I have been watching some (very) old Doctor Who episodes, including the first ever serial featuring the archetypal villains, the Daleks. In this story, the Daleks share a planet with their long-time enemies, the Thal. After a war culminating in the denotation of a neutron bomb, both races experience very different mutations. The Daleks have become shrunken beasts that get about in robotic shells, which the more fortunate Thals mutated into peace-loving blondes.
The Thals hope to make peace with the Daleks, but the Daleks have more fiendish plans and plot to lure the Thals into their city with a gift of food and then ambush them. It is a good plan, but it is the choice of gifts that left me bemused. There is plenty of fruit and some large tins whose contents remain undisclosed. These may be reasonable choices, although I do find it hard to picture the Daleks stacking melons with their plunger hands. But the trap also appears to feature stacks of toilet paper. Granted, toilet paper may be an appealing luxury for the Thal, who have been trekking through the jungle for a year, but the real question here is, why do Daleks even have toilet paper?
With three children, I have my own laboratory at home for performing psychological experiments. Before anyone calls social services, there is an ethical committee standing by (their mother).
This evening, I tried out one of my favourites: testing the perception of randomness. Here is the setup: I gave the boys two pieces of paper and a 20 cent coin. I was to leave the room, then they had to decide which of the two sheets of paper would be decided by the boys and which by a coin. Having made their choice, they then had to write down on one of the sheets their best attempt at a “random” sequence of 100 heads (H) and tails (T). Having done that, they were then to toss the coin 100 times, writing down on the other page the sequence of heads and tails that came up. I would then return to the room and guess which one was determined by the toss of the coin, and which by the boys.
I identified which sequence was which in less than 30 seconds. How did I do it?
The trick is to look for the longer sequences. Much like the gambler at the roulette wheel, the kids assume that a run of heads cannot last too long. One of the sheets had three runs of 5 in a row and two runs of 4, while the other had only one run of 5 and one run of 4. I correctly picked that the sheet with more long runs was determined by the coin toss.
Try it yourself sometime. If you see a run of 6 or more (which is in fact quite probable in a sequence of 100 coin tosses), you can quite confidently pick that as the coin toss, unless your subject has been well schooled in probability.
Our intuition struggles with randomness. We tend to assume randomness is more regular than it is. On the other hand, we also try to find patterns where there is only randomness, whether it is the man in the moon, clouds that look like things, the face of Mary on a piece of toast or, perhaps, an explanation for the disappearance of MH 370.