Information theory provides a quantitative conceptual framework for understanding the flow of information from the world into and through brains. It focuses our attention on the sets of possible messages a brain's anatomy and physiology enable it to receive. The meanings of the messages arise from the inferences licensed by the brain's processing of them. Different meanings arise at different levels because different representations of the input license different inferences.

Numbers are symbols manipulated in accord with the axioms of arithmetic. They sometimes represent discrete and continuous quantities, but they are often simply names. Brains, including insect brains, represent the rational numbers with a fixed-point data type, consisting of a significand and an exponent, thereby conveying both magnitude and precision.

Shannon's theory lays the foundation for understanding the flow of information from world into brain: There must be a set of possible messages. Brain structure determines what they are. Many messages convey quantitative facts. It is impossible to consider how neural tissue processes these numbers without first considering how it encodes them.