The ‘chaos’ introduced in the following pages reflects phenomena in mathematics and the sciences, systems where (without cheating) small differences in the way things are now have huge consequences in the way things will be in the future. It would be cheating, of course, if things just happened randomly, or if everything continually exploded forever. This book traces out the remarkable richness that follows from three simple constraints, which we’ll call sensitivity, determinism, and recurrence. These constraints allow mathematical chaos: behaviour that looks random, but is not random. When allowed a bit of uncertainty, presumed to be the active ingredient of forecasting, chaos has reignited a centuries-old debate on the nature of the world. The book is self-contained, defining these terms as they are encountered. My aim is to show the what, where, and how of chaos; sidestepping any topics of ‘why’ which require an advanced mathematical background. Luckily, the description of chaos and forecasting lends itself to a visual, geometric understanding; our examination of chaos will take us to the coalface of predictability without equations, revealing open questions of active scientific research into the weather, climate, and other real-world phenomena of interest.
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