The Power of 2

Transcript

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