The Power of 2

The Power of 2

A4b95be2145cc46f891707b6db9dd82d?s=128

Igor Wiedler

April 12, 2017
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  1. the power of 2 @igorwhilefalse

  2. 2n

  3. 2×2×… n

  4. 2 4 8

  5. 2 4 8 16 32 64 128 256

  6. 2 4 8 16 32 64 128 256 512 1024

    2048 4096 8192 16384 32768 65536
  7. 2 4 8 16 32 64 128 256 512 1024

    2048 4096 8192 16384 32768 65536 131K 262K 524K 1M 2M 4M 8M 16M 33M 67M 134M 268M 536M 1B 2B 4B 8B 17B 34B 68B 137B 274B 549B 1T 2T 4T 8T 17T 35T 70T 140T 281T 562T 1Q 2Q 4Q 9Q 18Q 36Q 72Q 144Q 288Q 576Q 1Quint 2Quint 4Quint 9Quint 18Quint
  8. 18'446'744'073'709'551'616

  9. 18'446'744'073'709'551'616 grains of rice

  10. alot by @alliebrosh

  11. 2 4 8 16 32 64 128 256 512 1024

    2048 4096 8192 16384 32768 65536 131K 262K 524K 1M 2M 4M 8M 16M 33M 67M 134M 268M 536M 1B 2B 4B 8B 17B 34B 68B 137B 274B 549B 1T 2T 4T 8T 17T 35T 70T 140T 281T 562T 1Q 2Q 4Q 18Q 36Q 72Q 144Q 288Q 576Q 1Quint 2Quint 4Quint 9Quint 18Quint
  12. 2 4 8 16 32 64 128 256 512 1024

    2048 4096 8192 16384 32768 65536 131K 262K 524K 1M 2M 4M 8M 16M 33M 67M 134M 268M 536M 1B 2B 4B 17B 34B 68B 137B 274B 549B 1T 2T 4T 8T 17T 35T 70T 140T 281T 562T 1Q 2Q 4Q 9Q 18Q 36Q 72Q 144Q 288Q 576Q 1Quint 2Quint 4Quint 9Quint 18Quint
  13. 2 4 8 16 32 64 128 256 512 1024

    2048 4096 8192 16384 32768 65536 131K 262K 524K 1M 2M 4M 8M 16M 33M 67M 134M 268M 536M 1B 2B 4B 8B 17B 34B 68B 137B 274B 549B 1T 2T 4T 8T 17T 35T 70T 140T 281T 562T 1Q 2Q 4Q 9Q 18Q 36Q 72Q 144Q 288Q 576Q 1Quint 2Quint 4Quint 9Quint 18Quint
  14. 2 4 8 16 32 64 128 256 512 1024

    2048 4096 8192 16384 32768 65536 131K 262K 524K 1M 2M 4M 8M #cafeee 33M 67M 134M 268M 536M 1B 2B 4B 8B 17B 34B 68B 137B 274B 549B 1T 2T 4T 8T 17T 35T 70T 140T 281T 562T 1Q 2Q 4Q 9Q 18Q 36Q 72Q 144Q 288Q 576Q 1Quint 2Quint 4Quint 9Quint 18Quint
  15. 2 4 8 16 32 64 128 256 512 1024

    2048 4096 8192 16384 32768 65536 131K 262K 524K 1M 2M 4M 8M 16M 33M 67M 134M 268M 536M 1B 2B 4B 8B 17B 34B 68B 137B 274B 549B 1T 2T 4T 8T 17T 35T 70T 140T 281T 562T 1Q 2Q 4Q 9Q 18Q 36Q 72Q 144Q 288Q 576Q 1Quint 2Quint 4Quint 9Quint 18Quint
  16. 2 4 8 16 32 64 128 256 512 1024

    2048 4096 8192 16384 32768 65536 131K 262K 524K 1M 2M 4M 8M 16M 33M 67M 134M 268M 536M 1B 2B 4B 8B 17B 34B 68B 137B 274B 549B 1T 2T 4T 8T 17T 35T 70T 140T 281T 562T 1Q 2Q 4Q 9Q 18Q 36Q 72Q 144Q 288Q 576Q 1Quint 2Quint 4Quint 9Quint 18Quint
  17. 2 4 8 16 32 64 128 256 512 1024

    2048 4096 8192 16384 32768 65536 131K 262K 524K 1M 2M 4M 8M 16M 33M 67M 134M 268M 536M 1B 2B 4B 8B 17B 34B 68B 137B 274B 549B 1T 2T 4T 8T 17T 35T 70T 140T 281T 562T 1Q 2Q 4Q 9Q 18Q 36Q 72Q 144Q 288Q 576Q 1Quint 2Quint 4Quint 9Quint 18Quint
  18. 2n

  19. exponential growth • population growth • infection (zombie apocalypse) •

    economic growth (mod humans) • moore's law
  20. crypto • one char = { 0 1 2 3

    4 5 6 7 8 9 a b c d e f } • possible values: 161 = 16 • two chars = {
 00 01 02 03 04 05 06 07 08 09 0a 0b 0c 0d 0e 0f
 10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f
 20 21 22 23 24 25 26 27 28 29 2a 2b 2c 2d 2e 2f
 ...
 } • possible values: 162 = 256 • 64 bit key: 264 = 1616 = 18Quint
  21. we scaled up let's scale down

  22. log2 n

  23. n÷2÷…=1 y

  24. dress shopping

  25. dress shopping

  26. dress shopping

  27. dress shopping

  28. dress shopping

  29. dress shopping

  30. dress shopping

  31. binary search

  32. database

  33. log2 n

  34. log2 (18'446'744'073'709'551'616) = 64

  35. atoms • atoms in a human body: 7×1027
 
 =>

    7'000'000'000'000'000'000'000'000'000
 => log2 = 92 • atoms in observable universe: 4×1079
 
 => 40'000'000'000'000'000'000'000'000'000
 '000'000'000'000'000'000'000'000'000
 '000'000'000'000'000'000'000'000
 => log2 = 264
  36. recap • 2n
 grows large fast
 232 = 4B
 264

    = 18Quint • log2 n
 decreases quickly
 log2 4B = 32
 log2 18Quint = 64 yay crypto and grains of rice yay databases and dresses
  37. thank u zine: igor.io/pow @igorwhilefalse