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Saturday, June 4, 2011

Goedel, Escher, Bach - Lecture 4(1)

My brain ran those neural network algorithms.

Justin Curry

The reading assignment was chapter 6 'The location of meaning'. It is basically about coding and decoding. Of course Hofstadter mentioned the Rosetta Stone in this context, the key to ancient Egypt. It contained a parallel text in three languages and was deciphered in 1821 by Champollion.

A recent example in the context of chapter 6 is space archeology. Archeologists and Egyptologists were able to interpret satellite pictures of Egypt which lead to the sensational discovery of new pyramids.

Let's go to the lecture. ( This is a 1h46m lecture and will be discussed in two posts. )

Curry talked about Goedel numbering again, a method Goedel used to code strings in formal number theory to numbers. What Curry said about coding a string in formal number theory, playing with it and then code it back is only true in theory. Simply because Goedel numbers become -extremely large-. Think of numbers built from pages full of digits. ( Would Curry ever have calculated a Goedel number? This reminds me of a DBA course I attended once. The trainer talked about all the beautiful properties of the then new RMAN from Oracle as if backups could be recovered in an instant. It turned out that he never worked in the trenches of 7 x 24 administration of large databases. )

Dialog "Contracrostipunctus" on page 75 of GEB is discussed. How this dialog has meaning on several levels. The dialog refers to itself that it contains a hidden message. The concept of 'Self' is introduced here.

Starting with what does "Snow is white" mean? he builds an argument that there is an isomorphism between electrical activity in the brain and the interpretation of symbols. ( Thought reading might be possible after all, one day. Isn't it true that man can create everything he is able to envision? )

Adam and Eve

There are at least two phases in the proces of assigning meaning two a string. The first is parsing the string, the second is the interpretation of the parsed words. Interpretation depends on the context of the interpreter.

Message in a bottle

He introduces the concept of information. For example how physicists reduce complex physical behaviour to a small sequence of symbols. Like for example how a pendulum works.

Pendulum ?

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