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We propose a new systematic method of studying correlations betweenparameters that describe an astronomical (or any) physical system. We recallthat behind Dimensionless scaling laws in complex, self-interacting physicalobjects lies a rigorous theorem of Dimensional analysis, known widely as theBuckingham theorem. Once a {\it catalogue} of properties and forces that definean object or physical system is established, the theorem allows one to select acomplete set of Dimensionless quantities or {\it Numbers} on which structuremust depend. The internal structure takes the form of a functionally definedmanifold in the space of these Numbers. Simple and familiar examples arediscussed by way of introduction. Correlations in properties of astronomicalobjects can be sought either through the constancy of these Numbers or betweenpairs of the Numbers. In either case, within errors, the functional dependencestake on an absolute numerical character. As our principal application, we studya well defined sample of galaxies in order to reveal the implied Tully Fisherand Baryonic Tully Fisher relations. We find that $L\,\propto\,v_{rot}^4$ forthe former and $M_b\,\propto\,v_{rot}^3$ for the latter, suggesting that theserelations may have different causal origins.

A `Numbers' Approach to Astronomical Correlations I: Introduction and Application to galaxy Scaling Relations