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Game of Life • Grid of binary elements, arranged on a 2-D plane, like pixels on a computer screen • Each cell belongs to a neighborhood including its 8 immediate neighbors. • Each cell follows simple local rules • Cohesive patterns form out of apparent randomness • Emergence Cellular automata • Very simple virtual machine that results in complex, even lifelike, behavior • A cell is a bit-position on a binary string • State of a cell at the next time step is determined by its state at the current time and by the states of cells in its neighborhood • Simplest neighborhood includes a cell and its neighbor on either side (a neighborhood of 3) Dawkins’ biomorphs • Richard Dawkins, The Blind Wathmaker, and biomorphs • Form was encoded in a chromosome of 9 genes, each could take values from 0 to 9. • These encoded rules for the development of the biomorph, e.g. angle or length of a branch • Each gene can change on step by mutation • User could generate a random population, select one that looked interesting, nad use it to generate a new population, and so forth Evolution • Dawkins found that, though he expected his population to look like trees, he discovered that insect forms were also possible • Incremental and unpredictable change in a desired direction: evolution Accomplishments of Social Insects • An insect may have only a few hundred brain cells (compared to hundreds of trillions of brain cells in a human), but insect organizations are capable of architectural marvels, elaborate communication systems, and terrific resistance to threats of nature • A central question in the sociobiology of insects is: how does mass behavior emerge from the behaviors of single ants Termites • Termites build domes by thru simple rules • Autocatalytic or positive feedback cycle • Termite builders are a self-organizing system, there is no central control, the members of the population are unaware of the “plan” they are carrying out • Stigmergy: communication by altering the state of the environment in a way that will affect the behavior of others for whom the environment is a stimulus Ants • • • • Ant cemeteries Formation of piles of woodchips by termites Live ant experiment: ants find shorter path If the length is changed during the experiment, some species re-discover the shorter path and some don’t • Flies trapped in a jar Fish Schools • Many species of fish swim in schools that seem to take on an emergent life of their own • A fish school appears to move as one, with hundreds if not hundreds of thousands changing direction, darting at what appears to be the same exact instant • Experiment with a solitary fish in divided tank • c=kNt (e.g. k=0.355, t=0.818) • Effect of t<1: sublinear increase with groupsize Social Impact • Latane’s experiments on social impact find that the impact of a group on an individual is a function of the Strength, Immediacy, and Number of sources of influence • Nervousness of participants in a college talent show shown to be a function of number of people in audience (similar formula to fish) • Do we humans exhibit herding behavior? • Craig Reynolds bird flocking simulation Fish Schooling • Biologists have shown that fish seem to regulate their schooling behavior using visual information and information from the fish’s lateral line • Vision guides the flock-centering tendency • Lateral line enables collision avoiding • Blinded pollock swim farther from their neighbors • Fish with lateral lines removed swarm closer to their neighbors than normal fish Herds and birds • Possible explanation for herd-centering behavior: an animal at the edge of the herd is more likely to be picked off by a predator • Biologists carried out an experiment: bird flocks were filmed with movie cameras filming at 3 frames per second. • Watching these one frame at a time, they could distinguish specific features of flocking • For example, there was no leader to the flock. Any bird could lead a maneuver at any time Shannon’s experiments • First-order: each letter is selected probabilistically based on its frequency • Second-order: based on probability that letter x will be followed by letter y • Third-order: based on probability that a 2letter sequence is followed by another • Experiments up to fifth order • Second-order word approximation Conformity and social norms • Sherif placed subjects in a dark room with a point of life projected (autokinetic effect) • Asch experiments: subjects asked to rate relative lengths of some lines (about a third agreed with group) • Subsequent experiments: subjects in booths, so they could not see rest of group Are humans herd animals? • Economist Brian Arthur has noted that it is impossible for people to reason deductively in complex situations; there are just too many linkages of facts for anyone to keep them straight. • People end up floundering in a pool of subjective beliefs, including subjective beliefs about subjective beliefs. • The rationality that is assumed by classical economists cannot hold Drunk Irishmen • El Farol is a bar that has Irish music on Thursday nights • Each irishman wants to go when it is not crowded; prefers not to go if more than 60 are there. Each would gladly go to El Farol, if only he knew those other noisy bastards would stay home • One hundred agents set up, and each was allowed to evolve a different strategy. Result: attendance was nearly 60% over time Drunk Irishmen Agents • No agent dominated or performed any better on average than any others • Some very sophisticated deceptive strategies had evolved • Agents were allowed to report their intentions and they were allowed to lie if they wished (of course, if they lied too often, they lost credibility) Conformity • Another experiment: students were asked to choose one-side of a debate question to argue for • Student was told he was free to choose either side, but was subtly persuaded to choose the unpopular side (while still believing he freely chose that side) • Afterward the assignment was over, the student was found to have incorporated some of the beliefs of the side he had argued Adaptive Culture Model • Axelrod: “Agents who are similar to each other are likely to interact and become more similar • Experiment: each individual is represented as a string of numerals (one might be 42237, another 99217) • A matrix of individuals is initialized • An individual and one of its four neighbors are selected at random Adaptive Culture Model • Based on flipping a biased coin (biased by degree of intersection), they interact. • One individual copies one numeral from the other • Sociologists say this is similar to humans, we pick up habits from those who are similar to us • But, perhaps in humans, we pick up habits from those who are similar to what we would like to be (e.g. success of Seven Habits) Adaptive Culture Model • Experiment: optimize a simple function • Experiment: Sum of first three digits equal to sum of last two • Requires complex coordination of entire vector of elements • Experiment: 8-city TSP. • Global optimal found in 11 of 20 trials Cultural Adaptation • Process of cultural adaptation, at the lowestlevel, includes three principles: – Evaluate your neighbors – Compare to yourself – Imitate your betters Swarm Intelligence • A system in which many individual agents with limited intelligence and information are able to pool resource to accomplish a goal beyond the capabilities of the individuals. Particle Swarm • • • • Binary PSO Real-valued PSO Train a neural network or a fuzzy rule system No Free Lunch Theorem