Reduction

Reduction is a general term used across disciplines to describe the act of making something smaller, simpler, or lower in a specified sense. It often implies transforming a complex state into a more basic or more easily managed form, but the exact meaning depends on the context, from chemistry and physics to mathematics and philosophy.

In mathematics and related fields, reduction encompasses simplifying representations and problems. Examples include reducing fractions to lowest terms, normalizing data, reducing a matrix to row-echelon or reduced row-echelon form, and expressing a problem in a form that is easier to analyze or solve by applying a sequence of simpler steps.

In chemistry, reduction refers to a redox process in which an element or compound increases its electron count or decreases its oxidation state. It is the opposite of oxidation. Reducing agents donate electrons. Classic examples include the reduction of metal oxides to metals by carbon or hydrogen.

In science and engineering, reduction often means lowering complexity. Dimension reduction (for example, principal component analysis) compresses data into fewer features while preserving important structure. Model reduction seeks simpler representations of complex systems. In computing and logic, problem reduction maps a difficult problem to a simpler one, or reduces code size via refactoring or compression.

Philosophically, reductionism seeks to explain higher-level phenomena wholly in terms of their fundamental parts, though it is debated in light of emergence and holism. The term also appears in linguistics and computer science with specialized meanings, but all share the core idea of transforming something into a simpler or more fundamental form.