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Det påvises at opbygningen af Kurt Gödels ufuldstændighedsteorem ligner mønstrene i M.C. Eschers tegninger og i Johann Sebastian Bachs fugaer, og at der er analogier til datamater, hjernen, genetikken, fysikken, zenbuddhismen og meget andet.
Zaklog: Cryptonomicon strikes me as the kind of book that Hofstadter would write if he wrote fiction. Both books are complex, with discursive passages on mathematics and a positively weird sense of humor. If you enjoyed (rather than endured) the explanatory sections on cryptography and the charts of Waterhouse's love life (among other, rarely charted things) you should really like this book.… (mere)
EerierIdyllMeme: An obvious suggestion (surprised it's not here already). Both are creative and fictional riffing off of formal logic and incompleteness.
heidialice: GEB is a thousand times as intense, but if you enjoyed the parts about self-referentiality it's worth a skim. Conversely, if GEB is just too much, Paulos' concise introduction to the theme is very accessible.
Lorem: Things in 4D I consider a more accessible version of GEB in its breadth and how it does get to complex topics. If you enjoyed the more complicated parts of 4D, definitely look at GEB and if GEB was a little too much, 4D might remind you why math(s) are never boring… (mere)
P_S_Patrick: Arturo Perez-Reverte has recieved inspiration for his excellent mystery thriller from Hofstadter's Godel Escher Bach, even without some of the chapter introduciton quotes, that much is clear. He uses the bewildering Escherian theme of worlds within a world, Godels incompleteness theorum is alluded to in the monologue of one character, and Bach is discussed in relevance to the mystery too, along with a few miscellaneous paradoxes which are also slipped in, in a similar spirit in which they permeate the more complex non-fictional work. Non-fiction readers who have enjoyed GEB should be amused by the Flanders panel, and I think they should enjoy it even if they do not often dip into fiction. It would be harder to recommend GEB to fans of the Flanders Panel, due to its sheer length, but if you were intrigued by the themes in the story then it should at least be worth finding GEB in a library and dipping into it.… (mere)
Oplysninger fra den engelske Almen VidenRedigér teksten, så den bliver dansk.
To M. and D.
Første ord
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Frederick the Great, King of Prussia, came to power in 1740.
Citater
Oplysninger fra den engelske Almen VidenRedigér teksten, så den bliver dansk.
In its absolute barest form, Gödel's discovery involves the translation of an ancient paradox in philosophy into mathematical terms. That paradox is the so-called Epimenides paradox, or liar paradox. Epimenides was a Cretan who made one immortal statement: “All Cretans are liars.”
Whereas the Epimenides statement creates a paradox since it is neither true nor false, the Gödel sentence G is unprovable (inside P.M.) but true. The grand conclusion? That the system of Principia Mathematica is “incomplete”—there are true statements of number theory which its methods of proof are too weak to demonstrate.
Sidste ord
Oplysninger fra den engelske Almen VidenRedigér teksten, så den bliver dansk.
Tortoise: Reentering Introduction Creates Endlessly Rising Canon, After RICERCAR.
Det påvises at opbygningen af Kurt Gödels ufuldstændighedsteorem ligner mønstrene i M.C. Eschers tegninger og i Johann Sebastian Bachs fugaer, og at der er analogier til datamater, hjernen, genetikken, fysikken, zenbuddhismen og meget andet.
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Intelligent tour-de-force af Hofstadter. Nogle af rablerierne er ret syrede, men der er som regel en intelligent tanke bagved. ( )