Monthly Archives: July 2017

Natural Knack for Numbers

In Oliver Sacks’ book ‘The Man Who Mistook His Wife for a Hat’ he describes the behaviour of two twins, John and Michael, who had been previously diagnosed as “autistic, psychotic and severely retarded”. What he observed in them, on the other hand, was closer to genius. Their mathematical abilities were so outstanding and unusual that they still provoke questions about our own innate mathematical ability.

Completely incapable of performing simple addition or subtraction, and lacking any concept of multiplication or division, these twins had an extraordinary ability to ‘feel’ or ‘see’ numbers. For example, Sacks recalls an occasion in which both twins said the number 111 aloud when a box of matches fell to the floor. On counting, it was realised that this number had been present in the box. The twins even repeated ‘37’ three times, showing recognition of this as a factor, despite their inability to perform any calculations.

The abilities of the twins also extended to other areas of maths, for example, listing prime numbers of twenty figures or telling the week day of any given date!

This is clearly unusual. For most people, using maths in everyday life is somewhat of a bugbear. Even figuring out the date of next Wednesday can cause a mild headache, let alone a date years into the future. However, we do have some mathematical capability that is seemingly not learnt through school. Children as young as five months have been shown to have an understanding of addition (study by Karen Wynn, University of Arizona). This experiment also relied on attention-grabbing Mickey Mouse dolls, as babies are not exactly known for their mathematical interest. The innate ability to see numbers is known as subitization, but, for most of us, applies only to embarrassingly small quantities.


A further way of learning about mathematical understanding comes from cultural studies. I can’t remember the day on which the chanting of times tables began. Having been drilled into my head so early, since so far back in childhood, I can’t imagine a life without these concepts. For all I know, they could have always been sitting there in my mind, a natural thinking process.

Through studying societies where education and language differ, we can reveal surprising truths about our own abilities and how they arise:
Do we rely on language for mathematical thinking?
Do we have the ability to see numbers?
What about numerical patterns?
Or geometry?

The Mundurukú are an Amazonian tribe, living an isolated life in the forest with a rich culture, full of traditions. Their terminology for numbers is extremely limited, only reaching up to 5, with even some of these words appearing to translate to rough estimates, such as four-ish. So how does this affect their lifestyle and understanding? It’s easy to think of language and arithmetic as separate capabilities and people often consider themselves talented at one but not the other, however we rarely think about the way in which they interact. We now understand that human babies and other animals use this rough estimation of numbers, named ‘analogue representation’, rather than exact counting, which is only demonstrated by older humans. For example, when Pica showed Mundurukú individuals different numbers of dots on a screen, their answers were wildly different from those given in the west, for example the number 5 was identified only 28% of the time. It is the innate number recognition ability, differing from our counting system, that is reflected in the Mundurukú language.

Pica himself also provides a fascinating case study of the way in which numerical language can influence culture. On returning from his studies of the tribe he experienced extreme culture shock, having lost track of numerical concepts, causing great problems with timekeeping, among other things.

A further study of this same tribe has revealed findings related to geometry; a concept completely absent from their language. The study, however, found that their ability matched that of US children, suggesting that understanding images such as right angles and equilateral triangles was unaffected by language. Geometric understanding therefore seems to extend more widely across cultures, being less dependent on language. Other studies have also found that young children and tribes have a greater ability to recognise ratios and plot logarithmic scales, than carry out stepwise counting in the way we are accustomed to.

These results may be interpreted from an evolutionary perspective. In the natural environment, we perhaps rely on recognising ratios and rough estimations of numbers. This allows us to, at a flash, recognise which patch of berries it might be more profitable for us to collect etc. An understanding of geometry can be highly beneficial in navigation and other activities. Our style of numeracy, on the other hand, does not have a place in this lifestyle. It is only in modern routines, where exact counting of minutes, pennies or G&Ts has become a necessity.

The Man Who Mistook His Wife for a Hat
Alex’s Adventures in Numberland



Blue Zones – Healthy, Happy and Spreading

Live to 100, stay healthy and skip the meds! Dan Buettner has led research into the five locations where people around the world live longest, remaining healthy:
-Sardinia, Italy
-Okinawa, Japan
-Loma Linda, California
-Nicoya Peninsula, Costa Rica
-Ikaria, Greece


What secrets can be learnt from these 5 ‘Blue Zones’ with the longest lived residents? Could studying these locations have revealed any keys to extending life expectancy?
Teams of researchers have investigated common factors shared among these residents in search for possible answers. The lifestyle factors that have been highlighted are referred to as the ‘Power 9’:

Well who would have guessed? Although it is in no way surprising that exercise is good for your health, it is interesting to note that high intensity exercise rarely features in the daily lives of these individuals. Their exercise is incorporated into daily routines, often in an enjoyable way and as a necessity. This is exercise in a style far different from a rushed gym session which may often be considered to make up for an otherwise sedentary day.

2.Fullness vs satisfaction
Sopping eating when nearing fullness is a practise encouraged in many diets for weight loss. This practice appears to be commonly followed in these locations, being partially responsible for maintenance of a healthy weight. The Okinawan mantra ‘Hara hachi bu’ captures this tradition precisely, reminding them to stop eating when feeling only 80% full. It seems that culture here is a huge factor promoting healthy dietary habits.
A further unusual routine shared among these locations is to eat the smallest and final meal of the day in the afternoon or early evening, therefore leaving an extended period of fasting overnight compared to most societies. Intermittent fasting has recently received a large amount of both research and media attention. Several studies have linked this to preventing and reversing obesity, as well as related metabolic issues. For example, a paper published in Cell Metabolism 2014 reported that fasting for at least 12 hours in mice resulted in them remaining healthier and lower in weight than others, despite their calorie intake remaining the same. The optimal way to practice of intermittent fasting is still under debate, for example low calorie days vs overnight fasts. Evidence also exists to suggest that to boost the benefits, fasting should be combined with high intensity exercise on an empty stomach.

3.Fresh and fibrous
The majority of these individual’s diets consist of fresh fruit, veg and wholegrains. Beans and nuts are also regularly eaten as a protein source, with meat and fish only being consumed in moderation in most areas. Residents of Loma Linda, however, are pescetarian, avoiding meat all together. Nuts are a popular snack, adding a wide variety of vitamins and minerals to the diet.

4.Dine with wine!
Opinions on the relationship between alcohol and health seem to swing almost daily in the media, largely fuelled by the intense interest among readers.

“Half a glass of wine a day ‘can increase breast cancer risk’”
“drinking tequila is good for your bones, science says”
“drinking wine engages more of your brain than solving maths problems”
“drinking a pint of beer a day linked to reduced risk of a heart attack”

People’s relationship with alcohol in the Blue Zones is far different from that in many societies, however this gives us no reason to encourage abstinence. In four of these locations, alcohol is regularly consumed in moderation, for example 1-2 glasses of wine per day. In Sardinia the preference is for cannonau wine, which is high in antioxidants and polyphenols which are known to be preventative of many diseases.

5.Tackling Stress
Although stress may be inevitable in any life circumstances, an important feature of lives within Blue Zones is routine practices to reduce stress, for example, happy hour in Sardinia, napping in Ikaria and preying in Loma Linda by seventh day Adventists. Chronic stress is associated with many inflammatory diseases and is therefore linked to many of the problems experienced in old age.

6.Family Time
Forming close relationships with loved ones is an essential part of life in these locations. This comes in many forms, such as commitment to a single partner, love and care for children and also valuing aging relatives. Older members of the family are, in general, respected and looked after within the family home. Other studies have separately investigated the effects of social structure on mortality. For example, a paper published in the Journal of Health and Social Behaviour found a lower likelihood of death among individuals with social ties with relatives, friends and the community. This can even be as simple as the influence of loved ones in promoting healthy behaviours, such as eating habits or quitting smoking etc.

In these areas 258 out of 263 centenarians belong to a community of shared faith. Membership in these communities involves attendance of services and other activities which help promote a sense of belonging. The association between sense of community-belonging and health has also been noted in other studies, such as of self-reported health in Canadian citizens in 2002.

“Ikigai” in Okinawa and “plan de vida” are both terms used to describe a person’s reason for waking up. In 2014 a study was led by UCL of 9050 people in England, measuring eudemonic wellbeing (related to sense of purpose and meaning in life). A key finding was that eudemonic wellbeing is associated with increased survival. 29.3% of people in the lowest wellbeing quartile died during the study period, compared to 9.3% of the highest quartile. It is estimated that those with highest eudemonic wellbeing live an average of 2 years longer. Sense of purpose has often been highlighted as important to happiness, which is further associated with lower risk of death. Just having a reason for living is therefore implicated in increasing life expectancy.

9.Positive Influence
Healthy habits are contagious. Carrying out these dietary and exercise routines, as well as holding these values is simply part of the culture in certain social groups. Close friendships within these societies are an encouragement to continue with these life-lengthening customs.

Lifestyles in each of these zones revolve around simplicity, compared to modern standards. The stress and rush of modern lifestyles, leaving little time for exercise and, quite literally, a need for “fast” food, might be inevitable in most societies, but also responsible for all kinds of chronic illnesses with which they are plagued.

The Blue Zones Project
The findings of the Blue Zones research is now being applied to help new communities adopt healthier behaviours and live longer. Taking inspiration from these healthy and happy areas, the project aims to make changes to the environment which will encourage residents to live out more of these 9 practices.
Policies have been transformed, such as encouraging dietary changes and preventing smoking. The food available to the community, from restaurants and supermarkets has also been altered in accordance with the recommendations made from the original Blue Zones. Infrastructure changes have also been made to public spaces and homes to encourage people to exercise more and eat less. The formation of strong relationships, sense of community, finding purpose and stress management are also key to these schemes.

For example, the Blue Zones Project has already begun in three communities of Southern California: Redondo Beach, Hermosa Beach and Manhattan Beach. Within two years, a 14% decrease in obesity and 30% decrease in smoking was already apparent. Exercise has also been on the increase, for example through the organisation of morning activities and walking school busses in Manhattan Beach community.

The main findings of Dan Buettner’s research is detailed in several books, such as ‘The Blue Zones’, ‘The Blue Zone Solution’ and ‘Thrive’.

References and Further Reading:
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