I don=92t understand something that is very basic. In Geometric Algebra/ Clifford Algebra I don=92t understand why the scalar in an M vector is not considered a dimension as the vectors are. My confusion comes from three different viewpoints, each of which show the scalar to be a vector: 1. Complex numbers separate the real and imaginary numbers and assign each a dimension such that the number 3+4i is plotted as 3 units in the X direction and 4 units in the Y direction. Yet adding two more complex dimensions =96 j and k, give us three not four dimensions plus a scalar. An example is a quaternion used for rotations in 3D graphics which is considered as being 3D plus a scalar which is zero dimension. 2. So a scalar is said not to be a vector because it has magnitude but no direction and so can=92t be a reference vector in a coordinate system. However, the radial direction in circular and spherical coordinates can be represented by a scalar and is considered a dimension. 3. In a 1D system, magnitude alone represented by a scalar is sufficient to give a position. Multiplying by i gives a 90 degree rotation and a 2D space represented by a complex number (see 1 above). What am I missing?