Abstraction

"It frequently happens that in studying the properties of a mathematical system S we come to recognize that the results obtained do not depend essentially upon the precise definition of S but only upon certain formal relations holding between its elements. In that case it may be useful to select a suitable set R of such relations and then consider a system Σ of entities of which nothing is presupposed except that they, too, satisfy all relations in R. The system Σ constructed in this way is said to be derived from S by a process of abstraction. If we now investigate the properties of Σ, the conclusions at which we arrive will, of course, hold for S, since S is a special case of Σ. In this way we obtain results more general than those relating to the system S only; and we are able, moreover, to distinguish between the basic structure of S, and its more superficial features."

- An Introduction to Linear Algebra, by L. Mirsky (OUS 1955) (italics by author, links by me (natch))

And they say mathematicians don't have a sense of humour...

Abstractions of life events serve as a mnemonic to trigger the warehouse of empirical studies that make up our life. As such, these abstractions provide the key to recombining personal experience into new abstract theories.

Ideas get stored in long term memory separately. It takes the recalling of ideas into short term memory to draw the conscious connections between element to form integrated theories.

Once a sufficient amount of study and life analysis has been performed, often the best source of ideas is our own mind. Before and after researching other sources, introspection and brainstorming can provide the best sources of ideas. It is an essential tool for integrating and drawing interconnections between ideas.

Rumbaugh sees abstraction as the fundamental attribute of certain aspects of a problem and the goal is to segregate those chief aspects. On the other hand, Booch describes abstraction as an important characteristic of an object that identifies it from all other variety of objects. To sum this all up, abstraction provides a crisply defined conceptual boundary, relative to the perspective of the view.

Abstraction as an entity
- denotes some representation of an actual entity.

Types of Abstraction
Fundamental Abstraction- concentration on the function *but* ignoring its implementation.
Data Abstraction- extension of the concept of functional abstraction; underlying implementation's particulars and the data are not of interest to the client.

...and there are two different forms of data abstraction

That's all.

Ab*strac"tion (#), n. [Cf. F. abstraction. See Abstract, a.]

1.

The act of abstracting, separating, or withdrawing, or the state of being withdrawn; withdrawal.

A wrongful abstraction of wealth from certain members of the community. J. S. Mill.

2. Metaph.

The act process of leaving out of consideration one or more properties of a complex object so as to attend to others; analysis. Thus, when the mind considers the form of a tree by itself, or the color of the leaves as separate from their size or figure, the act is called abstraction. So, also, when it considers whiteness, softness, virtue, existence, as separate from any particular objects.

⇒ Abstraction is necessary to classification, by which things are arranged in genera and species. We separate in idea the qualities of certain objects, which are of the same kind, from others which are different, in each, and arrange the objects having the same properties in a class, or collected body.

Abstraction is no positive act: it is simply the negative of attention. Sir W. Hamilton.

3.

An idea or notion of an abstract, or theoretical nature; as, to fight for mere abstractions.

4.

A separation from worldly objects; a recluse life; as, a hermit's abstraction.

5.

Absence or absorption of mind; inattention to present objects.

6.

The taking surreptitiously for one's own use part of the property of another; purloining.

7. Chem.

A separation of volatile parts by the act of distillation.

Nicholson.

© Webster 1913.