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In this video, I go over the GEB's ideas related to self-reference, computer science, formal systems, and strange loops, but I didn’t talk about the link with Bach nor the exploration of meaning and how meaning is created. Also not mentioned in this video, the book discusses Artificial Intelligence, although this section is a little bit dated, as AI research has progressed quite a bit since the 1970s.
On the whole, this video is to be taken as a taster of the book and some of the ideas it explores, rather than a ‘correct’ or faithful explanation of them. If you notice any misunderstandings I’ve communicated in the video, please comment below, as I don’t want to unintentionally create any misunderstandings of any ideas in people’s minds.
1:01 Self-referential paradox
2:51 Isomorphism, analogy, mapping
6:14 Levels and level of abstraction
9:42 Halting problem, appling Cantor’s Diagonalisation to computer programs
27:07 Formal systems - MIU and pq system
38:46 Use/mention distinction, linguistic quines and self-containing statements
43:50 Formal system that Gödel applies his technique to
49:14 Consistency and Completeness
52:00 Gödel numbering and the isomorphism between formal system and integers
58:41 Gödel’s uncle and the Gödel string
1:07:15 Gödel string’s meaning, interpretation and truth value
1:10:41 Self-reference and looping back of hierarchy
1:12:00 Strange loops, Heterarchy and Escher
1:16:20 Heterarchies in computer programming
1:21:04 Computer quines
1:21:57 Subject-object merging