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A Dimension, in the mathematical sense, is any direction in which a point can be moved.

A two dimensional plane has 2 directions: up/down, left/right (diagonals are not counted as dimensions)

A three dimensional plane has up/down, left/right, forward/backward

Scientists currently work with the model that we live in 4 dimensional space: up/down, left/right, forward/backward, past/future (3 spatial dimensions +1 dimension of time)

However, there are scientific models (such as string theory) which have more than 4 dimensions.

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