Where does forcing collide?

Thistlethwaite and Campbell's 1960 Regression-discontinuity analysis introduced a design in which units receive a treatment only when a measured score crosses a fixed cutoff, so that comparing units just above and just below the threshold estimates the treatment's effect. In modern econometrics that score is called the forcing variable, the running score whose value alone decides who is treated (Lee & Lemieux, 2010). Here forcing names a data column in an observational study, the quantity that pushes a case onto one side of a boundary, and it has nothing to do with a proof method in logic or a perturbation of the planet's heat budget.[1][2]

Unit

One observation's value on the assignment score relative to the cutoff

Recovery means

Not applicable

Measured by

Recorded as the running score, with the treatment effect estimated from the jump in outcomes at the cutoff

Paul Cohen's 1963 The independence of the continuum hypothesis introduced forcing, a method for extending a model of set theory by adjoining a carefully controlled new object, so that a target statement can be made to hold or fail in the enlarged model. Building on the constructible universe of Gödel, forcing let Cohen prove that the continuum hypothesis can be neither proved nor disproved from the standard axioms, and it became the central tool for independence results in mathematical logic. In this field forcing is a construction on formal structures, unrelated to a variable that assigns treatment in a study or to an energy imbalance driving the climate.[3]

Unit

A single forcing construction over a given model of set theory

Recovery means

Not applicable

Measured by

Carried out as a proof, verifying which statements hold in the extended model

Hansen, Sato, and Ruedy's 1997 Radiative forcing and climate response defined radiative forcing as an externally imposed change in the balance between incoming solar energy and outgoing heat at the top of the atmosphere, measured in watts per square meter. A positive forcing, such as added carbon dioxide, traps heat and warms the surface until the balance is restored, and putting different influences on this common scale lets them be ranked by their warming power. Here forcing is a physical quantity of energy flux acting on the whole planet, not a statistical cutoff variable or a model-building step in set theory.[4]

Unit

A change in net energy flux at the top of the atmosphere, in watts per square meter

Recovery means

The surface warms or cools until outgoing heat rebalances the imposed change

Measured by

Computed from radiative transfer models and observations of greenhouse gases, aerosols, and solar output