I think people sometimes think of dimensions as some other realms where there are fantastic things and whatnot. I think to get back down to earth a little, you should think of dimension as something that explains where you are. We exist in 4 dimensions and to explain the exact location of yourself at a point in time, you need to explain it by those 4 dimensions. If you imagine there being coordinates for everywhere in the universe, then in theory you could give your position by x, y, z coordinates and the point of time which for me now could be about ~15:41 on june 23rd 2009.
Some particles behave differently and are unpredictable when viewed or measured from those 4 traditional dimensions. Then you can start to think wether there is one or more other dimensions you need to know about before you can fully understand and predict them.
However, I don't think it means that we or these particles can potentially or occasionally exist in wonderful realms where humans can exist with 12 copies of their chromosomes. I'd love to see some logic behind this stuff, though. If this passes for pseudo scince, then the "pseudo scientists" should be embarassed, possibly more than usual.
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