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How many dimensions are there, and what do they do to reality?

Reading this article is the closest I have ever come to understanding what is meant by having more than four dimensions.

Imagine… you are an ant living on a long, very thin length of hose. You could run along the hose backward and forward without ever being aware of the tiny circle-dimension under your feet. Only your ant-physicists with their powerful ant-microscopes can see this tiny dimension.