## Discussion

### introduction

Why are there so many equations in this book? Why can't physicists be content with the written word like everyone else? Wouldn't it be easier just to speak directly instead of cloaking ideas behind mathematical cryptograms?

Modern mathematical notation is a highly compact way to encode ideas. Equations can easily contain the information equivalent of several sentences. Galileo's description of an object moving with constant speed (perhaps the first application of mathematics to motion) required one definition, four axioms, and six theorems. All of these relationships can now be written in a single equation.

When it comes to depth, nothing beats an equation.

Well, almost nothing. Think back to the previous section on the equations of motion. You should recall that the three (or four) equations presented in that section were only valid for motion with constant acceleration along a straight line. Since, as I rightly pointed out, "no object has ever traveled in a straight line with constant acceleration anywhere in the universe at any time" these equations are only approximately true, only once in awhile.

Equations are great for describing idealized situations, but they don't always cut it. Sometimes you need a picture to show what's going on — a mathematical picture called a graph. Graphs are often the best way to convey descriptions of real world events in a compact form. Graphs of motion come in several types depending on which of the kinematic quantities (time, displacement, velocity, acceleration) are assigned to which axis.