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Apiological: mathematical speculations about bees (Part 3: Travelling Salesman)

This is part 3 of a three-part series of mathematical speculations about bees. Part 1 looked at honeycomb geometry, and part 2 looked at how bees estimate nest volumes.

The sight of bumblebees roaming around British gardens, foraging for nectar, is common and comforting. The movement of these fuzzy bees between flowers and plants can often seem deliberate yet erratic. Charles Darwin was intrigued by “humble-bee” routines, and observed them with the assistance of his six children, but always regretted not attaching strands of cotton wool to the bees so he could follow them more easily.

Within the last decade there has been renewed interest from a number of collaborating researchers into studying bumblebees’ movement between flowers and their foraging techniques. The prevailing journalistic spin on this research seems to be ‘Bees solve the Travelling Salesman Problem – a problem that mathematicians and computers cannot solve’. This is unfortunate, not least because it is gleefully misleading, confusing various meanings of ‘solve’, but also it obscures a lot of the fascinating underlying scientific investigations.

π and The Simpsons

Simpsons-Packshot white mini

In “The Simpsons and Their Mathematical Secrets”, I documented all the mathematical references hidden in the world’s favourite TV show. Look carefully at various episodes, you will spot everything from Fermat’s last theorem to the Riemann hypothesis, from the P v NP conjecture to Zorn’s lemma.

All these references are embedded in the show, because many of the writers have mathematical backgrounds. To temper their nerdy enthusiasm, the general rule was that they could include as much mathematics as they fancied, as long as it was well hidden or only visible for a fraction of a second (a so-called freeze-frame gag).

However, if the mathematical reference is not particularly obscure, then it can be included at the heart of the action, and can even be included in the actual dialogue. π, of course, falls into this category, because everyone learns about it in school.

There are at least ten π references in “The Simpsons”, and here are my top three favourites, in reverse order:

Apiological: mathematical speculations about bees (Part 2: Estimating nest volumes)

This is part 2 of a three-part series of mathematical speculations about bees. Part 1 looked at honeycomb geometry.

Honeybees scout for nesting sites in tree cavities and other nooks and crannies, and need to know whether a chamber is large enough to contain all the honey necessary to feed their colony throughout the winter. A volume of less than 10 litres would mean starvation for the whole colony, whereas 45 litres gives a high chance of survival. How are tiny honeybees able to estimate the capacity of these large enclosed spaces, which can be very irregular and have multiple chambers?