Sunday, August 10, 2014

Ian Stewart. Nature’s Numbers (1995)

     Ian Stewart. Nature’s Numbers (1995) A guide into the uses of mathematics, and a glance at how mathematics has changed as our understanding of the world around us has changed. Stewart doesn’t like the divide between applied and pure math, he points out that each prods the other into ever new insights. His exemplar is the calculus, a mathematics invented in order to deal with rates of change of rates of change, prompted by Newton’s insights into how things move. Newton’s model of motion was a new way of thinking about it. To formalise that he needed more math than was available to him, so he invented it. Leibniz invented it, too, using a different notation. Newton’s notation has won out, barely, because it’s somewhat easier to use.
     We now can’t get along without the calculus, which informs all our technology. I learned how to integrate and differentiate years ago, and can’t do it any more, But the way of thinking it taught me is with me still. That’s the enduring legacy of learning math that you won’t use: it changes the way you think, more precisely, it increases the ways you can think about the world. Since then, more new math has been developed.
     The book is also an attempt to change the average person’s notion that math is calculation, but that it’s about patterns. The kinds of patterns that math can deal with now may be called patterns of patterns. We can’t calculate the weather accurately beyond a few days, but we can say a good deal about what kind of patterns to expect. These patterns are the climate (Stewart doesn’t say this, I’m building on his insights). It’s the changing patterns of the weather that’s meant by “climate change”. And although we experience only weather, we also have an uneasy sense that the patterns of weather are changing. The climate models put numbers to these changes, telling us that while we may not have more rain, for example, the rain will fall less frequently and in smaller areas, so we will see more flooding. Thinking in terms of patterns of patterns is a way of dealing with many more variables than we can handle by thinking merely about patterns.
     A good book, but it lacks pictures. Stewart is a poet, he thinks in images, but many people (most?) need actual pictures to understand metaphors. Like some other popular science books, this requires some background. You have to be able to think mathematically, not merely arithmetically, in order to fully get Stewart’s theses. Nevertheless, I recommend it. **½

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