Greek mathematicians termed this ratio of incommensurable magnitudes "alogos", or inexpressible. Competing paradigms are frequently incommensurable; that is, they are competing and irreconcilable accounts of reality. Of incompatible languages, rival paradigms are "incommensurable". In moral theory, Raz defends value pluralism and the idea that various values are incommensurable. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. However, the discovery of incommensurable lengths contradicted their philosophical views. In addition, they made the profound discovery of incommensurable lengths and irrational numbers. Euclid uses this algorithm to treat the question of incommensurable lengths. On the other hand actor interaction time is vectorial with components that are incommensurable. The result is an "alternate, asymmetric and incommensurable" program of sociological inquiry. The part which nature has in any work of man, is indefinite and incommensurable. Later he reflected "Time is incommensurable for Actors". As a result the time vector has incommensurable components. "a" and "b" are incommensurable. Otherwise the pair "a" and "b" are incommensurable.