Nature's Numbers: The Unreal Reality of Mathematics

Being a mathematics teacher I was used to repetitive Math texbooks, but this book helped me acquire a new and more complete vision of our physical world. It's content has helped me develop much more attractive lessons for my students and to offer very interesting conferences to my colleagues, besides motivating me to go further in the study of such themes.

Nature's Numbers is a valuable resource and, I think, a new doorway of scientific philosophy. (I think some reviewers didn't like this because they expected more, but as I said, its a doorway to a field, and by no means a complete study in itself) From the very beginning, it is promised to the reader that a new pair of glasses, a mathematicians, will be provided to look at your life in the universe a bit differently. Ian Stewart attempts to grasp the mathematical hypostasis of the natural macrocosm. Objectively, simplicity still likely underlies all external phenomena, however a outward branching tree of complexity translates this core into our manifested world, appearing fairly simple again as the laws which govern the cosmos. However, in Stewart's universe, mere laws and equations do not suffice. He strives for a new field of mathematics that is intertwined with natural science. It is obvious, as he shows from the science of flowers, dripping water, etc., that math determines the observed phenomena of science. Even in apparently haphazard systems, the source remains as deterministic principles by nonlinear dynamics. (This is what you should know as chaos theory) And the shibboleth of "the butterfly effect" is an epitome of the need to comprehend the governing mathematics of systems. Take biological adaption and evolution for example. Some biologists believe that DNA and genetics is the sole shaper of organisms. This does not appear to be fully adequate alone, because then we would in turn need to explain why biology followed symmetries and patterns. But as he notes on pp. 137 "Maybe evolution started with the mathematical patterns that occurred naturally, and fine-tuned them by natural selection." By opening our horizons of our attempts to comprehend the universe fully in our quest for absolute knowledge of nature's numbers, the final sentence in Stewarts work admirably states the scientist's philosophy with the same type of mere simplicity that Mother Nature holds at her core, "We may never get there. But it will be fun trying." Gotta love that.

Pros: Many interesting philosophical observations; lucid language.Cons: Not enough details on the math; not enough pictures / diagrams that would support verbal descriptions of examples from nature; in some cases, insufficient explanation of the ideas (e.g. What is qualitative theory, and how can it be an advance rather than a retreat?).Notable Quotes:"There is much beauty in nature's clues, and we can all recognize it without any mathematical training." "Patterns possess utility as well as beauty." "One of the strongest features of the relationship between mathematic and the 'real world,' but also one of the strongest, is that good mathematics, whatever its source, turns out to be useful." [begs the question WHY?]".. goal-oriented research can deliver only predictable results."".. the dreamers and the mavericks must be allowed some free rein, too." [on the tension between pure and applied research]A Question: There are many instances where the book talks about nature doing this or that. For instance, consider the following discussion of 'broken symmetry': "Nature, too, seems to be attracted to symmetry, for many of the most striking patterns in the natural world are symmetric. And nature also seems to be dissatisfied with too much symmetry, for nearly all the symmetric patterns in nature are less symmetric than the causes that give rise to them." HOW IS IT POSSIBLE FOR NATURE TO BEHAVE IN A CONSISTENT MANNER? IS THERE A CENTRAL INTELLIGENCE TO NATURE? HOW IS NATURE ABLE TO CONTROL EVERYTHING TO MAKE THESE CHOICES AND IMPLEMENT THEM? In scientific literature statements like this are frequently made, without any scientific basis. I don't know why, and I hope people can discern truly scientific from academic speculation.A difference of opinion: I do not think the nature is "mass produced." Everything in it seems very special to me.

This book is a hint that math can be both fun and useful. Understandable even to the non-mathematical reader, it tells in an entertaining style what mathematics is about and what it is good for. It shows how math helped us understand nature and our world in general, how it was used in mankind's most important inventions and developments; how it threaded through our history and what can we expect in the future. Both enlightening and enjoyable reading.

Mr. Stewart delivers an excellent insight into the role mathematics plays in the everyday world. Ever easy to understand, the author takes us on an exciting journey into the role math takes on in the places we may least expect. A truly enjoyable read for the non-mathematical and a must for the serious or amateur mathematician. Riveting from the onset, this book keeps your attention and wraps up in a climatic section on chaos theory with some remarkable insights in the epilogue.