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Triple-Twisted Möbius and Ant Foraging

Two recent news stories that involve mathematics...yes, despite a previous rant on this website, math stories do make the news.

First, a research team from the University of Jyväskylä (Finland) and the University of Kiel (Germany) announced their construction of a triple-Möbius molecule (i.e. annulene), the "most twisted fully conjugated molecule to date."

I assume you know what a single twisted Möbius molecule would look like; the much harder-to-visualize triple-twisted Möbius molecule still has only one side but resembles the well-known recycling logo...but with three twisted corners. The researchers note that their constructions are "merely scientifically intriguing topological objects and far from practical application" but have future promise in the areas of molecular electronics and optoelectronics.

The second news story involves an argument that ants are capable of complex problem-solving strategies that suggest optimization techniques. Though an individual ant walks in random directions when searching for food, the same is not tyrue when viewing the the collective food-search behaviours of ants. That is, a definite order or pattern efficiently emerges from the apparent chaos.

The key factor seems to be the ants' nest, which they need to return to...and which totally random movements would prevent. As described by the Chinese-German research team, there seem to be three stages of the complex feed-search movements of an ant colony: (1) scout ants circle around in a chaotic manner, looking for food, (2) when an ant finds some food, it carries a tiny piece of it to the nest and leaves a trail of a scent-emanating substance called pheromones, (3) other ants follow that trail to find the food and bring some of it home.

The mathematical key is that the last step involves some initial chaos because the trail scent is weak but due to the large number of ants and their separate ways in retrieving food and leaving new scents, an optimal path to the food source is eventually established.

Why care? The researches claim that their mathematical model of ant movement applies to other animals (e.g. Albatrosses) and "behavioral patterns of humans in areas as diverse as the evolution of web services and smart transportation systems."

So there...mathematics is in the news! Share it!

Source: ScienceDaily.com, May 26, 2014