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Study General Is God a Mathematician, or How can people be so stupid? Godel, Escher, Bach, and Eternal Golden Braid
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Godel, Escher, Bach, and Eternal Golden Braid
Welcome, Everyone!

I have decided to re-read a book that I recommended. It has turned out to be a very timely choice for me, for a lot of reasons. I am hoping very sincerely that there are others on this site with knowledge of the book, or with the time and curiosity to take it up, so that this discussion may bear fruit.

Godel, Escher, Bach; an Eternal Golden Braid  by Douglas Hofstadter.
                   (is there a way to type umluauts in Pdnls? please tell me if there is...)

THINQon has been a wakeup call for me. I have been dormantly slogging through simple work for years without much contact with other seekers of truth. This has been bad for my attitude, and I want to heartily apologize for my display of that. I have been too critical of Academics; too dismissive of their true worth. This is my own fault for not excelling at school and I know it. Picking up this work of genius again has put me in my place! Hofstadter has run circles around me; he is fluent in many languages and has succeeded in most of the fields of intellectual inquiry that have ever appealed to me at all. I stand in awe of his accomplishments.

This book is simultaneously light and heavy, easy and hard. To attempt to say what it is about is a Sysyphian task of sorts; the sheer breadth of it, for all it's unity of focus, has defied summary by reviewers since it's inception. Hofstadter himself, when the book was re-released in 1999, undertook to summarize it in his preface. It runs to 23 pages! It is with some amusement that I note that this act of self-reference, this lossy isomorphism of the work in total, is itself a strange loop of just the sort which this book is about.

I have branched this topic off of a thread about the question 'Is God a Mathematician...' This is partly because I recommended the book to everyone there; also partly because I made an assertion about the nature of formal systems in that thread which was apparently misunderstood. But mostly because it approaches that very question more closely than any other way of looking that I have found in all my searchings of the halls of knowing.

In truth, the question of God has no bearing whatever on the content of the book (or the thread I just referenced, incidentally). Hofstadter is an Academic of such calibre that he is above making such divisive claims. This book is a reach at a star no less distant. This book is a brilliant foray into the nature of consciousness by way of self-reference.

So today, I put out the call: Any who have read this book, I invite you to come here and share your experience of it. Any person with an interest in the fields of Mathematics, computer programming, artificial intelligence, or the study of symbol and meaning generally, I hope you will take my recommendation and purchase and consume this lively book! I can safely guarantee that there is no other book of similar content ever written(though if I'm wrong, I hope someone will tell me so!) This book is easy to read, for all it's very difficult content, and I heartily recommend it to young persons as much as everyone else.

I will be reading the book again as I go. I am hoping that the subject matter of our thread follows the chronology of the book to some extent. This is no rule, of course; feel free to write whatever you wish about it and in whatever order.

Isomorphism and translation are themes and subjects of the book. This is why I have included every foreign language translation I could find in the 'books referenced'. Any who have read it will understand!

Against that last intimidating statement, I want to balance this caveat: This book is so easy that anyone can read it. I think everyone should, particularly those in High School. Avoid the trouble I caused myself by finding fascination early.
Books Discussed
by Douglas Hofstadter
Gödel, Escher, Bach. Ein Endloses Geflochtenes Band
by Douglas R. Hofstadter
Gödel, Escher, Bach: Un Eterno y Gracil Bucle (Spanish Edition)
by Douglas R. Hofstadter
Gödel, Escher, Bach: Les Brins d'une Guirlande Eternelle
by Douglas Hofstadter

Well, I'm in a few chapters now, I guess I had better lay out a few words.

I have no intention of explaining the book, of course, but it is riddled with little secrets. I am going to make mention of as many as I'm able to notice.

There is an inscription in a very ancient looking script at the end of the list of illustrations. Somewhere along the line DH made mention of the decipherment of the 'Linear B' script. I suspect he had some contact or collaboration with whatever academics cracked that code. He hinted that to view it as a formal system was a key to it's decipherment. It appears to be some sort of alphabet, with words of 3 to ten characters separated by signs that look like colons. I bet this inscription is in 'linear B'.

The introduction begins with a story about J.S.Bach in the court of King Frederick the Great of Prussia. Apparently King Frederick was quite the musician in his own right. Many interesting things are discussed here, like the invention of the piano-forte (of which King Frederick was a major patron) and the visit by Bach to his palace to try them out. There is a discussion about Fugues and Canons in music; and a lot of discussion of counterpoint. The art of MCEscher is introduced, showing in particular some circular arrangements of water which appear to be falling at all points in the circuit.

I was surprised to hear that this was an invention of Roger Penrose in 1958. I have been chewing on a book by that author which was published in 2004. A very busy man! I was not aware of the connection between his work and Escher's before.

A quick synopsis of the work of Kurt Godel follows. We learn about the Principia Mathematica, a terribly dry sounding tower of math meant to banish the possibility of self-reference. Self reference is pointed at as the root of paradox by way of some interesting examples. We are then given fairly solid assurance that we will never have a use for the PM ever again. Thank goodness.

One item made me drop the book and start laughing. It is an example of an adjective which describes itself:  Awkwardnessful.       this is the sort of genius that DH brims with.

This is all in the introduction. In some ways this is the most integrated part of the book. Subsequent chapters are more focused. The whole concept of 'eternal golden braid' is laid out here and pretty much nowhere else that I remember. In essence, the self-referential nature of the works of all three of the title characters are laid out and compared and contrasted and interwoven.

One could comprehend much of the book by this one chapter, so long as one *understood* well enough! I cheated and read the whole thing ten years ago, so it's going a lot smoother this go round!
Umlauts anyone?

Gödel, Escher, Bach (GEB)

"An analogy has NOTHING to do with reasoning."

"Israel is the Mecca of tourism."

Cognition as a matter of comparison? Relativity?

In response to PiPhD PiALOGUE
That was %^$#@% awesome! thanks for that, Pi!

Doug's 'crushed hopes' over subscripts called to mind an experience I had with MAD magazine when I was about 8...

having been fascinated by codes, I demanded that my father explain the nonsense characters used in place of curse words. I understood that they were curse words, and as such, it took him some time to convince me that he was not withholding the true decoding of the symbols! I was quite disappointed that I had not found a real secret code!

His words about 'blends' of words arising from competitive choice of concepts brought to mind the recent flap about Sarah Palin. 'Refudiate' was the mash-word, in case you missed it. Comparing herself to Shakespeare in her own defense seemed a stretch, however...    
I hope DH put that incident in his notes!

I kept thinking of the poem I wrote to Perfect Black while all this was playing along. All the simple and complex things I was hinting at and spelling out. In poetry, a lot of thought goes into meter. This was not spoken of by DH in this talk, but in my mind it is very important to the process. I am much too wordy when I am explaining things straight. In poem, I am careful to lilt along at a purpose.

This talk bears more on DH's more recent work than on the drier mathematical content of GEB. I say drier, but in truth it is no less lively! But because he confines himself to formal systems for much of the book, it's bearing on mathematics is evident. This man is a wizard at the translation between languages, and this talk relates more clearly to those subjects.

I am embarrassed to admit, I was unable to figure out how to type umlauts from the wiki page. This was not the first time I have read that page in pursuit of the method, either! I am using a Linux based computer, and as such there is a good chance that it must be done a different way than on Pi's machine.

I can, however, cut and paste!

I am more convinced of DH's wizardry than ever. GEB is a masterwork in bootstrapping analogy machines out of nearly nothing. That he has taken it so very far since is no disappointment. Had I never read GEB, I might not be so impressed; there was something vaguely unsettling about some of his 'categories'...
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