Chaos - A Very Short Introduction - Leonard A. Smith
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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SacredFeather (4 )
The majority of people who are new to spell working will acknowledge that for them common sense backed up by practical action is normally more productive than theoretical or mystical thinking. In magical working, as in everyday life, when we have to handle a wide range of circumstances, common sense in dealing with them will normally produce the best results. However, when we are confronted with the unusual or difficult, or are faced by extreme anxiety, even the most practical minded among us will theorize in order to make sense of what is happening. We have not moved such a long way since those times, in the distant past, when our ancestors and people around the world routinely believed that if the crops failed then the gods must be angry. Practices carried out then are still with us in the form of many of the festivals and feasts, which still have relevance in the societies where they began. Some of you may choose not to use the spells in this section, but they do offer a return to basics and give fascinating insights into how our ancestors dealt with everyday challenges.
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