ABSTRACT
In ancient Greece the word logos covered a cluster of concepts involving speech: language, reason, explanation, and number. It is the root of our word logic and all the words ending in -ology. Logos and alogos were translated into Latin as rationalis and irrationalis, and first used in mathematics by Cassiodorus, secretary of the Ostrogoth king Theodoric, around 500 CE. The discovery of irrationality in geometry was a terrible blow to the dream of a world governed by natural numbers. As long ago as 1585, the Dutch mathematician Simon Stevin railed against using the words "irrational" and "absurd" for numbers Stevin appreciated the existence of irrationals, and aggressively asserted their equal rights with rational numbers. In this broadside, Stevin avoids using absolute terms for numbers, like "irrational," by using the relative term incommensuraule.
