Dimensional symmetry seems to follow a rule of the senses. For one dimension of U(1) gauge symmetry, there are the positive and negative senses. For SU(2) gauge symmetry, there are the east sense, the west sense, the north sense, and the south sense. For SU(3) gauge symmetry, there are the top-front-right sense, top-front-left sense, top-back-right sense, the top-back-left sense, bottom-front-right sense, bottom-front-left sense, bottom-back-right sense, and bottom-back-left sense. In other words, 3 dimensions have 8 distinct senses.

The rule for higher dimensions can be expressed as the n-power of 2. 2°=1 for zero dimension, 2=2 for 1 dimensions, 2=4 for 2 dimensions, 2=8 for 3 dimensions, 2=16 for 4 dimensions. This last is exactly the number of elements in the metric tensor of general relativity. If these elements represent 1st power mass and energy then U(1) represents electron and positron, SU(2) represents photon, W+, W-, and Z0 (however, this is a broken symmetry since W± and Z0 are massive while photon is massless), SU(3) represents the 8 massless gluons. O(4) orthogonal real symmetry would then represent 16 distinct types of graviton but none was ever detected. The difference between complex unitary (U), complex special unitary (SU), and real orthogonal (O) symmetry matrices is that the first two can have elements that are real, complex, or imaginary while that of O-symmetry matrices can be real including zero elements. Nevertheless, a true rule of the sense must be made of square matrices of positive definite elements without zeros.