Look closer...
Extra dimensions that are so small we can't see them - sounds pretty hard to get your head around.But maybe it's not - imagine an ant crawling on a hose. From a distance, the hose looks like a line - with just one dimension. But close up, you see that the ant can move from side to side, as well as along the hose - it can travel in two dimensions.
So if we look closer at particles, we might see them moving in extra dimensions.
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