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While no scientific theory is ever (or should be) closed to controversy, the answer currently accepted by most Physicists (thanks to Einstein) is that the fourth dimension is time, or that time is the way we experience the fourth dimension.

It depends on your concept of what exactly is a dimension. Initially dimension, as a concept, was determined by a measured displacement or finite movement. Typically one experiences going from Point A to Point B, as a change in placement. As one travels, some x amount of distance has been covered, the same is true of time, as it has passed as the distance was traveled. Typically in math the number of dimensions available, is only limited by your computer and you imagination. But I digress, dimensions are about how many perpendicular lines can cross at any one Point. Volume and space are words that describe 3D type dimensional concepts. The 'D' in 3D stands for 'dimension'. We all know up and down, left and right, and forward and reverse. So then, what else is there, in a linear displacement type distance environment?

The definition : hyper- pref. 1. Over; above; beyond: hypercharge. 2. Excessive; excessively; relates more to your question, and in terms of Extension that Creates Dimension, 'Hyperspace' is a more correct Label for the 4th dimension.

In Hyperspace, one can have four lines intersect at one point, each perpendicular to the others.

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