formal system? Does the universe behave deterministically? 0:52:15
7 Music in Gödel, Escher, Bach An overview of the role music plays in Gödel, Escher, Bach 0:56:40

## Lecture 2 Video: (RM - 220k)

Video lecture table.
SEG # SEGMENT TITLES SEGMENT TOPICS STARTS AT (HR:MIN:SEC)
1 Introduction to recursion and fractals Definition of recursion and recursive functions (function which calls itself), with the examples of factornial numbers and the Fibbonacci sequence 0:00:00
2 Recursive Tree Function Modeling the branches of a tree using a recursive function 0:11:16
3 Koch Curve Modeling shorelines as self similar fractals. Unexpected result of a shape with finite area, but infinite perimeter length 0:16:36
4 Serpinski Triangle Another famous fractal example 0:26:40
5 Fractal Fern Modeling a fern using a recursive function. Coordinate transformation. 0:37:15
6 Answers to student questions Answers to student questions on recursion 0:42:40
7 Mandlebrot Set Equation that defines this famous fractal. Graphing the Mandlebrot Set, and zooming in on interesting features 0:56:08
8 Recursion in music Discussion of recursive elements in music, with examples from J.S. Bach 1:09:22

## Lecture 3 Video: (RM - 220k)

Video lecture table.
SEG # SEGMENT TITLES SEGMENT TOPICS STARTS AT (HR:MIN:SEC)
1 Gödel's Incompleteness theorem There exist things which are true, but not provable. Any system as powerful as number theory, which can prove its own consistency, that system is necessarily inconsistent.  Any system as powerful as number theory is necessarily incomplete 0:00:00
2 Alternate Geometries Alternate geometries explored. Hyperbolic and spherical geometries 0:27:48
3 Little Harmonic Labyrynth Discussion of the dialogue and the patterns within 0:39:40
4 The Development of Calculus The discovery of calculus, and its early study by Jesuits. The Jesuits thought the concepts of infinity in calculus would aid in their understanding of the divine 0:42:17
5 Recursion and Isomorphism Introduced and defined. Also the example of Kasparov playing chess and losing to Deep Blue, a super-computer 0:53:50

## Lecture 4 Video: (RM - 220k)

Video lecture table.
SEG # SEGMENT TITLES SEGMENT TOPICS STARTS AT (HR:MIN:SEC)
1 Introduction Introduction and adminstration 0:00:00
2 The Meaning of Meaning What do we mean when we say 'Snow is white'? Does that sentence mean the same thing to everyone? 0:02:30
3 Contracrostipunctus Revisted Exploration of the multiple layers of meaning in this passage 0:18:13
4 Defining Meaning Meaning is the relationship between an object and its referrent 0:24:15
5 Encoding Information How complex phenomena can be modeled using simple equations 0:29:00
6 Lindenmeyer Systems Definition (formal grammar with self-similarity) with examples (Serpinski Gasket, Koch Snowflake). Self-similarity in nature 0:43:23
7 Cellular Automata The game of life and other cellular automata 1:06:57

## Lecture 5 Video: (RM - 220k)

Video lecture table.
SEG # SEGMENT TITLES SEGMENT TOPICS STARTS AT (HR:MIN:SEC)
1 Apology for the reading Justin apologizes that the reading was difficult 0:00:00
2 Theory of Meaning A review of the theory of meaning introduced in the last class. How exactly do we go about ascribing meanings to a word? Everyone has different meaning of words, based on their own experience of it. Would aliens be able to enjoy our music, or is it particular to our culture? Hofsteder argues that there is something fundamental in the patterns of music that cause it to be enjoyable 0:02:36
3 Universal Information Would aliens enjoy our music? Hofstatder argues they would, because the patterns of information encoded are universal and inherently beautiful 0:06:40
4 Information and Entropy Information theory 0:13:10
5 Number Theory Outlining typographical number thoery, or TNT 0:29:30
6 Context Free Grammar Graphical demonstration of context free grammars, using the open source computer program "Context Free" 1:01:06

## Lecture 6 Video: (RM - 220k)

Video lecture table.
SEG # SEGMENT TITLES SEGMENT TOPICS STARTS AT (HR:MIN:SEC)
1 Review of last class Review of Gödel's incompleteness theorem. Justin answers a students question 0:00:00
2 Emergent Properties Layers of meaning, example of computers, from the phsycial transistor level to operating systems. Example of neurons in the brain 0:09:33
3 Human Consciousness Evolution and human consciousness. Excessive self reflection may not be evolutionarily beneficial. Maslow's heirarchy of needs. Justin answers student questions 0:40:34
4 Class Wrap-up and Discussion More on emergent properties. Modeling particles using a few simple physics rules. The robustness of the human brain.  Justin and Curran field questions from students, and show more computer simulations 0:53:45