Introduction

As I write this in the early morning (February 28, 2002), only a few hundred meters from the beach in Byron Bay Australia, I want to share an important idea with you.

I am presently enjoying a book called "Where Mathematics Comes From" by George Lakoff and Rafael Nunez, published in 2000. The central premise of the book is that the ideas of mathematics are structually similar to other ideas that we have formed as a result of living. Our brains, and hence our minds, have evolved to meet the changing demands of life on this planet. In simplistic terms, we have developed neural patterns which predispose us to many actions (e.g. walking, talking) and to many thoughts (e.g. love, fear, beauty). We then also have a predisposition for certain ways of thinking, most notably the use of analogy and metaphor, to conceptualize some ideas in terms of other ideas that have underlying similarities.

What does this have to do with this course? Everything. According to Lakoff and Nunez, the idea of metaphor is the foundation of thought. I like the idea. This naturally and neurologically leads to the question, What would be an appropriate metaphor for this course?

My first thought was construction. Philosophically I tend to find myself in agreement with a constructivist position for learning. I believe that each of us builds or constructs their own knowledge. You construct this by living, by forming an almost infinite number of neural pathways and connections, as you experience each day. This metaphor of construction is a good one. Don't forget it. But for this course I want something richer, something that captures the subtle ideas of beauty and aesthetics. I then thought of the various crafts: pottery, woodworking, quilting, etc.. I like the idea of making and molding something, of shaping it into a desired product. This led to the idea of art, which in today's world implies a unique form of creativity. I do not want to make a strong distinction between art and craft, rather I want to emphasize what they have in common. And I want each of us to take that metaphor and apply it, not only to this course, but to all of our future learning activities. We are all artists and crafts-people. Let us create beautiful music and beautiful knowledge. This is the metaphor I am looking for as I create this course and this web-site. I am both artist and engineer. We all are.