If there's one bit of maths you remember from school it's probably Pythagoras' theorem. But what's a Pythagorean triple? How many triples are there and how do you find them? And what about quadruples, quintuples, sextuples....
In the previous article we looked at a psychological study which claims to provide evidence that certain types of extra-sensory perception exist, using a statistical method called significance testing. But do the results of the study really justify this conclusion?
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.
When 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.
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.