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Dimensions have units of distance! Movement is a change in distance in time, with units of speed, not distance, so movement is not directly a dimension. However, movement times time is a distance and in that sense movement defines the fourth dimension as r=ct where r is the fourth dimension, a real dimension composed of the speed of light c and time t, r is a distance.

The other three dimensions of the Universe are not real dimesnions they are vector dimensions meaning that they are displacements, Ix + Jy + Kz where I,J and K are unit vectors defining directions. Vectors I,J and K have the property that their square is a negative one, I^2 = J^2 = K^2 = -1.

A point in four dimensional Universe is p= r + Ix + Jx + Kz = r + V, (r for real and V for vector). Time is expressed in p= ct + Ix + Jy + Kz = ct + V, this point is mathematically called a Quaternion, invented by Willaim Rowan Hamilton in 1843, before the idea of four dimensional spacetime (Einstein, 1905).

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