The origin of the concept of a molecular complex between oxygen and hemoglobin can be traced to Stokes, a century and a half ago. Subsequently, physicochemical concepts of equilibria provided a path to quantitative formulations of these ligand-receptor interactions. Then, it took a quarter of a century before a proper format was prepared in terms of four stoichiometric equilibria and their associated binding constants. Since then, experimental measurements of these stoichiometric binding constants have consistently disclosed that successive values of K(1) to K(4) are accentuated above those expected if every subunit of hemoglobin maintained the same, intrinsic, unchanging affinity for oxygen. An alternative analysis of the observed cooperative interactions has been obtained by extracting the roots of the polynomial of the stoichiometric binding equation and deriving an alternative binding equation containing constants that for O(2)-Hb are complex numbers. These constants have the dimensions and properties of equilibrium constants. They provide some novel phenomenological insights into ligand-receptor equilibria.