Reading crossword #2

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Across
  1. 6. mathematician who tried to measure the angles in a 46d determined by three mountain peaks to determine the actual 62a of the universe
  2. 8. Escher's lithograph with many staircases, reprinted in the chapter
  3. 9. these have two levels of meaning in 35a
  4. 10. collection of musical pieces by Bach referenced in the dialogue
  5. 13. what the isomorphism from letters to 40d is an example of
  6. 15. adjective for 62a unwittingly studied by 7d; also gotten by asserting the existence of two lines 4d to a given line and containing a given point not on the given line
  7. 17. location of a building in a woodcut by Escher featured in the chapter
  8. 19. see 16d
  9. 20. like viewing Godel's theorem as a discovery of a difference between human reasoning and mathematical reasoning, according to Hofstadter
  10. 21. physicist whose "general" theory said that matter content determines the universe's 62a
  11. 25. Record Player ___, 54d's invention, which can change its own structure
  12. 26. one level of meaning had by the 9a in the dialogue
  13. 27. formal systems can be ___ into one another
  14. 28. low-___, like a record player incapable of making the sounds that would cause it to be 52a
  15. 30. the sequence of these induced in a record player by a record is the second level of meaning had by 9a in the dialogue
  16. 31. see 39d
  17. 35. the dialogue that we read for today
  18. 36. like 64a
  19. 38. J. ___ Bach
  20. 41. one of five given by 61a
  21. 42. room in the Tortoise's house where the dialogue takes place
  22. 43. piece in 10a referenced in the dialogue
  23. 48. ___ arithmetic, the core of number theory which will be formalized in Chapter 8
  24. 50. the only surviving work of 61a
  25. 52. Like 54d's first record player, after it tried to play Tortoise's first composition
  26. 53. avocation for Bach, according to Achilles
  27. 55. the opposite of 37d
  28. 56. adjective to describe 54d's record player, according to its salesman
  29. 57. kind of poem proposed by Tortoise like 73a but where the initial letters are to be read backwards
  30. 61. he systemized 62a in 300 BC
  31. 62. one of three nouns in the chapter title, from the Ancient Greek for "land measurement"
  32. 63. Hungarian mathematician who co-discovered non-61a-ian 62a
  33. 64. it's no 64a that this word appears twice in the dialogue!
  34. 65. composer of "Wellington's Victory"
  35. 68. providing this allows one to see that the answers to the questions in the clues 29d and 33d are "no" and "no"
  36. 70. like supposed proofs of 61a's 23d 41a from the first four
  37. 71. isomorphisms are the key element in Hofstadter's answer to the question "what is ___?"
  38. 73. kind of poem written by 60d+72d where the first letters of the lines spell out a hidden word or phrase
  39. 74. adjective for 62a that follows from only 61a's 23d 1,2,3 and 4.
Down
  1. 1. adjective for 62a gotten by asserting the existence of no lines 4d to a given line and containing a given point not on the given line
  2. 2. virtue found in 50a
  3. 3. 45d for Tortoise from Achilles
  4. 4. adjective describing a line that does not intersect a given line
  5. 5. what salesmen notoriously are, according to Achilles
  6. 7. he assumed the negation of 61a's 23d 41a and tried to find a contradiction
  7. 11. key verb in the definition of 56a
  8. 12. Hofstadter's 68a understands "q" in the pq-system as meaning "___ than or equal to"
  9. 14. Godel's ___ theorem
  10. 16. playing the 47d B-A-C-H in this way does not change it, if it is also played 19a
  11. 18. the kind of reasoning Godel's theorem applies to
  12. 22. what the conversion of 40d to sounds is an example of
  13. 23. 61a's ___ 23d was neither terse nor elegant
  14. 24. one of three nouns in the chapter title, the property a formal system has under an interpretation when its theorems are true statements
  15. 29. the modified pq-system is inconsistent with the ___ world?
  16. 32. what Tortoise's first composition cannot be, at least by record player 1
  17. 33. the modified pq-system is features ___ inconsistency?
  18. 34. Hofstadter lets Bach's last page serve as this for the late composer
  19. 37. like meaning that a very simple or very familiar isomorphism allows us to see
  20. 39. what the 3d does when Tortoise plays a 31a
  21. 40. the letters in Bach's last name, in Germany at least
  22. 44. like 54d's expectations regarding record players
  23. 45. what Tortoise's first composition is for 54d
  24. 46. polygon with three sides
  25. 47. what Bach's surname constitutes, on one interpretation
  26. 49. counterpart to the mechanical mode and the intelligent mode, briefly
  27. 51. general term for a maker of dialogues which appears in the dialogue
  28. 54. friend of the Tortoise whom Achilles hasn't met yet
  29. 57. one of three nouns in the chapter title, the property a formal system has under an interpretation when all true statements are theorems of it
  30. 58. item collected by Tortoise
  31. 59. how the dialogue ends
  32. 60. first name of 72d
  33. 66. Hofstadter gives a so-called ___ 46d to illustrate 33d inconsistency
  34. 67. Escher work mentioned but not shown in the chapter wherein gravity is present like usual but space itself is abnormal
  35. 69. record player
  36. 72. last name of 60d