Notation

Notation is a system of symbols, signs, and rules used to express information, ideas, or data in a compact and unambiguous form. The term comes from Latin notare, meaning to mark. Notation systems span many disciplines and can be universal or domain-specific.

The primary purpose of notation is to encode complex concepts so they can be communicated, reasoned about, computed, or performed. A notation defines a set of basic symbols and syntactic rules for combining them, and it often requires shared conventions to avoid ambiguity. Some notations are naturalistic and intuitive within a culture; others are highly formal and technical.

Mathematics and logic rely on formal notation such as f(x), ∑, ∫, ∀, ∃, and various logical connectives. In science, chemical formulas, reaction arrows, and SI prefixes provide compact representations of phenomena. In music, staff notation encodes pitch and rhythm. In programming, syntax and operators convey instructions to machines. Writing systems, phonetic notation like the International Phonetic Alphabet, and diagrammatic notations in electronics or geometry illustrate the broad use of notation.

Notations are shaped by historical development and standardization. Early symbols evolved into modern alphabets, and mathematical notation advanced through contributions across centuries. Today, standard bodies and digital encodings such as Unicode support global interoperability. Clarity, consistency, and ease of learning are central design goals in notation.

The study of notation intersects education, cognition, and information design. The choice of notation can influence comprehension, computational efficiency, and cross-disciplinary communication.