Where does dynamics collide?

In music, the aspect of a piece concerned with loudness and how it changes over time, from soft to loud, marked by terms and signs such as piano, forte, and crescendo. Thiemel's 2001 entry Dynamics in the Grove dictionary of music traces how composers came to notate graded and shifting levels of volume as an expressive dimension of a work. The referent is the intensity of sound in performance, an expressive and notational category, and it has nothing to do with motion under physical force, the forces at play inside a social group, or a rule that evolves a mathematical state.[1]

Unit

A notated or performed level of loudness, such as piano or forte

Recovery means

Not applicable

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Marked in a score by terms and signs like p, f, and crescendo, and realised as changes in the intensity of the performed sound

The processes and forces that operate within a social group and shape how its members think, feel, and act together, including cohesion, conflict, leadership, and change. Lewin's 1947 Frontiers in Group Dynamics in the journal Human Relations treated the group as a whole held in tension by interdependent social forces, borrowing the language of fields and forces from physics to model the life of a group. The referent is a pattern of social and psychological forces among people, described by analogy to physical force rather than by literal mechanics, and it is distinct from Newtonian motion, musical loudness, or a mathematical rule of change.[2]

Unit

The pattern of forces acting within a group taken as a whole

Recovery means

Not applicable

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Studied by observing group behaviour, mapping the interdependence of members, and, in Lewin's field theory, modelling the forces in the group's life space

The mathematical study of systems that change over time according to a fixed rule, where the object of interest is the long-run behaviour of trajectories through a space of possible states: fixed points, cycles, attractors, and chaos. Smale's 1967 survey Differentiable dynamical systems in the Bulletin of the American Mathematical Society helped organise the modern, geometric theory of such systems. The referent is an abstract rule of evolution and the shape of the paths it generates, applicable to any changing quantity, and it should not be confused with the physical forces of mechanics, the loudness of music, or the forces within a social group.[3]

Unit

A system's trajectory through its state space under a fixed rule

Recovery means

Not applicable

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Analysed through the geometry of trajectories in state space: fixed points, attractors, measures of stability, and the onset of chaos