One of the paradoxes he mentions is the lotto. Take for example a 6 digit lotto. Every number has an equal chance of winning, right? Not true. Numbers which are in an easy-to-remember form like 234543 or that could be dates e.g. 140297 win the lotto more often. Put like that it’s baffling. But think about how the lotto works. If the number drawn has not been chosen by anyone, another number is drawn. And so on until a number is drawn for which there is a winner. Many people choose their birthday etc. as their number, and so these types are over-represented. Paradoxes like this can appear in covert ways when we apply maths to reality, and usually so as to reinforce the beliefs held by the person making the argument.

Paulos writes about the application of maths to court cases, and in particular to the infamous O.J. Simpson trial. He describes some of the twisting of statistics by the defence in that trial. It is implied that if the jury had been a little more aware they wouldn’t have been as easily fooled. “We’re so often cocksure of our decisions, actions and beliefs because we fail to look for counterexamples, pay no attention to alternative views and their consequences, and distort our memories and are seduced by our own explanatory schemes.”

And we will become more and more so. The O.J. Simpson trial is only the beginning. The rule of reason is at an end. Reason is boring. An investigation into whether Clinton ejaculated on a dress, a car chase televised live: these are things that never happened on earth before. There will be more of them. Does anyone still believe that education is bringing us towards a better society, that the insights Paulos is bringing to the masses will improve them? At what point was it in the late twentieth century that insight and reasoning ceased to be something to strive for and became a lifestyle choice?

At certain points in the book it becomes clear that Paulos is aware of – what should we call it? The crisis of the modern? He writes: “We’re content to pick up small bits of pattern if ever and wherever they might be found. Indeed this book’s piecemeal, episodic structure is due to a similar impatience with lofty claims and simplistic theories.” Yes, but your plea that we should have more reason in our lives is one of those lofty claims.

It’s a strange universe we have arrived at, where a book on how a little analytic thinking can help us in our lives comes across as old-fashioned, willfully naive, out of place in this era.

I was wondering why he didn’t have a brief account of yet another point of interface between mathematics and society that mathematicians love to talk about – the 2000 presidential election where Gore got the majority of votes but Bush got elected. The president is elected on the number of “electoral votes” he gains, and the number of electoral votes is only roughly proportional to the population of a state. The Bush campaign conserved resources by campaigning hard in the marginal states. That could be taken as an application of mathematical reasoning.

I looked at the inside cover and found it was published in 1998. It made me wonder if his faith in commonsense (supported with mathematical insight), would be the same if it was written today. The call to listen to reason seems weaker now. Pointing out to readers the perversions in logic that sold the war to the common people would seem a necessary task, but one to be undertaken stoically, not in any hope that things will get better.

I examined the library slip pasted on the front leaf. The book has been borrowed 5 or 6 times a year for the past three years. That’s about the maximum in fact, because people can renew online for up to two months.