Godel, Escher, Bach
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This document provides an overview of the book "Gödel, Escher, Bach: an Eternal Golden Braid" by Douglas R. Hofstadter. It discusses key topics from the book like isomorphism, recursion, paradox, infinity and formal systems. It also references works by M.C. Escher like "Mosaic II", "Drawing Hands", and "Metamorphosis II" that are relevant to the book's exploration of mathematical and artistic themes. Finally, it directs readers to an online video of Bach's Crab Canon composition for additional context.
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Godel, Escher, Bach
- 1. Gödel, Escher, Bach: an Eternal Golden Braid by Douglas R. Hofstadter George Carstocea IML 555: Digital Pedagogies
- 3. I avoid speculating about futuristic sci-fi AI scenarios, because I don’t think they respect the complexity of what we are thanks to evolution. – interview with Wired, March 2007
- 5. Isomorphism Recursion // Strange Loops Paradox Infinity Formal Systems
- 6. XKCD # 468, “Fetishes”
- 7. “Mosaic II” M.C. Escher, 1957
- 8. “Drawing Hands” M.C. Escher, 1948
- 9. “Metamorphosis II” M.C. Escher, 1940
- 13. This slide initially contained a visualization of Bach’s Crab Canon, which you can find at http://www.dailymotion.com/video/x82en4_ bach-s-crab-canon_music
- 14. George Carstocea University of Southern California @uncertainblume
Hinweis der Redaktion
- Godel Escher Bach first came out in 1979, having been written by Douglas Hofstadter during and after his extended work in the PhD program in Physics at the University of Oregon. By the time it had been published, Hofstadter had already been employed by the University of Indiana, and he has been teaching cognitive science and AI-related issues there ever since.
- Not your usual technoapologistSkeptical of the SingularityNot very interested in computers (he says this in several interviews). Hofstadter sees them as tools, and the interesting work for him is in dealing with the general formal systems that those tools might bring to life“I avoid speculating about futuristic sci-fi AI scenarios, because I don’t think they respect the complexity of what we are thanks to evolution.” – interview with Wired, March 2007Interested in beauty and how we create it, the concept of the soul and how we couldretheoretize it by working through our knowledge of the brain, of formal systems., as well as practices of meditation and zen Buddhism
- Structure: 20Dialogues, 20 chapters, and an intro to the new edition at the beginningEach dialogue playfully introduces the issues that are to be discussed in terms of formal logic in the subsequent chapter. The second dialogue, Two-Part Invention, was not written by Hofstadter – it is, instead, one of the inspirations for this book, a dialogue between Achilles and the Turtle, written by Lewis Carroll in “Mind” in 1895. Carroll himself took these characters from Zeno of Elea, who used them in a famous thought experiment we know now as the “runner’s paradox” –
- Isomorphism – “information-preserving transformation” - preservation of formally mappable structure from an object to another, from a formal system to anotherRecursion - Strange loop = level-crossing feedback loop;a recursive loop that takes palce in a hierarchical formal systems. In a strange loop, as we parse the hierarchies moving to a higher level, we find ourselves back at the lower level – that is, the lower level is tangled to the highest one. “I am lying” – most paradoxes are strange loops – you keep going from the discursive to the metadiscursive level and back again. Same with Grelling’s paradox: autological (self-describing – English, finite, pentasyllabic) vsheterological words (monosyllabic, French). Is “heterological” heterological “I” as strange feedback loop – evolves over time, but comes back to the present, to the now of lived experience -> start with the example!ParadoxInfinityFormal Systems
- Step back: We know who Escher and Bach are, but who is Kurt Godel?Austrian logician and mathematicianBertrand Russell and Albert Whitehead’s Principia Mathematica, which sought to find a way to prevent paradoxical self-reference in mathematicsGodel showed that self-referentiality cannot be avoided in formal systems, showing (in the case of PM) that any metamathematical thinking can be turned towards the inside of the system of mathematics as well. Godel shows that a formal system, when making statements about reality, is also making a statement about itself, crossing the boundaries of its exterior. In simple terms, if a system is consistent, it can’t be complete, and its axioms cannot be proven completely within the system itself.
- The illustration for one dialogue, the Sonata for Unaccompanied Achilles. Here, Achilles speaks the words of one side of the conversation with the Turtle, while we are left to reconstruct the other side of it. Not only is this what Bach’s Sonatas did (playing one part of a contrapuntal structure and allowing the listener to fill in the gaps with the counterpoint), but it is also what M.C. Escher touches upon with the contrasting tensions between the foreground and background constituting themselves into white and black figures.
- “reality” of photorealistic rendering vs the page as a support(does, in some ways, what Magritte did in “La Trachison des Images” – “this is not a pipe”