A thermodynamic system consisting of a single phase, in the absence of external forces, in its own state of internal thermodynamic equilibrium, is homogeneous. This means that the material in any region of the system can be interchanged with the material of any congruent and parallel region of the system, and the effect is to leave the system thermodynamically unchanged. The thermodynamic operation of scaling is the creation of a new homogeneous system whose size is a multiple of the old size, and whose intensive variables have the same values. Traditionally the size is stated by the mass of the system, but sometimes it is stated by the entropy, or by the volume. For a given such system Φ, scaled by the real number λ to yield a new one λ Φ, a state function, X (.), such that X (λ Φ) = λ X (Φ), is said to be extensive. Such a function as X is called a homogeneous function of degree 1. There are two different concepts mentioned here, sharing the same name: (a) the mathematical concept of degree-1 homogeneity in the scaling function; and (b) the physical concept of the spatial homogeneity of the system. It happens that the two agree here, but that is not because they are tautologous. It is a contingent fact of thermodynamics.