Humans will always recognize these patterns when they’re sufficiently obvious. Nowhere in your body is the number “9.3” coded if you can run 100 yards in 9.3 seconds. Perhaps the mind can be understood without understanding the lower levels on which it both depends and does not depend. Knowledge doesn’t come in sentence like “packets,” it’s more abstract. There is a “calculus of thinking” where concepts can suddenly merge and split, such as when you find out that the person next to you in the bathroom is also your friend from the gym. Or do you have to go down to the level of the nerve cell to understand the mind? They just pop out at us. It’s not as if a man could successfully imitate a computer! The course covered some of the content from Douglas Hofstadter’s book, so I watched it in part as a precursor to reading the book. Requirement of Formality: You must not do anything outside the rules of the system. You don’t read every individual letter and then put them together into words, you can read whole words at once, despite the composite letters having no inherent meaning. Early in the twentieth century, Alfred North Whitehead and Bertrand Russell set about devising a mathematical system that would be consistent and complete, one that could generate every true statement about number theory without producing any false ones. Bach’s endlessly rising canon gives the musical form of strange loopiness, continuing forever. A Brief History of Time by Stephen Hawking, Astrophysics for People in a Hurry by Neil Degrasse Tyson, The Beginning of Infinity by David Deutsch. Hofstadter’s Law: It always takes longer than you expect, even when you take into account Hofstadter’s Law. Is it the writer? We feel self-programmed, but we have no access to our lower levels. Isomorphism: An information-preserving transformation. Epimenides Paradox: Another form of strange loop, contained in statements like “This statement is false.” It is a “one step strange loop.”, Russell’s Paradox: Most sets are not members of themselves. When you see the pipe painting in the pipe painting, you think that the pipe that’s a level “higher” is “more real,” but that’s absurd, they’re equally fake since they’re both in the painting you’re looking at. But you cannot quite break out of yourself and be outside of yourself. You divide the world, artificially, into parts and thereby miss the Way. A work of half a million words treating such esoteric matters as the propositional calculus, typographical number theory, Zen koans, and operator languages might easily overwhelm the typical reader. Such as in the famous Escher paintings like the infinite staircase. In this dialogue, they discuss modifying a tune to get different tunes but with the same ratio of note changes, e.g. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more. Symbols interact via fission and fusion. To “pop” is to jump back out to the previous task you were doing. Gödel Escher Bach by Douglas R. Hofstadter. Yes, if you go down to the lowest level, the hardware, to find the rules. or frogs?” make us step out a bit towards ism, recognizing the inherent absurdity that they’re not anything at all. Incompleteness Theorem and DNA: It is always possible to design a strand of DNA which, if injected into a cell, would, upon being transcribed, cause such proteins to be manufactured as would destroy the cell (or the DNA), and thus result in the non-reproduction of that DNA. Self-reference and loopiness is likely at the core of understanding minds and developing AI. The symbols among people with the same native language will likely be similar, but how does that change in new languages? Hofstadter claimed that the book expressed his religion; it certainly seems to encapsulate his extensive education. In large part, such wide appeal is attributable to Hofstadter’s style and presentation. One big difference between machines and humans is that it is possible to program a machine to do a routine task, while noticing no higher order to what it’s doing. Along the way he offers pleasant but instructive digressions and challenging problems, allowing one to pause and reflect during his journey through the development of modern technology. In this dialogue, Tortoise and Achilles end up being abducted into a hot air balloon off of the ferris wheel. “There exist formal systems whose negative space (set of non-theorems) is not the positive space (set of theorems) of any formal system.”. Surely there won’t be isomorphisms on the neural level, but could there be on the symbol level? The other is to explain the high-level traffic of symbol activation in its own terms, to make a theory which does not talk about the low-level neural events. The koan helps you “step out” and break the rules of thought you’re normally constrained by. Home > Highlights for High School > Humanities and Social Sciences > Gödel, Escher, Bach: A Mental Space Odyssey > Lecture Notes Lecture Notes Course Home Knowledge is not stored explicitly, but implicitly, in a spread out manner, rather than as a local packet of information.

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