Where does distortion collide?

An optical aberration in which the magnification of an image changes across the field of view, so that straight lines in the scene appear curved, bowing outward as barrel distortion or inward as pincushion distortion. Seidel's 1856 Zur Dioptrik derived the five primary aberrations of a lens system, of which distortion is the one that shifts image points without blurring them, and later optical texts kept his classification as the standard account. The referent is a geometric defect of an imaging system, measured as a percentage shift of image position, and it has nothing to do with a loss in an economy, a fidelity measure in a code, or an error in a person's thinking.[1]

Unit

One imaging system's geometric warp, given as percent distortion at the field edge

Recovery means

Correctable in software by remapping pixels, or reduced by lens design

Measured by

Measured as the percentage displacement of image points from their ideal positions, often on a grid target

A departure of a market from the allocation that would use resources efficiently, so that prices no longer equal marginal social cost and some feasible gains from trade go unrealised. Pigou's 1920 The Economics of Welfare traced such losses to a divergence between private and social value, arising from taxes, monopoly, or effects on third parties, and Lipsey and Lancaster's 1956 The General Theory of Second Best named these deviations distortions and showed that removing one while others remain need not improve welfare. The referent is a gap between an actual and an efficient economic outcome, measured as lost welfare, and it is unrelated to a warped image, a coded signal's error, or a biased thought.[2][3]

Unit

One market's departure from efficiency, scaled as lost welfare

Recovery means

Reduced by corrective taxes, subsidies, or removing the underlying wedge

Measured by

Estimated as deadweight loss, the welfare triangle between supply and demand at the distorted quantity

A quantitative measure of how far a reconstructed signal departs from the original when information is compressed and cannot be sent perfectly. Shannon's 1948 A Mathematical Theory of Communication introduced the idea of transmitting a source relative to a fidelity criterion, and his 1959 Coding Theorems for a Discrete Source with a Fidelity Criterion defined a distortion measure and the rate-distortion function that gives the fewest bits needed to hold average distortion below a chosen bound. The referent is an expected numerical difference between a source and its reproduction, measured in units such as mean squared error, and it is not a warped image, a loss to an economy, or a faulty belief.[4][5]

Unit

One expected distortion value between a source and its reproduction

Recovery means

Lowered by spending more bits, tracing out the rate-distortion curve

Measured by

Computed as an average of a distortion measure such as mean squared error over source symbols

A systematic error in thinking that leads a person to interpret events in a negative, inaccurate way, such as overgeneralising from one setback or reading disaster into an ambiguous remark. Beck's 1963 Thinking and Depression identified these recurring errors as cognitive distortions in depressed patients, and his 1976 Cognitive Therapy and the Emotional Disorders made correcting them central to treatment. The referent is a habitual bias in an individual's reasoning, identified from thought records and self-report, and it bears no relation to a warped image, a welfare loss in a market, or a fidelity measure in a code.[6][7]

Unit

One habitual pattern of biased thinking in a person

Recovery means

Addressed in cognitive therapy by testing and reframing the thought

Measured by

Identified through thought records, clinical interview, and self-report inventories