Randomness Does Randomness Rule Our Lives SDGs14 bRANCarlos

Randomness: Does Randomness Rule Our Lives? (SDGs/14 b-RAN)©Carlos Lemmi, Ph. D Stock market 1987 Average: 2562 1 SD – 68 % : 2468. 8 – 2655. 2 2 SD – 95 % : 2375. 6 – 2748. 4 3 SD – 99. 7 % : 2282. 4 – 2841. 6 Black Monday October 19, 1987 Dropped 508 points 1, 738 20 SD (8. 8) 1 x 10 -50

Randomness: Does Randomness Rule Our Lives? (SDGs/14 b-RAN)©Carlos Lemmi, Ph. D Is there life after 3 Standard Deviations…? Standard Deviation % ± 1σ 68. 268, 949, 213, 708, 6 ± 1. 5σ 86. 638, 559, 746, 228, 4 Frequency 1 in 3 1 in 7 Approx. frequency for daily event Twice a week Weekly ± 2σ ± 2. 5σ 95. 449, 973, 610, 364, 2 98. 758, 066, 934, 844, 8 1 in 22 1 in 81 Every three weeks Quarterly ± 3σ ± 3. 5σ 99. 730, 020, 393, 674, 0 99. 953, 474, 184, 192, 9 1 in 370 1 in 2, 149 Yearly Every six years ± 4σ ± 4. 5σ 99. 993, 665, 751, 633, 4 99. 999, 320, 465, 375, 1 1 in 15, 787 1 in 147, 160 Every 43 years (twice in a lifetime) Every 403 years ± 5σ ± 5. 5σ 99. 999, 942, 669, 685, 6 99. 999, 996, 202, 087, 5 1 in 174, 427, 8 1, 744, 278 1 in 263, 302, 54 26, 330, 254 Every 4, 776 years (once in recorded history) Every 72, 090 years ± 6σ ± 6. 5σ 99. 999, 802, 682, 5 99. 999, 991, 968, 0 1 in 506, 797, 346 Every 1. 38 million years (history of humankind) 1 in 124, 501, 973, 93 12, 450, 197, 393 Every 34 million years ± 7σ 99. 999, 744, 0 1 in 390, 682, 215, 445 Every 1. 07 billion years

Randomness: Does Randomness Rule Our Lives? (SDGs/14 b-RAN)©Carlos Lemmi, Ph. D Stock market 1987 Average: 2562 1 SD – 98 % : 2468. 8 – 2655. 2 2 SD – 95 % : 2375. 6 – 2748. 4 3 SD – 99. 7 % : 2282. 4 – 2841. 6 Black Monday October 19, 1987 Dropped 508 points 1, 738 20 SD (8. 8) 1 x 10 -50

Randomness: Does Randomness Rule Our Lives? (SDGs/14 b-RAN)©Carlos Lemmi, Ph. D Los Angeles Earthquakes Northridge Earthquake January 17, 1994 Magnitude 6. 7 Property damage: > 20 billions Oct. 17, 1988 Loma Prieta, CA (San Francisco Bay Area) Mag. : 6. 9

Randomness: Does Randomness Rule Our Lives? (SDGs/14 b-RAN)©Carlos Lemmi, Ph. D Phone Traffic - Internet Traffic Scale X-axis m. Sec 0– 6

Randomness: Does Randomness Rule Our Lives? (SDGs/14 b-RAN)©Carlos Lemmi, Ph. D Phone Traffic - Internet Traffic Scale X-axis m. Sec 0– 6 0 – 60

Randomness: Does Randomness Rule Our Lives? (SDGs/14 b-RAN)©Carlos Lemmi, Ph. D Phone Traffic - Internet Traffic Scale X-axis m. Sec 0– 6 0 – 600 (0. 6 sec)

Randomness: Does Randomness Rule Our Lives? (SDGs/14 b-RAN)©Carlos Lemmi, Ph. D Phone Traffic - Internet Traffic Scale X-axis m. Sec Scale Y-axis 60 – 160 0– 6 600 – 1, 600 0 – 600 (0. 6 sec) 6, 000 – 14, 000 0 – 3000 ( 3 sec. ) 40, 000 – 80, 000

Randomness: Does Randomness Rule Our Lives? (SDGs/14 b-RAN)©Carlos Lemmi, Ph. D 36 37 38 38 39 39 40 40 41 41 41 42 42 43 43 44 44 44 45 45 45 46 46 46 47 47 47 48 48 49 49 50 50 50 51 51 52 52 53 53 54 55 36 36 36 36 36 36 37 37 37 38 38 38 39 39 40 40 40 41 41 41 42 42 42 43 43 44 44 45 45 45 46 46 46 47 47 47 48 48 48 49 49 50 50 51 51 52 52 53 53 54 54 55 55 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 1 1 2 2 4 6 7 8 9 10 10 9 8 7 6 4 2 2 1 1 n = 100 10 8 6 4 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 22 12 9 7 6 5 5 4 4 3 3 2 2 2 2 n = 100 2 0 33 43 53 Normally Distributed Bell Shape Distributions 25 20 15 10 5 0 35 45 55 Power Law Distribution 65

Randomness: Does Randomness Rule Our Lives? (SDGs/14 b-RAN)©Carlos Lemmi, Ph. D 120 FREQUENCY 100 80 -0. 5 60 -0. 75 40 -1 20 0 0 50 100 MAGNITUDE 150

Randomness: Does Randomness Rule Our Lives? (SDGs/14 b-RAN)©Carlos Lemmi, Ph. D Normally Distributed Bell Shape Distributions People heights Body Temperatures Length of fingers Phone networks traffic Probability Mean – Median - Mode Standard Deviations Regression Analysis Power Law Non Bell Shape Distribution Fractal Power People incomes Earthquake intensities Stock market values Internet networks traffic Power Dimensions Slope in log – log plots Grid counting

Randomness: Does Randomness Rule Our Lives? (SDGs/14 b-RAN)©Carlos Lemmi, Ph. D The von Koch Curve

Randomness: Does Randomness Rule Our Lives? (SDGs/14 b-RAN)©Carlos Lemmi, Ph. D Dimensions as we know it D=1 D=2 D=3 Dimensions you may not think about… Koch D = 2. 3 Cesaro D = 2. 8 Solid D = 1. 98

Randomness: Does Randomness Rule Our Lives? (SDGs/14 b-RAN)©Carlos Lemmi, Ph. D divisions. D = Sp (Small Pieces) 11 = 1 12 = 1 13 = 1 21 = 2 22 = 4 23 = 8 31 = 3 32 = 9 33 = 27 log 3 0. 477 ------- = 1 log 3 0. 477 Log 9 0. 954 ------- = 2 log 3 0. 477 div. D = Sp log(div. D) = log(Sp) D x log(div. ) = log(Sp) D = ------log(div. ) Log 27 1. 431 ------- = 3 log 3 0. 477 ü log Small pieces log Divisions ü Power ü Dimension

Randomness: Does Randomness Rule Our Lives? (SDGs/14 b-RAN)©Carlos Lemmi, Ph. D X - Y log X - log Y Values – Freq. 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 22 12 9 7 6 5 5 4 4 3 3 2 2 2 2 Values – Freq. 25 20 15 10 5 0 35 45 55 Exponential Curve Linear-Linear Scales (1 – 2 – 3 – 4) Freq. = (Values)-D log(Values) D = --------- ~ -0. 33 log(Freq. ) 65 1. 556 1. 568 1. 580 1. 591 1. 602 1. 613 1. 623 1. 633 1. 643 1. 653 1. 663 1. 672 1. 681 1. 690 1. 699 1. 708 1. 716 1. 724 1. 732 1. 740 1. 332 1. 090 0. 949 0. 845 0. 763 0. 699 0. 653 0. 602 0. 556 0. 519 0. 491 0. 462 0. 431 0. 398 0. 380 0. 362 0. 342 0. 322 0. 301 0. 279 1. 550 X/Y = Slope Y 0. 275 X Logarithmic Curve Log – Log Scales (1 – 1000) ü Slope [log X/log Y] ü Power ü Dimension

Randomness: Does Randomness Rule Our Lives? (SDGs/14 b-RAN)©Carlos Lemmi, Ph. D What does all this has to do with Randomness? Cardano’s Law of the Sample Space SAMPLE SPACE : “THE SET OF ALL POSSIBLE OUTCOMES” 25 10 20 8 15 6 10 4 5 2 0 33 38 35 43 48 53 Sample Space Normally Distributed Bell Shape Distributions 0 58 57 35 0 45 55 Sample Space Power Law Distribution 65 ∞

Randomness: Does Randomness Rule Our Lives? (SDGs/14 b-RAN)©Carlos Lemmi, Ph. D Phone Traffic - Internet Traffic Black Monday October 19, 1987 Dropped 508 points 1, 738 20 SD (8. 8) 1 x 10 -50 Northridge Earthquake January 17, 1994 Magnitude 6. 7 LOSS RATIO: 2, 273 Property damage: > 20 billions

Randomness: Does Randomness Rule Our Lives? (SDGs/14 b-RAN)©Carlos Lemmi, Ph. D Some Interesting Examples Known Asteroids that travel near Earth Time June 9, 2014 David Morrison, who has the delightful title "director of space" at the NASA Ames Research Center, likes to say that the number of people searching for threatening astronomical objects is 11 times smaller than the staff of one Mc. Donald's restaurant. "

Randomness: Does Randomness Rule Our Lives? (SDGs/14 b-RAN)©Carlos Lemmi, Ph. D Some Interesting Examples People’s heights Average 57 countries 5 ft 8 in. St. Dev. : 3 in. - 4 σ …. . 4 ft 7 in. Chandra Bahadur Dangi of Nepal 1 ft 9 ½ in 16 Std. Dev. + 4 σ …. . 6 ft 8 in Robert Pershing Wadlow of USA 8 ft 11 in 13 Std. Dev.

Randomness: Does Randomness Rule Our Lives? (SDGs/14 b-RAN)©Carlos Lemmi, Ph. D y… Reall you s all i s i w? h t o n k lings h t r a at e e s e h t rned rsery a e l Nu We 2 1 6 the B hool… Sc Plato’s Allegory of the Cave Muth distribution Normal distribution Weibull distribution Gamma distribution Gumbel distribution Uniform distribution Gompertz distribution Chi square distribution Power Law distribution Right-truncated normal B-61 Log normal distribution Nurs 2 Log-logistic distribution e Exponential distribution Sch ry ool Half-normal distribution Exponential power distribution Ratio distribution of two uniform distributions Ratio distribution of two exponential distributions Ratio distribution of two half-normal distributions Ratio distribution of two right-truncated normal distributions Ratio distribution of two chi-square distributions (the F distribution) O Dist ther ribu of d tions ata

Finis