# The Improbability Principle

In my last blogpost, I touched on how chance and probability are major drivers of evolutionary phenomena. Around the same time I found “The Improbability Principle” by David Hand in the university library, a book that in part discusses the lottery of evolution.

If you’re first thought upon reading that intro was “That’s a strange coincidence!” then this book is for you. Hand, a Professor of Statistics at Imperial College London, uses his life-long expertise of statistical modelling to explain why seemingly improbable events occur with surprising regularity. Lotteries provide a good example of highly unlikely yet frequent events. Evelyn Marie Adams won the jackpot on the New Jersey State lottery twice; once in 1985, and again in 1986. Impossible? Then consider Maurice and Jeanette Garlepy of Alberta who won the jackpot the Canadian Lottery twice; the probability of that outcome is one-in-200 trillion. If dreams are more your cup of Earl Grey, then what explains déja vu, that strange feeling we sometimes get that we’ve lived through something before? Are these flashbacks just freak events, or the inevitable outcomes of each of us doing the same tasks, meeting the same people on a daily basis?

After a series of chapters outlining the basics of statistics and probability calculations, Hand offers five ‘laws’ to explain why seemingly impossible events arise with startling regularity. What could have been a dry book on statistical methods is instead a breezy and frivolous lesson on the roles probabilities play in our day-to-day lives, with each case richly illustrated using fun anecdotes. The five laws are:

• The law of inevitability: Put simply, something has to happen. Your personal chance of winning the National Lottery is vanishingly small, but someone usually wins every week due to the amount of people who play. Similarly, there’s…
• The law of truly large numbers: Given enough opportunities for something implausible to happen, it will happen. In 2010 a dog accidentally shot its owner after it stepped on his shotgun. A far-fetched story? Yet As Ben “Bad Science” Goldacre pointed out, two similar cases were reported in 2007, as well as in 2004. The world has plenty of dogs and guns, so puppycide will occur.
• The law of selection: You can make anything implausible seem inevitable if you state what you’re looking for after the event. Abraham Lincoln apparently dreamed that he was going to be assassinated a week before it happened. Yet how many other people have predicted their own death, but then lived a long life? What about those who foresaw the end of the world, then moped that they had ‘miscalculated’ when we all happily survived?
• The law of the probability lever: A slight change in circumstances can have huge impacts on predicted outcomes, making improbable events much more likely. Possibly the most infamous example of this law was used in the Sally Clark trial, a solicitor whose two children died young. Clark argued that both children died from natural causes (‘cot death’). The prosecution claimed that the probability of such an event was 1 in 73 million, and Clark was subsequently convicted of murder. However, the prosecutor’s calculation makes the erroneous assumption that each death was an independent event. In reality, if one cot death occurs in a family, subsequent deaths are much more likely so the 1 in 73 million claim is a gross overstatement. Clark was jailed for three years before her wrongful conviction was overturned.
• The law of ‘near enough’: Did you predict an unlikely event, but it didn’t arise? You can still claim it happened if something similar materialised instead. It’s exceedingly unlikely for someone to win a lottery jackpot twice, but how many compulsive gamblers have won two lesser prizes?

A bluebottle with compound eyes. Photo from Wikipedia Commons.

One of the fascinating aspects of evolutionary theory is that formation of complex adaptations essentially follows these laws. How did the eye, which started off as light-sensing proteins in unicellular bacteria, evolve into the complex camera-organ that all humans carry? If the rudimentary light-detecting organism were left to mutate by chance then it would be incredibly unlikely to form a complex eye. Natural selection however greatly skews these odds.

Consider a rudimentary bacterium, whose ‘eye’ was a collection of light-sensing proteins. This bacterium will reproduce many times, and eventually some offspring will be produced that will carry more developed ‘eyes’ (a variant of ‘the law of truly large numbers’). These individuals would be more able to survive, so these evolved eyes will persist in nature; rather aptly, this rule is an application of ‘the law of selection’. Repeat this process for millions of years (‘the law of truly large numbers’ in action, again) and eyes will eventually evolve into their complex modern forms. It seems that the Improbability Principle is living and breathing all around us in our natural world.