forcing

Forcing has multiple meanings depending on context. It is used across science, mathematics, and social discourse to describe the act of causing change by external input or pressure.

In physics, a force is an interaction that changes motion; forcing a system means applying such an interaction, causing acceleration per Newton's second law. External forces can be modeled as body forces or contact forces. In differential equations and fluid dynamics, forcing refers to an external input that drives the system, such as gravity, electromagnetic forces, or a prescribed velocity field.

In mathematics, forcing is a method used to prove that certain statements are independent of a given axiomatic system. Introduced by Paul Cohen, forcing involves extending a model of set theory by adding a generic filter to a partially ordered set (forcing notion). The resulting forcing extension can satisfy different propositions (for example, the continuum hypothesis) while preserving consistency with the original axioms. Forcing is a central technique in set theory and has many variants, including proper forcing, ccc forcing, and boolean-valued models.

In social and political contexts, forcing denotes coercive pressure to compel a person or group to act in a certain way, often through threats, punishment, or manipulation. This sense highlights power dynamics and ethical/legal concerns.

In all uses, forcing contrasts with voluntary action or internal causation; it describes an external input or pressure that produces change in a system, behavior, or belief.