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. 

The Haircut Trees

Deep in the Alto Alentejo, we are finding new terminologies for unfamiliar bits of landscape. Portugal produces half of the world's cork, and this sunscorched region is covered with the squat, silvery trees from which it is taken. "The haircut trees" is Isaac's name for the trees that have recently produced a harvest, with their orange-red underbark exposed in an odd kind of nakedness. He is thinking metaphorically. He notes a new phenomenon and wants to connect it to something he understands: the shedding of an overgrown covering, as in a haircut. Our ancestors probably thought in a similar way when they first named a flame tree or a spider plant, or first employed any of the other common names that have a similarly metaphorical root. 

Today he took the metaphorical connection to another level. Lacking a name for the eucalypts that give this part of Portugal a flavour of the Australian countryside, he extended his "haircut trees" label. The only connection that I can see between a stubby cork oak and a tall, skinny gum tree is that both are commonly short of bark. The name connects with the distinctive feature—the exposure of the tree's trunk—and brings both entities into his realm of comprehension. One connection leads to another, as he continues to loop together his conceptual network. 

When he's not indulging his passion for botany, he's having a typical four-year-old's holiday: swimming in the pool and smearing himself with ice-cream. It hasn't all been hard work. 

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We're off for a few days, so the next post might be from somewhere hot...

An immortality of the flesh

If the kids get back in time from their trip to the theatre with their grandparents, we will be sitting down together tonight to find out the fate of the Doctor and his companions. In her blog post on the trauma of seeing our favourite Time Lord regenerate, Jane Graham mentions the conversation we had when she was interviewing me about The Baby in the Mirror. She was interested in what I had said in the book about children's understanding of sadness that goes beyond their own immediate needs. I had argued that grief is, cognitively speaking, an almost uniquely complex emotion. (Actually, it's pipped at the last minute by regret, but for that you'll have to read the book.)

My kids certainly get the same emotional hit from Doctor Who as that observed by Jane in her little girl. When the Doctor's daughter appeared to die at the end of her eponymous episode, there wasn't a dry eye in the living room. However, there are moments, when you are paying attention to young children's feelings, when you wonder whether they are really grasping the full emotional story. For Isaac in particular, the stirring music that always accompanies a televisual trauma is a powerful cue to what the characters are feeling. Those swelling strings tell him that something is going on that is bigger than his understanding, but whose language he already knows. 

What interests Jane in particular is the ethical question for us as parents. Mums and dads want to protect their children from trauma, so why let them watch things that will upset them? On balance, I agree with her that young children probably take more positives from these experiences than negatives. I argued in the book that children have the cognitive and emotional capacity to come to terms with death far earlier than Freud and others wanted us to believe. This may be in part because, as Paul Bloom has argued, they are dualists, wired up to see the body and spirit going different ways. 

Which just leaves me wondering what we will be left with tonight, once the Doctor has stopped pulsating on the floor of the Tardis. With supernatural beings such as Time Lords and Santa Claus, the facts of life after death become more complicated. The Doctor will still be the Doctor (if we have read the clues correctly), but he won't be the David Tennant Doctor. We will all have to get our heads around a certain immortality of the flesh. 

One thing we can be sure about, though, is that there will be more empathetic tears. I am as much of a blubberer as any of them, having once even been reduced to tears by an episode of Baywatch (it was those damned strings, I tell you). And we will probably have to rethink our ideas about the afterlife as well. A few months ago, Isaac was telling us that heaven is full of dragons, and how, when you get to heaven, you can't 'get died'. That sounds like a Doctor Who version of paradise.