Articles

Understanding uncertainty: ESP and the significance of significance

In March 2011 a highly respected psychology journal published a paper claiming to provide evidence for extra-sensory perception (ESP). The claim was based largely on the results of a very common statistical procedure called significance testing. The experiments provide an excellent way into looking at how significance testing works and at what's problematic about it.
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Understanding the unseenWhen NASA first decided to put a man on the Moon they had a problem: once the Apollo spacecraft was in flight, they would not be able to observe its exact location and neither would they be able to predict it using physics. How could they send astronauts to the Moon if they didn't know where they were? An ingenious mathematician came up with an answer.
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The quest to simplifyString 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.
Taking on a 10-D Universe with 8-D mathsA 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.
synthesiser
Kaluza, Klein and their story of a fifth dimensionSpace 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.
The ten dimensions of string theoryString 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?
Why the answer to any sum is 10Learning 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.
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Mixing doublesAndy Murray and Laura Robson made a good team at London 2012, bringing home silver in the mixed doubles. But how do you make sure that the competing pair is the best you can pick from the team?
The logic of drug testing London 2012 vowed to be the cleanest Olympics ever, with more than 6,000 tests on athletes for performance enhancing drugs. But when an athlete does fail a drug test can we really conclude that they are cheating? John Haigh does the maths.
Schrödinger's equation — what does it mean?

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?
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Schrödinger's equation — in action

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.
Schrödinger's equation — what is it?In the 1920s the Austrian physicist Erwin Schrödinger came up with what has become the central equation of quantum mechanics. It tells you all there is to know about a quantum physical system and it also predicts famous quantum weirdnesses such as superposition and quantum entanglement. In this, the first article of a three-part series, we introduce Schrödinger's equation and put it in its historical context.