Grasping Infinity

Grasping Infinity

Slide #37 is a mistake! I think it caused me to mispeak and led to confusion!

From Bacon 2013
http://devslovebacon.com/conferences/bacon-2013/talks/grasping-infinity

5c1252cee710e2cec785ec999a130fe6?s=128

thattommyhall

April 12, 2013
Tweet

Transcript

  1. @thattommyhall Theatre fan, occasional mountaineer, part time runner, thoroughly nice

    chap, available in fine bookstores everywhere http://www.thattommyhall.com
  2. None
  3. (img from http://world.mathigon.org/Infinity.html)

  4. None
  5. None
  6. None
  7. None
  8. Tours

  9. 1 -> 1 2 -> 4 3 -> 9 ...

  10. 1 -> 10 2 -> 100 3 -> 1000 ...

  11. Cardinality

  12. None
  13. Countable? ..., -3, -2, -1, 0, 1, 2, 3 ...

  14. Countable?

  15. None
  16. None
  17. None
  18. Powersets P(S) = The set of all subsets of S

  19. S = {a,b,c} P(S) = { {}, {a}, {b}, {c},

    {a,b},{b,c},{a,c}, {a,b,c} }
  20. Is Countable?

  21. Is (0,1) countable?

  22. Is (0,1) countable? 1 -> 0.165198165161681681681681681... 2 -> 0.1565516516816543576432135... 3

    -> 0.516516846516598498468498468... 4 -> 0.516168489465435473543214354354... 5 -> 0.1 6 -> 0.454648976874354672546849846...
  23. Is (0,1) countable? 1 -> 0.165198165161681681681681681... 1 -> 0.1565516516816543576432135... 1

    -> 0.516516846516598498468498468... 1 -> 0.516168489465435473543214354354... 1 -> 0.1 1 -> 0.454648976874354672546849846... r = 0.267219.....
  24. Is 'larger'?

  25. None
  26. Is 'larger'?

  27. Is 'larger'? 0.8236... 0.2146...

  28. Is 'larger'? 0.8236... 0.2146... 0.82213466...

  29. None
  30. None
  31. None
  32. None
  33. Convergence

  34. None
  35. Building everything from nothing

  36. None
  37. S(n) = P(n)

  38. None
  39. None
  40. Ordinality one, two, three VS first, second, third

  41. To , and beyond!

  42. None
  43. None
  44. None
  45. Climbing Mount

  46. None
  47. None
  48. None
  49. None
  50. None
  51. None
  52. Monkey Puzzle Monkey 1: Opens all the doors Monkey 2:

    Starts at 2, goes up in 2s and 'toggles' each door. ... Monkey N, Starts at N, goes up in Ns and 'toggles' each door ... What doors are left open?
  53. None
  54. None
  55. None
  56. None
  57. None
  58. None
  59. Everything would be in its blind volumes. Everything: the minutely

    detailed history of the future, the archangels' autobiographies, Aeschylus' The Egyptians, the exact number of times that the waters of the Ganges have reflected the flight of a falcon, the secret and true nature of Rome, my dreams and half-dreams at dawn on August 14, 1934, the proof of Fermat's last theorem, the paradoxes Berkeley invented concerning Time but didn't publish, the premature epiphanies of Stephen Dedalus, which would be meaningless before a cycle of a thousand years, the Gnostic Gospel of Basilides,the commentary on that gospel, the commentary on the commentary on that gospel, the true story of your death, the translation of every book in all languages, the interpolations of every book in all books, the song the sirens sang, the complete catalog of the Library, thousands and thousands of false catalogues, the demonstration of the falsity of those catalogues, the demonstration of the falsity of the true catalogue, Everything. but for every sensible line or accurate fact there would be millions of meaningless cacophonies, verbal farragoes, and babblings. Everything: but all the generations of mankind could pass before the dizzying shelves ever reward them with a tolerable page,.
  60. Refs • http://world.mathigon.org/Infinity.html • http://naturelovesmath-en.blogspot.co.uk/2012/07/infinity-and-transfinite- numbers.html • http://scientopia.org/blogs/goodmath/category/surreal-numbers/ • http://maskofreason.files.wordpress.com/2011/02/the-library-of-babel-by-

    jorge-luis-borges.pdf •