Do the maths: the science behind the numbers that govern our lives

Eat five portions of fruit and veg, drink eight glasses of water, exercise five times a week… these figures grab our attention, but do the numbers really add up?

In the mid-60s, the psychiatrist Charles Hofling wanted to know more about the way nurses and doctors interact with one another, so he devised an experiment, in a real hospital. While on duty, the nurses would receive a telephone call from a doctor, who ordered them to give a 20mg dose of medicine to a patient. The doctor said he'd sign the paperwork when he got in. Despite clear instructions on the bottle of medicine that explained a 20mg dose could be fatal, 21 out of 22 nurses were prepared to give the drug. And none of them had met the doctor who made the call.

Hofling's paper became a textbook classic. People were shocked by the nurses' readiness to trust the authority of the doctor, but other, similar experiments have shown that most of us are all too ready to accept what we're told, particularly if there's a suggestion that the advice came from an expert.

Think about your average day as a series of choices. You'll get up, you'll choose what to eat, whether to go for a run, whether or not to indulge in a glass of wine or a second helping of dessert. You're constantly making decisions based on what you want versus what you think is good for you. And how do you know what's good for you? Because somebody told you so.

On average, we are given 123 different pieces of advice every week, from sensible government guidelines to scare stories about what gives us cancer. Actually, that's not strictly true: I found that statistic on the internet, but it rather proves the point that you can assign a number to just about anything. Numbers work because they get our attention, but they're also fairly easy to manipulate. Here's the latest thinking about the science behind the numbers that govern our lives.

5 portions of fruit and vegetables a day

"It's a lot more useful than 'eat a varied diet'," says Mike Rayner, director of the Nuffield Department of Population Health, "because how do we know what that really means? Health messages tend to work if they capture the public's imagination. There's a mixture of art and science in setting them at the right level, between what's ideal and what's pragmatic."

And so it was with the five-a-day campaign, which began in 1994. "We adopted a five-a-day message because the Americans had a similar scheme, and the World Health Organisation's recommendation was 400g a day, which was about 50% more than the average person in the UK was eating," Rayner says. But in the countries where the WHO had found the lowest levels of heart disease and cancers linked to diet, the average person was eating far more fruit and veg – around 10 portions a day – and other countries recommend greater amounts: in Denmark, it's 600g; in Greece, it's six portions of vegetables and three of fruit. So although five will do you good, more might be better. It's estimated that most people in the UK still average only three portions. "Based on this rate of increase," Rayner says, "it will take decades before we're hitting the target."

However, there has been a huge growth in another area, thanks to the five-a-day message: the processed food industry. According to the campaign group Sustain, we spend around £54bn on food a year, and £12bn of that is on food we believe to be healthy. "People trust food labels, opting for those that carry some form of 'health halo'," Sustain says, and there's little regulation around what can technically be allowed as a one-of-your-five-a-day claim. If you eat more portions of processed fruit and veg, you're also likely to be eating a lot more salt, sugar and saturated fat.

35 is the upper limit for women having children

"Have your babies before this clock strikes 12," Professor Mary Herbert, a specialist in reproductive biology, told an audience at the British Science Festival this year. "I would be getting worried about my daughter if she hadn't had a child by 35."

Herbert's Cinderella analogy may raise a few eyebrows, but she's certainly not the only expert keen to tell women who want to be mothers to get on with it. "I read one paper that referred to eggs as 'best used by 35'," says the economist Emily Oster. "Thanks; it's really helpful to know my sell-by date."

Oster became interested in the so-called fertility cliff when researching her book Expecting Better, which tackles the data behind some of the most common (and controversial) pregnancy advice. She found that the main research on fertility rates comes from data collected in the 19th century, based on the age of women at the time of their marriage. The theory being that "couples would pretty much get down to business right after the wedding… Researchers found the chance of having any children was very similar for women who got married at any age between 20 and 35. Then it began to decline: women who got married between 35 and 39 were about 90% as likely to have a child. Women who got married between 40 and 44 were only about 62% as likely."

So, yes, there is a decline, but only a 10% difference between the first two age groups, a century before IVF. Perhaps that clock isn't going to chime 12 quite as soon as you think.

8 glasses of water a day

The claim that we should drink eight glasses of water a day is widely attributed to a report from 1945, from the American National Academy of Sciences' Food and Nutrition board, which estimated we needed one millilitre of water for every calorie of food.

"What it meant was that daily fluid turnover is 2.5 litres, which is the equivalent of eight glasses of water," sports scientist Timothy Noakes says. "But the fluid does not need to be water. About 750ml comes from food eaten each day."

The eight glasses idea might seem fairly harmless, but it has fed into the belief that we should all be drinking more water, that it is healthy to be proactive about "staying ahead of our thirst". It's an idea that is now widely promoted in sport, but as Noakes details in his book Waterlogged: The Serious Problem Of Overhydration In Endurance Sports, even athletes weren't really encouraged to take on more fluids while training until the late 70s. It was then that sports drinks first appeared and more funding was given to research that promoted the "science of hydration". There have been no reported deaths from dehydration in sport, but there have been several deaths caused by hyponatremia, or water intoxication. These cases are rare, but they indicate how confused we've become about what our bodies need. If you're thirsty, have a drink. If not, you're probably fine.

2,000 calories a day for women, 2,500 for men

In the documentary Super Size Me, Morgan Spurlock's camera crew ask people on the street to define "calorie". Most can't. As Marion Nestle and Malden Nesheim recount in their book Why Calories Count: From Science To Politics, Spurlock's crew "could not find even one person who could come up with a reasonable definition".

There are actually five different measurements for calories as a unit of energy. The guideline we most commonly think of – 2,000, or 2,500 a day – is in calories with a small c. Around two-thirds of the total calories you need are defined by your basal metabolic rate (BMR) – the amount of energy you expend just existing: that's breathing, brain function, blood circulation. On top of that, anything you do, including shivering or fidgeting, let alone walking or running, will increase the number of calories you need.

Your BMR is affected by your weight and height (different formulae will give different totals) and the amount of activity each of us does each day will vary greatly. So do the average calorie guidelines really apply to any of us? "It's hard to arrive at anything approaching the correct number without doing expensive tests involving non-radioactive isotopes," admits Nestle. So, would we be better off using one of those online calculators that gives us an individual number? "Good grief, no," she says. "If you are going to buy anything, get a scale that works. And use it. By adulthood, people know whether or not they have a weight-gain problem. If they do, they need to eat less. This isn't rocket science. It's just figuring out how to balance food intake against calorie needs, and a scale tells you everything you need to know."

So why do we bother having recommended averages at all? Because, Nestle says, most of us dramatically underestimate how many calories there are in food and, therefore, what a portion size should look like. "If I had one thing to teach the world, it would be that larger portions have more calories," she says. "I wish this were as intuitive as it sounds, but it's not."

14 units of alcohol a week for women, 21 for men

Most of us who are old enough to drink probably still think of the 14/21 units per week rule, but the official recommendations are now subtly different. Men should not exceed three to four units per day; for women, it's two to three. The adjustment, says Dr Sarah Jarvis of Drinkaware, was to shift people's perception that they could somehow save up all their units for a big drinking session at the end of the week.

Jarvis believes the official recommendations are still the best advice, if you can stick to them. "The problem is, people fundamentally misunderstand the difference between short-term tolerance and long-term harm. If you drink every day, you might not feel that six units makes you particularly drunk, but that doesn't mean you're less susceptible to damage in the long-term."

Even though we know that a drink no longer amounts to a single unit, Jarvis says we still tend to underestimate the amount we're drinking, particularly at home. "A unit of wine is 110ml, which looks teeny. No one pours that," she says. "It's more likely that if you have a couple of large glasses of wine at home, you'll be having somewhere in the region of six units, which is classified in the league of binge-drinking. That's the level at which we see an increase in physical symptoms such as raised blood pressure, as well as violent behaviour."

8 hours' sleep a night

For every person who will tell you that Margaret Thatcher got by on four hours a night, a study will show that the average person needs between seven and nine hours of sleep to function well. If you regularly average less than seven hours, then you have an increased risk of depression, diabetes and heart problems. But sleeping for more than nine hours a night has also been associated with an increase in the likelihood of physical and mental-health issues.

Myths about our sleep abound. Is every hour of sleep before midnight worth more than the hours after? There's little evidence to support this, although one study showed that people performed better when they'd had more sleep after midnight, contradicting the myth. Do you need to get your sleep in one block? Again, this may not be true. Some historians believe that "segmented sleep" used to be the norm. Roger Ekirch made a study of sleep throughout the ages in his book At Day's Close, and found many references in different languages to a "first" and "second" sleep. People would get up between the sleeps, and use the time to pray, reflect on their dreams, have sex or even visit neighbours. Dr Thomas Wehr of the US Institute of Mental Health asked patients to spend a month living without artificial light. By the end of his experiment, the patients had all fallen into a pattern of sleeping for three or four hours, waking for an hour or so then sleeping for another four hours or so, and they reported never having felt so rested. What is almost certainly important, though, is going through the different stages of the sleep cycle, from light, to "slow wave", to REM (the average person goes through about four or five sleep cycles of 90-120 minutes a night). If your sleep is constantly interrupted, your body may not be reaching the right state of sleep it needs in order to repair itself.

30 minutes' exercise, 5 times a week

Despite our 2012 Olympic summer, a report from Sport England found that the number of adults playing traditionally popular sports such as football, rugby and squash has fallen in the past year.

You've probably heard that the recommended amount of exercise is half an hour's moderate aerobic activity at least five times a week. The official guideline from the Department of Health is at least 150 minutes a week, so it suggests you break it up into five half-hour sessions. But, within that, there are other suggestions. On two days or more a week, your physical activity should include strengthening exercises that work all the major muscle groups. Oh, and instead of 150 minutes of moderate exercise, you could do 75 minutes of vigorous intensity activity, "such as running or a game of singles tennis" (plus your muscle strengthening). Or, if you like, you can do a mix of the two. Not exactly catchy, is it?

"Sometimes messages are refined for the sake of making them more accurate, but it means people can't always remember what they are," Nuffield's Mike Rayner says. "These things only need to be changed lightly and only when they are overwhelmingly out of date."

Even if you're meeting the recommended quota, it will only count for so much if you then drive to work and sit at a computer for nine hours. A review by the American Journal of Clinical Nutrition conceded that the average of 30 minutes daily "may be insufficient to prevent unhealthful weight gain for some, perhaps many, but probably not all, persons".

2 hours a day screen time for children

Given the amount of panic there is about children watching TV, playing computer games or going online, there is surprisingly little research into the long-term effects of screen time. That's not to say studies don't exist, but they are scattered and the quality of the sample sizes and data gathered varies. This is also an area where the research we do have is likely to be sensationalised (such as the claim, in 2009, by Dr Aric Sigman that the isolation caused by social networking sites could give you cancer).

It's widely accepted that being sedentary for too long contributes to physical health problems – although no one worries whether children are reading for more than two hours a day – so the more difficult question to answer is: should we limit screen time to protect our children's emotional health?

In August this year, Public Health England, a government body, published a briefing that analysed a number of existing datasets on children's wellbeing. It included research from the Millennium Cohort Study, which collected reports from the mothers of 11,000 children in the UK at age five, and then again at seven, making it one of the largest data samples available. That study found that watching TV for three hours or more at age five predicted a 0.13 point increase in behaviour problems at seven, but there was no link between playing computer games and behaviour problems, and "no associations were found between either type of screen time and emotional symptoms, hyperactivity/inattention, peer relationship problems or prosocial behaviour".

So, instead of worrying that our children's attention spans are shrinking, should we marvel at the way the new generation of digital natives effortlessly parse information on their phones and start online uprisings that change the world? It's probably too early to tell.

"The field is so new, it is rash to draw conclusions, either apocalyptic or utopian, about how the internet is changing our brains," says Clive Thompson, author of the recently published Smarter Than You Think. Rather than hunt for a definitive answer, we have to use our own judgment about what's best for our children – and for ourselves.

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