Backreaction: The cube of physical theories
To our best present knowledge these constants are indeed constant, but you can imagine varying them and ask what happens to the theory then. In many cases this corresponds to some physical limit. For example, if your theory contains terms in v/c, where v is velocity, then the limit of velocities small compared to c (i.e. non-relativistic) formally corresponds to taking c to infinity, ie 1/c to zero.
To unite classical and statistical thermodynamics you need Boltzmann’s constant, as stated in the comments- a tesseract rather than a cube. Thermodynamics plus the Beckenstein bound is GR. Is one of the four a dependent variable? (x,y,z,t) naïvely should be fit with three.
http://en.wikipedia.org/wiki/Bekenstein_bound
http://en.wikipedia.org/wiki/Theodore_Jacobson
We live in a world of infinite possibilities. Theory enumerates what is interesting, experiment discloses what is useful. Science is observed fact being observably factual.