Modified large number theory with constant G

The inspiring ''numerology'' uncovered by Dirac, Eddington, Weyl, et al. can be explained and derived when it is slightly modified so to connect the ''gravitational world'' (cosmos) with the ''strong world'' (hadron), rather than with the electromagnetic one. The aim of this note is to show the following. In the present approach to the ''Large Number Theory,'' cosmos and hadrons are considered to be (finite) similar systems, so that the ratio R-bar/r-bar of the cosmos typical length R-bar to the hadron typical length r-bar is constant in time (for instance, if both cosmos and hadrons undergo an expansion/contraction cycle: according to the ''cyclical big-bang'' hypothesis: then R-bar and r-bar can be chosen to be the maximum radii, or the average radii). As a consequence, then gravitational constant G results to be independent of time. The present note is based on work done in collaboration with P.Caldirola, G. D. Maccarrone, and M. Pavsic