News from the world of maths

The death toll from wars around the globe in the second half of the twentieth century should be increased by a factor of three, according to a recent mathematical study by Ziad Obermeyer and colleagues at the Institute for Health Metrics and Evaluation in Seattle, Washington.

Estimating a war death toll is usually done by a mixture of eyewitness reports and media coverage. This involves extrapolating large numbers from sketchy data — read more about how this is done in the Plus article Body count.

Uppsala University in Sweden, and the Peace Research Institute in Norway, both keep death toll records estimated from media coverage, but Obermeyer's study suggests that the recorded death toll for 20th century wars could have been up to three times higher than they record.

The researchers looked at the death toll estimates gathered by the World Health Organization (WHO) — these numbers are extrapolated from telephone interviews with individuals with family members who may have died. This method is considered to be more accurate than gathering information from media reports.

In most cases, the WHO surveys recorded much higher numbers of dead than the Norwegian and Swedish databases. For example, the WHO figures suggest that more than twice the number of people died in Vietnam than previously thought — currently recorded at two million. On average, across 12 countries, the WHO figures are three times bigger. If true, then the average annual death toll for wars between 1985 and 1994 was 378,000.

During the 50 years covered by the study, Obermeyer suggests that there were 269,000 deaths in Bangladesh and 141,000 in Zimbabwe — nearly five times more than previously thought — and conflicts in Sri Lanka, Bosnia, Georgia and Laos are also estimated to be more costly than previously thought. However, in other countries, such as Burma, Ethiopia, Guatemala, Namibia and The Philippines, the death tolls dropped.

The study also found that a controversial report in 2006, which estimated the death toll after the invasion of Iraq at 655,000, may have been an over-estimate. You can read more about this study in the Plus article Body count. Obermeyer revises this number down to 184,000.

One downside of the study is that it only counts conflict fatalities and not deaths that have arisen from infectious diseases, which often afflict poor countries after war.

No matter how many friends you have on Facebook and MySpace, you won't have more real-life friends than the average person. Using mathematics to model online social networks is an evolving field, with techniques that have been used to model human interaction, such as network modelling, moving into the online world. Users of online social networks tend to build up long lists of "friends" with whom they only occasionally interact, if at all. Given that we can maintain more weak relationships online than we can in real-life, it is an interesting question to ask whether or not online social networks create as many close friendships as in real life. According to Will Reader of Sheffield Hallam University, the answer is no, and in this there is an interesting scientific and social point to be found.

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If we are to believe the latest signs from outer space, the local aliens are keen mathematicians. A new crop circle appeared on the 1st of June this year in a barley field near Barbury Castle in Wiltshire, England, measuring 150 feet in diameter and correctly representing the first 10 digits of the irrational constant pi.

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Issue 47 of Plus is our biggest issue ever and a mathematical showcase! Not only are we bringing you the best young writing talent with the winners of the Plus new writers award, but we are overloaded with features about the ways maths influences and shapes our lives. We investigate the overlap between the arts and maths, find out why mathematicians are always portrayed as mad in the movies, and learn about the nature of infinity and of prime numbers. We also challenge 118118 with some mathematics, uncover the mathematics of surprise and respond to recent newspaper reports that maths is no longer relevant. There are also all our usual puzzle and teacher package.

And if you want to give you eyes a break, tune your ears into our podcast, with 3 new episodes out today.

More information:

The 2008 Plus new writers award has been run and won. This year's competition saw an exceptional standard of writing. The winning entries include biographies of two of the greatest mathematicians of the last 100 years, as well as articles on the mathematics of Google, ants that do maths, why we should (or should not) woo brunettes, the dangers of probing the infinite, and joining the mathematical mile-high club...

We are releasing 3 new podcast episodes in conjunction with the stories in this issue:

1. Podcast 11, June 2008: Catching waves
   The magical Fourier transform;
2. Podcast 10, June 2008: Maths in the Movies
   The maths film festival at the Edinburgh science festival;
3. Plus Careers Podcast 2, June 2008: Exhibition Curator
   Exhibition design is not a career that the mathematically inclined tend to think about, let alone pursue.

Happy reading from Plus!

A damning new report into maths education blames an over-politicised system for narrow teaching, uninterested students and demotivated teachers.

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Mathematics is used in interesting, and often less than accurate, ways. Newspapers present graphs showing apparently correlated variables, but with a little thought, some of the time you will find that whilst it looks like two variables are connected, there is actually no cause and effect. An unscrupulous media can draw connections where they don't exist for political ends and politicians have been known to confuse cause and effect entirely. So what really is behind the rise in oil prices? Could it be the humble game of cricket?

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A boomerang has been thrown in space, and lo and behold, it returns to its thrower, just like on Earth.

Japanese astronaut Takao Doi threw the boomerang on request from world boomerang champion, compatriot Yasuhiro Togai onboard the International Space Station.

"I was very surprised and moved to see that it flew the same way it does on Earth," Doi was quoted as saying in the Mainichi Shimbun.

Thanks to wawawamovie for the following video of the boomerang.

If you would like to read more about the physics of throwing a boomerang (and why it is no surprise that it should fly in microgravity as long as there is air), read the Plus article Unspinning the boomerang. And to make your own boomerang, read the Plus article Bang up a boomerang.

Mathematicians are known to be good musicians. Here is a mathematical parody of the Gloria Gaynor song, "I will survive". I particularly like the lyrics:

It is one of my favourite times of year, and I'm not even European.

The Eurovision Song Contest to Australians is a strange mix of bad 80s music, songs about "joy", "love" and "unity", amazingly good-looking hosts, scantily dressed Eastern Europeans and reality TV winners from Western Europe.

But another reason I love it is because it is about politics and maths. For the first time in my life, living in the UK, I get a chance to vote for the winner and watch it live instead of having to ignore radio reports (of course it's all over the news) till the Sydney Sunday evening replay.

The voting of Eurovision is a complex interaction of politics and voting blocks. Each country votes in a popular vote, in which they cannot vote for themselves, and each country has equal voting power. Voting is often based on politics — Cyprus and Greece nearly always exchange votes — and I can remember the days when Ireland and the UK were similarly connected. On the other hand, France does not vote for the UK and the Balkan states have mixed allegiances.

Eurovision is a perfect example of what mathematicians call a complex system. This consists of a group of objects (countries) which interact with each other (by giving each other points for their songs), and this interaction can be tracked over time. A statistical analysis of the system can then give some insight in the nature of the interaction. For example, it can show whether certain countries form cliques that always vote similarly, or whether a country's voting is largely "in tune" with that of the whole group.

Some time ago a team of Oxford scientists performed statistical tests to see whether the voting behaviours of different countries are in some way related. In every statistical test you need a "control experiment" to compare your results to. Suppose, for example, that two countries always seem to vote the same way. Then, before you can deduce that their musical tastes are indeed related, you need to show that the two countries vote the same way significantly more often than would happen in a song contest in which the countries' voting is truly independent. To create such a control experiment, the team simulated a "random song contest", in which each country assigns its points randomly to 10 other countries. They then compared the results of all their tests to the random contest.

One such test involves seeing whether voting relationships between countries persists over time. If, for example, country A gives and/or receives points from another country B over a long period of time, then we can deduce that in some way the musical tastes of the two countries are related. Carrying out the same analysis between country A and all other countries in turn will show whether or not country A is "in tune" with the rest of Europe.

Another test observes the number of countries to which a given country A has awarded points and from which it has also received points. If a country has many such "reciprocal links", then one might deduce that its musical taste harmonises well with that of Europe in general.

The remaining tests were devised to identify cliques of countries whose voting behaviour is correlated. For example, the team checked to see whether two countries that have both received and/or awarded points to a third country are likely to give or receive points from each other.

And the results of the study? Well, you'll just have to read our Plus article United Kingdom - twelve points for more information on the statistical tests, and don't forget to vote!

Maths in the movies is obviously in vogue these days.

The following video comes from Triple J in Australia, and is a nice summation of how maths has been used as a tool for plot development over the years.

Thanks to Marc Fennell, the host of the show, for the permissions.