Jake DiBello > Recent Status Updates

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?

Easily best description for where the inverse square law comes from

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)

Cantor sets and recursion in solid state physics. Note: recursion is seen within a graph called INT(x). Which is representative of a continued fraction and used to describe energy levels of allowed states of electrons in crystal lattices and magnetic fields ?

Today it explored recursivity through finishing the “pushing and popping” dialogue between Achilles and the tortoise and then further through Hofstadter’s own explanation. Things of note are the points on expanding the nodes in recursive systems that can resemble fractals but in practical computing scenarios there is a least one end point to avoid infinite regress

Today was a dialogue between the tortoise and Achilles that was very meta inside an Escher painting and a meta genie

…A perfect formal system should be able to produce every statement including the one that proves itself wrong and by that very statement it is itself wrong. This was told through a dialogue.

(Idk if this is right so far but that’s what I’ve gotten from it)

The following thread through the book so far has been on the importance and unimportance of isomorphisms.

Most importantly so far as Gödels incompleteness theorem is concerned it discussed how a “formal system” that is “perfect” should be able to produce a theorem that “destroys” the system and by that definition it is not perfect because it “breaks itself”

So far this has been about (in small part) fugues in relation to Bach and strange loops which refer to the recursive properties that many systems seem to have.

Even more recently in the book it has mostly been about formal systems and how they work. How formal systems often use definitions for terms that may not perfectly align with the real world. Some Formal systems don’t align perfectly with the external world

Describing simple harmonic oscillators and how the equations are formed and used to describe them

2 minute rule for starting habits