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I totally disagree. I mean for a start you seem to think the book was about Godel's theorem. It was about something more general, that's Godel's theorem was m

by samh 17y ago

I totally disagree. I mean for a start you seem to think the book was about Godel's theorem. It was about something more general, that's Godel's theorem was merely one instance of, what exactly that general thing is..... is probably the heart of almost all philosophy. But that's just my take :)

Tichy 17y ago
It's been more than 20 years since I read it. But please explain - because to be honest my hunch is that the book just leaves one with a vague feeling that something cool is going on ("the heart of all philosophy"?), but not with real understanding. Looking at a three page formal proof of Goedel's theorem somehow helped me understand a lot more than reading GEB.
- samh 17y ago
  Well obviously I can't communicate the full idea of "The Greatest Book Ever Written" in a comment, but I'll try :) Strange things happen when you have 'recursion' / 'strange loops' / 'self reflection' / 'mirroring' / 'strange entanglement' / 'entangled heirachies' etc. What are some examples ? - "This statement is false" is true or false ? - The Heisenberg uncertainty principle, position and momentum of a particle cannot both be known because they each influence each other. - Turing Halting problem proof when a program is executed using itself as input. - Human self awareness ? If I think about what I'm thinking about what am I thinking about ? - Godel's proof that any formal system strong enough to be useful is either incomplete or inconsistent, to use an analogy he proves this by stating in the language of the system the statement "this statement cannot be proved in this system". If it can be proved the system lied (is inconsistent) or if it cannot be proved the statement is a truth that the system cannot prove and hence the system is incomplete. (Obviously he doesn't use statements like that, he uses facts about the natural numbers but the same principle applies) - Chandelier cells in the brain, thought to contain an internal model of the brain's state. A model of the brain within the brain. Do they contain a model of themselves ? Ok, so if this 'recursion' / 'strange loops' business is mysterious, present at the heart of all interesting systems it must be pretty special, it must require magic or devine intervention to come about, surely ? Nup, simple examples such as the 'game of life' can show amazing complexity and even this sort of 'self awareness' emerging from a simple initial state and a simple set of rules. Best I've got at the moment.

by samh 17y ago

Tichy 17y ago

It's been more than 20 years since I read it. But please explain - because to be honest my hunch is that the book just leaves one with a vague feeling that something cool is going on ("the heart of all philosophy"?), but not with real understanding. Looking at a three page formal proof of Goedel's theorem somehow helped me understand a lot more than reading GEB.

samh 17y ago
Well obviously I can't communicate the full idea of "The Greatest Book Ever Written" in a comment, but I'll try :) Strange things happen when you have 'recursion' / 'strange loops' / 'self reflection' / 'mirroring' / 'strange entanglement' / 'entangled heirachies' etc. What are some examples ? - "This statement is false" is true or false ? - The Heisenberg uncertainty principle, position and momentum of a particle cannot both be known because they each influence each other. - Turing Halting problem proof when a program is executed using itself as input. - Human self awareness ? If I think about what I'm thinking about what am I thinking about ? - Godel's proof that any formal system strong enough to be useful is either incomplete or inconsistent, to use an analogy he proves this by stating in the language of the system the statement "this statement cannot be proved in this system". If it can be proved the system lied (is inconsistent) or if it cannot be proved the statement is a truth that the system cannot prove and hence the system is incomplete. (Obviously he doesn't use statements like that, he uses facts about the natural numbers but the same principle applies) - Chandelier cells in the brain, thought to contain an internal model of the brain's state. A model of the brain within the brain. Do they contain a model of themselves ? Ok, so if this 'recursion' / 'strange loops' business is mysterious, present at the heart of all interesting systems it must be pretty special, it must require magic or devine intervention to come about, surely ? Nup, simple examples such as the 'game of life' can show amazing complexity and even this sort of 'self awareness' emerging from a simple initial state and a simple set of rules. Best I've got at the moment.