Data from our man Zipf Zipf in brief Principles of Complex Systems - PowerPoint PPT Presentation

Data from our man Zipf Data from our man Zipf Zipf in brief Principles of Complex Systems Zipfian empirics Course 300, Fall, 2008 References Prof. Peter Dodds Department of Mathematics & Statistics University of Vermont Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License . Frame 1/20

Data from our man Outline Zipf Zipf in brief Zipfian empirics References Zipf in brief Zipfian empirics References Frame 2/20

Data from our man George Kingsley Zipf: Zipf In brief: Zipf in brief Zipfian empirics ◮ Zipf ( ⊞ ) (1902–1950) was a linguist at Harvard, References specializing in Chinese languages. ◮ Unusual passion for statistical analysis of texts. ◮ Studied human behavior much more generally... Zipf’s masterwork: ◮ “Human Behavior and the Principle of Least Effort” Addison-Wesley, 1949 Cambridge, MA [2] ◮ Bonus field of study: Glottometrics. ( ⊞ ) ◮ Bonus ‘word’ word: Glossolalia. ( ⊞ ) Frame 3/20

Data from our man Human Behavior/Principle of Least Effort: Zipf Zipf in brief Zipfian empirics References From the Preface— Nearly twenty-five years ago it occurred to me that we might gain considerable insight into the mainsprings of human behavior if we viewed it purely as a natural phenomenon like everything else in the universe, ... And— ... the expressed purpose of this book is to establish The Principle of Least Effort as the primary principle that governs our entire individual and collective behavior ... Frame 4/20

Data from our man The Principle of Least Effort: Zipf Zipf in brief Zipfian empirics References Zipf’s framing (p. 1): “... a person in solving his immediate problems will view these against the background of his probable future problems as estimated by himself .” “... he will strive ... to minimize the total work that he must expend in solving both his immediate problems and his probable future problems.” “[he will strive to] minimize the probable average rate of his work-expenditure ...” Frame 5/20

Data from our man Rampaging research Zipf Within Human Behavior and the Principle of Least Zipf in brief Effort: Zipfian empirics ◮ # new items by dateline References ◮ City sizes ◮ weight moved between ◮ # retail stores in cities cities by rail ◮ # services (barber ◮ # telephone messages shops, beauty parlors, between cities cleaning, ...) ◮ # people moving vs. ◮ # people in occupations distance ◮ # one-way trips in cars ◮ # marriages vs. and trucks vs. distance distance ◮ Observed general dependency of ‘interactions’ between cities A and B on P A P B / D AB where P A and P B are population size and D AB is distance between A and B . Frame 6/20

Data from our man Zipfian empirics: Zipf ◮ vocabulary balance: f ∼ r − 1 → r · f ∼ constant Zipf in brief ( f = frequency, r = rank). Zipfian empirics References Frame 7/20

Data from our man Zipfian empirics: Zipf ◮ f ∼ r − 1 for word frequency: Zipf in brief Zipfian empirics References Frame 8/20

Data from our man Zipf’s basic idea: Zipf Zipf in brief Forces of Unification and Diversification: Zipfian empirics ◮ Easiest for the speaker to use just one word. References ◮ Encoding is simple but decoding is hard ◮ Zipf uses the analogy of tools: one tool for all tasks. ◮ Optimal for listener if all pieces of information correspond to different words (or morphemes). ◮ Analogy: a specialized tool for every task. ◮ Decoding is simple but encoding is hard ◮ Zipf thereby argues for a tension that should lead to an uneven distribution of word usage. ◮ No formal theory beyond this... Frame 9/20

Data from our man Zipfian empirics: Zipf Zipf in brief ◮ Number of meanings m r ∝ f 1 / 2 where r is rank and r Zipfian empirics f r is frequency. References Frame 10/20

Data from our man Zipfian empirics: Zipf ◮ Article length in the Encyclopedia Britannica: Zipf in brief Zipfian empirics References Frame 11/20 ◮ (?) slope of − 3 / 5 corresponds to γ = 5 / 3.

Data from our man Zipfian empirics: Zipf ◮ Population size of districts: Zipf in brief Zipfian empirics References Frame 12/20 ◮ α = 1 corresponds to γ = 1 + 1 /α = 2.

Data from our man Zipfian empirics: Zipf ◮ Number of employees in organizations Zipf in brief Zipfian empirics References Frame 13/20 ◮ α = 2 / 3 corresponds to γ = 1 + 1 /α = 5 / 2.

Data from our man Zipfian empirics: Zipf ◮ # news items as a function of population P 2 of location in the Chicago Tribune Zipf in brief ◮ D = distance, P 1 = Chicago’s population Zipfian empirics References ◮ Solid line = +1 exponent. Frame 14/20

Data from our man Zipfian empirics: Zipf ◮ # obituaries in the New York Times for locations with population P 2 . Zipf in brief ◮ D = distance, P 1 = New York’s population Zipfian empirics References ◮ Solid line = +1 exponent. Frame 15/20

Data from our man Zipfian empirics: Zipf ◮ Movement of stuff between cities Zipf in brief ◮ D = distance, P 1 and P 2 = city populations. Zipfian empirics References ◮ Solid line = +1 exponent. Frame 16/20

Data from our man Zipfian empirics: Zipf ◮ Length of trip versus frequency of trip. Zipf in brief ◮ Solid line = -1/2 exponent corresponds to γ = 2. Zipfian empirics References Frame 17/20

Data from our man Zipfian empirics: Zipf ◮ The probability of marriage? Zipf in brief ◮ γ = 1? Zipfian empirics References Frame 18/20

Data from our man Recent Zipf action: Zipf Zipf in brief Zipfian empirics 1.0 c d References 0.6 ◮ Probability of people P ( L ) 0.4 being in certain 0.2 0.1 locations follows a P ( L ) 1 2 3 4 5 6 Zipfish law... L ◮ From Gonzàlez et al., 0.01 5 loc. Nature (2008) 10 loc. 30 loc. “Understanding 50 loc. ~( L ) –1 individual human 0.001 240 mobility patterns” [1] 1 10 100 L Frame 19/20

Data from our man References I Zipf Zipf in brief Zipfian empirics References M. C. González, C. A. Hidalgo, and A.-L. Barabási. Understanding individual human mobility patterns. Nature , 453:779–782, 2008. pdf ( ⊞ ) G. K. Zipf. Human Behaviour and the Principle of Least-Effort . Addison-Wesley, Cambridge, MA, 1949. Frame 20/20