It’s one of the three Rs (’rithmetic), but many of us fail to see the relevance of mathematics in our modern world. We associate it with geniuses such as Einstein and don’t see not being good at maths as a slur. Think again, says Kit Yates, whose book The Maths of Life and Death shows how maths really does make all the difference.
How do zebra fish get their stripes? How do you stop locusts swarming? How do ants make decisions? These are all questions of biological mathematics. And there was I thinking that – apart from addition, multiplication and percentages – maths was an abstract concept: equations on a chalk board, layered calculations, endless numbers.
But mathematics is all around us, says Kit Yates, senior lecturer in mathematical biology at the University of Bath, whose job consists of taking real-world phenomena and uncovering the mathematical truths behind them. “Maths is the language of science, so you can use maths to describe any area of science,” says Kit. “The seeming dichotomy is that biology seems to be messy and real world and people traditionally think of maths as pure and abstract and irrelevant, but actually they come together in the middle.”
How many snails?
Kit relates a scenario where his four-year-old son asked him how many snails there were in the garden. Kit didn’t know, but calculated this by a method called capture/ recapture. Kit and his son searched the garden and found as many snails as they could in 10 minutes – the result was 23. They marked them all with a cross using an indelible pen. A week later, they did the same thing, found as many snails as they could in the garden over a 10-minute period. This time they found 18 snails and just three of them had the cross on their shells. The capture/recapture method says that the proportion of marked individuals in the second sample – 3/18 or 1/6 – should be representative of the proportion of marked individuals in the garden as a whole. So the number of marked individuals caught on the first day, 23, are scaled up by a factor of six to find an estimate for the total number of snails in the garden – 138.
“So it’s a really simple multiplication,” says Kit. This method can be used to calculate in all sorts of scenarios, including estimating the number of war dead in conflict zones where not all the bodies can be rescued, the number of drug addicts in the United States, the number of fish in an ocean to research how intensively to fish the seas, the number of raffle tickets bought at a fair, the crowd number at a football ground or the number of visitors to a website.
The maths behind the biology
One of Kit’s current areas of research is looking at the mathematics of how embryo patterns and pigmentation patterns form. “The reason why some cats have a white belly but a black coat can be explained through mathematical modelling,” he says. He describes how he works with experimental biologists – one recent study compared the movement of cells in an embryo to a mathematical model in which cells jump between the sites of a grid. “It’s not hugely complicated; it’s more like a computer game, like a game of Tetris, where you are trying to fill up a domain with cells.”
This is one thing – apart from mathematics obviously – at which Kit excels, making maths problems and mathematical calculations sound really interesting to those who are not mathematicians. “I realised that this was the way into mathematics for people who haven’t been interested in mathematics or didn’t enjoy it at school – to tell the story of real people’s lives and how it affects real people.” In his book The Maths of Life and Death, published this month, Kit explains how maths underpins everything we do, and how, quite literally, it is often a matter of life or death.
Take the famous case of Sally Clark, one of the real-life examples that Kit uses in his book. Sally and her husband Steve lost their son at 11 weeks. Then a year later, they lost their second son at eight weeks. After the second death Sally was charged with the murder of both her sons. This was a complex trial, Kit says, with conflicting evidence and it was characterised by a number of mathematical mistakes, which would contribute to what has been described as Britain’s worst miscarriage of justice.
One of the miscalculations involved a statistic given by an expert witness, Professor Sir Roy Meadows, who testified that the chance of two children from an affluent family suffering sudden infant death syndrome (SIDS), also known as cot death, was one in 73 million. Meadows had multiplied the probability of an individual event (the death of Sally Clark’s first baby) by the probability of another similar event (the death of another baby). The calculation assumed that SIDS cases were independent events. But there are many known risk factors associated with SIDS, including smoking and premature birth, and genetic factors, which makes the assumption, and the calculation, wildly off the mark.
Combined with other mathematical mistakes, and the fact that the evidence was conflicting and the case not clear cut, the jury were heavily influenced by Meadow’s statistic and assumed that it was extremely likely that Sally had murdered her two children. Sally’s defence didn’t question the figure. The jury found Sally guilty and she was sentenced to life imprisonment in 1998.
“Meadows took the probability of one death in a family and multiplied that by itself, which made it look far more likely that Sally Clark had murdered her kids. That is the worrying thing – we see someone who we perceive to be an expert and in a position of authority and they produce a figure and we are blinded by the figure. We need to learn to question these figures.”
“There are plenty of other instances in the book where slight mathematical understandings have caused deaths in some instances or serious inconveniences, or sent people to prison,” says Kit. A fatal example was a nurse who calculated the insulin she needed to administer to a diabetic patient as 10 times the dose that was required. Another example was in 1936 when pollsters estimated that the Republican presidential candidate in the US election would beat Theodore Roosevelt, but they got their sampling method wrong and Roosevelt won by a massive majority. A more lighthearted example is of a builder who was mistakenly paid £400,000 instead of £400, and ended up going to prison because he spent the money.
Is the maths in the book challenging to understand? “I don’t think people will find any of the mathematical concepts difficult, it’s more the detail,” explains Kit. “I’ve tried to steer away from much of the detail and focus on the broad concepts. I want the book to be mainstream. It is written for people who are intelligent, smart and interested, but that applies to a huge number of people. There are no equations in the book – the bits of maths that we do are explained with analogies, with metaphors and through stories, and the really important part of the book is not the details of the maths, it’s the concepts.”
“There are so many stories around life and death which have a mathematical implication, and it’s a good place to get people’s attention where you think that something is in the balance because of mathematics. Also life and death – although they are important – are everyday experiences, and that is what the book is about, trying to get to grips with people’s everyday experience where maths can make a huge difference.”
It seems that my memories of chalk marks on a board are not abstract concepts – such calculations give meaning and relevance to everything around us.
The Maths of Life and Death by Kit Yates, published by Quercus Books, £20