Aggregation and Emergence

Dave Ackley, Ackley Associates
January 23, 1995

The concept of "emergence" is useful for understanding the structure and source of complex objects. This paper describes the relationship between emergence and aggregation, and argues that an understanding of the nature of aggregation is a prerequisite for explaining emergence. It asserts that the "wholeness that emerges is simply one characteristic of aggregation. The unique properties of an aggregate object emerge from the nature of its individual components, together with the constraining relationships that have been formed to join them into a whole. Examples are provided to show how this idea can be applied to both physical and abstract situations.

Background

Aggregation is one of several distinctly different forms of abstraction. To illustrate the differences in viewpoint, two forms of abstraction are considered: generalization and aggregation.

Techniques for modeling generalization have been clearly defined and documented, but the nature of aggregation is not well understood. The remainder of the discussion focuses on the nature of aggregation and its intimate relationship with "emergent" properties. It is argued that aggregation and emergent properties are fundamental to our understanding of complex objects, relationships, and evolution.

Generalization

Generalization is used to emphasize the general character of a group of things, rather than focus on their specific individual details. Things that share common general characteristics are designated as "subtypes" of a higher level "supertype." The entire group of subtype objects is abstracted into a single supertype object.

Generalization provides an economical way to think about similar things. We can say "A Car is one type of Motor Vehicle," and later follow up with "A Truck is another type of Motor Vehicle." This aids in efficient communication by allowing a discussion to take place in the context of a generalization hierarchy. Similarities between two things can be quickly identified by referencing their common supertype. When only the common characteristics are of interest, focus can shift to the supertype, hiding the complexity of the individual subtypes.

Generalization also provides an economical way to store data. The common properties of a group are assigned to the supertype, to be inherited by each of the subtypes. Each subtype then needs to store only its unique individual properties. The relationship between subtype and supertype is often expressed in two ways:

Subtype is-a-kind-of Supertype. "A Car is a kind of Motor Vehicle."
Instance of a Subtype is-an Instance of Supertype. "Every Car is a Motor Vehicle."

Generalization involves no action on the physical things being grouped together. It is a technique for organizing information about the things.

Generalization Example: A Department of Motor Vehicles wants to license all motor vehicles, including passenger cars, trucks, motorcycles, buses, vans, etc. All motor vehicles are to have certain operating rules in common, such as "motor vehicle must be licensed and display current license plates." Different kinds of motor vehicle are to have their own unique properties. For example, buses are to have designated passenger capacity limits. All subtypes are to inherit the common motor vehicle properties, such as a requirement to be licensed and to display current license plates.

Aggregation

Aggregation is used to gather a group of interrelated things into a whole. The result is an aggregate object with unique characteristics that were not present in its constituent parts. This form of abstraction provides an effective way to think about large complex structures or systems, by elevating the frame of reference to a higher level of detail. There are two aspects of aggregation that need explanation, actual creation of an aggregate object, and perceiving one that has already been created.

Creation of an aggregate object requires physical action on its components, as in "assembling an automobile." In this case, a physical process is used to join the components together to construct an aggregate automobile.

Perceiving an aggregate object requires mental action, as in "seeing the forest instead of just the trees." There must be some degree of recognition that the forest ecosystem has components with interdependencies. No physical action is taken on the physical components, which are simply observed in their assembled state. However, a mental process is required to revise the viewer’s internal model to appreciate that the forest is made up of interrelated animals, plants and bacteria. The mental process abstractly visualizes the earlier physical process that created constraining relationships among the forest components over time.

In both cases, the resulting aggregation can be seen to have unique properties that are different from those of its components. These new properties are often said to "emerge" from the nature of the components and their constraining relationships. In generalization, the subtype object inherits common properties from its supertype. In aggregation, there is no inheritance because both components and aggregate object each have their own unique properties.

The emergent properties of aggregations do not just appear. Component objects must in some way be bound together and assembled into an aggregate whole. This is done by forming constraining relationships, such that each component in some way limits the freedom of movement of the other. If the automobile frame did not constrain the engine such that its rotation is constrained by the wheels, the drivability of the automobile would not emerge. Without constraining relationships, the group of components that make up an automobile would look like a kit of parts lying in a disconnected pile, waiting for the forces of assembly to join them together.

As they become connected together, each component looses some freedom of movement. Its ability to change from one state to another is limited by one or more constraining relationships. In the automobile example, a wheel’s ability to change between its "stopped" and "turning" states is constrained by the car’s engine and brakes. In the case of the forest ecosystem, the ability of a tree to proliferate and root its seeds is constrained by the presence of animals, other plants and bacteria-laden soil that make up the forest floor.

It is helpful to contrast "aggregation" with "object." A simple object has properties, but it is opaque, with no visibility into its internal structure. To be an aggregation, some degree of perception of its components and their relationships must be present. The observer must be able to appreciate the connections among the components that cause the aggregate object’s properties to emerge.

In aggregation, two kinds of structural relationship are involved, and both are necessary to cause the properties of the aggregate object to emerge.

Component Object is-a-part-of Aggregate Object. "Engine is a part of Automobile."
Component A is-constrained-by Component B. "Engine is bolted to Frame."

Aggregation Example: Jimmy decides to make a slingshot. He finds a suitable "Y" branch from a tree and attaches rubber bands with a leather pocket for holding small rocks. The result can now be perceived as a crude weapon, with its own emergent properties. It has the capability of being used to kill a small animal from a distance. None of the components by itself had that capability.

Three Approaches to Aggregation

Aggregation can be applied to different kinds of situation, where the constraining of component parts is accomplished in different ways. For example, the assembly of an aggregate object may be accomplished by:

Intelligent Design
Mutual Consent
Evolution

In each case, some kind of force must act on the components to form constraining relationships, and cause the aggregation’s properties to emerge. The following sections illustrate three different ways that aggregations can be created.

Aggregation by Intelligent Design

An automobile company wants to build passenger cars. The company decides to assemble the cars out of available components, such as frame, engine, body, seats, wheels, etc.

The components are welded, bolted or otherwise fastened together, in a certain sequence. Human employees, computers and robots provide the force necessary to create the constraining relationships. Once established, the constraining relationships allow the unique properties of the resulting car aggregation to emerge. These include top speed, road handling capability, stopping distance, gas mileage, etc.

Aggregation by Mutual Consent

A company wants to hire a person as an employee. The company and the person enter into an employment contract, where the person agrees to do assigned work for which the company agrees to provide compensation.

Under this "employment" aggregation the company is constrained to assign a certain type of work to the employee, and then provide compensation for work performed. Similarly, the person is constrained to be present at the company premises at certain times and days to carry out work assignments.

These constraining relationships allow the properties of the resulting employment aggregation to emerge. These include fairness of the exchange, adequacy of the work performed, and adequacy of the compensation paid.

Suppose that after a while the person begins to perform poorly on the job. Suddenly, the emergent properties of the employment aggregation change. The work being performed is no longer adequate. If the employee cannot do the work required by the company, the company is not required to provide compensation, and the contract is void.

Aggregation through Evolution

A one-celled organism has evolved into a frog, a complex aggregation of interdependent components. Mutation and a natural selection process have provided the slow moving forces necessary to create the components and form constraining relationships among them.

Mutation causes new components and aggregate organisms with new properties to emerge, while natural selection limits survival to those that behave effectively within their environment. The eventual result is a new aggregate species with effective emergent properties: a frog that has long legs and webbed feet, with the ability to swim, jump and catch flies.

Conclusion

The concept of "emergence" is helpful for understanding the nature of complex objects, but the "wholeness" that emerges when a complex object is constructed has not been adequately explained. By recognizing wholeness as a characteristic of aggregation, a new structural architecture can be introduced to define the nature of emergence. The properties that comprise the wholeness of an aggregate object emerge from the nature of its components and the relationships that have been formed to constrain them. This same viewpoint can be applied to improve understanding in a very wide variety of situations, including the manufacturing of physical objects, establishment of contracts, and evolutionary development.