What if you discover that what you know about math physic is wrong? That would be quite a surprise, but it is what actually is if you haven’t studied chaos theory.In fact I felt quite surprised when I read this book by Ian Steward. Surprised and Enlightened. The book is an educational essay on the math physic history and the most recent advances on the so-called theory of chaos.
Basically the core concept is that the classic equations describing system motions have been developed in the 17th century properly describes only ideal cases. It was thought that the real world effects, being small could be considered negligible.
What the real world insistently taught us in these years is that those small contribution can not be ignored for given enough time they will sum up and will turn you neat and smooth equations into the negligible part. The worst part is that for most system, even after a short time the system becomes unpredictable.
The author is a university professor and does a great job in presenting the matter, there are few equations, but they are thoroughly explained. Still with my aging university math (I studied analysis in 1988) I found I could follow easily the topic.
This book is fascinating under many aspects – historical and philosophical. I also found very enlightening some ideas. For example everyone knows the so-called butterfly effect – a butterfly flaps her wings in Tokio and your weather forecast on the East Coast are totally messed up. Now I always thought about this effect as an annoyance in getting the right weather forecast. But correctly you may see on the other side – it is an amazing mean of control. With so little energy you may control huge phenomena.
I also loved the part at the end of the book where Steward defends mathematicians against the popular belief they are closed in their Ivory Towers without doing anything useful. As he – correctly – points out, they are doing their work (as anyone else on the World) and their work usually has useful applications in everyday life even though they could not happen immediately.
(Italian title: “Dio gioca a dadi? La nuova matematica del Caos”)