Programming Complexity - Speaker Deck

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Programming Complexity Modeling Complex Systems with Go and React Chang Sau Sheong sausheong@gmail.com

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Complexity The behavior that emerges from a group of interacting parts, that is not directly the result of interactions between individual parts

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Modeling cultural interactions

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The Dissemination of Culture American political scientist, complexity theory researcher, National Medal of Science laureate Robert Axelrod

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Cultures who are similar to each other are likely to interact

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When cultures interact, they become more alike each other

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Agent-‐based model where each agent represents a culture

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Culture = Set of Features language, religion, style of dress etc

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Trait = possible values of a feature

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36 x 36 grid each cell has a culture culture

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5 4 3 2 1 0 Each culture has 6 features

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Each feature has 16 possible traits 0 1 2 3 4 5 6 7 8 9 A B C D E F

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8 neighbours

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Algorithm •At every tick, randomly pick n cells •Compare features of the culture with each of its neighbours •If the trait difference for the same feature between 2 cultures are < t, randomly select either culture and copy the trait of the feature to the other culture

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A B A and B are 2 neighbouring cultures

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difference is 5 – 2 = 3 culture B culture A A 0 5 5 F 6 F A D 2 D 0

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A 0 5 5 F 6 F A D 2 D 0 culture B culture A Difference between 2 cultures = 34 5 A 8 3 2 6 + + + + + = 34

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F F F F F F 0 0 0 0 0 0 culture B culture A 100% different = 96 F F F F F F + + + + + = 96

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A 0 5 5 F 6 culture B culture A Difference between 2 cultures that are 100% similar = 0 0 0 0 0 0 0 + + + + + = 0 A 0 5 5 F 6

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The more similar 2 cultures are, the more likely there will be cultural exchange Probability of cultural exchange = 1 -‐ difference between 2 cultures ÷ 96

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Probability of cultural exchange: 1 − 34 96 = 1 − 0.354 = 64.6%

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culture B culture A Randomly choose to copy one of culture A’s features to culture B or vice versa A 0 5 5 F 6 F A 5 2 D 0 When interaction happens

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What do we want to measure? •Average feature distance tells us how far apart (different) the cultures are •Uniques tells us the number of unique cultures at any given point in time •Changes tells us how vibrant the cultural exchanges are

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Observations •Eventual equilibrium is only a few dominant cultures •Dominant cultures can be quite different from each other •Smaller areas results in faster equilibrium and smaller number of dominant cultures •A culture that is more dominant at a point in time doesn’t mean it will be dominant in the end

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Modeling racial segregation

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Chicago

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Washington D.C. New York City Detroit Los Angeles

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London

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Dynamic Models of Segregation American economist, 2005 Nobel Prize in Economics Thomas Schelling

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36 x 36 grid each cell has a household

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8 neighbours

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Algorithm •At every tick, check every cell •If at least n number of its neighbours are of the same ‘race’, do nothing •Otherwise, randomly pick an empty cell and move there

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Parameters •Acceptable number of neighbours (n) •Number of ‘races’ in the grid (r) •Percentage of vacant cells (v) •Policy limitation – cannot have more than (l) number of neighbours of the same race

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Observations • Segregation happens even if there is weak preference for neighbours of same type • The weaker the preference, the less segregated (smaller clusters) • The stronger the preference, the more segregated (larger clusters) • At a threshold, stronger preference results in an unstable but non-‐ segregated state (occupants always moving to another cell) • Number of races have no impact of segregation • Number of vacant cells have no impact on segregation • Policy enforcement has limited impact on segregation (stronger policies result in unstable state)

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Modeling bystander effect

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Game Theory

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The study of mathematical models of conflict and cooperation, often used in economics and political science

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Volunteer’s Dilemma

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V = value gained if at least 1 person volunteers C = individual cost of volunteering A = overall cost if no one volunteers

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You volunteer You don’t volunteer I volunteer I don’t volunteer V - C V - C V - C V V - C V V - A V - A Payoff matrix for a 2-‐player game

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You volunteer You don’t volunteer I volunteer I don’t volunteer V - C V - C V - C V V - C V V - A V - A If I volunteer

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You volunteer You don’t volunteer I volunteer I don’t volunteer V - C V - C V - C V V - C V V - A V - A If I don’t volunteer

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Mixed strategy Nash equilibrium V – C = pV + (1 – p)(V – A) where p = probability of volunteering

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For an N-‐player game Probability of volunteering = p x p x … x p = pN-‐1 N – 1 times

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For an N-‐player game Probability of not volunteering = (1 – p)N-‐1

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V = value if at least 1 volunteer C = individual cost of volunteering A = overall cost if no volunteers N = number of people involved p = probability of getting at least 1 volunteer 1-‐ p = probability of getting no volunteers V – C = (pN-‐1)V + (1 – p) N-‐1(V – A)

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Monte Carlo simulation

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Observations •Decrease individual cost of volunteering •Increase the overall costs/impact of not volunteering (??) •Increase difference between individual cost and overall costs •Reduce number of ‘players’ •Increasing number of players have negative or no impact

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@sausheong sausheong@gmail.com http://blog.saush.com http://github.com/sausheong