Where does shadow collide?

In Carl Jung's analytical psychology, the shadow is the part of a person's psyche that the conscious self will not recognise: the traits, impulses, and memories pushed out of awareness because they clash with the self-image a person wants to hold. Jung carried the idea through his work from his early writings (On the Psychology of the Unconscious, 1917) to its fullest account in Aion (1951), where a chapter is given to it and confronting the shadow is treated as a step toward becoming whole. Here the shadow is a hidden layer of one human mind, not the marginal worth of a scarce resource, a region a rendering engine marks as unlit, or a dark patch in the image of a collapsed star.[1][2]

Unit

One person's disowned psychic content, described qualitatively

Recovery means

Not applicable

Measured by

Explored through analysis of dreams, projections, and slips rather than a numeric scale

In economics, a shadow price is the amount by which the best achievable outcome would improve if a binding limit were loosened by one unit: the implicit worth of a scarce resource that carries no posted market price. Leonid Kantorovich set out the idea in 1939 in his work on planning production (translated in Management Science in 1960), where such implicit valuations fall out of the optimisation itself, and Dorfman, Samuelson, and Solow's 1958 Linear Programming and Economic Analysis fixed the term in Western economics. This shadow is a number attached to a constraint in a model, unrelated to a buried part of the mind, a computed dark region on a screen, or the silhouette of a black hole.[3][4]

Unit

A change in the objective per one-unit relaxation of a constraint, in the objective's units

Recovery means

Not applicable

Measured by

Read off as the dual variable or Lagrange multiplier when an optimisation problem is solved

In computer graphics, a shadow is the set of surfaces a light source cannot reach because something blocks the path, computed so that a rendered scene looks lit correctly. Lance Williams's 1978 paper Casting Curved Shadows on Curved Surfaces introduced shadow mapping: the scene is first drawn from the light's own viewpoint to record how far the nearest surface lies in each direction, and any later point farther away than that recorded distance is treated as shadowed. This shadow is a per-pixel occlusion test inside a renderer, not a hidden part of a personality, the worth of a scarce input, or a dark feature in a telescope image.[5]

Unit

A set of occluded surface points, resolved per pixel or per fragment

Recovery means

Not applicable

Measured by

Determined by comparing each point's distance from the light against a stored depth map rendered from the light

In astronomy, the shadow of a black hole is the dark central region an observer sees in the glow around it, left because light rays that pass too close are captured and never reach the eye, so a rim of bent light surrounds an apparent void larger than the event horizon. Falcke, Melia, and Agol named and predicted it in 2000 for the black hole at the centre of our galaxy, and in 2019 the Event Horizon Telescope Collaboration published the first image of such a shadow, around the black hole in the galaxy M87. This shadow is a feature of light bending near collapsed matter, measured as an angle on the sky, not a repressed part of the mind, a valuation on a constraint, or an occlusion test in a renderer.[6][7]

Unit

An angular diameter of the dark region on the sky, in microarcseconds

Recovery means

Not applicable

Measured by

Imaged by very long baseline interferometry at radio wavelengths and compared with general-relativistic predictions