Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter
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Book Reviews of Gödel, Escher, Bach: An Eternal Golden Braid
Book Review: Worth Working Through!
Summary: 5 Stars
Overall, the book looks at the author's views on how consciousness and a sense of self can arise from what is nothing more than the mind, a collection of neurons that follow fairly precise rules at a granular enough level. How can something as complex as a symphony be produced by what is nothing more than a collection of cells?
What made the book such an enjoyable read was the author's ability to meld these three individuals' lives (Godel's, Escher's, and Bach's) and work together into a seemingly finely interwoven mosaic. In virtually every chapter there's multiple works by Escher that, upon seeing them within the context of the chapter's topic, makes you think Escher created that work for Hofstadter's book. Similarly, I learned a lot about music structure and the little games and slieghts of hand Bach's works contain.
One unique thing about this book was the structure. Between each chapter the author included a dialog between, typically, Achilles and the Tortoise. These two chums would have discourses on topics that played into the material presented in the following chapter. These dialogs are worth the price of admission alone. In particular the Crab Canon is a piece where a new character, the crab, is introduced, and he has one line right smack dab in the middle of the dialog. The first half and second half of the dialog, however, are identical in words, but shifted in meaning. For example, the dialog starts with Achilles saying, "Good day!" as a greeting, and ends with the Tortoise saying "Good day!" as a goodbye. It's amazing how well it all works together. (You can read this particular dialog in its entirety here - http://www.barryland.com/canon.html) In music, a crab canon is a kind of canon in which one line is reversed in time from the other (e.g. FABACEAE <=> EAECABAF).
Hofstadter explores these ideas in part by looking at Goedel's incompleteness theorem, which states that given a complex enough of a formal system (such as number theory), there are theorems in the system that are true but cannot be expressed in the system. In other words, interesting formal systems are incomplete. The canonical example used to illustrate Goedel's theorem is the statement, "This sentence is false." Goedel's theorem is founded in number theory, not English, but the point is that given a complex enough system, there are things that are "beyond" the system.
The chapters I enjoyed included:
* The one on Zen Buddhism, which I knew little to nothing about beforehand, but like the explanation that the author provided. Sounds like a very interesting philosophy. (How honest/complete an overview the author gave, I don't know, not being familiar with the philosophy myself.)
* The chapters describing the basics of the cell, how cell's replicate and how DNA, RNA, mRNA, and ribosomes work together to create the proteins used by the cell.
* The final chapter, as it posed many open-ended questions about "strange loops and tangled hierarchies" (a concept discussed throughout the book) in everyday life.
Overall, I would highly recommend this book to those who are interested in a discussion on what might constitute consciousness, thought, the soul, and existence, and how these concepts can be materialized from lower-level mechanical processes. Furthermore, the author examines how he views things like true artificial intelligence - a computer with a soul, with a sense of self - would have to be accomplished. Understand that the author does not get to these concepts right off; rather, he spends significant time building up the base of understanding to have a discussion on these topics, and the topics are not fluff ones. At times it can take several minutes just to get through a single page (at least for me).
But if you put the time in, I think you'll reap the reward by the book's end. Personally I liked every chapter except for the few close to the end that detailed the "progress" in AI research. (I use "progress" in quotes because this book was written back in 1979.)
Book Review: GEB: EGB puts the I in Intelligence
Summary: 5 Stars
GEB: EGB is basically an exploration of the idea of intelligence, artificial and otherwise. Hofstader's goal is to shed some light on how intelligence / consciousness / self-awareness happens. I would call him a materialist, in the sense that he believes that there is a physical basis for thoughts, feelings and emotions. He is dismissive of "soulists," who believe that there is some sort of inexplicable metaphysical aspect to consciousness.
The question, in Hofstader's mind, is, "If the human brain is made of essentially the same stuff as a kitchen table or a pocket calculator or a tree, why does the first have a sense of of self -- of being an 'I' -- whereas the others do not? Hofstader explores how physical activity in the brain, which seems completely mechanistic and completely unlike the process of thought that we experience, can in fact give rise to a qualitatively different sort of activity occurring at the "higher levels" of the brain. He gives several examples of such systems, such as an ant colony: the individual ants are stupid, acting in response to basic stimula, but the colony as a whole is much smarter.
This kind of qualitative difference between the different levels of a system is key to Hofstader's thesis that critics of the possibility of artificial intelligence have misinterpreted the implications of such limitative notions as Godel's theorem. Godel's theorem states, in essence, that any sufficiently powerful system will contain truths that are not provable within the system. The problem with computers, these critics charge, is that they are stuck within a particular system -- there is no way to program them to realize that there is no solution to a particular problem within the system, even though such a fact would be perfectly obvious to an intelligent person who can "jump out of the system." So the computer is stuck trying to solve the problem with a method that is doomed to fail.
Hofstader argues, on the other hand, that there is nothing magical about being able to jump out of the system and reflect on whether it is the appropriate system to be using. In fact, in doing this one is still "in" a system -- it's just a bigger system, one that has the ability to think about lower level systems. And one can jump out of that top level system and reflect on it as well -- but then of course one has entered a new system again. There's always another system, at a higher level, no matter how high up you go.
At a certain point these levels blur together, because they are recursive -- meaning they reflect back on themselves. Hofstader uses the works of Escher and Bach to illustrate the concept of recursivity. For example, there is Escher's stairway that goes up and up until you are back where you started, or the two hands, each of which is drawing the other.
Hofstader believes that self-awareness -- the "I" -- arises from this kind of recursivity. To put it very simply, at the highest levels the brain is a system that deals with symbols, and the "I" is the symbol for the system itself.
There is much, much more to this book. There are lengthy tangents into mathematics, philosophy, biology (the section about the recursion that takes place in the copying of DNA is particularly fascination), etc.
Thankfully the book is organized into sections that alternate between straight exposition of some concept and a fictional dialogue that illustrates the concept. Still, it's not light reading, and I did wish at points that there was a Reader's Digest version that would just give me the main points without going off on a tangent for 30 pages about wasps or something.
Godel, Escher, Bach made me rethink a lot of my preconceptions about consciousness and artificial intelligence, and is well worth reading the next time you have three months to spare.
Book Review: A Profound Meditation On Human Creativity
Summary: 5 Stars
Gödel, Escher, Bach: An Eternal Golden Braid debates, beautifully, the question of consciousness and the possibility of artificial intelligence. It is a book that attempts to discover the true meaning of "self."As the book introduces the reader to cognitive science, the author draws heavily from the world of art to illustrate the finer points of mathematics. The works of M.C. Escher and J.S. Bach are discussed as well as other works in the world of art and music. Topics presented range from mathematics and meta-mathematics to programming, recursion, formal systems, multilevel systems, self-reference, self-representation and others.
Lest you think Gödel, Escher, Bach: An Eternal Golden Braid, to be a dry and boring book on a dry and boring topic, think again. Before each of the book's twenty chapters, Hofstadter has included a witty dialogue, in which Achilles, the Tortoise, and friends discuss various aspects that will later be examined by Hofstadter in the chapter to follow.
In writing these wonderful dialogues, Hofstadter created and entirely new form of art in which concepts are presented on two different levels simultaneously: form and content. The more obvious level of content presents each idea directly through the views of Achilles, Tortoise and company. Their views are sometimes right, often wrong, but always hilariously funny. The true beauty of this book, however, lies in the way Hofstadter interweaves these very ideas into the physical form of the dialogue. The form deals with the same mathematical concepts discussed by the characters, and is more than vaguely reminiscent of the musical pieces of Bach and printed works of Escher that the characters mention directly in their always-witty and sometimes hilarious, discussions.
One example is the "Crab Canon," that precedes Chapter Eight. This is a short but highly amusing piece that can be read, like the musical notes in Bach's Crab Canon, in either direction--from start to finish or from finish to start, resulting in the very same text. Although fiendishly difficult to write, the artistic beauty of that dialogue equals Bach's music or Escher's drawing of the same name.
As good as all this is (and it really is wonderful), it is only the beginning. Other topics include self-reference and self-representation (really quite different). The examples given can, and often do, lead to hilarious and paradoxical results.
In playfully presenting these concepts in a highly amusing manner, Hofstadter slowly and gently introduces the reader to more advanced mathematical ideas, like formal systems, the Church-Turing Thesis, Turing's Halting Problem and Gödel's Incompleteness Theorem.
Gödel, Escher, Bach: An Eternal Golden Braid, does discuss some very serious topics and it can, at times, be a daunting book to handle and absorb. But it is always immensely enjoyable to read. The sheer joy of discovering the puns and playful gems hidden in the text are a part of what makes this book so very special. Anecdotes, word plays and Zen koans are additional aspects that help make this book an experience that many readers will come to feel to be a turning point in their lives.
Like every other book written by Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid, has an index and a bibliography that must be noted as exceptionally well done.
Although filled with English wordplay, this book is in no way tied to the American origin of its author. For years, it was thought that Gödel, Escher, Bach: An Eternal Golden Braid, would be impossible to translate, but so far, it has successfully been translated into French, German, Spanish, Chinese, Swedish, Dutch and Russian.
A profound and beautiful meditation on human thought and creativity, this book is indescribably gorgeous and definitely one of a kind.
Book Review: Book Stands on its Own Merits
Summary: 5 Stars
This book first came out when I was entering graduate school. Intrigued by reviews, I vowed to pick it up and see what all the fuss was about, but that intention continued to be overruled by the time constraints of graduate research, as well as various other life experiences. Eventually, a few other misadventurous choices I made sucked a lot of time out of life, and I gradually forgot about GEB.
Then, a little more than ten years ago, an internet acquaintance I had met in a newsgroup referred to GEB, and I was intrigued enough at that time to seek out and purchase an out-of-print copy at a used book store. What a life saver, literally! How? Bear with me, and I will explain...
It would be hyperbole to credit GEB solely for giving me the inspiration to change a very bad personal situation several years ago, without also crediting family, friends, myself, and a bit of good luck as well, but it would also be negligent to not credit GEB at all. After purchasing the book, I started reading short passages occasionally and working through various mental challenges and puzzles, albeit secretly, lest my activity be perceived as futile and thus evoke the ire of a certain someone in my life at the time. I certainly did not want my dearly sought, out-of-print (at the time) book to end up being destroyed.
If you are still with me here, you are probably thinking by now, she needed a few self help books, new locks on the doors, court orders, and maybe even a baseball bat; not GEB! Well, this is a book review, so let me continue. It sounds trite, but Hofstadter's book helped me realize the truth of "I think, therefore, I am." Of course, it certainly helped that I have always enjoyed puzzles in mathematics and logic, but by going through GEB, I began to recover a certain sense of self that I had pretty much neglected. It was a defining moment in turning my life around.
Now, with regard to the book itself...
Some reviewers here have critiqued GEB as if they are reviewing a paper for journal publication. Excuse me, but the book is what it is. Surely if these reviewers are as serious and scholarly as they present themselves to be, they could stroll over to their nearest university library and find all sorts of very scholarly writing with which they could impress themselves. However, I do not understand why they seem to expect GEB to be in the same category as peer reviewed journals. The ideas presented in the book are most definitely impressive, but GEB was published to be read and enjoyed by an educated public, not just by a scholarly few within one discipline.
I will not pretend to have found the "hidden message" of the entire book, though I think I have a pretty good idea what it is. I find that I enjoy the book most by slowly taking in various ideas to be savored and digested. It is a meditative work. Indeed, as someone now well along in a career as a computer professional, e.g., programmer analyst (hey, my life really did change!), I sometimes find the development in my thinking skills nurtured by GEB, and I also find my understanding of GEB nurtured by the development of my thinking skills. This understanding extends into all areas of life.
GEB is very inspirational on multidimensional levels, e.g., serious, recreational, challenging, etc. If you enjoy logic, puzzles, philosophy, and knowledge in general, I think you will enjoy this book. If you have a reasonably good grounding in mathematics, you will probably enjoy GEB even more, but if you do not have such a background, do not let that stop you from diving in anyway. Peruse a few passages, and see if you like it!
Book Review: A Crystal Bead
Summary: 5 Stars
In honor of the 20th anniversary, I put up a review I wrote 11 yearsago, for a school assignment:
When I am feeling that life is pointless
or unwondrous, I read Douglas Hofstadter's =Godel, Escher, Bach=; time
and time again, this book leaves me in awe over the interconnectedness
of several "unrelated" subjects, over order arising from
apparent chaos. This book made me regain my faith in and admiration of
the beauty of math, art, music, and the universe -- the beauty that is
almost never shown in a class or revealed in a "scholarly"
work; after reading it, the isolation of those subjects from the rest
of the conceptual world seems simply ludicrous. Each time in reading I
am challenged to discover more connections, more self-references, more
meaning in the several subjects presented. In short, reading this book
is like a religious experience for me -- I love it.
From GEB:
"The Buddhist allegory of 'Indra's Net' tells of an endless net
of threads throughout the universe...At every crossing of threads is
an individual and every individual is a crystal bead. The great light
of 'Absolute Being' illuminates and penetrates every crystal bead;
moreover, every crystal bead reflects not only the light from every
other crystal in the net -- but also every reflection of every
reflection throughout the universe."
Hofstadter's book is the
perfect example of one of those crystal beads; Hofstadter portrays (or
"reflects") several subjects in his work, e.g., formal
systems, Zen, moplecular biology, the art of fugues and canons, model
of the brain, various geometries, number theory, Holism
vs. Reductionism, and much more, and then shows the
"reflections" of the subjects in one another -- truly a
large task. For the most part, he comes across quite well; his
dialogues which encapsulate and discuss ideas to be presented, his
"dogmaps" which outline parallel ideas and "map"
them onto one another, and his relatively simple language enable him
to communicate his ideas quite easily. However, this book is quite
weighty -- almost 800 pages long, full of digressions and
perspective-blowing ideas; many ideas and underlying themes must be
sought out within the dialogues, many open-ended questions are left
for the reader to ponder. If you aren't used to flexible or abstract
thinking, and you don't want to work very hard in reading, this book
isn't for you.
GEB is an unique "nonfiction" book -- it does
not address one subject, or even several "closely related"
subjects. Even though published in 1979, many parts deal with research
still going on today [this is still true in 2001, as it was in
1990]. For example, Hofstadter presents a possible model for a brain
to be used in artificial intelligence in computers -- one of many
models being studied today in that field. In one short section, he
presents recursive graphs that were generated in theoretical
experiments -- graphs that bear some similarity to the modern study of
fractals. Especially in the area of computer science, Hofstadter
leaves several goals for people to attain -- goals that may never be
realized, but perhaps goals that will enlighten us as we seek to
attain them.
The ideas in this book shall live long past its authorr;
I can say no more but that the people who awarded the Pulitzer Prize
to this book made no mistake.