Elasticity as a mathematical concept finds its origin in mechanical physics. Mechanical physics describes macroscopic features of the universe, how forces such as friction and gravity can morphologically alter the structure of physical items. It defines stress, strain, and other forms of mechanical deformation and their properties. Elasticity refers to a property wherein a body can be distorted to some degree and still retain some salient characteristic, however that characteristic is defined, and be able to return it to its original state. This suggests a maintenance of relationship. Typically, elasticity applies to spatial distortion that nonetheless maintains some relationship between two points in the system being distorted. Jelly, rubber and spandex offer everyday examples. However, there will be a point, as a material endures multiple or extreme distortions, at which it will not be able to return to it original shape and either remains in a distorted state or breaks at the point of most strain such as an elastic band that snaps at the limit of its stretching capacity.
Loss of elasticity may affect the system as a whole. With the loss of elasticity, there is a global change in a structural state (so the concept of a global state variable would apply) that changes the nature of the material. However, it does not always strictly apply to the whole system. It may take place locally, as with a sharp edge, area of impurity, or other site. However, in that case our focus is on a system within a system. In metal fatigue a small crystallized area will have, within the metal matrix, a modulus of elasticity different from that of the rest of the system. However, with certain qualifications (e.g. a very short length scales such as the context of molecular structure) it is fair to speak about the crystallized area as an entirely separate system and to ignore the surrounding metal.
Language can be shown to behave similarly. Elasticity in language is lost over time. Early instances of a vocable can be thought of as the stage of the system before its extension is stretched. Later instances correspond to a system that has stretched to the point of structural change and has lost its elasticity. Because we are interested in changes in language, we focus on the aspects of the system that become structurally different. We turn to physics as we enquire about the specific ways in which these changes occur in physical systems. 4.2