Edward Lorenz described Chaos as follows: Chaos: When the present determines the future, but the approximate present does not approximately determine the future.
Chaos is deterministic yet unpredictable without random elements. This sounds self-contradictory but this is essentially why the area of chaos theory has become so interesting. It deals with systems which fully obey physical laws yet whose future is not easily predictable from simple observation.
This book helped me to truly understand what chaos is mathematically (as opposed to socially). The fact that a system can be simultaneously deterministic and yet unpredictable opened my eyes. The book is written very much from a personal view of the author and even includes some swipes at proponents of other sciences (such as biology) being "lesser" sciences but whoever can look past that level of unprofessional bias will find a very understandable explanation of what chaos is and how it is of great importance to modern science.
I have to admit that I found the book hard to read at times but I really did feel like I got a proper introduction to the proper notion of chaos.
Looks like a very interesting read.
It's from 1987 though - does anyone know if it's current enough? I know that huge strides have been made in chaos theory over the last 28 years, among other things to make game theory more practically applicable to our everyday problems like traffic and population growth.
I can't edit my post any more, but I found an updated version of the book.
It's from 2008 so I presume (although I've found no clear evidence that it is so) it incorporates some new information since the original book I read (Publish date 1996). It's true that the original book is dated from the '80s. It's still a highly-rated book.
I must order his newer book:
I've no idea how it is, but it's guaranteed to be more current than the book linked to above. I still maintain that, for the uninitiated, reading a book from 1987 on Chaos is not a bad start. It can help pave the way to more current titles. Because without the "aha" moment, chaos theory is just incredibly obscure and hard to fathom.
"The Information" is a good popular read on information theory. There is nothing ground breaking in it but it is a very good overview and shows the wide applicability. His book on Chaos Theory is dated and there have been a lot of good experimental and theoretical advances since then. I don't know a newer reference on it, but will check around.
In this theme (whatever it is) there is always the classic "Goedel, Escher Bach" by Hoffstader and his other book "The Minds I". Both very good discussions of the limits of math and analysis with special attention to recursive systems.