Thursday, July 31, 2008

Scissors, paper, stone

Isaac learned a new game today. The interesting thing about Rock, Paper, Scissors* is that each of the three possible selections is equally powerful: it defeats one other and is also defeated by one. The hand configurations are pretty transparent—'Paper' is flat like a sheet of paper, for example—making them easy for a four-year-old to pick up. The only other requirement is understanding the need to present your choice at exactly the same time as your opponent, so that neither of you gets an unfair preview. Simple rules and no props: the recipe for a popular game. 

I wrote a little in the book about the toddler Athena's developing understanding of rules: 
Armed with a rule, a little person can exert awesome control over a bigger one. ‘You have to run holding hands,’ she barks at me, as we while away some moments in a playground. ‘You have to stand at the top of the steps and when I reach the tree you can come down.’ A rule is not just Mummy or Daddy telling you to do something; it comes from somewhere transcendental, like God. Under the democracy of a rule, everyone is an equal.
As well as being a way of exerting control over others, rules provide a vital means of organising our own experience. They let you know where you are in the game. Rules are conditionals: if this, then that. Paradoxically, submitting yourself to their yoke is a profound liberation. By understanding what the rules are, Isaac knows when he has won—and lost. 

It's one thing to have a rule, but quite another to have a strategy. Athena has quickly worked out that Isaac will base his next play on whatever gesture was successful next time round. If he wins it with Rock, he will choose Rock himself next time. If Athena wins it with Paper, then he will copy her for the next bout. His big sister has sussed this, and is representing her opponent's strategy as a way of guiding her own selection. Although Isaac has sophisticated theory of mind abilities, he has not quite progressed as far as second-guessing his opponent's intentions, or trying to instigate double-bluffs. 

For him, a better strategy at the game might be to pick a gesture at random, and so prevent his opponent from getting any handle on his intentions. But children find randomness hard to understand. In a classic study, Piaget and Inhelder presented children with an experimental set-up which modelled raindrops falling on paving stones, and asked children to predict where the next drops would fall. They found that the children gave responses that credited rainfall with too much organisation. They would assign the same number of raindrops to each paving stone, creating patterns where none would be seen in nature.

Adults struggle with randomness too. The Piaget and Inhelder study reminds me of the story of a friend of mine who asked a builder to arrange some red and black floor-tiles in a random pattern. The builder was at a loss: he spent his life trying to impose order, regularity and precision, and going against system in this way was too much for him. Misunderstanding the laws of chance is a failing we are all prone to, as the gambler's fallacy demonstrates. In fact, one way of producing cognitive load in psychological experiments is to ask participants to generate random numbers or letters, a task which puts great strain on people's minds. Producing a truly random sequence of actions, where the randomness of the sequence is assessed by mathematical analysis, is something that most people would score poorly on. 

Perhaps it's the formalising power of rules, those recently acquired marshals of order, that makes Isaac prefer systematicity to blind chance. When he is allowed to cheat at dominoes, say by peeking at the pieces before choosing them, he goes for a pattern, such as taking all the doubles. That's actually a pretty bad hand for that game, and it's one example of his preference for order putting him at a disadvantage. Young children's actions may frequently seem haphazard, but removing all elements of order from their behaviour is something they won't achieve until later in life, if at all. 

*For me, as a child, it was always Scissors, Paper, Stone—hence the title of this post. 

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