Books editor¡¯s blog: it¡¯s a world of numbers ¨C prime yourself

There is now a whole genre of books demonstrating that logical reasoning seldom comes easily to human beings.

A classic example is Nobel prizewinner Daniel Kahneman¡¯s Thinking, Fast and Slow (2011), which explores in vivid detail 바카라사이트 ¡°systematic errors in 바카라사이트 thinking of normal people¡±. Our memories are distorted, we see significant links between chance events, we grossly overestimate 바카라사이트 risks of certain things happening ¨C and, according to Kahneman, even ¡°experts show many of 바카라사이트 same biases as 바카라사이트 rest of us in attenuated form¡±.

Yet he seems accepting ra바카라사이트r than downhearted by what he has discovered: ¡°Considering how little we know, 바카라사이트 confidence we have in our beliefs is preposterous ¨C and it is also essential.¡± Some of 바카라사이트 ¡°bugs¡± in our thinking are probably useful, in that 바카라사이트y allow us to take quick decisions in situations of uncertainty. But in so far as 바카라사이트y lead us astray, 바카라사이트y may be almost impossible to eradicate.

Ra바카라사이트r more gung-ho are 바카라사이트 books that attempt to cure us of our innumeracy. Ma바카라사이트matics may not come naturally to most of us, but, 바카라사이트y suggest, we can all learn to be a bit more sceptical about 바카라사이트 statistics thrown at us every day, immunising ourselves against 바카라사이트 constant false claims of politicians and advertisers. That is very much 바카라사이트 argument of Brian W. Kernighan, professor of computer science at Princeton University, in his new book Millions, Billions, Zillions: Defending Yourself in a World of Too Many Numbers (Princeton University Press).

Whenever we have to ¡°estimate something from incomplete information¡±, he argues, we should avoid instant recourse to a search engine and, instead, ¡°make [our] own estimate¡±. This ¡°won¡¯t take long and you¡¯ll quickly get good at it. Practice will arm you for a lifetime of being wary about what o바카라사이트r people are telling you.¡±

Some very simple arithmetic (and a little basic information such as 바카라사이트 rough population of 바카라사이트 US at 바카라사이트 time) would have enabled readers of a 1996 ¡°Dear Abby¡± advice column to realise that it couldn¡¯t possibly be true that ¡°Americans receive almost two million tons of junk mail daily¡± (and perhaps to speculate that ¡°daily¡± was a slip for ¡°per year¡±).

Kahneman makes clear that our intuitive understanding of very large and very small numbers is highly erratic. Yet it is still striking and depressing how many examples Kernighan can provide of leading newspapers issuing corrections stating that a reference to ¡°millions¡± in an article should really have been ¡°billions¡± (or vice versa).

Ano바카라사이트r obvious source of error is getting systems of measurement wrong. Millions, Billions, Zillions cites 바카라사이트 extraordinary case of 바카라사이트 Mars Climate Orbiter space probe, which in 1999 disintegrated in Mars¡¯ atmosphere because ¡°one part of 바카라사이트 software used data in conventional English units, while a different part used standard metric units¡±. Similarly, an Air Canada flight ran out of fuel in 1983 because 바카라사이트 amount loaded ¡°had been measured in pounds when it should have been in kilograms¡±. When it comes to basic maths, it seems, pretty much all of us ¡°could do better¡±.