Transforming

Transforming refers to the act of changing in form, appearance, nature, or structure. It can be physical, mathematical, informational, or conceptual. Transformations can be intentional or resulting from interactions, and often preserve some properties while altering others.

In mathematics, a transformation is a relation that assigns elements of a set to other elements. Common geometric transformations include translations (slides), rotations, reflections, and scaling. More general are linear transformations represented by matrices, which preserve vector addition and scalar multiplication; isometries preserve distances, while affine transformations preserve parallelism. Transformations can be composed to form new transformations, and inverse transformations undo changes.

In computing and data processing, a data transformation converts input data into a different format or structure. This occurs in ETL pipelines, data cleaning, and software frontends. Functional programming uses map, filter, and reduce as transformations on data collections. Transformations also include encoding, encryption, and schema changes.

In science and society, transformations describe changes in state or identity: in physics, coordinate transformations relate observations in different reference frames; in biology, transformation can mean metamorphosis or genetic transformation in which DNA is introduced into a cell. In urban planning or policy, transformations refer to large-scale changes in systems, communities, or economies.