Intelligent Systems And Their Societies Walter Fritz

Concept of a Society


In the same way that the mathematical concept of triangle helps to calculate some properties of natural objects that are similar to a triangle, our concept of society will permit us to calculate certain properties of natural societies. Since we are most interested in human societies, we will define "society" in such a way that it may be a useful concept for understanding these societies. The way we define a concept has effects on what we can possibly predict from that concept. A concept has to have a relationship with the object in the environment, but a richer or poorer concept can say more about the object or only very little.


Suppose we define "society" just as a system. It seems that we can now predict those properties of a society that are properties of a system, but no more. Such a society has:


But suppose we define "society" as being an Intelligent System. It seems that we can now predict properties in addition to those above:


On the other hand, if we define "society" as a system composed of many sub societies and Intelligent Systems, it seems that we should be able to deduce and make calculations with the following properties:

This seems a much more useful definition of society, and thus better suited to our purposes. Therefore here is our formal definition of the concept "society":see Definitions (For continuous reading, like a book - do not enter here now).


A Society:

Here "very many" is a gradual concept. A million is always "very many". But in some simple societies, for instance a medieval rural society, "very many" could be as little as 50. The above concept of society is fully applicable to those having a million members and only partially applicable (according to the type of society), to societies with lower amounts of members. Specifically, a governing subsociety and several levels of subsocieties, exist only if there are very many members.

Some examples of societies are: states, provinces, municipalities, industrial enterprises, political parties, religious organizations and clubs. Also a wolf pack, a heard of reindeer, being composed of intelligent systems, as we have defined them, are societies. Ant hills and beehives are only societies if we find members (ants or bees) that are intelligent systems, i.e., that can learn.

You may ask: "Why just this definition of society and not another". On one hand this concept permits working with a number of interesting aspects of a human society and also we can model it on a computer. There is another aspect. In physics we use as fundamental concepts those of force, distance and time. It has been shown that all physical formula can also be written with the fundamental concepts of mass, distance and velocity. All formulas, including those of electromagnetism can be rewritten with these as fundamental concepts and give the same valid results. It seems that it is not of so great an importance what fundamental concepts we use, but it is of the highest importance that we define them well and that they form a coherent system, so that we can treat them mathematically. Also, as has been shown, different definitions permit us to treat different aspects of societies. If, in the future, we note that we cannot treat some important aspect with the present concept of society then we should modify this concept.

In the following we will show a few mathematical formulas. We wrote them only as examples to show the possibility of using formulas. Much more detailed study is needed to write really useful formulas. But without calculation and prediction of the variables of a society, sociology is an art, not a science.


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Last Edited 5 July 2013 / Walter Fritz
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