Chapter 4 Abstraction

In our study, we will frequently use the notions "abstract", "abstraction", "concrete" and "instantiation". To avoid confusion about the meaning of these words, and because the notions are closely related to some fundamental mechanisms, we have a closer look to their meaning in this context.

4.1 Abstraction versus instantiations.

When recognizing a similarity between two phenomena, the similarity itself is something more general than each of the phenomenon. Because it is more general, we call it abstract. Each of the phenomena can be considered as an instance of the more abstract principle.

We notice a joke is spreading. We notice also that a manufacturing technique is spreading. We can express the recognized similarity in a more general, a more abstract statement: "Information is spreading".

The action of the generalization we call abstraction. The opposite action is the application of the general information under specific circumstances. This action we call instantiation. The result can be called an application, an example, an instance or an instantiation. I prefer to use the word instantiation because it implies a temporary aspect; at a certain instant, the abstract information manifests itself as an instantiation. In other words, an abstract information being expresses itself in a given environment by instantiating itself. It's like the information being grabbing some elements of the environment to pull them into a specific constellation to make itself clear.

"Information is spreading" is an abstract statement. "Jokes are spreading" is a first instantiation, and "Manufacturing techniques are spreading" is a second instantiation.

Because the laws governing information are applicable to all information and there is a very wide variety of information, our study of behavior of information is very abstract.

4.2 Building an abstraction.

The basic mechanism for building an abstraction is surprisingly simple. However, building a new and stable abstraction which will spread and survive for a long time is not so simple.

When removing some details from a set of information, we obtain a more abstract set of information.

Suppose we have a story about Jim and Julia. By removing the details about the names and replacing them by "a boy" and "a girl", we obtain a more abstract story which can be instantiated in many ways by filling in some names.

However, there is more to making useful abstractions than cutting away some details. When removing elements from an information set, it can happen that the obtained information set has no use anymore and has thus no chance on survival.

The princess is going to marry a controversial politician... When replacing "the princess" by "a girl", The entire story looses its gossip aspect and by this it looses its chance on fast and wide spreading.

In the coming chapters we will return to the propagation and evolutionary forces influencing abstract information sets.

4.3 Abstraction and learning.

When learning how to cook an omelet, it may be demonstrated in a red frying pan. Fortunately, most of us will understand that the color of the pan is irrelevant and memorize the technique of preparing an omelet separately from the details of the demonstration.

When learning something, we observe a way of doing it in a very specific context. We take it for granted that we memorize the essence of what we see separated from all the details.

Suppose we learn a witchcraft trick by receiving one single demonstration. When we do not have a general knowledge about witchcraft, it is very difficult to evaluate the importance of the individual details. Therefore we try to memorize all of them. Once we can systematically reproduce the trick, we are able to evaluate the importance of each detail in experiments. By this, we learn about the subject.

To be able to remove the right (irrelevant) details, there must be a general understanding of the process. If we do not have this base, we can only try to memorize all details. Later on, we can attempt to remove details one by one and see if it still works. This process of removing details and testing the result contributes largely to the understanding of the subject.

4.4 Use of existing abstractions helps.

When the information concerns a subject we are familiar with, we know already abstractions of some details of the subject. We obtain new abstractions by replacing details by the already known abstractions of these details.

When we are familiar with cookery, we have probably discovered already that the color of the pot is not so important. So besides the notion of "a red pot", "a green pot", etc., we have also a more abstract notion of "a pot". Once this abstraction is discovered, we will attempt to use it whenever it is possible.

4.5 Generalizations and hypothesis.

The technique of replacing some details by abstractions of the details causes a generalization because the abstract elements can be instantiated in new ways.

Out of the expressions: "Jokes are spreading" and "Manufacturing techniques are spreading", we can built the abstract expression: "Information is spreading."

The element "information" can be re-instantiated in many different ways. This leads to new statements such as: "Tales are spreading," "Knowledge is spreading," etc.

This illustrates how an abstraction causes a generalization.

Generalizations can of course lead to mistakes. It is not because a few instantiations of something more abstract correspond with our observations that all instantiations are possible. It is not sure that the choice of the instantiation of the elements is irrelevant or independent from each other. Because of these possible problems, new generalizations are called hypothesis.

When experimenting with our new witchcraft trick we can replace the brown stick with a green stick. When the trick still works, we could conclude that the color is irrelevant. However it might be that all colors work except for red.

4.6 Conscious use of hypothesis in science.

As soon we feel there is a similarity between two phenomena, we have discovered some more abstract information (the similarity), even when we have no name for it.

The observed similarity suggests that there exist some more abstract information of which we have observed two instantiations. Based on this, an attempt can be made to express the common part without mentioning one of the phenomena. Because the abstraction is more general than the observed phenomena, there can be a mistake. Verifying an abstract rule would imply the verification of the correctness of the rule in all possible instantiations to check if there are no exceptions to the rule. Therefore all abstractions are at first hypothesis. As the hypothesis is applied (tested) with good result under different circumstances, we become more confident in the hypothesis and we start considering the hypothesis as a law. The described abstraction mechanism is part of our common sense. As all parts of our knowledge, we express it in our actions.

In scientific research, generalizations (abstractions) are formulated consciously as hypothesis. As the formulated hypothesis proves to be useful in the explanation of more phenomena, the hypothesis is gradually being considered as a law. Scientists are supposed to keep always in mind that all formulated laws remain hypothesis. The science of physics has been shaken several times by discoveries that hypothesis considered as laws since a long time suddenly proved to be incomplete or wrong.

4.7 Abstraction and classification.

All information which can be abstracted to the same, more abstract, information element is related. It seems that it makes part of one set. The process of assigning an element of information to a set is called classification. It is clear that any classification process is related with an abstraction.

More in next chapter on Instantiation

This is Chapter 4; Abstraction of Behavior of Information

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

Last updated on Nov 12, 1997