Gödel, Escher, Bach: An Eternal Golden Braid
From Hofstadter’s preface to the book’s 20th-anniversary edition:
GEB is a very personal attempt to say how it is that animate beings can come out of inanimate matter. What is a self, and how can a self come out of stuff that is as selfless as a stone or a puddle?
Somehow, I found this snippet interesting; it was written by Farkas Bolyai to his son János Bolyai, in an attempt to persuade him to stop investing so much effort to prove Euclid’s fifth postulate. It is fascinating how a plain letter to his son feels so well written, fraught with metaphors and similes.
You must not attempt this approach to parallels. I know this way to its very end. I have traversed this bottomless night, which extinguished all light and joy of my life. I entreat you, leave the science of parallels alone….I thought I would sacrifice myself for the sake of the truth. I was ready to become a martyr who would remove the flaw from geometry and return it purified to mankind. I accomplished monstrous, enormous labors; my creations are far better than those of others and yet I have not achieved complete satisfaction. For here it is true that si paullum a summo discessit, vergit ad imum [if it’s failed to make the grade, even by a smidgeon, it might as well be the worst]. I turned back when I saw that no man can reach the bottom of this night. I turned back unconsoled, pitying myself and all mankind…I have traveled past all reefs of this infernal Dead Sea and have always come back with broken mast and torn sail. The ruin nof my disposition and my fall date back to this time. I thoughtlessly risked my life and happiness—aut Caesar aut nihil [either Caesar or nothing].
Consistency: Everything produced by the system is true (in some imaginable world).
Completeness: Every true statement (which belong to the domain of the system) is produced by the system. More technically: it is when all statements which are true (in some imaginable world), and which can be expressed as well-formed strings of the system, are theorems.
There are 2 types of consistency: consistent with the external world vs internally consistent. The difference is that external consistency requires it to agree with the real world, whereas internal consistency of a system requires it to agree with any imaginable world. => This brings the question of what constitutes an “imaginable” world?
Decoding something is pulling information from an object - but how hard can we pull at it? Are we pulling so hard that we are adding information to it? An example is the decipherment of ancient text, which requires drawing on a large pool of knowledge:
Just how intrinsic is the meaning of a text, when such mammoth efforts are required in order to find the decoding rules? Has one put meaning into the text, or was that meaning already there?
In this case, intuition tells us that the meaning in the text was always there, since the text would have been deciphered by another group of people another time if it was not deciphered today - and it would have come out the same way, i.e. it acts upon intelligence in a predictable way.
Generally, we can say: meaning is part of an object to the extent that it acts upon intelligence in a predictable way.
We see the world as being outside ourselves even though it is only a mental representation of it that we experience inside ourselves.
Hofstadter seems to believe that consciousness is an emergent phenomenon, and that the creativity element in intelligence can emerge from higher and higher levels of “chunking”, where, although the bottom level is deterministic, it is obscured from view and the product exhibits creativity (like how software engineers rarely think of the physics in the hardware when coding–it is all obscured behind layers and layers of abstraction). I think the central thesis (proposition?) is that not only did consciousness arise from many neurons at the base level (through many layers of abstraction), the higher levels (consiousness and its symbols and ideas) also influence the base neurons in some way (a strange loop).