Gödel, Escher, Bach的笔记(27)

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  第160页

  zsh

  In order to convert genotype into phenotype, a set of mechanisms far more complex than the genotype must operate on the genotype. The various parts of the genotype serve as /triggers/ for those mechanisms. or instructions for a machine operation, a "program" (更多)

  In order to convert genotype into phenotype, a set of mechanisms far more complex than the genotype must operate on the genotype. The various parts of the genotype serve as /triggers/ for those mechanisms.

  or instructions for a machine operation, a "program" (收起)

  2012-03-24 03:12:40   回应

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  第94页

  zsh

  A full formalization of geometry would take the drastic step of making _every_ term undefined---that is, turning every term into a "meaningless" symbol of a formal system. I put quotes around "meaningless" because ... the symbols automatically pick up passive meanings in accordance with the theorems they occur in. It is another question, though, whether people discover those me... (更多)

  A full formalization of geometry would take the drastic step of making _every_ term undefined---that is, turning every term into a "meaningless" symbol of a formal system. I put quotes around "meaningless" because ... the symbols automatically pick up passive meanings in accordance with the theorems they occur in. It is another question, though, whether people discover those meanings, for to do so requires finding a set of concepts which can be linked by an isomorphism to the symbols in the formal system. If one begins with the aim of formalizing geometry, presumably one has an _intended_ interpretation for each symbol, so that the passive meanings are built into the system.

  consistency is not a property of a formal system per se, but depends on the interpretation which is proposed for it. By the same token, inconsistency is not an intrinsic property of any formal system.

  (收起)

  2011-12-04 09:35:44   回应

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  第79页

  zsh

  Tortoise: ... By the way, did you know that each of the four letters in Bach's name is the name of a musical note? Achilles: 'tisn't possible, is it? After all, musical notes only go from 'A' through 'G'. Tortoise: Just so; in most countries, that's the case. But in Germany, Bach's own homeland, the convention has always been similar, except that what we call 'B', they call 'H', and what w... (更多)

  Tortoise: ... By the way, did you know that each of the four letters in Bach's name is the name of a musical note? Achilles: 'tisn't possible, is it? After all, musical notes only go from 'A' through 'G'. Tortoise: Just so; in most countries, that's the case. But in Germany, Bach's own homeland, the convention has always been similar, except that what we call 'B', they call 'H', and what we call 'B-flat', they call 'B'. For instance, we talk about Bach's "Mass in B Minor", whereas they talk about his "H-moll Messe".

  (收起)

  2011-12-01 07:28:07   回应

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  第78页

  zsh

  By elaborate calculations, its little computer figured out what effects the sounds would have upon its phonograph. If it deduced that the sounds were such that they would cause the machine in its present configuration to break, then it did something very clever. Old omega contained a device which could disassemble large parts of its phonograph subunit, and rebuild them in new ways, so that it coul... (更多)

  By elaborate calculations, its little computer figured out what effects the sounds would have upon its phonograph. If it deduced that the sounds were such that they would cause the machine in its present configuration to break, then it did something very clever. Old omega contained a device which could disassemble large parts of its phonograph subunit, and rebuild them in new ways, so that it could, in effect, change its own structure. If the sounds were "dangerous", a new configuration was chosen, one to which the sounds would pose no threat, and this new configuration would then be built by the rebuilding subunit, under direction of the little computer. Only after this rebuilding operation would Record Player Omega attempt to play the record.

  This is like switching to a new gauge to avoid multi-valuedness in the wavefunction phase. Now, we know the flux can never be avioded simply by gauge transformations... (收起)

  2011-12-01 07:14:05   回应

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  第73页

  zsh

  xy DND x (DND: does not divide) this is essentially the reversal of Euclid's algorithm for Greatest Common Divisor (更多)

  xy DND x

  (DND: does not divide)

  this is essentially the reversal of Euclid's algorithm for Greatest Common Divisor (收起)

  2011-11-26 11:03:56   回应

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  第73页

  zsh

  1 3 7 12 18 26 35 45 56 69 See wikipedia entry Hofstadter sequence. 1) taking _difference_ of neighboring numbers generates: 2 4 5 6 8 9 10 11 13 2) taking _complement_ of the given sequence yields the same result as 1): 2 4 5 6 8 9 10 11 13 14 15 16 17 ... (更多)

  1 3 7 12 18 26 35 45 56 69

  See wikipedia entry Hofstadter sequence.

  1) taking _difference_ of neighboring numbers generates:

  2 4 5 6 8 9 10 11 13

  2) taking _complement_ of the given sequence yields the same result as 1):

  2 4 5 6

  8 9 10 11

  13 14 15 16 17

  ... (收起)

  2011-11-26 10:42:54   回应

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  第72页

  zsh

  The intuition underlying my belief is represented by the question: "How could a figure and its ground not carry exactly the same information? when the canvas is kind of infinite, or has some topological weirdness. (The intuition requires a "localized" complement of some sort. If the complement becomes "delocalized", then the original local set cannot capture the delocaliz... (更多)

  The intuition underlying my belief is represented by the question: "How could a figure and its ground not carry exactly the same information?

  when the canvas is kind of infinite, or has some topological weirdness. (The intuition requires a "localized" complement of some sort. If the complement becomes "delocalized", then the original local set cannot capture the delocalized complement) (收起)

  2011-11-26 10:02:56   回应

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  第70页

  zsh

  One may also look for figures and grounds in music. One analogue is the distinction between melody and accompaniment...Another figure-ground distinction exists in music: that between on-beat and off-beat. (更多)

  One may also look for figures and grounds in music. One analogue is the distinction between melody and accompaniment...Another figure-ground distinction exists in music: that between on-beat and off-beat.

  (收起)

  2011-11-26 10:01:30   回应

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  第60页

  zsh

  If we were to delve into Euclid's proof more and more carefully, we would see that it is composed of many, many small---almost infinitesimal---steps. If all those steps were written out line after line, the proof would appear incredibly complicated. To our minds it is clearest when several steps are telescoped together, to form one single sentence. the said vs. the unsaid (更多)

  If we were to delve into Euclid's proof more and more carefully, we would see that it is composed of many, many small---almost infinitesimal---steps. If all those steps were written out line after line, the proof would appear incredibly complicated. To our minds it is clearest when several steps are telescoped together, to form one single sentence.

  the said vs. the unsaid (收起)

  2011-11-26 04:20:55   回应

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  第58页

  zsh

  The best we could do would be to count primes for a while and concede that there are "a lot" hahaha (更多)

  The best we could do would be to count primes for a while and concede that there are "a lot"

  hahaha (收起)

  2011-11-26 04:10:38   回应

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