In the basic canon, the first voice enters, and after a period, the second voice enters at the same beginning as the first, layering on top of each other. There are also more complicated canons, where the second voice may enter at a different pitch as well. The transition is seamless, and allows it to continue rising forever. Such as in the famous Escher paintings like the infinite staircase.
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Not even its publishers or readers who just absolutely love it. A quick 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 Yes, quite a wonderful something indeed.
Or put less delicately, how are you supposed to know whether reading all 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. At 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 more 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 quickly 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 neuron? The 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. The title is a little misleading - this book is not at all about how when you get right down to it, Kurt Godel, M.
Escher, and J. 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.
The reverse is also true. And all this relates back to how a system can be more than the sum of its parts. These are definitely interesting ideas and very worth reading about, but whether GEB is worth reading is a harder question. 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.
The 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. 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.
If he trusted you to feel these things for yourself, the book would be maybe pages shorter. As it is, his constant pedagogical wordplay and artful brain teasers started out fun but after page 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.
In a short book or a movie, cleverness can be fun and exciting. In a page tome, not so much. I strongly recommend this book to a very narrow set of people. I enjoyed it and found it very fun and informative, overall.
Gödel, Escher, Bach: un Eterno y Grácil Bucle
The main chapters alternate with dialogues between imaginary characters, usually Achilles and the tortoise , first used by Zeno of Elea and later by Lewis Carroll in " What the Tortoise Said to Achilles ". These origins are related in the first two dialogues, and later ones introduce new characters such as the Crab. These narratives frequently dip into self-reference and metafiction. Word play also features prominently in the work. One dialogue contains a story about a genie from the Arabic " Djinn " and various "tonics" of both the liquid and musical varieties , which is titled " Djinn and Tonic ". One dialogue in the book is written in the form of a crab canon , in which every line before the midpoint corresponds to an identical line past the midpoint.
Godel, Escher, Bach: An Eternal Golden Braid
Not even its publishers or readers who just absolutely love it. A quick 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 Yes, quite a wonderful something indeed. Or put less delicately, how are you supposed to know whether reading all 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. At 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 more 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.
Gödel Escher Bach by Douglas R. Hofstadter
In , he moved to the University of Michigan in Ann Arbor, where he was hired as a professor of psychology and was also appointed to the Walgreen Chair for the Study of Human Understanding. In he returned to Bloomington as "College of Arts and Sciences Professor" in both cognitive science and computer science. He was also appointed adjunct professor of history and philosophy of science, philosophy, comparative literature, and psychology, but has said that his involvement with most of those departments is nominal. Other more recent models include Phaeaco implemented by Harry Foundalis and SeqSee Abhijit Mahabal , which model high-level perception and analogy-making in the microdomains of Bongard problems and number sequences, respectively, as well as George Francisco Lara-Dammer , which models the processes of perception and discovery in triangle geometry.