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Gödel, Escher, Bach > Chapter 2 - Meaning and Form in Mathematics

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message 1: by Erik (new)

Erik | 165 comments In plain words, the problem of the book is mentioned: "Do words and thoughts follow formal rules, or do they not?"

Isomorphism and Formal Systems are introduced and discussed using the p-q system. The video lectures I posted links to do a nice job of working through the p-q system in an easy to understand way. The book isn't too complicated, but might be difficult to follow. I watched the videos first and found the book challenging in areas.

Isomorphism and meaning are discussed. I think someone in one of the videos says something like "common sense can't exist, because meaning is not inherent". I really liked that statement. It adds a lot of depth to the "what is meaning and understanding" question.

Inferring meaning is discussed in the video too. They reference the Voynich Manuscript, which is a mysterious book that WWI and WWII code crackers worked on. It appears to be an alien language with images of things not found on Earth. It's very old and appears to have order and meaning. Read more about it here:

Euclid's proof of the "Infinite Primes" is very elegant. It is shown in the videos and discussed in the book.

The very last paragraph introduces several questions using the topics discussed in this chapter. These questions act as a cliff hanger.

message 2: by Brad (new)

Brad (bradrubin) | 264 comments Mod
Figuring out the overall problem the book is trying to adress is tough. I will comment on this more as we get farther into the book, but two major themes, for me, are the power of self-reference to create a complex something out of nothing, and the elusiveness of pure truth.

Interestingly, I just read Stephen Hawking's new book "The Grand Design", and he addresses these same two points, in the context of physics and cosmology!

message 3: by Steph (new)

Steph (SPThomp) | 20 comments I am seeing information in the discussion of formal systems relating to a personal interest: information space. At present it’s just a notion I want to know more about.

How do we “carve up” information space into meaningful concepts? In natural language we create concepts and use the terms for those concepts to communicate. I see the discussion of formal systems as a method for exploring that interest.

For example, in English we have the word ‘individualism’. However, I understand that in Chinese there is no equivalent because they have a more group-oriented culture. The idea of a lone, self-reliant person who ‘hears another drummer’ and follow his instincts is out-of-the-norm for a group oriented society. The closest term they have is “every-man-for-himself”. The latter is clearly different.

I am back to the metaphor of a cube of jello. The jello cube represents the part of information space dealing with the concepts of a sole person, self reliance, etc. It would also contain the parts that indicate selfishness as denoted by “every-man-for-himself”. So how and why do different cultures carve up the information-space-jello in different shapes?

I see formal systems to be a microcosm of rules defining a small universe of thought. This discussion can help me form a method of inquiry into the larger, natural system of defining concepts in information space.

message 4: by Erik (new)

Erik | 165 comments In one of the MIT videos, they do an exercise of word association. It seems similar to what Steph describes in meaning relationships.

They start with the word "Apple". One branch of the relationships goes to Newton and Gravity. They discuss how the meaning and relationships would be different for people before Newton. From Apple, they have another branch that goes Adam/Eve and God.

message 5: by Brad (new)

Brad (bradrubin) | 264 comments Mod

You might be interested in clustering-based information retrieval. Here is one example:

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