The concept of physical and fractal dimension I. The projective dimensions

The projective dimensional analysis based on the projective extension of scaling group and projective dimensional function is presented. We study the notion of self-similarity based on the physical quantities and not on topology. The projective analog of the classical theorem-π has been formulated in terms of (projective) numerical invariants. The additivity dimensions replacing fractal dimension are briefly discussed. Intuitive examples illustrate presented ideas.