Introductory

Abstract

The Philosophy of Engineering, if such a field existed, would concern itself with broad questions about how models relate to reality and how our mathematical and computational tools manage to be so useful. One of the topics that discipline would surely investigate is the nature and representation of physical dimensions, such as “length,” “voltage,” and “viscosity.” If a consensus were reached on that topic, this book would be much shorter, as there would be a firm spot from which to begin a discussion of multidimensionality. However, there may be as many different conceptions of dimension as there are scientists and engineers. So, lacking a suitable starting point, this work deals with two topics:

• i) How should we model physically dimensioned quantities and their relationships?

• ii) How do linear algebra and multidimensional system models behave in the context of dimensioned quantities?

This book of mine has little, need of preface, for indeed it is “all preface” from beginning to end. —D’arcy Thompson