Infinity is a pain. Its paradoxes easily ensnare the unsuspecting
reasoner. So over the centuries,
mathematicians have carefully constructed
bulwarks against its predations.
But now cosmologists have developed
theories that put them squarely outside
the mathematicians' "green zone" of
Remember Frank Lampard's disallowed goal in the 2010 World Cup match against Germany? The ball hit the crossbar, landed well behind the line but then bounced out again. And it all happened too quickly for the ref to spot it was a goal. How these kind of (non)-goals happen and what can we do about them?
Horses, like all animals, have a number of different gaits. But how can they perform these complicated leg movements without having to stop and think? And why do they switch to a new gait when they want to go faster? Mathematics can shed some light on these questions.
A simple question to ask about kayak races is whether having lots of paddlers helps or slows the boat down? The kayak with two paddlers has twice as many "engines" to power it but it also has twice as much weight to drag through the water. Which is the dominant factor?
Does it pay to be nice? Yes, it does. And we're not just talking about that warm fuzzy feeling inside, it pays in evolutionary terms of genetic success too. We talk to Martin Nowak about how the mathematics of evolution prove that being nice is unavoidable.
It does pay to be nice if you repeatedly deal with the same person. Martin Nowak explains why cooperation also wins in matters of reputation, neighbourliness and family. But can evolutionary game theory save the world?