mathematical reality

This book tells the fascinating story of strange geometric objects that have achieved some fame outside of maths and even inspired a Woody Allen joke: they're called Calabi-Yau manifolds. When Plus recently interviewed one of its authors he was adamant that maths should be brought to the masses without dumbing down or glossing over the tricky parts. And this is just what this books sets out to achieve.

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. And as Plus found out at a recent conference, studying these little creatures' quantum compass may help us achieve the holy grail of computer science: building a quantum computer.

The words quantum physics are usually associated with the weirder end of physics, including strange phenomena like superposition or quantum entanglement, the "spooky action at a distance" as Einstein called it. But it turns out that quantum mechanical processes occur in living systems too. Some species of birds use quantum mechanics to navigate and studying how they do it might actually help us with building quantum computers.

Quantum physics is a funny thing. With counterintuitive ideas such as superposition and entanglement, it doesn't seem to resemble reality as we know it, yet quantum physics is an incredibly successful theory of how the physical world operates. Plus attended the conference Quantum Physics and the Nature of Realtiy at the University of Oxford in September 2010. We spoke to Andrew Briggs, John Polkinghorne, Nicolas Gisin, David Wallace, Roger Penrose and Andrea Morello about how we can resolve the mysteries of quantum physics with our experience of reality. And we find out why quantum physics is just like riding a bike...

Benoît Mandelbrot, the father of fractal geometry, died last Thursday at the age of 85. Born in Poland in 1924, Mandelbrot had dual French and American citizenship and spent most of his working life in the US. He died of cancer in a hospice in Cambridge, Massachusetts.

Well, it goes to no-one because there isn't a Nobel Prize for maths. Some have speculated that Alfred Nobel neglected maths because his wife ran off with a mathematician, but the rumour seems to be unfounded. But whatever the reason for its non-appearance in the Nobel list, it's maths that makes the science-based Nobel subjects possible and it usually plays a fundamental role in the some of the laureates' work. Here we'll have a look at two of the prizes awarded this year, in physics and economics.

The human brain faces a difficult trade-off. On the one hand it needs to be complex to ensure high performance, and on the other it needs to minimise "wiring cost" — the sum of the length of all the connections — because communication over distance takes a lot of energy. It's a problem well-known to computer scientists. And it seems that market driven human invention and natural selection have come up with similar solutions.

One of the amazing things about life is its sheer complexity. How can a bunch of mindless cells combine to form something as complex as the human brain, or as delicate, beautiful and highly organised as the patterns on a butterfly's wing? Maths has some surprising answers you can explore yourself with this interactive activity.

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It is thought that the next great advances in biology and medicine will be discovered with mathematics. As biology stands on the brink of becoming a theoretical science, Thomas Fink asks if there is more to this collaboration than maths acting as biology's newest microscope. Will theoretical biology lead to new and exciting maths, just as theoretical physics did in the last two centuries? And is there a mathematically elegant story behind life?

Researchers have unveiled the first prototypes of robots that can develop emotions and express them too. If you treat these robots well, they'll form an attachment to you, looking for hugs when they feel sad and responding to reassuring strokes when they are distressed. But how do you get emotions into machines that only understand the language of maths?
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