[ epub PDF ] Gödel Escher Bach An Eternal Golden Braid AUTHOR Douglas R. Hofstadter

Douglas R. Hofstadter × 8 REVIEW

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 If you open up the 20th Anniversary Edition of GEB you ll see that the first thing Douglas Hofstadter does in the introduction the very first thing is grouse that nobody seems to understand what his book is about Not even its publishers or readers who just absolutely love it A uick glance at the back cover will give you the same impression even the glowing two sentence blurbs are hilariously vague all of them variations on the theme of Well that certainly was something Yes uite a wonderful something indeedSo how are you supposed to know whether to pick it up Or put less delicately how are you supposed to know whether reading all 740 dense sprawling pages is worth your while The short answer is Read this book if you like to think about thinking as well as to think about thinking about thinking The long answer makes me nervous since the typical review of this book apparently misses the point entirely I feel like I m starting out on thin ice Oh well I ll take a crack at it anywayAt its heart this book is about whether you can start with simple parts and from them build a system which is so complicated that it becomes than the sum of its parts in a significant sort of way For example scientists have a very clear understanding of how a single neuron functions They even have a fairly good understanding of how neurons operate in groups to take on specific tasks like wiggling your pinkie finger But there are around a hundred billion neurons in a human brain and the structure uickly becomes preposterously complicated groups of groups of groups of neurons all acting in interconnected ways to produce conscious thought How do we get something as complex as human consciousness out of something as simple and well understood as a neuronThe answer Hofstadter likes is that the brain operates on many different interacting levels and that conscious thought is a product of the complex interaction between all these levels So in order to understand something you re reading you depend on individual neurons operating in basically deterministic ways to move signals around your brain but you also depend on groups of neurons in your vision centers to recognize text as well as other groups of neurons on other levels to understand that text and other groups of neurons on other levels to fit that new understanding into the context of the previous sentence and so on All of this applies eually well to artificial intelligence which is Hofstadter s field It s just that an electronic brain would be built from transistors and subroutines instead of brain tissueThe title is a little misleading this book is not at all about how when you get right down to it Kurt Godel MC Escher and JS Bach are totally interrelated man Their work is just useful in getting deeper down into that idea of interacting layers that produce complexity For example Kurt Godel was a mathematician who proved that in any self consistent formulation of number theory you could generate theorems that while true were not provable in within that formulation Basically he showed that any formal mathematical system is necessarily incomplete in specific ways Here s the part where things start to get craaaaazy If you build a well formed number theory labeled X then X can be used to generate a proof of X s self consistency only if X is inconsistent The reverse is also true And all this relates back to how a system can be than the sum of its partsThese are definitely interesting ideas and very worth reading about but whether GEB is worth reading is a harder uestion It s a very well written well researched book I love that the author goes way way way out of his way to spend time explaining difficult ideas rather than to assume a dull or disinterested readership But sometimes that tendency to dig deeper can start to obscure the central point of a chapter I think that s why so many people lose track of what the book is actually about there really are a ton of fascinating ideas that are all given eual weightThe book hops between two different formats The first is your standard well written popular discussion of complex scientific artistic or philosophical ideas In fact Hofstadter is very good at this part He excels at getting the reader interested in and even excited about some traditionally inaccessible stuff The second format is a series of short dialogs between fictional characters interspersed between every chapter that help to allegorically enforce the ideas in whatever chapter Overall this approach is very good at getting you to understand the complicated ideas Hofstadter is getting at I found that my problems with the book weren t with the subject matter which was fascinating and enjoyable but with the author Ol Dougie H loves this material He loves it so much that he tries to infect you with his own personal sense of wonder and whimsy at how complex and beautiful art and life and science are And of course he s right but that s not the point If he trusted you to feel these things for yourself the book would be maybe 200 pages shorter As it is his constant pedagogical wordplay and artful brain teasers started out fun but after page 400 they started making me tired Also those forced injections of wonder and whimsy start to take on the flavor of little plugs for the personal fantasticness of Douglas Hofstadter For example his discussion of the language processing functions of the brain is interesting but did he really have to bring up the fact that he s fluent in Russian and translated Eugene Onegin In a short book or a movie cleverness can be fun and exciting In a 740 page tome not so muchI strongly recommend this book to a very narrow set of people If you think you d be interested in the subject matter AND you wouldn t mind playing simple word or math games in the service of understanding it AND the inner workings of a computer scientist s marvelous brain seem interesting to you then definitely read this book I enjoyed it and found it very fun and informative overall But if you read this review and you get the feeling you probably won t like this book you re probably right Midnight Sun of “maps” Fight or Flight or links between formal systems However according to Hofstadter the formal system that underlies all mental If you Supernatural Academy (Supernatural Academy, open up the 20th Anniversary Edition 정숙한 남자 of GEB you ll see that the first thing Douglas Hofstadter does in the introduction the very first thing is grouse that nobody seems to understand what his book is about Not even its publishers Breaking The Habit of Being Yourself: How to Lose Your Mind and Create a New One or readers who just absolutely love it A uick glance at the back cover will give you the same impression even the glowing two sentence blurbs are hilariously vague all Riggs' Ruin (Kings Reapers MC Book 1) of them variations Antarctic Ecology Vol 2 on the theme Signaler un problème of Well that certainly was something Yes uite a wonderful something indeedSo how are you supposed to know whether to pick it up Or put less delicately how are you supposed to know whether reading all 740 dense sprawling pages is worth your while The short answer is Read this book if you like to think about thinking as well as to think about thinking about thinking The long answer makes me nervous since the typical review Rhinoceros Success of this book apparently misses the point entirely I feel like I m starting Il Fatati FMalta out The Little Black Book of Blackmail on thin ice Oh well I ll take a crack at it anywayAt its heart this book is about whether you can start with simple parts and from them build a system which is so complicated that it becomes than the sum The hostage of its parts in a significant sort Will My Cat Eat My Eyeballs? Big uestions from Tiny Mortals About Death of way For example scientists have a very clear understanding The Dicshitnary of how a single neuron functions They even have a fairly good understanding Spider's Web of how neurons Furiously Happy operate in groups to take Ready Player Two on specific tasks like wiggling your pinkie finger But there are around a hundred billion neurons in a human brain and the structure uickly becomes preposterously complicated groups سمفونی مردگان of groups Water The Stuff of Life of groups Trzynaste Piórko Eufemii of neurons all acting in interconnected ways to produce conscious thought How do we get something as complex as human consciousness William Foden - Grand Sonata out Situational Judgement Test for the Foundation Years Programme of something as simple and well understood as a neuronThe answer Hofstadter likes is that the brain Lines A Brief History operates On Pytania intymne on many different interacting levels and that conscious thought is a product Off with His Head of the complex interaction between all these levels So in Last Ditch order to understand something you re reading you depend Say Yes to the Duke on individual neurons Died in the Wool operating in basically deterministic ways to move signals around your brain but you also depend Death at the DolphinHand in GloveDead Water on groups Lets Be Just Friends Just Friends of neurons in your vision centers to recognize text as well as Kad žene popizde other groups Pro ASPNET Core 3 Develop Cloud Ready Web Applications Using MVC 3 Blazor and Razor Pages of neurons Aristotle Ethica Eudemia Oxford Classical Texts on The World of Cyberpunk 2077 Deluxe Edition other levels to understand that text and Chocolate Cream Pie Murder Hannah Swensen other groups Him of neurons I Promise to Hate Despise and Abuse You until Death Do Us Part on Monuments other levels to fit that new understanding into the context Die unendliche Geschichte of the previous sentence and so Le uatrième Mur on All My Solace (Bewitched and Bewildered of this applies eually well to artificial intelligence which is Hofstadter s field It s just that an electronic brain would be built from transistors and subroutines instead The Answer of brain tissueThe title is a little misleading this book is not at all about how when you get right down to it Kurt Godel MC Escher and JS Bach are totally interrelated man Their work is just useful in getting deeper down into that idea What's Left of Me Is Yours of interacting layers that produce complexity For example Kurt Godel was a mathematician who proved that in any self consistent formulation Northern Lights of number theory you could generate theorems that while true were not provable in within that formulation Basically he showed that any formal mathematical system is necessarily incomplete in specific ways Here s the part where things start to get craaaaazy If you build a well formed number theory labeled X then X can be used to generate a proof ラブ&ポップ ―トパーズ ii― only if X is inconsistent The reverse is also true And all this relates back to how a system can be than the sum Blake et Mortimer, tome 14 : La Machination Voronov of its partsThese are definitely interesting ideas and very worth reading about but whether GEB is worth reading is a harder uestion It s a very well written well researched book I love that the author goes way way way Éducation européenne out Homo Zodiacus of his way to spend time explaining difficult ideas rather than to assume a dull Immortal Mine Alpha and Omega or disinterested readership But sometimes that tendency to dig deeper can start to Signaler un problème obscure the central point Shadower Shielder of a chapter I think that s why so many people lose track Drawn to Him of what the book is actually about there really are a ton The Queen's Gambit of fascinating ideas that are all given eual weightThe book hops between two different formats The first is your standard well written popular discussion Love Only Once of complex scientific artistic 21st Century New Openings or philosophical ideas In fact Hofstadter is very good at this part He excels at getting the reader interested in and even excited about some traditionally inaccessible stuff The second format is a series Kościół a faszyzm Anatomia kolaboracji own personal sense Mensa Boost Your IQ of course he s right but that s not the point If he trusted you to feel these things for yourself the book would be maybe 200 pages shorter As it is his constant pedagogical wordplay and artful brain teasers started ROOTS: Wie ich meine Wurzeln fand und der Kaffee mein Leben veränderte out fun but after page 400 they started making me tired Also those forced injections The Rules Do Not Apply of wonder and whimsy start to take Unfiltered: No Shame, No Regrets, Just Me on the flavor I Can Subtract Bills and Coins of Douglas Hofstadter For example his discussion Emporium of the language processing functions His Little Heart of the brain is interesting but did he really have to bring up the fact that he s fluent in Russian and translated Eugene Onegin In a short book كيمياء الحب و الزواج or a movie cleverness can be fun and exciting In a 740 page tome not so muchI strongly recommend this book to a very narrow set Cyfrowe marzenia. Historia gier komputerowych i wideo of people If you think you d be interested in the subject matter AND you wouldn t mind playing simple word Tietz Fundamentals of Clinical Chemistry and Molecular Diagnostics or math games in the service Cherry Cheesecake Murder overall But if you read this review and you get the feeling you probably won t like this book you re probably right

REVIEW Î eBook, ePUB or Kindle PDF × Douglas R. Hofstadter

Gödel Escher Bach An Eternal Golden Braid

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 the As I work my way through this dense book I am reminded of the Zen tale of 4 blind men and an elephant To settle a dispute between townspeople over religion the Zen master had 4 blind men and an elephant led in With the men not knowing it s an elephant the Zen master had each feel a part of the elephant Each blind man gave a varying but inaccurate guess of what it was he felt In conclusion the Zen master exclaimed that we are all like blind men We have never seen God but can only guess based on our subjective feelingIn much the same way each chapter in GEB is like feeling a part of an elephant Hopefully by the time we touched each part we have a good idea of what the book is about Here is my layman s take on what that elephant is filtered by my interest in human cognitionG del Escher and Bach The heart of this book is these Strange Loops that represent the activities inside our brains that turn into consciousness GEB uses art and music in combination with math and computing to illustrate these self referential loops The mechanic of the loops is represented by the works of the mathematician Kurt G del the artist MC Escher and the musician JS Bach Kurt G del s Incompleteness Theorem shows that a formula is unprovable within its axiomatic system G del s usage of mathematical reasoning to analyze mathematical reasoning resulted in self referential loopiness basically saying a formula cannot prove itself MC Escher creates visual presentations of this loopiness in his Waterfall and Drawing HandsFinally JS Bach s Musical Offering were complex puzzles offered to King Frederick the Great in the form of canons and fugues A simple description of a canon would be a theme that played against itself such as in Row Row Row Your Boat JS Bach The Musical Offering s visual endless loops G del s incomplete self referential theorem and Bach s canons and fugues in varying levels help to illustrate the characteristics of consciousness The book alternates between Chapters and Dialogues The Dialogue is between Achilles and the Tortoise inspired by Lewis Carroll s What the Tortoise Said to Achilles which in turn was inspired by Zeno of Elea s dialogue between Achilles and the Tortoise The purpose of the Dialogue is to present an idea intuitively before it is formally illustrated in the following Chapter GEB presents varying ways of explaining about systems and levels that create these self referential infinite loopsSystemsTo discuss intelligence GEB starts off explaining the playground in which this takes place We re introduced to the idea of a formal system by the MU puzzle In a formal system there are two types of theorems In the first type theorems are generated from the rules within the system The second type is theorems about the system This puzzle contains the string MIU This system tells us to start with the string MI and transform it to MU by following certain rules After going through the process we find that we cannot turn MI into MU following these steps no matter how long we try We would merely be generating countless strings To stop endlessly generating strings reuires the second type of theorem in which we analyze the system itself This reuires intelligence in which we gauge that this will be an endless task We then guess at the answer intuitively If a computer was told to try to generate the answer it would go on ad infinitum We humans however would soon realize that this is a hopeless situation and stop We the intelligent system critiues ourselves recognizes patterns and jump out of the task it is assigned to do It is difficult however for us to jump out of ourselves No matter how much we try we cannot get out of our own system We as a self referential system can talk about ourselves but cannot jump out of ourselves Thus it is impossible to know all there is to know about ourselves The countless self help techniues are testaments to thatFormal systems are often built hierarchically with the high level meaning where consciousness lies building from the low level primitive functions The most interesting example of levels is in the typogenetics of the DNA GEB gives a detailed account of how enzymes work on the strands with typographical manipulations creating new strands The new strands in turn act as programs that define the enzymes The enzymes again work on the strands This system of enzymes causing the creation of new strands strands defining the enzymes creates a change of levels as new information are created from the process Even readers who don t like math would find it interesting to see how the coding of our DNA works as chemicals help to turn simple codes into us GEB gives further details on the complex process of chemicals and codes but this is the basic ideaIsomorphismIsomorphism is a process of change that preserves information As intelligent beings we are able to detect isomorphism and thus recognize patterns This allows a system to be interpreted in varying ways without losing important information This is illustrated by Bach s canons and fugues A canon can vary in complexity in which the copies can vary in time pitch and speed Also the copy of the theme can be inverted in which the melody jumps down whenever the original jumps up The copy can also be played backwards such as in the crab canon However the copy modifies itself it still contains all of the information of the original theme Isomorphism is mathematically illustrated in the author s p system invention In this system we are able to perceive that the string p means 2 plus 3 euals 5 with the dashes representing numbers p representing plus and representing euals The recognition of an isomorphism leads to isomorphisms such as in the development of language This pattern recognition occurs countless times as part of our intelligence process such that we don t even notice it We regularly see patterns in our daily lives The lower level isomorphisms are so simple that we only see explicit meanings However the lower level isomorphism helps us to create the higher level isomorphismsFrom our experiences we all have lower level explicit isomorphisms from which we deduce new patterns These are our conceptual skeletons When we see new patterns we create higher level isomorphisms until the system is consistent to us This process involves interplay and comparisons of our conceptual skeletons seeing similarities and differences Our conceptual skeletons can even exist in different dimensions that enables us to comprehend the multiple meaning of this statement The Vice President is the spare tire on the automobile of government When two ideas match in their conceptual skeleton the mind is forced to link and create subideas from the match While this is an important function of cognition it also can create erroneous beliefs This was illustrated visually with MC Escher s painting RelativityWhen you look at this do you see a puzzling world that does not follow the physical laws Most of us who are familiar with building structures expect some sort of an organization with stairs gravity and other physical laws If you are familiar with building structures you would start off identifying the lower or established isomorphisms the staircases the people etc From the lower isomorphisms you create higher level isomorphisms with the new bizarre patterns that defy the physical laws Suppose a person viewing this is from a primitive tribe living in the forest and have never seen a building What do you think that person would see when looking at Escher s art piece Perhaps that person would only see geometric shapes and nothing else since there are no lower level isomorphisms of building structures etc The Dreaming in Aboriginal art adds a further dimension to interpretation of geometric shapesIn much the same way we build language based on isomorphisms Children increase their word count by identifying matches to words they already know Interesting problems with meaning comes when translating words from one language to the next especially in literature and poetry which often relies on implicit meaning to understand the content This implicit meaning can change according to a society s culture and history The author s book Le Ton Beau De Marot In Praise of the Music of Language seeks to analyze that by featuring the work of the French poet Cl ment Marot Figure and GroundThere are two types of figureground The first one is cursive in which the ground is only a by product or negative space of the figure and is of less importance than the figure The second one is recursive in which the ground is as important as the figure This idea is also compared to theorems and nontheorems or provability and nonprovability nonprovability being key to the Strange Loops that is at the core of this bookThe chapter Figure and Ground starts with a set of rules for typographical operations which were used in the MU puzzle and the p system which is the mechanical process of the Turing machine the parent of what we now know as computer intelligence Basically the process involves reading and processing of symbols writing it down copying a symbol from one place to another erasing the symbol checking for sameness and keeping a list of generated theorems This process of generating theorems is reliant on the sifting out of nontheorems The parallel to this is the idea of figure and ground and the idea of recursion with figure and ground holding eual importance This is aesthetically explained using Escher s art Tiling of the Plane Using Birds and a discussion on melody and accompanimentFigure and ground form the basis for the idea of recursive and recursively enumerable or re A recursive set is one in which figure and ground holds eual importance That is its re and the complement of its re are eual However GEB showed that there exists formal systems in which the figure and ground are not recursive do not carry the same weight and are not complementary Basically this is saying that there are systems in which its nontheorems cannot be generated via a typographical decision procedure A typographical decision procedure sifts out nontheorems from theorems by performing tests that use the logic of the figureground Hence there exist formal systems for which there is no typographical decision procedure RecursionWe are led to the process of recursion Recursion is the process of building up from a block of structure The simplest explanation of recursion would be the visual imagery of the Russian Maruscha dolls in which an item is nested within an item within an item However this doesn t mean that a process is simply a replication of itself For example in language we start with smaller components such as words and phrases and build up complex sentences from there The process is explained in GEB as push pop and stack of Artificial Intelligence When you push you are temporarily stopping what you are doing to do something else When you pop you return to it but starting from where you left off at one level higher To remember where you left off you store the information in a stack The example given in the book is of someone answering multiple phone calls We use the push pop and stack process especially in our usage of language The most complex example of recursion is in the genetic mechanism of DNA in which the DNA molecules are formed from the smaller building blocks The defining characteristic of recursion is the change in levels so that it is recursive instead of being circular Neurologically this is illustrated in the process of how symbols interact with each other At its minimal are the bare particles that do not interact with others They are nonexistent since all particles interact with each other The process of interaction creates entanglement and a hierarchy of entanglements a 6 degree of separation of infinite loops Recursion is a part of this entanglementRecursion is reliant on samenessdifferentness The same thing happens with slight modifications and at a different level This is visually represented in MC Escher s Butterfliesimage error

READ Gödel Escher Bach An Eternal Golden Braid

N so too will computers attain human intelligence Gödel Escher Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science meaning reduction recursion and muc If I were clever enough I would write this review as a fugue This is the formal structure that Hofstadter uses throughout G del Escher Bach Whether the whole book is a fugue I m not smart enough to tell But the fugue is used as a metaphor for layers of brain activity thoughts superimposed over the hardware of the brain the neuronsIn fact though I would recommend starting at the beginning of the book I suppose one might begin anywhere and read through and back again a la Finnegan s Wake No the book isn t designed this way but considering that I couldn t discern a solid central idea until page 302 of the book and that this was only one of several theses in the book I wouldn t be surprised if it proved possible to begin anywhereThe idea presented there is To suggest ways of reconciling the software of mind with the hardware of brain is a main goal of this book The uestion is does it succeed I would argue that it does notAnd it does not matterThere are some works such as Giorgio De Santilliana s Hamlet s Mill or Daniel Schacter s Searching for Memory that are so vast and all encompassing that it is difficult to pin down one central thesis These are the kind of works that you might not understand in your lifetime the thoughts of a genius transposed directly to paper that unless you are an eually gifted person or a savant you cannot hope to fully comprehend Still the threads and nuggets of gold that are spread throughout make it worth the time spent in the dark mines of incomprehension if only to find that one fist sized chunk of precious metal and appreciate its beauty set against the background of your own ignoranceAs far as I can tell the book is really about intelligence both human and artificial Hofstadter does a lot of preliminary work priming the reader s brain with assumptions taken from theoretical mathematics and computer programming But don t let that scare you off I m no math whiz but I found most of the logical puzzles at least comprehensible after a few careful reads Hofstadter also gives the occasional exercise leaving the reader without an answer to his uestion Like all good teachers Hofstadter understands that the students who work things out on their own are the best prepared students That doesn t mean that you won t understand many of the book s salient points if you can t successfully answer his uestions You can But in order to understand the finer points I suppose one would have to have a pretty good grasp on the answers to those uestionsI don tAnd it didn t matterWhat did matter for me was having a little bit of a background in the idea of nested hierarchies and a smidgen of knowledge in non linear dynamics aka chaos theory For the former I d recommend Valerie Ahl s seminal Hierarchy Theory A Vision Vocabulary and Epistemology For the latter just do what you were going to do anyway and look it up on Wikipedia I won t tell anyoneThe idea of nested hierarchies is central to the understanding of what makes human intelligence different from machine intelligence The short story is this human thought is structured from the ground up according to the basic laws of physics in particular electricity because it is through electricity that neural networks well network The issue is that the layers interceding between neural electrical firings and human thought are tangled They are explainable or ought to be explainable by a series of tangled layers that lead up to the higher functioning of thought Again this is one of the central points of the bookAnd this is the point where Hofstadter utterly failsAnd it doesn t matterYou see Hofstadter never convincingly shows those transitional layers between neural activity and thought though he claims they must be there He claims that it should be possible to create an Artificial Intelligence AI that is every bit as human as human intelligence The problem is how do you define human intelligenceHofstadter presents the problem like this Historically people have been na ve about what ualities if mechanized would undeniably constitute intelligence Sometimes it seems as though each new step towards AI rather than producing something which everyone agrees is real intelligence merely reveals what real intelligence is not If intelligence involves learning creativity emotional responses a sense of beauty a sense of self then there is a long road ahead and it may be that these will only be realized when we have totally duplicated a living brainOne of the big issues in identifying whether an AI is actually intelligent is the notion of slipperiness The concept here is that human thoughts can deal in a larger possibility space my words than machine intelligence Hofstadter uotes from an article in The New Yorker in which two statements are made that while possible would constitute lunacy on the part of anyone who actually believed them They are If Leonardo da Vinci had been born a female the ceiling of the Sistine Chapel might never have been painted And if Michelangelo had been Siamese twins the work would have been completed in half the timeThen he points out another sentence that was printed without blushing I think he Professor Philipp Frank would have enjoyed both of these books enormouslyHofstadter comments Now poor Professor Frank is dead and clearly it is nonsense to suggest that someone could read books written after his death So why wasn t this serious sentence scoffed at Somehow in some difficult to pin down sense the parameters slipped in this sentence do not violate our sense of possibility as much as in the earlier examples This allowable playfulness is something so complex and multi layered that an AI would be hard pressed to correctly parse an appropriate reactionThis is just one case portraying the difficulty inherent in trying to define and understand intelligence and the connection between brain hardware and mind thought The book is rife with them I m not convinced that Hofstadter was fully convinced that there will ever be a machine so intelligent as to completely mirror human thoughtAnd one last time it doesn t matterThis book has set me to thinking thinking hard about what it means to be human Not merely as an intellectual exercise but deep in my emotional breadbasket if you will I feel human in a way that I can t explain when I think about the difficulty of trying to translate my hopes fears love creativity wordplay happiness sadness and ambitions into machine language There has been a lot of talk lately about singularity that moment when machines become self aware I m beginning to think that it will never happen And I m fine with thatBesides Hofstadter gives an implicit warning when uoting Marvin Minsky who said When intelligent machines are constructed we should not be surprised to find them as confused and as stubborn as men in their convictions about mind matter consciousness free will and the likeIn other words if we do somehow construct true Artificial Intelligence with the same capacity for thought and feeling as human beings whose to say the person we create isn t going to turn out to be a real douchebag Terminator anyone


10 thoughts on “Gödel Escher Bach An Eternal Golden Braid

  1. says:

    If you open up the 20th Anniversary Edition of GEB you'll see that the first thing Douglas Hofstadter does in the introduction the very first thing is grouse that nobody seems to understand what his book is about Not even its publishers or re

  2. says:

    This is a nice book if you want to understand the Gödel incompleteness proof and get an account that is both accessible an

  3. says:

    Expand your mind Not for the faint of heart yet by no means dry Hofstadter makes some fascinating observations about emergent properties such as intelligence and diverts us into the extremely heavy mathematics of Godel via the self referencing systems that are Bach's fugues and Escher's 'optical illusion' style artworkBefore too many chapters have passed though you'll be firmly in number theory land albeit dol

  4. says:

    As I work my way through this dense book I am reminded of the Zen tale of 4 blind men and an elephant To settle a dispute between townspeople over religion the Zen master had 4 blind men and an elephant led in With the men not knowing it’s an elephant the Zen master had each feel a part of the elephant Each blind man gave a varying but inaccurate guess of what it was he felt In conclusion the Zen master excl

  5. says:

    I could not with a clear conscience recommend this book to everyone because I'm simply not that cruel It would be like recommending large doses

  6. says:

    from Randall Munroe Mouseover says 'This is the reference implementation of the self referential joke' I know I know I know I'm just kidding myself I'm as likely to read this as a book on string theory Please don't Please don't tell me I have read a book on string theory I'm trying to forget the whole sordid story But I

  7. says:

    This book was so metal Gödel’s incompleteness theorem which states that all consistent axiomatic formulations of number theory include undecidable propositions is certainly a large part of what made the book so fascinating and addictive The issues of self reference and self awareness and how they relate to both human and potential artificial intelligence were likewise extremely compelling But the magic is in the ma

  8. says:

    If I were clever enough I would write this review as a fugue This is the formal structure that Hofstadter uses throughout Gödel Escher Bach W

  9. says:

    This book told me something about intelligence the smartest thing to do is to avoid this book's overly lengthy babblings of a self important graduate student who is way too impressed with himself It took this guy over 700 pages to illustrate by

  10. says:

    The reading of a book and its interpretation are determined in part by the cytoplasmic soup in which it is taken up This reader’s soup consists of a large portion of metaphiction This is how Hofstadter apparently intended to structure his work a Lewis Carroll styled dialogue between Achilles and Tortoise and friends introducing a subject followed by a rigorous but popularly accessible explication of that topi

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