full transcript

From the Ted Talk by Alex Rosenthal and George Zaidan: The case of the missing fractals

Unscramble the Blue Letters

It was a night like any other night, except here I was climbing the platonic paeks like rmoeo on a second date. (ugh) I was there for the dame. She had eyes like imaginary numbers and curves that went on forever. Said she wanted to go home. Said I could help. Said the pay was good. Didn't say anything about climbing a... Voice: "Who's there?" Manny Brot: "Manny Brot, private eye." Voice: "What are you doing here?" "A pretty number sent me to find a soteln dnguis." Voice: "Well, to eetnr the cave, you must answer my riddles three." What was it with riddles, and why do they always come in threes? "Is it an egg?" "No. Why would it be an egg?" "It's usually an egg." "What can I hold in my hand, but has zero area?" "Is it a dodo egg?" "It's not an egg!" I took out the rock that had nearly bareind me before and gave it a hard ponder. The size of the rinsig bump on my conk said to me that this thing had area, and a lot of it. But what if I carved out a tinlgrae from this side here? As any mook could see, this triangle had a quarter of the area of the full triangle. I did the same thing again with each of the smaller triangles. Again, a quarter of the rnmaeiing area — gone. And I just kept going. After an infinite number of cuts, I was satisfied that my triangle had zero area. A bounded saphe with zero area. Now, it's not often that I surprise myself, but my own two mitts had created something czray, and new. "Very good. (ahem) Now, show me a shape with finite area, but an infinitely long perimeter." "Let me get this straight. If I want to make a snip in the border of this shape, smotoh it out, and lay it on the ground ... " "It would go on for ... " "Wait 'til I'm through, and then you can talk. It would go on forever." "Are you through?" "Yeah." "So show me that shape then." Mmm ... I hadn't been this stuck since the Rubik's Cube fiasco of '58. All the shapes I knew had perimeters. Circles: 2πr. Triangles: sum of their sdies. What's this? An agnle. An angle from heaven. What if I were to pinch each side, like so. A third of the way through, just so. And do it again, and again, and again. After each pinch, the pmirteeer got a third longer because where there had been three line segments, now there were four. As for the area, every pncih made more tegnialrs, that's true. But those triangles were getting slleamr and smaller. You could say that the area was converging, approaching a fixed number, while the perimeter was just getting bieggr and bigger, uncontrollably bnlonloiag like an overindulgent birthday clown. After itfinniy pinches, flimflam, there it was: Finite area, but intfiine perimeter. Now that is a piece of work. "Oh, you're good. (ahem) rdilde three: Show me a picture that if I magnify it under my microscope, I'll keep seeing the oiaingrl picture, no mtaetr how much I zoom in." "You're a strange little man." "Thank you." I was out of ideas, so I looked at my muse, my complex Dora. Voice: "Who's the dame?" And then it hit me. "She's a hreat breaker, my fractal fmmee fltaae. Will she do?" "Yes, she'll do just fine." (lightning) It was dark, and at first I thought the cave was empty, but then I noticed: the box. The dame had played me like a triangle. She had told me she wanted to go home. (Lightning) What she really wanted was to bring her home here. The fractals spread everywhere. Most of them the same no matter how deep you looked at them, like Dora's mugshot. Some had itneilfiny long perimeters, others were objects with no area or volume, all of them created through infinite repetition. So, you wanted to know what fractals are? Well, kid, they're the sftuf that dreams are made of. (Music)

Open Cloze

It was a night like any other night, except here I was climbing the platonic _____ like _____ on a second date. (ugh) I was there for the dame. She had eyes like imaginary numbers and curves that went on forever. Said she wanted to go home. Said I could help. Said the pay was good. Didn't say anything about climbing a... Voice: "Who's there?" Manny Brot: "Manny Brot, private eye." Voice: "What are you doing here?" "A pretty number sent me to find a ______ ______." Voice: "Well, to _____ the cave, you must answer my riddles three." What was it with riddles, and why do they always come in threes? "Is it an egg?" "No. Why would it be an egg?" "It's usually an egg." "What can I hold in my hand, but has zero area?" "Is it a dodo egg?" "It's not an egg!" I took out the rock that had nearly _______ me before and gave it a hard ponder. The size of the ______ bump on my conk said to me that this thing had area, and a lot of it. But what if I carved out a ________ from this side here? As any mook could see, this triangle had a quarter of the area of the full triangle. I did the same thing again with each of the smaller triangles. Again, a quarter of the _________ area — gone. And I just kept going. After an infinite number of cuts, I was satisfied that my triangle had zero area. A bounded _____ with zero area. Now, it's not often that I surprise myself, but my own two mitts had created something _____, and new. "Very good. (ahem) Now, show me a shape with finite area, but an infinitely long perimeter." "Let me get this straight. If I want to make a snip in the border of this shape, ______ it out, and lay it on the ground ... " "It would go on for ... " "Wait 'til I'm through, and then you can talk. It would go on forever." "Are you through?" "Yeah." "So show me that shape then." Mmm ... I hadn't been this stuck since the Rubik's Cube fiasco of '58. All the shapes I knew had perimeters. Circles: 2πr. Triangles: sum of their _____. What's this? An _____. An angle from heaven. What if I were to pinch each side, like so. A third of the way through, just so. And do it again, and again, and again. After each pinch, the _________ got a third longer because where there had been three line segments, now there were four. As for the area, every _____ made more _________, that's true. But those triangles were getting _______ and smaller. You could say that the area was converging, approaching a fixed number, while the perimeter was just getting ______ and bigger, uncontrollably __________ like an overindulgent birthday clown. After ________ pinches, flimflam, there it was: Finite area, but ________ perimeter. Now that is a piece of work. "Oh, you're good. (ahem) ______ three: Show me a picture that if I magnify it under my microscope, I'll keep seeing the ________ picture, no ______ how much I zoom in." "You're a strange little man." "Thank you." I was out of ideas, so I looked at my muse, my complex Dora. Voice: "Who's the dame?" And then it hit me. "She's a _____ breaker, my fractal _____ ______. Will she do?" "Yes, she'll do just fine." (lightning) It was dark, and at first I thought the cave was empty, but then I noticed: the box. The dame had played me like a triangle. She had told me she wanted to go home. (Lightning) What she really wanted was to bring her home here. The fractals spread everywhere. Most of them the same no matter how deep you looked at them, like Dora's mugshot. Some had __________ long perimeters, others were objects with no area or volume, all of them created through infinite repetition. So, you wanted to know what fractals are? Well, kid, they're the _____ that dreams are made of. (Music)

Solution

  1. stolen
  2. infinite
  3. dingus
  4. smooth
  5. infinity
  6. triangles
  7. perimeter
  8. femme
  9. ballooning
  10. crazy
  11. shape
  12. enter
  13. original
  14. peaks
  15. angle
  16. fatale
  17. sides
  18. remaining
  19. rising
  20. infinitely
  21. brained
  22. matter
  23. smaller
  24. heart
  25. romeo
  26. bigger
  27. triangle
  28. stuff
  29. pinch
  30. riddle

Original Text

It was a night like any other night, except here I was climbing the platonic peaks like Romeo on a second date. (ugh) I was there for the dame. She had eyes like imaginary numbers and curves that went on forever. Said she wanted to go home. Said I could help. Said the pay was good. Didn't say anything about climbing a... Voice: "Who's there?" Manny Brot: "Manny Brot, private eye." Voice: "What are you doing here?" "A pretty number sent me to find a stolen dingus." Voice: "Well, to enter the cave, you must answer my riddles three." What was it with riddles, and why do they always come in threes? "Is it an egg?" "No. Why would it be an egg?" "It's usually an egg." "What can I hold in my hand, but has zero area?" "Is it a dodo egg?" "It's not an egg!" I took out the rock that had nearly brained me before and gave it a hard ponder. The size of the rising bump on my conk said to me that this thing had area, and a lot of it. But what if I carved out a triangle from this side here? As any mook could see, this triangle had a quarter of the area of the full triangle. I did the same thing again with each of the smaller triangles. Again, a quarter of the remaining area — gone. And I just kept going. After an infinite number of cuts, I was satisfied that my triangle had zero area. A bounded shape with zero area. Now, it's not often that I surprise myself, but my own two mitts had created something crazy, and new. "Very good. (ahem) Now, show me a shape with finite area, but an infinitely long perimeter." "Let me get this straight. If I want to make a snip in the border of this shape, smooth it out, and lay it on the ground ... " "It would go on for ... " "Wait 'til I'm through, and then you can talk. It would go on forever." "Are you through?" "Yeah." "So show me that shape then." Mmm ... I hadn't been this stuck since the Rubik's Cube fiasco of '58. All the shapes I knew had perimeters. Circles: 2πr. Triangles: sum of their sides. What's this? An angle. An angle from heaven. What if I were to pinch each side, like so. A third of the way through, just so. And do it again, and again, and again. After each pinch, the perimeter got a third longer because where there had been three line segments, now there were four. As for the area, every pinch made more triangles, that's true. But those triangles were getting smaller and smaller. You could say that the area was converging, approaching a fixed number, while the perimeter was just getting bigger and bigger, uncontrollably ballooning like an overindulgent birthday clown. After infinity pinches, flimflam, there it was: Finite area, but infinite perimeter. Now that is a piece of work. "Oh, you're good. (ahem) Riddle three: Show me a picture that if I magnify it under my microscope, I'll keep seeing the original picture, no matter how much I zoom in." "You're a strange little man." "Thank you." I was out of ideas, so I looked at my muse, my complex Dora. Voice: "Who's the dame?" And then it hit me. "She's a heart breaker, my fractal femme fatale. Will she do?" "Yes, she'll do just fine." (lightning) It was dark, and at first I thought the cave was empty, but then I noticed: the box. The dame had played me like a triangle. She had told me she wanted to go home. (Lightning) What she really wanted was to bring her home here. The fractals spread everywhere. Most of them the same no matter how deep you looked at them, like Dora's mugshot. Some had infinitely long perimeters, others were objects with no area or volume, all of them created through infinite repetition. So, you wanted to know what fractals are? Well, kid, they're the stuff that dreams are made of. (Music)

Frequently Occurring Word Combinations

ngrams of length 2

collocation frequency
infinitely long 2

Important Words

  1. ahem
  2. angle
  3. answer
  4. approaching
  5. area
  6. ballooning
  7. bigger
  8. birthday
  9. border
  10. bounded
  11. box
  12. brained
  13. breaker
  14. bring
  15. brot
  16. bump
  17. carved
  18. cave
  19. climbing
  20. clown
  21. complex
  22. conk
  23. converging
  24. crazy
  25. created
  26. cube
  27. curves
  28. cuts
  29. dame
  30. dark
  31. date
  32. deep
  33. dingus
  34. dodo
  35. dora
  36. dreams
  37. egg
  38. empty
  39. enter
  40. eye
  41. eyes
  42. fatale
  43. femme
  44. fiasco
  45. find
  46. fine
  47. finite
  48. fixed
  49. flimflam
  50. fractal
  51. fractals
  52. full
  53. gave
  54. good
  55. ground
  56. hand
  57. hard
  58. heart
  59. heaven
  60. hit
  61. hold
  62. home
  63. ideas
  64. imaginary
  65. infinite
  66. infinitely
  67. infinity
  68. kid
  69. knew
  70. lay
  71. lightning
  72. line
  73. long
  74. longer
  75. looked
  76. lot
  77. magnify
  78. man
  79. manny
  80. matter
  81. microscope
  82. mitts
  83. mmm
  84. mook
  85. mugshot
  86. muse
  87. music
  88. night
  89. number
  90. numbers
  91. objects
  92. original
  93. overindulgent
  94. pay
  95. peaks
  96. perimeter
  97. perimeters
  98. picture
  99. piece
  100. pinch
  101. pinches
  102. platonic
  103. played
  104. ponder
  105. pretty
  106. private
  107. quarter
  108. remaining
  109. repetition
  110. riddle
  111. riddles
  112. rising
  113. rock
  114. romeo
  115. satisfied
  116. segments
  117. shape
  118. shapes
  119. show
  120. side
  121. sides
  122. size
  123. smaller
  124. smooth
  125. snip
  126. spread
  127. stolen
  128. straight
  129. strange
  130. stuck
  131. stuff
  132. sum
  133. surprise
  134. talk
  135. thought
  136. threes
  137. told
  138. triangle
  139. triangles
  140. true
  141. ugh
  142. uncontrollably
  143. volume
  144. wanted
  145. work
  146. zoom