Such as in the pair of statements âThe following sentence is false.â âThe preceding sentence is true.â. (Finite / Infinite Games). In October, I spent a few enjoyable evenings watching a series of lectures from the MIT course ‘ Gödel, Escher, Bach: A Mental Space Odyssey ’. Or maybe I just didnât focus on them deeply enough. Can a text have enough inner logic that its meaning is fully restored whenever intelligence comes into contact with it? You divide the world, artificially, into parts and thereby miss the Way. Already a member? Log in here. Certain rule sets are inviolate, they cannot be changed. Then consider joining the 25,000 other people getting the Monday Medley newsletter. Could we map part of one mind onto another one? Here they introduce the diagonals, first talk about DH himself, and make allusions to ending the discussion earlier than the written discussion ends. Home > Highlights for High School > Humanities and Social Sciences > Gödel, Escher, Bach: A Mental Space Odyssey > Lecture Notes Lecture Notes Course Home This is the dialogue where the crab can play mathematical statements as music, but they only sound good if theyâre true. Fugue: A fugue is like a canon, in that itâs based on one theme which gets played in different voices, but the notation is much less rigid and you can play with it more. A car will never pick up the idea that it is supposed to avoid other cars. We all perceive systems at different levels, and may try to convince others that theyâre operating within systems that theyâre blind to but that we observe. Constant level crossing is what creates our sense of self, it will be necessary to be able to slip between multiple levels comfortably to understand the full richness of the mind-brain system. Symbols interact via fission and fusion. People attribute inherent meaning to words, when their context is just as important. In zen we can see this idea of self transcendence. To get rid of strange loops, you have to get rid of self reference. Knowledge doesnât come in sentence like âpackets,â itâs more abstract. One objection might be that it puts too much challenge on the machine. What makes us call a system a âchoice makerâ is whether we can identify with a high-level description of the process which takes place when the program runs. You can âbootstrapâ a language by acquiring enough of it to keep teaching yourself more of it. Weâre all bundles of contradictions, and thatâs a natural function of our brain, being able to hold contradictions comfortably. Gödel’s so-called Incompleteness Theorem deeply disturbed mathematicians seeking a perfectly logical, ordered universe. Intelligence depends on the ability to create high-level descriptions of complex arrays, such as chess boards, printed pages, or paintings. The Offering has a three part fugue, a six part fugue, ten canons, and a trio sonata. 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. In this dialogue, the music and the piano are backwards, creating an odd feel to the sound. Hofstadter initially intended to write a short book about Gödel’s theorem, similar in content and brevity to Ernest Nagel and James R. Newman’s Gödel’s Proof (1958); in his bibliography, Hofstadter credits this work as the inspiration for his own. Most problems exist in a âproblem spaceâ and being able to step back and consider the space that youâve put the problem in is a core function of intelligence. Surely there wonât be isomorphisms on the neural level, but could there be on the symbol level? This new task is said to be âon a lower levelâ than the previous task. Such as in the famous Escher paintings like the infinite staircase. Start your 48-hour free trial to unlock this Gödel, Escher, Bach study guide. The Tortoise insists on Achilles proving with increasing certainty that itâs his birthday, âhow can I trust that I can trust you?â and so on. 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 itâs doing. This is the discussion of Koans and zen strings. Self-Rep: Self reproducing object or entity. The book ends on this dialogue involving six characters: Achilles, Tortoise, Crab, DH, Turing, and Babbage, and ends in the most appropriate way it possibly could. Once you begin to question your own sanity, you can get caught in an ever tightening vortex of self-fulfilling prophecies. The dust? The anteater is on good terms with the ant colonies, just not specific ants, since he eats ants, but doing so helps the colonies. No matter how much it twists and turns, it is still following the rules inherent in itself. Â© Nathaniel Eliason, 2020 |Â You're looking great today |Â This site built on, Get My Searchable Collection of 200+ Book Notes, Get My Searchable Collection of 250+ Book Notes.