## Plus Blog

December 13, 2011
Maths is a creation of our brains, so how come it describes the world around us so amazingly well? How is it that ideas from pure maths suddenly find real-world applications decades or even centuries after their discovery? Here are some articles exploring the "unreasonable effectiveness" of mathematics. When it comes to describing natural phenomena, mathematics is amazingly — even unreasonably — effective. This article looks at an example of strings and knots, taking us from the mysteries of physical matter to the most esoteric outpost of pure mathematics, and back again. It has often been observed that mathematics is astonishingly effective as a tool for understanding the universe. But why should this be? Is mathematics a universal truth, and how would we tell? The philosophy of applied mathematics We all take for granted that mathematics can be used to describe the world, but when you think about it this fact is rather stunning. This article explores what the applicability of maths says about the various branches of mathematical philosophy. |

December 12, 2011
You might not have thought it, but while you sit contentedly digesting your turkey and gazing at the telly, your brain is keeping up the hard work, making sure that everything in your body goes according to plan. And to understand this most amazing of nature's creations you need maths. Here are some of our favourite articles on brains, human and animal. Saying that someone is a chaotic thinker might seem like an insult, but, as this article shows, it could be that the mathematical phenomenon of chaos is a crucial part of what makes our brains work. Catching sight of a cockroach tends to make us behave chaotically, what with the running and screaming and throwing of shoes. But it appears that chaos might actually explain how we, and the cockroach itself, behave. The human brain faces a difficult trade-off. On the one hand it needs to be complex to ensure high performance. On the other hand it needs to minimise what you might call wiring cost — the sum of the length of all the connections — because communication over distance is metabolically expensive. It's a problem well-known to computer scientists. And it seems that market-driven human invention and natural selection, faced with similar challenges, have come up with similar solutions. Uncoiling the spiral: Maths and hallucinations Think drug-induced hallucinations, and the whirly, spirally, tunnel-vision-like patterns of psychedelic imagery immediately spring to mind. But it's not just hallucinogenic drugs that conjure up these geometric structures. People have reported seeing them in near-death experiences, following sensory deprivation, or even just after applying pressure to the eyeballs. So what can these patterns tell us about the structure of our brains? And you can find out more about mathematics and the biomedical sciences in our package Do you know what's good for you?. |

December 11, 2011
It may be Sunday but that's no excuse for resting your brain. The podcast: Does quantum physics really describe reality? With counterintuitive ideas such as superposition and entanglement, quantum mechanics doesn't seem to resemble reality as we know it, yet quantum physics is an incredibly successful theory of how the physical world operates. Flying home with quantum physics Quantum mechanics is usually associated with weird and counterintuitve phenomena we can't observe in real life. But it turns out that quantum processes can occur in living organisms, too, and with very concrete consequences. Some species of birds use quantum mechanics to navigate. Studying these little creatures' quantum compass may help us achieve the holy grail of computer science: building a quantum computer. You can also listen to the accompanying podcast. When it comes to the science of the very small, strange things start happening, and our intuition ceases to be a useful guide. Plus finds out about the crazy quantum world, and spin that a politician would die for. String theory: From Newton to Einstein and beyond Over the last few years the words string theory have nudged their way into public consciousness. It's a theory of everything in which everything's made of strings. Find out how these tiny strings offer hope for reconciling quantum mechanics with Einstein's theory of relativity. One of the many strange ideas from quantum mechanics is that space isn't continuous but consists of tiny chunks. Ordinary geometry is useless when it comes to dealing with such a space, but algebra makes it possible to come up with a model of spacetime that might do the trick. Quantum mechanics say that some physical processes are fundamentally random. The perfect set-up for a lottery! |

December 10, 2011
What would Christmas be without the unlimited eating? And even though you can't taste it, there's plenty of maths in food. Here's some yummy examples. Researchers are asking for a serve of fuzzy logic with their pizza. How risky is your daily bacon butty? Whenever you smell the lovely smell of fresh coffee or drop a tea bag into hot water you're benefiting from diffusion. Now researchers have finally found experimental confirmation for the most important concept underlying diffusion theory. Take a dive into the rather smelly business of digesting food, and how a crazy application of chaos theory shows the best way to digest a medicinal drug. More on the fluid mechanics of food travelling through the intestines |

December 9, 2011
With the weather cold and the nights very dark, it's the perfect time to curl up in front of the fire and do some philosophising. Here are some of our favourite articles on mathematics and the nature of truth ... or lack of it! Searching for the missing truth Many people like mathematics because it gives definite answers. Things are either true or false, and true things seem true in a very fundamental way. But it's not quite like that. You can actually build different versions of maths in which statements are true or false depending on your preference. So is maths just a game in which we choose the rules to suit our purpose? Or is there a "correct" set of rules to use? We find out with the mathematician Hugh Woodin. Read more... In the 1930s the logician Kurt Gödel showed that if you set out proper rules for mathematics, you lose the ability to decide whether certain statements are true or false. This is rather shocking and you may wonder why Gödel's result hasn't wiped out mathematics once and for all. The answer is that, initially at least, the unprovable statements logicians came up with were quite contrived. But are they about to enter mainstream mathematics? Read more... This is not a carrot: Paraconsistent mathematics Paraconsistent mathematics is a type of mathematics in which contradictions may be true.
In such a system it is perfectly possible for a statement If you like mathematics because things are either true or false, then you'll be worried to hear that in some quarters this basic concept is hotly disputed. This article looks at To read more about maths and philosophy, have a look at our package Mathematics and the nature of reality. |

December 8, 2011
We do love our many-legged friends and we know they're not just for Christmas. In fact, they're not only cute they have a whole lot of maths in them too. Here are our favourite animal articles. How does the uniform ball of cells that make up an embryo differentiate to create the dramatic patterns of a zebra or leopard? How come there are spotty animals with stripy tails, but no stripy animals with spotty tails? Read more... Finding your way home without knowing where you are Foraging ants have a hard life, embarking on long and arduous trips several times a day, until they drop dead from exhaustion. The trips are not just long, they also follow complex zig-zag paths. So how do ants manage to find their way back home? And how do they manage to do so along a straight line? Their secret lies in a little geometry. Read more... England's performance in the 2010 World Cup was thankfully overshadowed by the attention given to Paul the octopus, who was reported as making an unbroken series of correct predictions of match winners. David Spiegelhalter looks at Paul's performance in an attempt to answer the question that (briefly) gripped the world: was Paul psychic? Read more... Will an infinite number of monkeys with typewriters eventually produce the complete works of Shakespeare? Read more... Not all the animals we love are real: some are generated by computers, but they have us cooing with cuteness or trembling with terror nevertheless. Here's how they are made. Read more... Here's more about our six-legged friends, showing that having a small brain doesn't stop you from doing great things. Read more... |