Representations

Representations are models or stand-ins for real objects or phenomena, used to simplify, communicate, or reason about them. They encode essential properties while omitting many details, enabling analysis, comparison, and transmission across individuals and disciplines.

In mathematics, a representation is a concrete realization of an abstract object, usually a homomorphism from an algebraic structure to a set of transformations on a vector space. Representation theory studies how these mappings can be classified and decomposed. A classic example is a group acting by linear transformations on a vector space.

In computer science and information theory, representations encode data for processing and storage. Examples include binary encodings, graphs, and symbolic formats. The chosen representation affects efficiency, error handling, and the ease of performing operations on the data.

In cognitive science and psychology, mental representations are internal models of the world that support perception, memory, and reasoning. They can be symbolic, such as propositions, or analog, such as images and spatial layouts.

In linguistics and cultural studies, representations concern how meaning, identity, and social norms are encoded in language, media, and artifacts. Phonological, syntactic, and semantic representations underlie linguistic analysis, while broader cultural representations shape perception and action.

Representations are abstractions, not the things themselves. They enable inference but may introduce bias or error. Their usefulness depends on the balance between fidelity to the source and simplicity for analysis.