Mathematics is the science of measurement. Measurement is the basic form of abstract comparison, i.e. comparison that focuses selectively on attributes rather than whole percepts. More precisely, measurement is comparison between instances of the same attribute, done using units instead of percepts. Measurement is crucial to expanding the range of cognition beyond the perceptual level. Why? Consider: since, measurement consists of relating easily perceivable or conceivable units to the attributes observed in things, through measurement, we can potentially identify quantities that are not directly perceivable by a human — or even by any conscious being. For example, we may not be able to directly perceive a distance of 1000 kilometres, but we can define it using kilometres, which can be reduced to metres, which are directly perceivable by a human. Since measurement is so crucial, the importance of mathematics becomes more apparent: as the science of measurement, it is the study of how to measure quantities, how to apply logic quantitatively (e.g. applying logic to arrive at knowledge about quantities not directly measured), and how to validate one’s logic in quantitative terms.