The Pauli exclusion principle is the quantum mechanical concept that no two identical particles in all the Universe may occupy the same quantum state simultaneously. What does that mean, exactly? Well, for starters, it means that the butterfly effect has nothing on the consequences of the Pauli exclusion principle.
In this clip from BBC's A Night With the Stars, theoretical physicist Brian Cox uses the tenets of the exclusion principle to illustrate the interconnectedness of the Cosmos, in a demonstration that is at once elegantly straightforward and utterly mind-boggling.
UPDATE: Shock of shocks, it turns out the subtleties of quantum physics cannot always be summed up in neat, 90 second television segments — not even by the magnificent Brian Cox. Long story short: the physics in Cox's explanation are a bit off. Flat out wrong, even. Fortunately for all of us, Discover's Sean Carrol has put together a lengthy (albeit accessible and clarifying) explanation of where Cox went astray. You can check it out here.
And yes, this is from the same program wherein Cox recruits Simon Pegg and Jim Al-Khalili to demonstrate why atoms have so much empty space. What's that you ask? Why doesn't America have hour-long television specials hosted by science rockstars and attended by world-famous celebrities from the spheres of science and entertainment? That's a damn good question.