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By Peter L Duren; Richard Askey; Uta C Merzbach; Harold M Edwards

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The unpredictability of the weather, however, has nothing at all to do with randomnessa topic we will take up in chapter 8, when we discuss the concept of chaos. The role of mathematics goes beyond mere prediction. Once you understand how a system works, you don't have to remain a passive observer. You can attempt to control the system, to make it do what you want. It pays not to be too ambitious: weather control, for example, is in its infancy-we can't make rain with any great success, even when there are rainclouds about.

At every turn, new vistas WHAT MATHEMATiCS is ABOUT arise-an unexpected river that must be crossed using stepping stones, a vast, tranquil lake, an impassable crevasse. The user of mathematics walks only the well-trod parts of this mathematical territory. The creator of mathematics explores its unknown mysteries, maps them, and builds roads through them to make them more easily accessible to everybody else. The ingredient that knits this landscape together is proof Proof determines the route from one fact to another.

The difficulty was compounded in Galileo's time-and, indeed, in Newton'sbecause it was hard to measure these numbers directly. In actual fact, Galileo rolled a ball up a gentle slope to slow the whole process down. The biggest problem was to measure time accurately: the historian Stillman Drake has suggested that perhaps Galileo hummed tunes to himself and subdivided the basic beat in his head, as a musician does. The pattern of distances is a puzzle, but the pattern of velocities is much clearer.

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