Abstraction

Abstraction in its main sense is a conceptual process by which general rules and concepts are derived from the usage and classification of specific examples, literal ("real" or "concrete") signifiers, first principles, or other methods. "An abstraction" is the product of this process—a concept that acts as a super-categorical noun for all subordinate concepts, and connects any related concepts as a group, field, or category.

Conceptual abstractions may be formed by filtering the information content of a concept or an observable phenomenon, selecting only the aspects which are relevant for a particular purpose. For example, abstracting a leather soccer ball to the more general idea of a ball selects only the information on general ball attributes and behavior, eliminating the other characteristics of that particular ball. In a type–token distinction, a type (e.g., a 'ball') is more abstract than its tokens (e.g., 'that leather soccer ball').

Abstraction in its secondary use is a material process, discussed in the themes below.

Abstraction (computer science)

The essence of abstractions is preserving information that is relevant in a given context, and forgetting information that is irrelevant in that context.

In computer science, abstraction is a technique for managing complexity of computer systems. It works by establishing a level of complexity on which a person interacts with the system, suppressing the more complex details below the current level. The programmer works with an idealized interface (usually well defined) and can add additional levels of functionality that would otherwise be too complex to handle. For example, a programmer writing code that involves numerical operations may not be interested in the way numbers are represented in the underlying hardware (e.g. whether they're 16 bit or 32 bit integers), and where those details have been suppressed it can be said that they were abstracted away, leaving simply numbers with which the programmer can work. In addition, a task of sending an email message across continents would be extremely complex if you start with a piece of optic cable and basic hardware components. By using layers of complexity that have been created to abstract away the physical cables, network layout and presenting the programmer with a virtual data channel, this task is manageable.

Abstraction (mathematics)

Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena. Two of the most highly abstract areas of modern mathematics are category theory and model theory.

Description

Many areas of mathematics began with the study of real world problems, before the underlying rules and concepts were identified and defined as abstract structures. For example, geometry has its origins in the calculation of distances and areas in the real world; algebra started with methods of solving problems in arithmetic.