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mathematical reality
Travelling Salesman is an unusual movie: despite almost every character being a mathematician there's not a mad person in sight. Moreover, the plot centres on one of the greatest unsolved problems in mathematics. We were lucky enough to speak to the writer/director Tim Lanzone about creating drama from mathematics.
It's not often the very first person you meet in a movie is a mathematician. The second, third and fourth people on screen also being mathematicians is even rarer. But the movie Travelling Salesman is a rare movie: not only are almost all of the characters mathematicians, the central plot also hinges on the solution of one of the most important problems in mathematics.
A team of physicists have curbed the hope that quantum physics might be squared with common sense. At least if we want to hang on to Einstein's highly respected theory of relativity. Their result concerns what Einstein called "spooky action at a distance" and it may soon be possible to test their prediction in the lab.
String theory predicts there are more than the familiar four dimensions of space-time. But where do those extra dimensions come from? Eva Silverstein is looking for the answer.
A bizarre set of of 8-dimensional numbers could explain how to handle string-theory's extra dimensions, why elementary particles come in families of three... and maybe even how spacetime emerges in four dimensions.
Space is three-dimensional... or is it? In fact, we are all used to living in a curved, multidimensional universe. And a mathematical argument might just explain how those higher dimensions are hidden from view.
String theory has one very unique consequence that no other theory of physics before has had: it predicts the number of dimensions of space-time. But where are these other dimensions hiding and will we ever observe them?
The laws of symmetry are unforgiving, but a team of researchers from the US have come up with a pattern-producing technique that seems to cheat them. The new technique is called moiré nanolithography and the researchers hope that it will find useful applications in the production of solar panels and many other optical devices.
Learning mathematics involves a progression to higher and higher concepts, building on the foundations of what we have already learnt. But Andrew Irving and Ebrahim Patel explain that no matter how high your mathematical knowledge reaches you must never lose sight of your foundations, no matter how basic they may seem.
In the first article of this series we introduced Schrödinger's equation and in the second we saw it in action using a simple example. But how should we interpret its solution, the wave function? What does it tell us about the physical world?
In the previous article we introduced Schrödinger's equation and its solution, the wave function, which contains all the information there is to know about a quantum system. Now it's time to see the equation in action, using a very simple physical system as an example. We'll also look at another weird phenomenon called quantum tunneling.