An Information Principle Based on Partitions for Cognitive Data

Motivated by the deep connections that exist between brain activity analyzed through thermodynamics and cognitive processing measured by information, this paper proposes an information principle based on partitions for possible applications to cognition-based judgments with potential applications to artificial intelligence. Looking at information through the lens of variety, which is the set of distinguishable elements of the set, we propose that partitions with only one type of object are counted once, and partitions with k types of objects are counted k times. Put differently, multiple occurrences of an object are considered not to have significance for the observer, or we can say that the objects are indistinguishable unless they are distinct. We explore the implications of this many-to-one logic that has possible applications to cognition centered systems and present a result related to the frequencies of the objects and contrast them with the first digit frequencies as well as the Bose–Einstein distribution.