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The future belongs to crowds. ~ Don DeLillo
In a seminar on creativity, we tried an exercise with movement. There were 20 students in the small room. We put the chairs against the walls and started walking. There were no instructions other than ‘walk.’ The first thing to note was that the students did not walk randomly. There was significant synchrony and alignment. Most students walked along a counterclockwise ellipsoid near the chairs and walls. A few walked clockwise, against the current. These anadromous (like salmon) folk did not walk randomly either. Instead, their choice of direction seemed like a deliberate counterpoint to the majority current.
At this point, we had achieved a modest level of swarm intelligence. Like starlings in a flock or fish in a school, these students moved by individually following a small set of simple rules. ‘Do what your neighbors are doing and don’t bump into them.’ ‘Go with the flow.’ How does a flow pattern emerge? Not much is needed. It may be enough for one person to start walking with confidence to inspire others to follow, which easily leads to a cascading effect involving the whole group. The highly synchronized movement of the group becomes an emergent property produced by the aggregated and interdependent actions of the individuals.
At this point, our coach asked everyone to keep mentally track of one other person, trying to know at all times where that person was while not letting anyone know who we were keeping track of. This was easy and did not lead to any perceptible change in the overall flow. Then the coach asked that we keep track of a second person as well. This was more demanding, and I wonder if it made our movements more uniform.
The real intervention came when the coach asked everyone to move with the goal of forming an equilateral triangle with the other two chosen individuals. This turned out to be challenging. With 20 people in the room, and each having privately selected two reference persons, the probability that 3 individuals choose one another is small (1/19^3 = .00014579). In effect, any person’s move intended to form an equilateral triangle affected 2 other people, who in turn were most likely connected to still others in other triangles. This way, there was a good chance that the effects of any individual’s move would ripple throughout the entire group. With everyone affecting everyone else, the only certain outcome was that the smooth counterclockwise flow would end. There was a small probability that the group would find a neat pattern and that all movement would stop (with all triangles being established at the same time). This did not happen. Movements became more chaotic and the mood more frustrated. Yet, there was a clear lesson for us. Groups can self-organize following simple rules, and that complex patterns can emerge ‘spontaneously.’
Zoe Papakipos, one of the students in the class, created a computer simulation of the exercise. Using JavaScript and HTML, Zoe wrote a program that allows us to see the group members’ moves from a bird’s eye view. Instead of people, there are little red squares or points. These points can be instructed to move either randomly or to move “intentionally” with the goal of forming an equilateral triangle with 2 other points, which the program randomly selected. The program can show the lines connecting one point with its 2 reference points. It won't show the thrid line, though, which would complete the triangle. The number points and the speed with which they move can be varied. The display can be paused and reloaded. It is instructive to play a few simulations while holding number, speed, and instructions constant to appreciate how different the results are simply because of the random variation in the initial placements of the points.
Click here to open the Game of Zoe, which is copyrighted by Zoe Papakipos.
We suggest you begin with a group size (number of points) of 20, a velocity of .2, and a minimum distance between partner points of 0 (if you find the movements too slow, increase the velocity). Notice that the random-move setting results in the expected rhyme-and-reason-less migrations of points. Many points wander outside of the window. With the intentional setting, we notice a contraction effect. On most runs, points are more likely to move towards one another than away. Over time, this results in a compact final state of the group. When the minimum distance is set to 0, the points often end up all in one spot. This may not be surprising because points are programmed to take the shortest route to establish their triangle. Imagine 3 points dropped at random on a plane and then one point moving to make a triangle. The sum of the distances will be smaller when the triangle is completed than it was before. When all 3 points move, the result should not be much different. Run the simulation to see for yourself. Once a big crunch has been achieved, a big bang can be had by simply switching from the intentional to the random setting. When points move randomly, there is nothing that binds them together. With space being unlimited, they will soon lose sight of each other (and you of them).
Points on a plane are obedient to instruction. They are, after all, programmed to follow explicit rules. They do so perfectly. Humans are imperfect in this regard. They may disobey instructions deliberately or neglect them because they are not paying attention or because they find themselves compelled by other motives (e.g., to stay far away from Erika). In other words, Zoe’s game shows what humans would do if they made no errors and had no additional or contrarian motivations.
Unlike simulated points, people may be reluctant to be very near any other person. To simulate this motivation, you can increase the minimum distance between partner points to, say, 30 (although this does not affect the proximity among non-partnered points). Now triangles often form, and points can no longer collapse into a black hole. Over many repetition, some weird phenomena will appear: a few points moving out of the window or solutions failing to stabilize (as shown by continuous jitter). The most interesting observation, though, is that the group’s end state never seems to replicate. Every initial random setting (probably) leads to a different end state, and that end state is unpredictable unless one has vast computation power. The final state emerges from a few simple rules governing movement and from random differences in the initial state.
There are many ways in which the game can be extended, but they lie beyond this preliminary treatment. By dumb luck, some points will be popular; theyhave been chosen by many others as partners. When these popular points move, trying to form their triangle, they affect the group at large. At the other extreme, a point may only be part of the one triangle consisting of itself and the two chosen partners. This point could not wander off into space as it would be bound to the group by its partners. This point's effect on the group would be minimal and indirect (by affecting the moves of its partners, who in turn are connected to other points).
How might a graded group structure affect the efficiency of settling on a solution? A group with a highly graded structure would be the kind just described, with popular points and loners. Other groups might have a flat structure, where every point has two chosen partners and is chosen by two. The chosen and the chosee should not be the same, though, or group coherence would be lost. As noted above, there is a very small probability for choices to be mutual or reciprocal. If so, cliques would form, and this too is a possibility among humans.
The Game of Zoe bears some resemblance to Conway's Game of Life. In both games, "evolution is determined by its initial state, requiring no further input. One interacts with the Game of Life by creating an initial configuration and observing how it evolves or, for advanced players, by creating patterns with particular properties," as Wikipedia states. The Game of Zoe, though, simulates goal-directed motion, whereas in the Game of Life, motion is but apparent.
A simple lesson
The Game of Zoe teaches a simple lesson on what's interesting, important, and beautiful. The initial setting of randomness is entropic, uninteresting, and ugly. When the minimum inter-point difference is 0, the final outcome has no discernible structure either; it is equally uninteresting and unappealing, and perhaps even highly entropic if we believe Hawking and Bekenstein's theory of black holes. It is the middle stages that show emergent structure, which is interesting and appealing. Most of all, it is the flow of interdependent movement that conveys information, interest, and pleasure. In this way, the Game of Zoe is a truer game of life than Conway's Game of Life. Zoe, after all, is Greek for Life.
