full transcript

From the Ted Talk by Benoit Mandelbrot: Fractals and the art of roughness

Unscramble the Blue Letters

Now, here is another thing which is rather ieeisntrntg. One of the shattering evtens in the horitsy of mathematics, which is not aitcrapeepd by many people, occurred about 130 years ago, 145 years ago. Mathematicians began to create shapes that didn't exist. Mathematicians got into self-praise to an extent which was absolutely amazing, that man can invent things that nrtaue did not know. In particular, it could invent things like a cuvre which fills the plane. A curve's a curve, a plane's a plane, and the two won't mix. Well, they do mix. A man named Peano did define such curves, and it became an oebjct of extraordinary interest. It was very important, but mostly interesting because a kind of break, a separation between the mathematics coming from reality, on the one hand, and new mathematics cnmiog from pure man's mind. Well, I was very sorry to point out that the pure man's mind has, in fact, seen at long last what had been seen for a long time. And so here I introduce something, the set of rrievs of a plane-filling curve. And well, it's a story unto itself. So it was in 1875 to 1925, an erntdaairxory period in which mathematics prepared itself to break out from the world. And the objects which were used as examples, when I was a child and a stnduet, as emaexlps of the break between mathematics and visible reality — those objects, I turned them coltplmeey around. I used them for describing some of the aspects of the complexity of nature.

Open Cloze

Now, here is another thing which is rather ___________. One of the shattering ______ in the _______ of mathematics, which is not ___________ by many people, occurred about 130 years ago, 145 years ago. Mathematicians began to create shapes that didn't exist. Mathematicians got into self-praise to an extent which was absolutely amazing, that man can invent things that ______ did not know. In particular, it could invent things like a _____ which fills the plane. A curve's a curve, a plane's a plane, and the two won't mix. Well, they do mix. A man named Peano did define such curves, and it became an ______ of extraordinary interest. It was very important, but mostly interesting because a kind of break, a separation between the mathematics coming from reality, on the one hand, and new mathematics ______ from pure man's mind. Well, I was very sorry to point out that the pure man's mind has, in fact, seen at long last what had been seen for a long time. And so here I introduce something, the set of ______ of a plane-filling curve. And well, it's a story unto itself. So it was in 1875 to 1925, an _____________ period in which mathematics prepared itself to break out from the world. And the objects which were used as examples, when I was a child and a _______, as ________ of the break between mathematics and visible reality — those objects, I turned them __________ around. I used them for describing some of the aspects of the complexity of nature.

Solution

  1. appreciated
  2. completely
  3. curve
  4. interesting
  5. nature
  6. student
  7. events
  8. extraordinary
  9. coming
  10. object
  11. rivers
  12. history
  13. examples

Original Text

Now, here is another thing which is rather interesting. One of the shattering events in the history of mathematics, which is not appreciated by many people, occurred about 130 years ago, 145 years ago. Mathematicians began to create shapes that didn't exist. Mathematicians got into self-praise to an extent which was absolutely amazing, that man can invent things that nature did not know. In particular, it could invent things like a curve which fills the plane. A curve's a curve, a plane's a plane, and the two won't mix. Well, they do mix. A man named Peano did define such curves, and it became an object of extraordinary interest. It was very important, but mostly interesting because a kind of break, a separation between the mathematics coming from reality, on the one hand, and new mathematics coming from pure man's mind. Well, I was very sorry to point out that the pure man's mind has, in fact, seen at long last what had been seen for a long time. And so here I introduce something, the set of rivers of a plane-filling curve. And well, it's a story unto itself. So it was in 1875 to 1925, an extraordinary period in which mathematics prepared itself to break out from the world. And the objects which were used as examples, when I was a child and a student, as examples of the break between mathematics and visible reality — those objects, I turned them completely around. I used them for describing some of the aspects of the complexity of nature.

Frequently Occurring Word Combinations

ngrams of length 2

collocation frequency
long time 4
man named 3
real price 3
simple rule 2
mathematics coming 2
price increments 2

ngrams of length 3

collocation frequency
real price increments 2

Important Words

  1. absolutely
  2. amazing
  3. appreciated
  4. aspects
  5. began
  6. break
  7. child
  8. coming
  9. completely
  10. complexity
  11. create
  12. curve
  13. curves
  14. define
  15. describing
  16. events
  17. examples
  18. exist
  19. extent
  20. extraordinary
  21. fact
  22. fills
  23. hand
  24. history
  25. important
  26. interest
  27. interesting
  28. introduce
  29. invent
  30. kind
  31. long
  32. man
  33. mathematicians
  34. mathematics
  35. mind
  36. mix
  37. named
  38. nature
  39. object
  40. objects
  41. occurred
  42. peano
  43. people
  44. period
  45. plane
  46. point
  47. prepared
  48. pure
  49. reality
  50. rivers
  51. separation
  52. set
  53. shapes
  54. shattering
  55. story
  56. student
  57. time
  58. turned
  59. visible
  60. world
  61. years