Paul the Octopus got it right seven times in a row, and if he is now treated as a football oracle by some, there seems to be good reason for it. Since Paul has no knowledge of the histories of the teams involved, he should have no better than even odds of getting a prediction right. Under those circumstances, even for those who know a bit of probability, the odds of getting seven matches right is 1 in 128, which should make his achievement noteworthy.
But actually, the existence of a Paul is not surprising. When we look at such instances, we forget that there is no shortage of experts, human or not, making predictions across the world. Start with say, 128 such experts (there will be a thousand times more across the world) for the first match; at even odds, 64 get it wrong. Of the 64 who got it right, 32 get the next match right and 16 the third match. At this stage, someone in their locality starts paying attention. Of these, eight get the next match right, and by now, the local newspapers start paying attention. Carry on like this and what you get at the end is someone who has got seven matches right purely at random. There you have Paul.
If you read Alex Bellos’ book, you will gain some sense of the ease with which the random play of large numbers deceives humans. Bellos is a journalist who decided to return to his love for mathematics after a stint as a foreign correspondent in Brazil. Writers of books on popular mathematics are always caught in a bind: how much can they assume of the reader? To assume too much is to put off some potential readers, to assume nothing is to risk boring others. Bellos assumes nothing and the book takes us through addition, multiplications and logarithms to some very interesting mathematics, including the study of infinity.
My guess is many readers won’t last the course, and I’d advise them to persist. For those bored by the first half, skip to hit portions that hold your interest. But even the first half bears reading. Like any good journalist, Bellos has looked for stories that tell the tale of elementary mathematics in an interesting way. The trouble is that he must sometimes summon up enthusiasm for journeys that do not match up to the hype. A case in point is his visit to the Puri Shankaracharya, who expounds the ‘Vedic mathematics’ conjured up by one of his predecessors in the 20th century. There is nothing Vedic about the subject, and no real maths involved. Bellos tries hard to summon up enthusiasm for an elementary bag of tricks that amounts to nothing. In the process, he does not even take note of the fact that the very existence of this subject speaks of the intellectual humiliation of colonialism.
For men such as the Shankaracharya, if the ancient Indians knew their mathematics, there is nothing they could not have known. In attributing this knowledge to the ancients, what they could not find, they simply made up, only to end up paying an unwitting tribute to the centrality of mathematics in the modern world.