Nature's Numbers: The Unreal Reality of Mathematics (Science Masters Series)

Rating:
Summary: An interesting pop science book
Review: I first read the translated (Chinese) version of this book. I liked it a lot that I decided to buy the English version for my son, who is a 6-grader but has developed keen interest in numbers and patterns. The author brings up many interesting topics and let the "hidden rules" develop and unwind. The writing is with good pace and clarity. I recommend it.

Rating:
Summary: 'Nature's numbers' - Avoid
Review: Ian Stewart wastes an interesting subject with 'Nature's Numbers.' The book is bland, relatively uninformative, and shallow. While the book's superficiliaty makes it more accessible to non-mathetical readers, the final product is less palatable to all readers. It is impossible to introduce and explain the occurrence of numbers and patterns in the universe without using at least simple arithmetic. In striving to reach readers of all abilities, Mr Stewart has alienated the entire audience.

Mr Stewart's writing style, however, is admirable: clear, concise and precise. The reader is left with the impression that he would be an excellent teacher, and could adequately handle the topic. (Excluding his curious, defensive, intermittent apology for 'pure' (vs. applied) mathematical reserach.)

Ill-researched and ill-presented, 'Nature's Numbers' is a cursory review that is not worth the time it takes to read it. Readers are strongly advised to avoid.

Rating:
Summary: A mathematician with his head on straight
Review: 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.

Rating:
Summary: God does not play dice, nor vice versa..
Review: 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.

Rating:
Summary: Not enough information
Review: The Science Masters series is a very good idea, but, as with all multi-authored series, the individual books are very variable in content. This one's in the middle, not as good as Jared Diamond's 'Why sex is fun', but not as bad as Peter Atkins' 'Periodic Kingdom'. It's just too basic, this book won't stretch anyone who's read any other popular maths book

Rating:
Summary: God does not play dice, nor vice versa..
Review: This book promises to introduce the world of mathematics to the layman but doesn't quite deliver. It has a great premise and raises many interesting questions but fails to answer them in a concise manner (and one that the average Joe can understand). A few more diagrams and illustrations would do wonders for the clarity of the author's explanantions. A great bibliography leads readers to better work.