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Project work 1: The triangle game

This project investigates the game which Ian mentions in his talk. You should try the activities in Part A first, then quantify what you see. Suggestions are given in Part B. Part C gives extension work.

Part A

  • Play the game several times with the whole class. The rules are that each person chooses two other people WITHOUT saying who they are to anyone else. Everyone mills around. When told to do so, everyone tries to form an equilateral triangle with their two chosen people. Make your move, then stop and see what has happened. Don't move again until you are told to do so. This continues until everyone is happy, and equilibrium is reached - it may take seconds, it may take quite a long time. Compare how many moves, it takes, and discuss what makes a difference.
  • Sometimes not very much happens when people move, sometimes lots happens. Decide what "small", "medium" and "large" events are.
  • Repeat the basic game noting how many moves have taken place when different types of event take place.
  • Now divide the class into as nearly equal halves as you can. Each person has to choose someone who is in the same group as they are. Repeat the game and see if there is any difference.
  • Vary the size of the groups. You can have different numbers in groups, several groups ... Try to vary the groups in a systematic way so you can build up a picture of what is happening.
  • Only let one group move at a time. So one group makes a move, then the other group has a go, and so on, until equilibrium is reached.

Part B

  • Try to quantify how big the events are
  • There are lots of different ways to do this, and you should try to find your own
  • To get you started, you could think about having one person disrupt the equilibrium by taking one step
  • Then see how many steps are needed by everyone to reach equilibrium again
  • Try this again, and see if you can graph your results
  • When you've had a go at quantifying the game this way, try out variations of your own

Part C

  • Pick people who move once, then don't move again during that game - these people are "pins", who impede movement. How many people does it take to make a substantial effect on the number of moves it takes for equilibrium to occur? Again investigate systematically, and repeat the analysis in Part B
  • Pick two equal teams, the "red" team and the "green" team. First, have red people picking red, and green people picking green. Secondly, have red people choosing 1 red and 1 green, and green doing the same. Thirdly, let red pick 2 green, and green pick 2 red.
  • This time get red people to run to their next position, while green people go really slowly - you'll have to decide what "fast" and "slow" are - can you quantify these in some way? What difference do these variations make to the speed with which equilibrium is reached?
  • Try to graph the size of the events and the number of moves between events in each of the above cases.

Additional activities for triangulators

  • Pins. Some participants don't move. 1 in 10 is a good ratio to start with, then investigate the effect of changing the number.
  • Disruptors. Nominated participants take a single step once everyone is in the stable state. What effect does this have? What about if two people (or more) take a step simultaneously?
  • Pins and disruptors. Combine both these.

Note that all the triangle activities need to be done many (ideally 10+) times for valid statistics. It would be a good idea to rotate the observer duties to avoid people getting too bored.