Hofstadter - Godel, Escher, Bach

Tags: books

Preface

Book is not about math, art, and music relations
Book is about patterns, the more abstract layer on top of the raw information in the brain
Describes the self-referential “I”
- godel’s incompleteness theorem showed that it is impossible to construct a set of axioms that exist outside mathematics, all axioms are “incomplete”
Kurt Godel vs bertrand russel and alfred north whitehead in principa mathmatica

How do maeningless symbols give causal meaning in a rules-based meaning-free universe?
Similar to a TV camera pointed @ the TV screen
It’s the patterns that arise! Not the raw information stored, but how these patterns are arranged and laid out!

What is a melody vs harmony?

Crab canons and isomorphism (information preseriving transformations)

Strange loops -> moving upwards or downwards through a level results with what you started

Godel numbering and godel codes

Aristotle -> syllogism -> Boole and de Morgan Euclid -> Geometry -> non-enuclian geometry

Cantor set theory?

Mathematics and metalogic

hilbert wanted to demostrate that systems in princpa mathematica were consistent & complete

Babbage and his difference engine

Is there incompleteness in AI?

holfstander talks about rules based AI, but what about statistical AI?

Formal semantics do not need to be proved -> they are produced statements

Informal systems arise from axioms, which give birth to theorems

Computing is symbol shunting, and people tend to recongize the patterns

Intelligence is when you can jump out of a tax and surveil what has already been done