Gödel, Escher, Bach: an Eternal Golden Braid

I have been wanting to read Douglas R. Hofstadter's book Gödel, Escher, Bach: an Eternal Golden Braid for several years. I finally bought it earlier this year and started the task of reading it. Hofstadter, in the preface, describes the book as "a very personal attempt to say how it is that animate beings can come out of inanimate matter." It can be classified as being about metamathematics, consciousness, or artificial intelligence. It uses the concept of "strange loops" to describe how different levels of a system interact to produce unexpected properties. These comments can only be taken as a high level introduction to these concepts, as the book is very dense.

The structure of the book consists of chapters divided by dialogues, which are between the characters of Achilles and the Tortoise, and others who join in later on. the dialogues illustrate a concept that is expanded in the following chapters. For example, in the dialogue "...Ant Fugue", the Anteater tells Achilles and the Tortoise about how he interacts with an ant colony as if it were a sentient thing, even though the ants themselves are simple beings incapable of larger concepts of self or complex communication. The ants carry signals via chemicals, which in turn produce symbols, which create an end result such as "get food here" or "build there". In the following chapter, this is related to the brain and its concept of self, against the fact of neurons and the signals they carry, and the symbols they create, all the way to the super-symbol of self.

The three men of the title are chosen because each created things that were somehow strange loops. Bach created canons and fugues, which are musical notes arranged in a tightly controlled but elaborate pattern. The mathematician Gödel invented the Incompleteness Theorem, which uses a system's symbols to describe itself. And Escher created art that creates illusions on different levels.

The author first delves into a version number theory which he calls Typographical Number Theory (TNT), because it describes how to turn axioms into theorems by using typographical rules. The first big concept is the difference between I-mode and M-mode. M-mode is machine mode, where one mechanically applies different rules. I-mode is intelligent mode, where one can make a leap of intuition, to create an abstraction out of other rules. For example, a machine can transform different strings to make theorems until it reaches a certain one, but an intelligent person can step back and, using I-mode, intuit that either there is an easier way, or that the goal is unreachable.

He also talks about figure and ground, and how some things are best expressed as lacking a well-defined properties. One of his examples is prime and composite numbers. He discusses meaning and form, and introduces the concept of isomorphism, which is a map or translation to a different meaning.

He then gets into a description of recursion. The dialogue preceding this is an interesting one where Achilles and the Tortoise read a story about themselves, wherein they have adventures and find a book about themselves, which they in turn read, etc. The discussion of recursion moves into musical patterns, linguistic structures, and of course math and computer science. An interesting chapter centers on meaning and how it exists in a text, whether meaning is intrinsic to a text or whether it only has meaning in the proper context. It turns out context is crucial, of course, and is described as the writing on a bottle which contains the actual message. The most interesting point in this discussion is that a message in Japanese might have to have an explanatory note saying that the text is in Japanese, but that note would have to be in a different language, or it would be pointless. The fact that the message is in Japanese is in effect the bottle, or context, and understanding this is the key to understanding the text itself.

Hofstadter then gets into a discussion of levels of meaning, specifically inside a computer. He describes the difference between transistors, registers, machine code, assembly language, and higher level languages. He then relates this to the brain and neurons, using the ant colony analogy. Then the discussion segues into finite searches and infinite searches, and the more abstract question of how to determine whether a search is infinite or finite. (I must admit I got a little lost around this point.)

Then he starts to tie it all together, using the TNT to talk about itself. This point about self-reflection is a key point in the whole book. Examples abound in Escher's work, such as the picture of the dragon trying to escape from a two-dimensional space, though it is in fact always two-dimensional, or his picture of two hands drawing each other (kind of a mutual reflection). Other examples are sentences which comment on themselves, like "This sentence is true." Or, more mysteriously, "This sentence is false." The truth/false nature of this last sentence is ambiguous, and in a way it transcends meaning. Another crucial sentence is "This sentence has not proof." He comes up with a method, following Gödel, of letting TNT talk about itself, and creates a sentence in TNT which as an ambiguous meaning like the one above. This is a bit of a paradox, since part of TNT's claim (like the Principia Mathematica) is that it is complete, and the lack of proof for this statement, G, or it's negation, ~G, means that it is really incomplete.

This can only make so much sense in the limited way I'm describing it, and there are so many other levels. Hofstadter then goes on to see if TNT can be superseded, but it turns out that there is no system that can be described as complete. Even if you made a system called TNT+G, it would suffer from the same limitations, and likewise TNT^G, or TNT^G^G.

He then describes how DNA works, and the process that turns it into RNA, and into proteins, which then perform functions. Some of these functions include making the DNA replicate itself, so that part of the message of DNA is a message to create more DNA. One question is, is DNA data, or is it program, or is it both?

The last chapters talk about the implications for artificial intelligence, how an intelligence might be formed out of circuits and software instead of neurons and impulses. He questions whether the seemingly infinite nature of recursion and self-reflection that is consciousness means that intelligence is not able to be produced in a limited system. He then wraps it up by talking about systems that are self-referential and the implications.

This book is a definite A+. I have always been interested in intelligence and AI. Hofstadter clearly brought a lot of different theories together in this book. All the concepts build on each other, creating a symbol linkage that is very complex in the mind. One of the most fascinating illustrations is of Bongard problems, puzzles of two different sets of six boxes. The sets are different, but not easily differentiated. One might have a certain number of shapes, and the other one might have another number of shapes, but the boxes have different sizes and shapes, so it is difficult to tell exactly what the difference is. These puzzles require deep abstract thinking and problem solving skills, the type of skills which are difficult to program into software.

Hofstadter describes these curious connections and references as strange loops. How does an intelligent being make sense of such abstractions and use them to solve problems? How are concepts related? How does the mind think about itself? How does a camera look at itself? I must admit that my mind started clouding over at some of the concepts. The math is just on the edge of my abilities, but I don't think it's necessary to be a math whiz to appreciate the book, especially the language centric parts. Anybody who has thought about thinking will enjoy this book. This one will stay on my bookshelf, and I hope to read it again to see if I understand it any better in the future. In the meantime, Hofstadter has a new book coming out, called I Am a Strange Loop.

Gods and Pawns

Gods and Pawns is a collection of short stories by Kage Baker. The stories are all about the Company, an institution that has figured out how to travel back in time and use that power to enrich themselves. They recruit children who are lost to history, give them treatments to make them immortal cyborgs, and use them as agents throughout history.

The first story is "To the Land Beyond the Sunset"., about two cyborgs names Lewis, a literature preservation specialist, and Mendoza, a cyborg woman who is a botanist. Lewis is attracted to Mendoza, but he is shy and she is bitter about the death of a mortal lover. They live in a Company compound in 17th century South America. When Lewis wins a week off, he decides to offer Mendoza a trip to the Amazonian wilderness. While camping, they encounter a family claiming to be ancient gods. They end up in an amusing cat and mouse game with the family, and Mendoza discovers the secret to a biological substance that's a super fertilizer.

Another story, "The Angel in the Darkness", is about Porforio, an immortal who has followed and protected the descendants of his brother for centuries. In 1991, he has to protect Maria and her niece and grandnephew when a rogue agent from a secret organization that plots against the Company. The rogue agent starts a plague in a nursing home, in a recreation of a plague he started decades earlier. Poforio has to explain who he is to his mortal relative, and why he looks the same as he did in the fifties when she was a girl.

"Welcome to the Olympus, Mr. Hearst" is a long story about Lewis and Joseph, two immortals who visit William Randolph Hearst's estate in 1933 to let them hide an autographed manuscript in a piece of furniture. They have to deal with a visitor who claims to be a mystic, her dog who suspects Lewis is different, the theft of the manuscript, celebrities such as Greta Garbo and Clark Gable, and a very demanding Hearst. Joseph discovers that he has a much bigger time dealing with Hearst, and finds out a big secret of the Company.

There are some shorter stories, about a man who is turned into an immortal and goes insane; Joseph and Mendoza on the trail of a special type of gold in San Fransisco in 1950; the Company's work to create works from a Dutch master to suit the bland twenty-fourth century taste in art; and Lewis's trip to a private library in 1774, and the secret rites he experiences.

The stories all have common themes of how immortals deal with long lives and the loss of mortal friends, how the Company twists the little known pieces of history to its advantage, and how the agents suffer through the machinations and dealings of their masters.

The characters are all interesting. Lewis in particular comes off very well, almost a naive version of a manipulative agent. He is always earnest and enthusiastic. Mendoza is more cynical, holding a grudge against the Company for the loss of her mortal lover. Joseph is the capable agent, who knows that he is only part of a large process. The plots are also captivating. The stories manage to weave through time without causing disruptions. And yet big things happen. It's an A-.

Monsters, Gods, and Heroes: Approaching the Epic in Literature

Monsters, Gods, and Heroes: Approaching the Epic in Literature
is a course from the Modern Scholar library. The lecturer is Professor Timothy Shutt.

The professor distinguishes between two kinds of epics. Primary epics are those based directly on oral tradition, having been written down from a poem created over many tellings. Secondary epics are those with a more literary tradition, based on primary epics and each other. All epics reflect grand themes of their society.

Shutt describes the major epics of Western literature, starting with the Iliad the the Odyssey. The them of individual achievement, or arete, pervades these works. Achilles is the finest example of a warrior, and Odysseus is the most crafty man. Both exemplify personal excellence. Virgil's Aneas, on the other hand, exemplifies a leadership and sacrifice for the common good. Aneas leads his people to their destiny, sacrificing his own desires.

Beowolf is the other primary epic discussed. Beowolf's confrontation with Grendel and his mother represents triumph over the murderous nature of men. His fight with the dragon shows the inevibility of fate and death for all men.

Shutt's favorite epic is Dante's Divine Comedy. He traces the geography of Hell, Purgatory, and Heaven. Dante's creation is truly inspired. The circles of Hell show a constricting of spirit, and the mountain of Purgatory shows an ever increasing spirit as lesser sins are purged. Along the way, Dante puts his political enemies and friends in their places.

The last two epics are Spenser's The Fairie Queen and Milton's Paradise Lost. Both are Christian epics, though with different Protestant viewpoints. Spenser's work is a vast allegory, where each person or item represents another concept in religion. Milton's poem is the story of Lucifer's fall from Heaven. Lucifer's anger and defiance of God is a quintessence of man's separation from God.

All of these epics have themes that are significant in their own culture. And thus they are good examples of the culture's literature. Shutt does a pretty good job of elucidating the plot, style, and themes of the epics. It made me want to read the Aeneid and Paradise Lost, and perhaps reread The Inferno and read the rest of the Divine Comedy.

I especially liked the description of Hell, Purgatory and Heaven fromt Dante's imagination. The linking of the map of these places to the soul is very illuminating. This lecture gets an A.

Wicked

Gregory Maguire's Wicked is a retelling of the story of the Wicked Witch of the West, from Frank Baum's Oz. It is an inventive story that delves into the psychology of the witch and her sister.

The story starts in Munchkinland, where Elphaba is born as a green baby to a Unionist minister and his wife. She is born inside a clock of the Time Dragon, which has caused unrest in the lands. Everybody is surprised that she is green, and she is naturally afraid of water. She ends up in Shiz, the university in Oz, where she meets Galenda and others. They get caught up in politics, trying to stand up for the rights of Animals, who can talk. When her professor, a Goat, is killed and Galinda's guardian dies, Elphaba runs away to the Emerald City to be an insurgent.

There she ends up having an affair with Fiyero, a young prince who was also a classmate. Things end badly when her insurgent plans go awry, and Fiyero dies. After years in a nunnery, she travels to Fiyero's lands to meet his widow and try to get forgiveness. There her powers start to grow. She goes to visit her sister one day, who has become a leader in Munchkinland, called the Eminent Thropp, since it is hereditary and Elphaba has rejected the title. Her sister, Nessa Rose, was born without arms, but has managed to walk a lot better since her father gave her some special ruby shoes. When Elphaba returns to Fiyero's family, she finds that they have been kidnapped by the wizard's troops.

Years later, she visits her father after a house drops on her sister. She is enraged at Glenda for giving the shoes away to the girl in the house. She obsesses over the shoes and the wizard, until the girl throws water on her and kills her.

There is a lot more to the story. It delves into the conflict between the Unnamed God of the Unionists, the pagan Lurlene, and the Pleasure Faith. There's also the wizard, who has grabbed power from the Princess Ozma. There's the sisters' wanton mother and conflicted father. The wizard takes away the rights of the Animals. There's also the snobbishness of Galinda, and how she and Elphaba become attached.

The witch is a misanthrope through and through. It is amazing that she ends up in bed with a man at all. She treats her son from Fiyero, who she doesn't remember giving birth to, with neglect and hostility. Yet her character arc is a growth from a child who can't relate to other children (in fact the children shun her), to a young adult who acts with wit, humanity, and even charm, to an adult who bears an awful burden and takes on the needs of those around her. It is telling that she treats the Animals and other downtrodden humans with more humanity than her fellow humans.

The land of Oz is vast, and we get to see the lands of Munchkinland and the Thousand Year Grasslands, and more in between. The story is infused with a wonderful mysticism, giving it a deeper and broader meaning. Between that and the insights into the personality of the witch, the book gets an A.