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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. 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 doled out as painlessly as is possible with such stuff leavened with imagined philosophical debates between ancient Greeks and other proxies I seem to remember Achilles spends a lot of time talking to a tortoiseNumber theory reuires no great resource of mathematical knowledge just an extremely agile and open mind If you let him Hofstadter will show you how Godel destroyed Betrand Russell s Principa Mathematica his attempt to logically deduce all of mathematics from a set of axioms Godel shows us that I paraphrase drastically that all logical systems allow statements about natural numbers that are true but unprovable within the systemAnd somehow this isn t even what the book s about As the pages turn you will be steadily tested and at some point it will become apparent you ve not been paying close enough attention However even without taking pen to paper and labouring through the instructive exercises you can get a pretty decent glimpse at some exciting and fundamental thinking Join my 3 emails a year newsletter prizes

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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. 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 analogy his not particularly novel theory which he sums up finally as followsMy belief is that the explanations of emergent phenomena in our brains for instance ideas hopes images analogies and finally consciousness and free will are based on a kind of Strange Loop an interaction between levels in which the top level reaches back down towards the bottom level and influences it while at the same time being itself determined by the bottom levelDuh Icebergs pages to illustrate by analogy his not The Line particularly novel theory which he sums up finally as followsMy belief is that the explanations of emergent Your Naughty Playmate 3 - Cuckolding Fantasy phenomena in our brains for instance ideas hopes images analogies and finally consciousness and free will are based on a kind of Strange Loop an interaction between levels in which the top level reaches back down towards the bottom level and influences it while at the same time being itself determined by the bottom levelDuh

Douglas R. Hofstadter Á 9 free download

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


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 readers who just absolutely love it A uick glance at the back cover will give you the same impression ev

  2. says:

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

  3. says:

    Expand your mind Not for the faint of heart yet by no means dry Hofstadter makes some fascinating observations a

  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 i

  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 of LSD to everyone some small minority will find the experience invaluably enlightening but for most people it's just going to melt their brainWhile you do not need to be a professional mathematician to appreciate this you really have to like math a lot You can't just s

  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 hope you like thisA friend of mine established The Harvester Press in the 1970s He did it

  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 mathHere is a brief su

  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 Whether the whole book is a fugue I'm not smart enough to tell But the

  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

  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 topic This is how I read

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