An abstraction is a model that serves as a general description or definition of a set of specific instances. Note that the idea of an abstraction is, itself, an abstraction. This property of the abstraction meme gives rise to an infinite regression of meta-abstraction memes. Compare metameme.

Abstraction is the most powerful tool used in programming, as well as useful in life. The steering wheel is a good example, a user doesn't need to understand it at a low level, it just turns their car. Using information hiding, a good abstraction crates an intuitive interface and separates it from the implementation. The underlying structure can be changed
without affecting the user.
A steering wheel turns a car or boat, though in very different ways.

"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...

A poem by Lady Ise, a Heian era poet

A flower of waves
Blossoms in the distance
And ripples shoreward
As though a breeze
Had quickened.

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.

In light of software engineering, particularly in object-oriented analysis and design, Abstraction can be seen and defined as a process and as an entity.

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 a process
- denotes the withdrawal of important details about an item or group of items while disregarding the unimportant details. It draws a boundary line around an object, where its important attributes are within the boundary. By having a boundary, we can concentrate more on the real issues concerning the object.

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

Abstraction of the fundamental structure of the data- the different forms of data are identified in terms of operations that apply to the objects of the type though the only setback with this kind of data abstraction is that values of such objects can be altered and observed only by the use of the native operations.
Abstraction of items held in the data type- the model of the data type is alienated from the structure of the items held in the data type.

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.

[Modern]

7. Chem.

A separation of volatile parts by the act of distillation.

Nicholson.

 

© Webster 1913.

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