Saturday, September 12, 2009

When is a number not a number?

The other day, it seems, some magician 'predicted' the lottery results. I'm surprised no one's tried it before, actually, given the interest the lottery always seems to attract. From the article it would appear that the trick was well done, impressive and entertaining, and the audience liked it.

How did he do it? Well, I wouldn't know, of course. There are two basic types of prediction trick, one in which you control the outcome of the event (pick a card, any card) to get the result you want, and the other is when you delay the prediction until after the outcome is known. I think we can assume this Brown chap didn't rig the lottery, and in any case, when it's the outcome that is fixed you make the prediction in advanced, whereas he only made his prediction after the draw.

As entertainment it seems to have worked, which is the point of magic, and people who know rather more about these things than me have discussed how he might have done it. That isn't why it caught my attention. I was interested, rather, in the explanation the man himself gave- he said that he had asked a number of people in the audience to make predictions and had then taken the average of the numbers. He described this as the 'wisdom of crowds' and compared it to guessing the weight of a pig.

Now, if a hundred people who are used to dealing with pigs, guess the weight of a pig that's standing in front of them, the average of the guesses is likely to be close to the true weight of the animal. But this, as Mr Brown is no doubt well aware, has nothing to do with predicting lottery numbers, for two reasons:

firstly, and most obviously, the crowd has no knowledge of the numbers that willm be drawn, and thus has no wisdom it can possibly pool to give some kind of approximate answer;

secondly, and much more interestingly, the numbers in a lottery draw don't represent quantities, they are simply abstract symbols, with no relation between them or between any instances of their being drawn. Their sole purpose is to be different from each other so as to serve to distinguish the balls. The lottery organizers could have used colours, or regular polygons, or the outlines of fjords copied from a map of Norway, or or pictures of songbirds, or of names taken at random from the Basingstoke telphone directory. It is as meaningful in the context to speak of the average of these numbers as to refer to the average of those people from Basingstoke- there is nothing it can mean that is relevant to the problem.

Derren Brown is an entertainer, and apparently a good one; this explanation was part of the misdirection which allowed him to pull off the trick. I just wanted to spell put why the 'explantion' he gave is rubbish.

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