Multi-dimensional space - and dance
In Flatterland* the 'Spacehopper' explains that a bicycle has seven dimensions:
The Spahehopper nudged the bicycle handlebars through a small angle. "There - a fourth dimension!"
"But you just moved it in three dimensions."
"Yes, but it has changed shape - if it had stayed the same shape, you could make it fit its current position by rigid motion."
"So if it has moved through a new dimension, in which direction does that dimension point?"
"The turn-the-handlebars direction." said the Spacehopper "Different from the turn-the-front-wheel direction and the turn-the-back-wheel direction and the turn-the-pedals direction. That makes seven dimensions in all."
So every time we change shape, we enter a new dimension. Dance is a truly multi-dimensional art-form.
* Flatterland (Like Flatland only more so) by Ian Stewart
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