Disorganized Territory

In this book, you find math presented in a fairly unorganized manner, as though it might be regarded as a conversation that you join whenever you feel like it. Visual Formula complements this disorganization. It provides a context in which you can play a game that addresses conversational mathematics. It is designed to draw you into an activity that forces you to set aside notions that you can do only what you do well. There is none of that here. You just do what you do and leave it at that.

To gain the most from such an experience, play with Visual Formula and learn how to set up equations and view the values and graphs that result from them. Then change the equations. Each time you change an equation, you extend your explorations. Each time you change an equation, you make something familiar strange but at the same time something strange familiar.

Likewise, from the first realize that it is not necessary to be systematic. The chapters in this book may convey a sense of disorganization. View your study of math along the lines of a novel by Joseph Conrad. You can venture from island to island, finding new adventures on each one. Just because one proves a little strange just now does not mean that you cannot go on to another and return later. Chance can prevail.

One way to understand this approach to the topic at hand is to consider that in the vast majority of instances, people study grammar and composition only after they have learned the language. Along the same lines, if you have a way of visualizing and playing with math before you pursue a systematic knowledge of it, your adventure becomes one of recognizing familiar features in new and more intricate ways.

This provides a way that you can increase the chance that you can acquire knowledge and feel confident about the knowledge you acquire. It also allows you to review what you have learned with greater confidence. Along with these benefits, Visual Formula can serve as a special sort of map that allows you to explore a new territory in a way you find more comfortable.