Definition

1. Adjective:
   • Capable of being measured by a common standard: Refers to two or more quantities that can be compared or measured using the same unit or standard, implying a shared basis for measurement.
   • In mathematics: Specifically refers to numbers or quantities that have a common measure; that is, their ratio can be expressed as a rational number (a ratio of integers).

Usage Examples

• General Use:
  • The concepts of justice and fairness are not always commensurable, as they can be interpreted differently.
  • For a valid comparison, the economic outputs of the two countries must be commensurable.
• Mathematical Use:
  • The lengths of the two sides are commensurable because their ratio is 3:2.
  • In ancient geometry, it was discovered that the side and diagonal of a square are not commensurable.

Advanced Usage

• "commensurable with": Measurable by or comparable to a specific standard.
  • The value of the artwork is not directly commensurable with its material cost.
• "mutually commensurable": When multiple quantities share a common measure among themselves.
  • In the equation, all variables were mutually commensurable, simplifying the analysis.

Variants and Related Words

• Commensurability (n): The quality or state of being commensurable.
  • The scientist questioned the commensurability of the two different measurement scales.
• Commensurate (adj): Corresponding in size, degree, or extent; proportionate. (Note: This is a related but distinct word often implying proportionality rather than just a shared measure).
  • Her salary was commensurate with her experience.

Synonyms

• Comparable: Able to be likened to another; similar enough to allow comparison.
• Measurable: Capable of being measured.
• Proportionate (in some contexts, when implying a rational ratio).

Antonyms

• Incommensurable: Not measurable by the same standard; lacking a common basis for comparison. In mathematics, having an irrational ratio.
  • The philosopher argued that scientific and ethical values are incommensurable.
• Incomparable: So different that comparison is impossible.

Related Phrases and Concepts

• Common Measure: A quantity that can be used to measure two or other quantities exactly a whole number of times. This is the core concept behind commensurability.
  • Finding a common measure was essential to prove the lines were commensurable.
• Rational Ratio: A ratio that can be expressed as a fraction of two integers. This is the mathematical condition for commensurability.

Adjective

1. capable of being measured by a common standard
   • hours and minutes are commensurable