The Power of 2

Transcript

1. the power of
   2
   @igorwhilefalse
   

   View Slide

2. 2n
   

   View Slide

3. 2×2×…
   n
   

   View Slide

4. 2 4 8
   

   View Slide

5. 2 4 8 16 32 64 128 256
   

   View Slide

6. 2 4 8 16 32 64 128 256
   512 1024 2048 4096 8192 16384 32768 65536
   

   View Slide

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
   

   View Slide

8. 18'446'744'073'709'551'616
   

   View Slide

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

   View Slide

10. alot by @alliebrosh
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

18. 2n
    

    View Slide

19. exponential growth
    • population growth
    • infection (zombie apocalypse)
    • economic growth (mod humans)
    • moore's law
    

    View Slide

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
    

    View Slide

21. we scaled up
    let's scale down
    

    View Slide

22. log2 n
    

    View Slide

23. n÷2÷…=1
    y
    

    View Slide

24. dress shopping
    

    View Slide

25. dress shopping
    

    View Slide

26. dress shopping
    

    View Slide

27. dress shopping
    

    View Slide

28. dress shopping
    

    View Slide

29. dress shopping
    

    View Slide

30. dress shopping
    

    View Slide

31. binary search
    

    View Slide

32. database
    

    View Slide

33. log2 n
    

    View Slide

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

    View Slide

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
    

    View Slide

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
    

    View Slide

37. thank u
    zine: igor.io/pow
    @igorwhilefalse
    

    View Slide