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In mathematics, two non-zero real numbers a and b are said to be commensurable if their ratio a / b is a rational number; otherwise a and b are called incommensurable. (Recall that a rational number is one that is equivalent to the ratio of two integers.)
Two concepts or things are commensurable if they are measurable or comparable by a common standard.. Commensurability most commonly refers to commensurability (mathematics). ...
In ethics, two values (or norms, reasons, or goods) are incommensurable (or incommensurate, or incomparable) when they do not share a common standard of measurement or cannot be compared to each other in a certain way. There is a cluster of related ideas, and many philosophers use the terms differently. On one common usage:
In 1962, Thomas Kuhn and Paul Feyerabend both independently introduced the idea of incommensurability to the philosophy of science. In both cases, the concept came from mathematics; in its original sense, it is defined as the absence of a common unit of measurement that would allow a direct and exact measurement of two variables, such as the prediction of the diagonal of a square from the ...
The distortion changes the band structure, in part splitting the bands up into smaller bands that can be more completely filled or emptied to lower the energy of the system. This process may not go to completion, however, because the substructure only allows for a certain amount of distortion. Superstructures of this type are often incommensurate.
The history of aperiodic crystals can be traced back to the early 20th century, when the science of X-ray crystallography was in its infancy. At that time, it was generally accepted that the ground state of matter was always an ideal crystal with three-dimensional space group symmetry, or lattice periodicity.
If the new periodicity is a rational fraction or multiple of the lattice constant, the density wave is said to be commensurate; otherwise the density wave is termed incommensurate. A sketch in k-space of a (001) section of the Fermi surface of Cr.
Occupational stress can occur when workers do not feel supported by supervisors or coworkers, feel as if they have little control over the work they perform, or find that their efforts on the job are incommensurate with the job's rewards. [2]