Jake DiBello’s Reviews > Gödel, Escher, Bach: An Eternal Golden Braid > Status Update

Incredibly important when working with math: the books speaks about formal systems and the potential to formalize higher levels of a formal system and about why this cannot/should not be done. Note that a formal system is NOT THE SAME as the metalanguage in which we interpret its results.

Propositional calculus and the old koan gantos axe?

Is information a universal thing? Can it be stored in a message that will given a long enough time be discovered as truth? He says yes

“The inborn hardware is like a jukebox: it supplies the additional information which turns mere triggers into complete messages”

“Thoughts are produced by physical law”

Today: recursively enumerable sets, that is to say as set that can be generated from axioms by the repeated application of rules of inference, is an example of how emergence can appear from a seemingly fixed set of rules and how maybe a recursive “set” “carried further” (allowed to affect itself) may represent intelligence

This renormalization was paralleled to zenos paradox

Covered Feynman diagrams just to further illustrate how to world is based on everything being recursive. In Feynman diagrams to an outside observer it seems like a photon just moved from A to B but in reality we see inside how the decay of this photon into a electronn-positron pair can then in turn annihilate eachother and turn back into a photon

Nevermind that energy band graph is called G-plot which is build off of the principle of recursion seen in INT(x)