Here are the four rules of the puzzle rephrased for further clarity. Mu uses a breadthfirst, bruteforce method, and multimu the main version has multicore support. An eternal golden braid, also known as geb, is a 1979 book by douglas hofstadter. For example, in the mu puzzle hofstadter claims human intelligence was only able to recognize the pattern that all theorems must begin with m because human intelligence had to attempt the puzzle and follow the puzzles rules first. Hofstadter 1999 in this, the twentiethanniversary edition of hofstadters seminal work, we learn how it is that animate beings can come out of inanimate matter through strange loops of symbolic manipulation that result in consciousness. A bit of theory about the mu puzzle proposed by douglas hofstadter in his book godel, escher, bach of 1979. This demonstration lets you explore the miusystem and the mupuzzle 1. The texts range from early philosophical and fictional musings on a subject that could seemingly only be examined in the realm of thought, to works from. The mupuzzle in this series of blog posts, i will read and summarize the main points of godel, escher, bach. Full text of godel, escher, bach an eternal golden braid. Twenty years after it topped the bestseller charts, douglas r.
A musicological offering the mu puzzle meaning and form in mathematics figure and ground consistency, completeness and geometry recursive structures and processes the. The book is filled with puzzles, such as hofstadters mu puzzle. As stated, it is an example of a post canonical system and can be reformulated as a term rewriting system the puzzle. The order of the characters in a string does matter. Computer models of the fundamental mechanisms of thought is a 1995 book by douglas hofstadter and other members of the fluid analogies research group exploring the mechanisms of intelligence through computer modeling. No one knew what it was, but molly wasnt able to understand language or to speak nor is she to this day, and we never did find. I can only warmly invite the reader to take the time to enjoy this book a gr friend of mine stated that this is one of the very few books that he did read twice, and i perfectly understand why.
Escher, and composer johann sebastian bach, the book expounds concepts fundamental to mathematics, symmetry, and intelligence. Fantasies and reflections on self and soul is a 1981 collection of essays and other texts about the nature of the mind and the self, edited with commentary by popular science writers douglas r. For those of you who did the mu puzzle from godel, escher, bach. Escher and composer johann sebastian bach, geb expounds.
Mu finds whether you can derive one string from another, primarily using the rules printed in hofstadters godel, escher, bach. In a dialogue between achilles and the tortoise, the author hints that there is a contrapunctal acrostic in the chapter that refers both to the author hofstadter and bach. The number of is in the string will never be evenly divisible by 3. The following books are nice to have, but not at all required. An eternal golden braid, but other rules can be implemented by changing the transform method in rules. An eternal golden braid is still something of a marvel. Isbn 0465026567 a new preface by the author, but otherwise is a facsimile of the original edition, with the exact same 777 pages hofstadter. Goodreads helps you keep track of books you want to read. The minds i stanislaw lem wiki fandom powered by wikia. The mu puzzle was first described in douglas hofstadters book, godel, escher, bach. In this dialogue, they discuss modifying a tune to get different tunes but with the same ratio of note changes, e. I did the mu puzzle a very long time ago but i still have the book. This fantastic range of word, logic and number puzzles will engage even the most avid solver.
From this you try to derive the string mu, but you have to follow a few rules of course. Provide an example of how you used the mmode in considering the puzzle. Douglas richard hofstadter born february 15, 1945 is an american scholar of cognitive science, physics, and comparative literature whose research includes concepts such as the sense of self in relation to the external world, consciousness, analogymaking, artistic creation, literary translation, and discovery in mathematics and physics. Great books in computer sciences florida institute of. Provide an example of how you used the imode in considering the puzzle.
Were given a starting string mi, and some transformation rules. The chesscafe puzzle book 1 kindle edition by muller, karsten, polgar, susan, susan polgar. The chapter figure and ground starts with a set of rules for typographical operations which were used in the mupuzzle and the pqsystem, which is the mechanical process of the turing machine, the parent of what we now know as computer intelligence. Hofstadters motivation is to contrast reasoning within a formal system ie. This demonstration lets you explore the miusystem and the mu puzzle 1, an example formal system and accompanying challenge introduced by douglas hofstadter in chapter 1 of godel, escher, bach as a means of illustrating the important elements of formal systems axioms, theorems, rules of inference, the mechanical and intelligent modes of treating a formal system, and the concept. An eternal golden braid this chapter opens up with the mu puzzle as a prototype for us to better understand the underlying structure of formal systems. Piano music by douglas hofstadter audio cd isbn 1576771431, 2000 hofstadter, douglas r. A strange loop is a cyclic structure that goes through several levels in a hierarchical system. Douglas hofstadter and daniel dennett, the minds i. By exploring common themes in the lives and works of logician kurt godel, artist m. Download it once and read it on your kindle device, pc, phones or tablets.
Whether youve loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. It always takes longer than you expect, even when you take into account hofstadters law. Because geb is one of the most magnificent books ever written. An eternal golden braid is a 1979 book by douglas hofstadter. A simple formal system the miusystem is presented, and the reader is urged to work out a puzzle to gain familiarity with formal systems in general. The chesscafe puzzle book 1 kindle edition by muller. Fantasies and reflections on self and soul, bantam, 1985. Why is douglas hofstadters godel, escher, and bach so.
A any string containing only the letters m, i, and u is wellformed. It contends that the notions of analogy and fluidity are fundamental to explain how the human mind solves problems and to create computer. 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. If you came up with the answer yourself, feel free to share it now. The mu puzzle was first described in douglas hofstadter s book, godel, escher, bach. Hofstadter suggests that the numbers 3 and 2 play important roles in the miusystem. Invariant mathematics wikimili, the best wikipedia reader. The set of theorem is the set of string constructed by the rules and the axiom, is denoted by and can be built as follows. The mu puzzle is in essence about attempting to produce the string mu from an initially given string mi as one follows a certain set of rules that can be applied given some conditions.
The mu puzzle is a puzzle stated by douglas hofstadter and found in godel, escher, bach involving a simple formal system called miu. I strongly doubt that i understood them at any greater depth than that of the copy on the book jackets, but that fact didnt bother me. I remember reading hofstadters books as a young teen. You missed out on the mu puzzle, which means you lose. Logic level 3 in douglas hofstadters book, godel, escher, bach, he proposes the following puzzle about formal systems. The mu puzzle and godels incompleteness theorems there exists a book called godel, escher, bach, written by a man called d ouglas hofstadter. The tagline a metaphorical fugue on minds and machines in the spirit of lewis carroll was used by the publisher to describe the book. If you enjoyed rather than endured the explanatory sections on cryptography and the charts of waterhouses love life among other, rarely charted things.
This is an interface for producing derivations is hofstadters formal system called. I enjoyed it and found it very fun and informative, overall. Vintage books, a division of random house, 1980, 1980. Mu puzzle confusion submitted 3 years ago by petersonpersuasion this is my first run through geb, and i must misunderstand the rules of the mu puzzle but im not exactly sure how so. Provide an example of how you used the umode in considering the puzzle. The mu puzzle asks to start with a the axiomatic word mi and. The author leans primarily on the seemingly impossible recursion underlying. Welcome to the official i book of puzzles the book features brand new content throughout, with a collection of over 100 mixed puzzles that have been specially selected by the creators of the i puzzle page, for both existing fans as well as new.
For those of you who did the mu puzzle from godel, escher. You need it to be so that rule 3 can reduce it to 0 and thus acheive the goal. The puzzle asks one to start with the word mi and transform it into the word mu, using in each step one of the following transformation rules. You can apply one of these four transformations at a time. John gould, just for the record, i believe the solution is a single stroke. Harry gensler, introduction to logic, routledge, 2001. Other readers will always be interested in your opinion of the books youve read. It arises when, by moving only upwards or downwards through the system, one finds oneself back where one started. Through illustration and analysis, the book discusses how, through self. Hofstadters miu system the alphabet of the system contains three symbols m, i, u. The mu puzzle is a formal system puzzle that i first discovered when i read douglas r. The mu puzzle is a puzzle stated by douglas hofstadter and found in godel, escher, bach. Use features like bookmarks, note taking and highlighting while reading the chesscafe puzzle book 1. An example of this is the chapter titled contracrostipunctus, which combines the words acrostic and contrapunctus counterpoint.
Evidence without proof that its likely to be impossible. If you possess a string whose last letter is i, you can add on a u at the end. Hofstadter talks a lot about observ ing patterns, but who is doing the observing and from where. Strange loops may involve selfreference and paradox. This is the mupuzzle from one of my favourite books godel, escher, bach. You start with a string, mi, and you must transform it repeatedly until you obtain the string mu. The mu puzzle 8 is a good example of a logical problem where determining an invariant is of use for an impossibility proof.
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