Mathematics

When ants go exploring in search of food they end up choosing collective routes that fit statistical distributions of probability, according to a team of mathematicians who analyzed the trails of a species of Argentine ant.  It's unknown how flocks of birds, shoals of fish, lines of ants and other complex natural systems organize themselves so well when moving collectively so researchers from Spain and the U.S. analyzed the movements of Argentine ants (Linepithema humile, an invasive species in many parts of the world) while they forage or explore an empty space (a petri dish) and then…

It took human culture millennia to arrive at a mathematical formulation of non-Euclidean spaces - but that was not because of a limitation of our brains.  Instead, it's likely that even the brains of rodents get there very naturally every day. Euclidean geometry is the kind of geometry we normally study at school, whereas non-Euclidean geometries are all those that reject one or more of Euclid's five postulates. A geometry that unfolds on a curved surface is an example. Recent research has investigated how the brain encodes flat spaces and in 2005, Edvard and May-Britt Moser discovered…

There is not the slightest doubt that the the universe is real. It is three-dimensional. But one popular alternative notion has been the "holographic principle", which asserts that a mathematical description of the universe only requires two dimensions. What we perceive as three dimensional may just be the image of two dimensional processes on a huge cosmic horizon.  Up until now, this speculation has only been mathematically analyzed in exotic spaces with negative curvature. Math, like any language, can talk about lots of things that are not possible and such spaces are quite different…

The famous sunspots on the surface of the Earth's star result from strong magnetic fields. Their numbers are an important indicator of the state of activity on the Sun. At the Institute of Nuclear Physics of the Polish Academy of Sciences in Kraków, Poland, researchers have been conducting multifractal analysis into the changes in the numbers of sunspots and found that the graphs were asymmetrical in shape, suggesting that sunspots may be involved in unknown physical processes. Mathematical analysis of multifractals provides invaluable information on the dynamic phenomena, as they occur to…

One cornerstone of the Science 2.0 approach is the framework for making Big Data manageable. In fields from physics to biology, it's no longer a question of obtaining data, but managing it in ways that are relevant. It's been problematic in science just as it has been in business and the public sector because relationships between the different parts of a network have been represented as simple links, regardless of how many ways they can actually interact, and that results in a loss of valuable information in science. The Science 2.0 approach has advocated representing multilayer…

By Peter Gwynne, Inside Science – From raisins to fingerprints, and from tree bark to the surface of the brain, wrinkles appear throughout nature. But scientists have struggled to explain how wrinkles form. Now two independent research teams at the Massachusetts Institute of Technology in Cambridge have developed key insights into the process. One group has developed a mathematical theory, confirmed experimentally, that predicts how wrinkles take shape on curved surfaces. The other explains in more general terms how layered materials form different types of wrinkly patterns. Taken together,…

Many people have heard of the Golden Ratio, a ratio that is the midpoint between asymmetry and symmetry - when "the whole is to the larger as the larger is to the smaller". In numerical terms, it is 1.618.  Mark Barr used the Greek letter Φ (phi) to represent it and that has stuch. Because it is inherently pleasing to us, stairways, buildings, paper sizes and lots of other things use Φ in their designs. In music, the octave, fifth, and major and minor sixths are ratios of consecutive numbers of the Fibonacci sequence, making them the closest low integer ratios to the golden ratio.…

Pi Day – on March 14th – will be particularly memorable this year: the date can be written 3/14 by those who opt for the month then day format, which is Pi to two decimal places, 3.14. If you include the year this year then that gives 3/14/15, which is Pi to four decimal places, 3.1415. This happens only once a century, and the Museum of Mathematics in New York City, among others, is taking Pi Day 2015 one step further, by celebrating at 9:26 pm, adding three more digits to Pi, 3.1415926. You can personally celebrate the event 12 hours earlier at 9.26 am, wait a further 53 seconds to get 3.…

Why do people cooperate? This isn’t a question anyone seriously asks. The answer is obvious: we cooperate because doing so is usually synergistic. It creates more benefit for less cost and makes our lives easier and better. Maybe it’s better to ask why don’t people always cooperate. But the answer here seems obvious too. We don’t do so if we think we can get away with it. If we can save ourselves the effort of working with someone else but still gain the benefits of others’ cooperation. And, perhaps, we withhold cooperation as punishment for others’ past refusal to collaborate with us. Since…

It's that time of year - the NCAA tournament, called "March Madness", when office pools all across the United States have people researching teams and reading predictions to try and optimize their chances of winning money by predicting basketball games. They are, sadly, doomed to fail. Last year, Warren Buffett offered $1 billion for a perfect winning bracket, but the highest scoring bracket among ESPN.com subscribers was still 18 games off - and those people pay to know sports. Yet each year people will try again. Like with the lottery, people try even when there is no realistic chance of…