Book review by Anthony Campbell. The review is licensed under a Creative Commons Licence.

I quite often have the radio on when I'm writing. Occasionally I hear someone say the exact word that I'm typing at that moment; sometimes it's quite an uncommon one. Believers in Jung's synchronicity theory would no doubt attach some deep significance to such coincidences, but I'm quite sure that they are simply that—coincidences. Hand's book deals with such events and seeks to show how statistical principles can produce them without the need for any spooky underlying forces.

Hand is well qualified for the task, being an emeritus professor of mathematics and former President of the Royal Statistical Society. But his book is written for readers who lack any special mathematical expertise and contains only a few simple artithmetical examples. He illustrates his Improbility Principle by means of a number of 'laws., so we get the Law of Inevitability, the Law of Truly Large Numbers, the Law of Selection, the Law of the Probability Lever, and the Law of Near Enough. This is perhaps a bit artificial but it serves as a basis for discussion.

The 'law of inevitability' says that if you make a list of all possible outcomes, one of them must happen. As Hand remarks, this is completely obvious, but we often forget it for that very reason. It means that if all the possibilities are highly unlikely, one of them must nevertheless occur.

The 'law of truly large numbers' says that if the range of possibilities is large enough an unlikely outcome will occur sooner or later. He provides a striking example of this: if you choose any abitrary sequence of six numbers, such as the date of your birth in days, months, and years, you will find it somewhere in the expansion of pi; he gives a link to a site where you can try it out.

The 'law of selection' says that you can make probability as high you
like (certain,in fact) if you choose *after* the event. Here he
gives the example of scoring a bullseye by shooting an arrow at a barn
door and then drawing a target round the arrow.

The 'law of the probability lever' says that a slight change in circumstances can have a huge impact on probabilities. The earth appears flat to us, but if we keep going in one direction we will eventually end up at our starting point.

The 'law of near enough' says that we tend to regard events that are fairly similar as identical—we over-interpret near coincidences.

An important reason for Hand's writing this book was to show that apparent coincidences are not a reason to believe in miracles, prophecies, or the paranormal. I doubt that any believers in these things will be persuaded by his arguments to change their views, but sceptics who are already disbelievers will find rational justification here for their scepticism.

17 May 2014

%T The Improbability Principle

%S Why coincidences, miracles, and rare events happen every day

%A David J. Hand

%I Scientific American / Farrar, Straws and Giroux

%C New York

%D 2014

%G ISBN 9780374175344

%P xii + 269pp

%K statistics

%O hardback

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