unattainability

Unattainability describes a state in which a goal or value cannot be achieved under a given set of constraints. It is the opposite of attainability and is used across disciplines to denote that certain targets are forever out of reach within the relevant system, whether due to physical laws, logical limits, or practical obstacles.

In physics and thermodynamics, unattainability often arises from fundamental limits. A classic example is the unattainability of absolute zero, as stated by the third-law form known as the Nernst unattainability principle, which holds that cooling to exactly 0 kelvin requires infinite steps. Unattainability also appears in measurement and control limits, such as the precision limits implied by quantum mechanics or in idealized states that cannot be prepared without disturbance.

In mathematics and engineering, unattainability can refer to limits of optimization problems where the optimum value cannot be realized by any feasible solution, or is only approached in the limit (for example, asymptotic bounds or discrete constraints). It can also describe models that assume perfect information or instantaneous signals, which in practice cannot be achieved.

In philosophy and ethics, unattainability is used to describe ideals that are valued but cannot be fully realized given human nature or social conditions, prompting discussions about aspiration, practicality, and reform. The concept helps distinguish what is impossible by the structure of a system from what is merely difficult or economically costly.