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Abstraction

An abstraction is a representation of something independent from a its specific details or context, a building's blueprint such as this would be a good example

An abstraction is a representation of something independent from its specific details or context, a building’s blueprint such as the above would be a good example

Abstraction is the process of considering something independently of its associations or attributes.1 The use of abstraction involves removing successive layers of detail from a representation in order to capture only the essential features that are generic to all entities of that kind and independent of their specific form.

Abstraction involves the use of inductive reasoning, that is to say identifying common attributes to a variety of instances of some entity and the formation of a generic model that captures the fundamental aspects of it without reference to any specific instance or context. An algebraic equation, an architect’s master plan of a building, or a non-figurative painting would be good examples of abstract representations. They all have in common the aim of capturing and communicating only the most essential feature to the system they are representing by removing the specific, concrete details of their form or function.

Abstract Thinking

To think in the abstract is not to see the world in terms of concrete instances but instead to see the categories or general types that a specific instance forms part of. A concrete thinker can see that a particular house is big; a more abstract thinker can think about the concept of size or scale in general. A concrete thinker can recognize that Jane is a friend of Kate; a more abstract thinker can reflect on relationships and friendships. Someone thinking in a concrete form can count five birds; but by thinking in the abstract, one can reason about numbers in general.

Origins

The usage of abstract reasoning is one of the key characteristics of modern human beings, which is believed to have developed between 50 to 100 thousand years ago. Its development is likely to have been closely connected with the development of human usage of symbols and language, which—whether spoken or written—appears to both involve and facilitate abstract thinking.2

Developmental psychologist Jean Piaget argued that children develop abstract reasoning skills as part of their last stage of development, known as the formal operational stage. This stage occurs between the ages of 11 and 16.3 During the adolescence years, the developing teenager acquires the ability to think systematically about logical relationships within a problem. However, the beginnings of abstract reasoning may be present earlier, and children advanced in their cognitive capabilities frequently develop abstract reasoning at an earlier age.

Synthesis

Abstract reasoning often involves synthesis, the putting together of disparate ideas or instances to define a more generic abstract form

Abstract reasoning often involves synthesis, the putting together of disparate ideas or instances to define a more generic abstract form

Abstraction involves the synthesizing of disparate qualities attributes or forms, putting together things that in their concrete form are different. In this sense, the process of abstraction entails the identification of similarities between objects, and associating these objects with an abstraction type. Thus, an abstraction can be seen as a compact representation and in order to create it one must “compress” information into a more condensed form. The final abstraction must contain less information or data than the original set of instances that it is designed to represent. This requires mapping multiple different pieces of constituent data to a single piece of abstract data. In an article in Scientific America, Gregory Chaitin talks about this as such: “A useful theory is a compression of the data; comprehension is compression. You compress things into computer programs, into concise algorithmic descriptions. The simpler the theory, the better you understand something.”4

Abstraction and Reification

Abstraction involves the induction of ideas or the synthesis of particular facts into one general theory about something. It is the opposite of reification, which means to make something real, bringing something into being, or the making of something concrete.5 Whereas abstraction removes the specific, reification involves specification, which is the analysis or breaking-down of a general idea or abstraction into concrete, specific facts.

For any abstraction to have real application it must go through a process of reification and specification in which the detail of the abstraction is specified in order to create a real instance of that form, as all real instances must have specific attributes. This process may also be called instantiation.

Application

Abstraction is key to dealing with complexity through encapsulation of parts in a hierarchical fashion that give structure and order

Abstraction is key to dealing with complexity through encapsulation of parts in a hierarchical fashion that give structure and order

Due to the fact that an abstract idea or model cannot have application in the real world without going through a process of specification, they are often seen as lacking in utility. Abstract reasoning is seen to be disembodied from the “real world” and limited in its capacity to affect change. Although abstract reasoning, by definition, does not have immediate application in the world in the way that concrete thinking does, it is however often the foundation for major transformation. Abstract scientific theories about thermodynamics may not help one fry an egg or fix a central heating system, but it was the abstract reasoning of the scientific revolution and the Enlightenment that transformed societies from pre-modern to modern and enabled the building of the cookers and central heating systems in the first place. So, whereas abstractions may not have immediate application in the world, through synthetic reasoning upwards towards creating an abstraction and then back down through reification and specification, it is possible to overcome some major hurdle and achieve a major transformation or break through.

Complexity

Abstraction is central to dealing with complexity. Where complexity represents a large number of diverse elements, abstraction can be used to find common attributes and functions that simplify this complexity. For example, money works as an abstraction of an item’s value. Without this common abstraction, we would have to deal with the large amount of complexity engendered in evaluating every single item for exchange relative to every other. Through this abstraction of a monetary system, we automatically interpret the value of all items across the economy by giving each one a single price, thus significantly reducing the complexity involved in computing the exchange rate between every single specific item by developing a single platform.

 

Cite this article as: Joss Colchester, "Abstraction," in Complexity Labs, July 31, 2016, http://complexitylabs.io/abstraction/.
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2017-05-23T11:58:31+00:00