Three dimensions are needed to specify the centre of the object. Three more are required to specify location and position of the object in motion. Spin groups whose dimension are square root of that vector in n-dimensional space give four more dimensions.A particle is treated as of dimension 0 and a brane as of dimension 1 as some dimensions curl up.There is a spending symmetry from degrees of freedom, then holding distributivity there is an impact grading with k* algebra. With affine space and no preferred origin, the gamma starts time flow and alpha is dimensionless, as in string theory.Applying to capital asset pricing , a positional scalar inhibits the length of vector and beta determines the risk and the range of shape of yield curves.

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