Chapter 6 Mapping

6.1 Mapping.

An abstract element instantiates itself by assigning a concrete element to each of its abstract components. Such set of assignments is called a mapping.

Abstract statement: "Information spreads."

Abstract element 1. `Information' as an abstraction of:

`a joke', `a manufacturing technique', `a tale', etc.

Abstract element 2. `Spreading' as an abstraction of:

`being told', `being thought', `propagate', etc.

Instantiation 1. "A joke is told."

Instantiation 2. "A manufacturing technique is thought."

Mapping 1. Information <==> Joke,

Spreading <==> Telling (of the joke).

Mapping 2. Information <==> Manufacturing technique,

Spreading <==> Teaching (of the manufacturing technique).

6.2 Restriction of possible instantiations.

Complex abstract information makes use of a number of smaller abstract elements. Each of these elements can be instantiated in a number of ways. However, not all combinations do make sense.

Each combination of instantiations of the elements is a mapping. The memory of what mappings make sense and what mappings have been failing in the past is called experience. The use of experience plays an important role in the instantiation of complex information.

Experience can also be described as the restriction of the instantiation of one element imposed by the instantiation of other elements.

6.3 Need for experience.

We can imagine an ideal situation in which each aspect of an abstract information element can be instantiated independently. However, in a real situation, the choices of the instantiation of the several elements are not independent.

Because an information element spends energy in attempting to find a proper mapping, less energy is wasted when successful mappings are remembered.

6.4 Link between worlds.

Suppose information life and biological life are two instantiations of some more abstract principles of life. By consciously building a mapping between both concrete life forms (information life and biological life) and the abstract notion of life, we build some indirect links between these worlds. Once these links are established, we can transpose some of our knowledge from one world to the other.

Transposing knowledge of one world to another by means of mappings can of course lead to serious mistakes. Better understanding of the underlying mechanisms can reduce the number of mistakes.

6.5 Offspring of instantiated information.

When an abstract element propagates while it is instantiated, only the instantiated part is copied. The copy or offspring is an instantiation with no direct link with the abstract source.

When only telling that manufacturing techniques are thought, an offspring of the abstract statement is spreading without the abstract element itself.

6.6 Spreading of the building blocks.

Complex abstract information is an organization of more elementary abstract elements. These smaller elements are smaller generalizations used by many abstract structures. Because these building blocks are used so often, they are widely spread.

The spreading of the complex abstract information depends largely on the presence of the building blocks in the receiver.

The understanding of an utterance as "paint exists in different colors" depends on the presence of the small abstract notion of "color" (among others).

The spreading of the building blocks is obtained by the spreading of small sets of information containing several times the same information except for one element which is replaced by several instances of the small abstract element which is to be communicated.

Red is a color,

Green is a color,

Blue is a color,


6.7 Propagation of abstract information.

Once the building blocks for a larger abstraction are communicated, the larger abstract information can be communicated by the communicating a few instances of the more abstract information.

6.8 Mapping for communication.

To facilitate the communication of abstract information by means of language, we first prepare a number of smaller abstractions by conditioning them (see chapter 5). After this preparation, we communicate an instantiation of the abstract information. The concrete elements of the instantiation correspond with the conditioned abstract elements. By this, the communicated element is immediately represented as the instantiation of the abstract element in the receiver.

The combination of all the conditioning prepared in the receiver defines the mapping relating the abstract element to the communicated instance.

More in next chapter on Induration of information

This is Chapter 6; Mapping of Behavior of Information

Author: Luc Claeys. All comments welcome, mail to lcl at this site:

Last updated on Nov 12, 1997