A TUTORIAL ON NETWORKS AS AN INTRODUCTION TO RELATIONAL SYSTEMS THEORY

Don Mikulecky

Fellow, ISCE

Professor of Physiology

Virginia Commonwealth University

OBJECTIVES:

1.                  To define “network” as a way of modeling relations in the real world.

2.                  To explore different networks and the kinds of real world things they can model.

3.                  To use network models to illustrate the difference between mechanistic world views and relational world views and to explore the relationships between them.

INTRODUCTION:

Network theory arose out of  an area of mathematics that did not make the list of  mathematical things we need to know in order to be modelers of the world (scientists). We believe that this is intimately related to the world-view promoted by reductionist science, since the focal point of network theory is the relations between things rather than the things themselves.  This tutorial is aimed at providing a partial cure for that situation.  We start with some little known facts about the situation.

SOME LITTLE KNOWN FACTS ABOUT THE SITUATION:

1)      Network theory, based in algebraic topology and graph theory, contains the vector calculus as a subtopic.

2)      Electrical networks and circuits are a part of a much broader class of physical networks which can be used to model the              material world.

3)      Even electrical networks are based on thermodynamic concepts to a large extent.

4)      In the broader class of “physical networks”, chemical reactions play the role that transistors do in the electronic version.              This means that electronic networks, such as those in computers, are a special case of a set of material networks which              also can compute and do what computers can.  Physical networks have “memory” and can manipulate “data”.

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