Gödel, Escher, Bach: An Eternal Golden Braid
by Douglas R. Hofstadter
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Book Summary Information
Author: Douglas R. HofstadterBrand: Baker and Taylor
Edition: Paperback
Audio: English (Unknown); English (Original Language); English (Published)
Published: 1999-02-05
ISBN: 0465026567
Number of pages: 832
Publisher: Basic Books
Product features:
- Music
- Art
- Mathematics
- Meditation on Human Thought and Creativity
- Artificial Intelligence
Book Reviews of Gödel, Escher, Bach: An Eternal Golden Braid
Book Review: One of the great popular science books
Summary: 5 Stars
This book richly deserved its Pulitzer prize. It's one of the great pieces of popular science writing and it's remarkable that it has lost so little in 25 years. You learn the intricacies of Bach's music, of Godel's Incompleteness theorem, Escher's drawings and DNA replication. Although his purpose seems to have been very general, with everything tied together loosely as ideas for his future work in artifical intelligence, one could view this as a book about some parts of cognitive psychology-- how the templates we inherit in our DNA create and interpret sounds and images and theorems and how these seem to relate to one another via the concepts of recursiveness, tangled hierarchies, and incompleteness. It is mostly the lack of these inference engines that accounts for the fact that to this day AI has still not been able to make a machine with the brains of an ant(ie, go out into an arbitrarily complex world, recognize and deal with friend and foe, eat, reproduce, and stay out of the sun and rain and keep doing it for years).
His followup the next year with Daniel Dennet--`The Mind's I` complements this book nicely(see my review).
So one could say that this is really a psychology text. It is about human behavior and reasoning-about why we think and act the way we do. But(like all such discussions until recently) none of the explanations are really explanations. Nobody at that time had much understanding of the mental mechanisms involved. Like most 'explanations` of behavior, the comments here are often more interesting for what kinds of things he tries to use (and omits) than for the actual content. As with all reasoning and explaining, art, math, music, etc, one now wants to know which of the brains inference engines are activated. This book and most books and AI research were largely oblivious to such explanations until quite recently.
Cognitive and evolutionary psychology are still not evolved enough to provide full explanations but an interesting start has been made. Boyer's `Religion Explained` is a good place to see what a modern scientific explanation of human behavior looks like,and works on art, music and math are sure to appear soon. Pinker's `How the mind Works` is a good general survey. They do not explain all of intelligence or thinking but give an idea of how to start. See several of the recent texts(ie, 2004 onwards) with evolutionary psychology in the title or the web for further info.
We now recognize that the bases for art, music, math, philosophy, psychology, sociology, language and religion are found in the automatic functioning of templates or inference engines. This is why we can expect similarities and puzzles and inconsistencies or incompleteness and often, dead ends. The brain has no general intelligence but numerous specialized modules, each of which works on certain aspects of some problem and the results are then added, resulting in the feelings which lead to behavior. Hofstadter, like everyone, can only generate or recognize explanations that are consistent with the operations of his own inference engines, which were evolved to deal with such things as resource accumulation, coalitions in small groups, social exchanges and the evaluation of the intentions of other persons. It is amazing they can produce philosophy and science, and not surprising that figuring out how they themselves work together to produce consciousness or choice or spirituality is way beyond reach.
He does not try to deal with the endlessly vexing issue of whether these correlations are out there in the world or in here in the mind. Yes, we use our templates, but why did we evolve those and was there another possibility? Some will say this will all become clear when psychology and genetics are sufficiently advanced, while others say the same of physics and mathematics or programming. And, did they all evolve from some prototype engine in a precambrian invertebrate or did they come much later and from many sources?
It occurred to me that some of the most complex products of human reasoning --superstring theory and the associated math--are recursive( in some nontrivial sense) to quantum field theory, subatomic particle behavior and the entire universe. Physics unites many areas of the most advanced math because it needs self consistent structures, but since we know math is logically proven to be inescapably incomplete and math is a product of the mind, it seems reasonable that there must be a sense in which the mind is incomplete also. We expect since they use math that computers must be incomplete. We know that Turing's halting theorem for computation(we can not discover in advance when a computer will stop) is logically equivalent to Godel's incompleteness theorem. It might follow that physics will be incomplete as well and there will be many physical laws or phenomena that will never be compatible with or derivable from the others. Or perhaps physics can be complete and selfconsistent in one universe but not in others
Just as he did not go very far into the many realms of psychology or physics, neither did he venture far into philosophy. Perhaps the book could have benefited greatly from an understanding of the infinitely subtle relationships between language, thought and reality. An acquaintance with Wittgenstein would have helped immensely, especially his 'Lectures on the Foundations of Mathematics: Cambridge, 1939' edited by Cora Diamond(1990). It is better to get this one rather than the earlier `Remarks on the Foundations of Mathematics, Vol. 1` edited by Rush Rhees( as they are based on different sets of notes if you are really into it you should get both).
Although I've never seen anyone say so, W can be regarded as a pioneer in cognitive psychology. All of his research was thought experiments and introspection into the relations between language, thought and reality. Perhaps nobody ever approached his talent for describing the mind at work. The point is that Hofstadter is trying to understand how the mind works as a preliminary to making programs that work the same way(or at least get similar results) so anyone who is interested in this book(or nearly any area of philosophy, language, psychology, or intellectual discourse) can look into W with great profit(but be forewarned W may seem very shallow, but if you jump in you may never stop swimming)!
Just after reading this book I happened to read Wittgensteins ``Culture and Value``(published the same year(1980), but written decades earlier), and, though it's his least interesting book, I picked out a few comments that may be regarded as pertinent to much of this book and of course to a large part of modern intellectual life.
``There is no religious denomination in which the misuse of metaphysical expressions has been responsible for so much sin as it has in mathematics.``
``People say again and again that philosophy doesn't really progress, that we are still occupied with the same philosophical problems as were the Greeks. But the people who say this don't understand why is has to be so. It is because our language has remained the same and keeps seducing us into asking the same questions. As long as there continues to be a verb 'to be' that looks as if it functions in the same was as 'to eat' and 'to drink', as long as we still have the adjectives 'identical', 'true', 'false', 'possible', as long as we continue to talk of a river of time, of an expanse of space, etc., etc., people will keep stumbling over the same puzzling difficulties and find themselves staring at something which no explanation seems capable of clearing up. And what's more, this satisfies a longing for the transcendent, because, insofar as people think they can see `the limits of human understanding', they believe of course that they can see beyond these.``
Whenever one gets philosophical it is relevant to take a step back from time to time and see just what is really going on. Hofstadter is not a philospher and he does not seem to take that step. Incompleteness seems well defined in math but what about elsewhere? In what sense is music or art or biology incomplete? And exactly what will count as a tangled hierarchy, and recursiveness or self referencing in such different realms(and as W would say, such different language games)? Its not really so clear that the recursiveness in art, music, biology and math are the same sort of thing at all an, insofar as they are, what exactly that means. What should count as ``same` here?
H does not address these questions in any depth but one might find them by far the most interesting theme of the book. We are tantalized at the seeming connections but do they mean anything? Do they go to the core of our being(how the mind works)? Are they merely the result of the use of some of the same templates by art, math, and music? Do they relate to the molecular structure of matter or to particle physics and string theory? Is it useful to extend these analogies(or are they homologies?)almost endlessly further into philosophy, language, psychology, biology(e.g., not only the recursive nature of DNA, RNA and proteins, but the many levels of feedback in the nucleus, cytoplasm, intercellular, interorgan, intracerebral, exchange of chemicals and genes between nucleus, mitochondria and chloroplasts as well as with the bacteria and viruses that wander in out of our bodies into other bodies and other organisms happily picking up and dropping off genes as they go--tangled, recursive, hierarchical and in some sense, incomplete).
Or, to take it further, one might find yet more connections between art and music, math and biology, computer programs, physics and chemistry and biochemistry and add such dimensions as color, geometric shapes, measurements , self organizing abilities, chaos, and other temporal, spatial or purely psychological ways(emotions, sensations, dreams etc). There are many books in art, music, math, biology, psychology, physics and chemistry that already touch upon these themes but I think the most progress is being made in cognitive psychology. The brain is highly recursive in many ways. We converse with ourselves internally and many times externally. The schizophrenic commonly hears voices, but they rarely say nice things.
One is reminded of the cut-ups that William Burroughs and Byron Gysin created. They cut up books or even newspapers and stuck them back together randomly. There was usually some perverse kind of logic to the result showing the hidden threads in discourse. Burroughs later did the same thing with films, with similar results.
Of course pursuing hidden relationships between seemingly unconnected things quickly leads to numerology, pyrimidology and madness. One can find codes or algorithms to connect or derive anything from anything. Hofstadter does not go into this here but he mentions it in his next book, The Minds I(1981). I am reminded of string theory which has math so powerful it can probably explain any possible universe and so it is very suspect as an explanation of ours.
He suggest that incompleteness, tangled hierarchies etc may be responsible for the emergence of higher phenomena which do not exist and cannot be explained at lower levels(eg, consciousness and in fact, everything)and seems to be something of a holist( but in other places he seems clearly behaviorist or reductionist). You might say he is suggesting we look for the explanation of emergence in the bizarre phenomena of the foundations of math, rather than in those in the foundations of physics. Given a universe where life is possible, is it not inevitably full of recursiveness, tangled hierarchies, incompleteness etc.
As H is well aware, Zen can be regarded as using these aspects of the world to trick the mind into stopping-- at which point all relationships become irrelevant. However he was just starting in Zen at the time so he does not go very far with it. For those who want to go into it further, probably the best and most readable recent books on Zen are the various volumes by Osho.
Its a pity he has not been able to write another book like this as there is now a vast amount of information available about DNA and RNA, the inflationary theory of the universe, quantum theory, and the beautiful fusion of string theory and advanced math, which could greatly extend and amplifiy the themes of recursion, tangledness, hierarchies, and incompleteness. One could make a good case that the basic structure of the universe has these properties at its smallest and largest scales. Both quantum physics and string theory have complex sets of laws that appear tangled,nested, hierarchical and incomplete-- and so far no one can unify them, unless one accepts string theory on faith-but nobody can solve string theory and physics, like mathematics which it mirrors (or expresses?)may remain forever incomplete( Kaku's `Hyperspace` gives a summary up to 1994-see my review).
It was one of the few times he stuck his neck out when he predicted that the future of AI would involve recursive programs but are neural nets and fuzzy logic recursive? And do these relate at all to how the brain works or to anything Wittgenstein has to say about language and reality? The diligent might want to look at B.A. Worthington's book--`Self Consciousness and Self Referencing:an interpretation of Wittgenstein's Tractatus`.
Since this book appeared, mathematician Gregory Chaitin has made major extensions of incompleteness and alsodeveloped the amazing omega number defining the limits of math(his popular and tech books easy to find on the net and his most recent on omega-- Meta Math --appeared in 2005).
Some readers will find interesting a vaguely similar book ``Labyrinth`` by Peter Pesic (2000) which uses the form of the triple fugue to link symbolic mathematics to the pursuit of science.
He does not mention that Godel showed that (if the universe is rotating) time travel is possible(ie, time is recursive), nor that all theories of physics, including quantum field theory, remain incomplete. Also the highest product of the mind--Superstring Theory is recursive to quantum field theory and the behavior of particles and the entire universe. A good bit of this was known in 1980 and Hofstadter was a physicist so it''s surprising it does not appear here. We know that the most advanced physics and the most advanced math fuse in superstring theory and this seems amazingly holistic. Physics must have the self consistent structures of mathematics but as math is inescapably incomplete does it follow that physics is also? And worse, as math is a product of the mind is not the mind forever incomplete too? Does this mean there will always be physical laws or phenomena that are not deriveable from(compatible with) the others or can physics be complete and self consistent in one universe(however we delimit or describe that) but inconsistent in others? All these questions seem likely to go on forever.
Summary of Gödel, Escher, Bach: An Eternal Golden Braid
Douglas Hofstadter?s book is concerned directly with the nature of “maps? or links between formal systems. However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel Escher and Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.
Twenty years after it topped the bestseller charts, Douglas R. Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid is still something of a marvel. Besides being a profound and entertaining meditation on human thought and creativity, this book looks at the surprising points of contact between the music of Bach, the artwork of Escher, and the mathematics of Gödel. It also looks at the prospects for computers and artificial intelligence (AI) for mimicking human thought. For the general reader and the computer techie alike, this book still sets a standard for thinking about the future of computers and their relation to the way we think.
Hofstadter's great achievement in Gödel, Escher, Bach was making abstruse mathematical topics (like undecidability, recursion, and 'strange loops') accessible and remarkably entertaining. Borrowing a page from Lewis Carroll (who might well have been a fan of this book), each chapter presents dialogue between the Tortoise and Achilles, as well as other characters who dramatize concepts discussed later in more detail. Allusions to Bach's music (centering on his Musical Offering) and Escher's continually paradoxical artwork are plentiful here. This more approachable material lets the author delve into serious number theory (concentrating on the ramifications of Gödel's Theorem of Incompleteness) while stopping along the way to ponder the work of a host of other mathematicians, artists, and thinkers.
The world has moved on since 1979, of course. The book predicted that computers probably won't ever beat humans in chess, though Deep Blue beat Garry Kasparov in 1997. And the vinyl record, which serves for some of Hofstadter's best analogies, is now left to collectors. Sections on recursion and the graphs of certain functions from physics look tantalizing, like the fractals of recent chaos theory. And AI has moved on, of course, with mixed results. Yet Gödel, Escher, Bach remains a remarkable achievement. Its intellectual range and ability to let us visualize difficult mathematical concepts help make it one of this century's best for anyone who's interested in computers and their potential for real intelligence. --Richard Dragan
Topics Covered: J.S. Bach, M.C. Escher, Kurt Gödel: biographical information and work, artificial intelligence (AI) history and theories, strange loops and tangled hierarchies, formal and informal systems, number theory, form in mathematics, figure and ground, consistency, completeness, Euclidean and non-Euclidean geometry, recursive structures, theories of meaning, propositional calculus, typographical number theory, Zen and mathematics, levels of description and computers; theory of mind: neurons, minds and thoughts; undecidability; self-reference and self-representation; Turing test for machine intelligence.
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