Where does trajectory collide?

The path traced through space by a moving body under the forces acting on it, most famously the curved flight of a projectile shaped by its launch velocity and by gravity. Galileo's 1638 Dialogues Concerning Two New Sciences showed that a projectile, once released, follows a parabola, combining a steady horizontal motion with a uniformly accelerated fall. The referent is a geometric curve in physical space, fixed by initial conditions and forces, and it is not a person's path through life, a modeled curve of change over time, or the advancing edge of a technology.[1]

Unit

One body's path through space, as a curve of position over time

Recovery means

Not applicable

Measured by

Predicted from launch velocity, angle, and the forces acting, and observed by tracking position over time

A long-term sequence of the states and roles a person moves through over the lifespan, such as a work career, a family path, or a sequence of health states, shaped by timing, by earlier events, and by the historical setting. Elder's 1998 The Life Course as Developmental Theory set out the trajectory as a central idea, a line of development marked by shorter transitions and turning points along the way. The referent is a person's ordered path through social roles across years, not the flight of a thrown object, a statistical curve fit to data, or the path a technology follows.[2]

Unit

One person's sequence of roles or states across the lifespan

Recovery means

Not applicable

Measured by

Traced with longitudinal life histories and panel data on roles, timing, and transitions

A modeled path of change in some measured attribute over time, estimated from repeated measurements and often summarized as a smooth curve or as a small set of typical curves within a population. Nagin's 1999 Analyzing developmental trajectories: A semiparametric, group-based approach gave a method that sorts individuals into groups, each with its own estimated trajectory of change. The referent is a fitted mathematical curve describing how a variable moves over time, not a projectile's flight, a lived path through social roles, or the advance of a technology.[3]

Unit

One estimated curve of a measured attribute against time

Recovery means

Not applicable

Measured by

Estimated from repeated measures by growth-curve or group-based trajectory modeling

The cumulative direction of improvement that a technology follows within an established way of framing its problems, so that progress runs along a shared line rather than in all directions at once. Dosi's 1982 Technological paradigms and technological trajectories defined the trajectory as the pattern of ordinary problem-solving carried out inside a technological paradigm. The referent is the direction a field of technical work advances over time, set by a paradigm and by economic pressures, not a body's flight through space, a person's path through life, or a curve fit to data.[4]

Unit

One line of cumulative technical advance within a paradigm

Recovery means

Not applicable

Measured by

Traced through patents, performance metrics, and the pattern of successive improvements in a technology