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The Geometry of Biological Time (Interdisciplinary Applied Mathematics) [Hardcover]

by Arthur T. Winfree
4.0 out of 5 stars  See all reviews (2 customer reviews)

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Book Description

June 8, 2001 0387989927 978-0387989921 2nd
Dealing with dynamics of processes that repeat themselves regularly, this revised and updated edition extends the thread from 1980 to the present day, concentrating on areas of interest where there will be much activity in the future. This involves going through spatial biochemical, electrophysiological, and organismic dynamical systems and patterns that were discovered by pursuing the theme of phase singularities introduced in the original book. In particular the work on excitability in cell membranes will be thoroughly updated as will the references throughout the book.

Editorial Reviews


From the reviews: "This book is a wonderful exposition about his life’s work and is presented with such clarity that the reader gains an insight into details of his manner of thinking…the reader is taken on a quest to solve biological mysteries and travels from the intricate beginnings of formulating the questions, through the apices and troughs of analyzing, and on to the discovery of the holy grail, that which yields biological predictions and answers. One leaves with a sense of understanding that hopefully can be applied to one’s own work…this book could easily serve a dual purpose. First, through the introduction of basic mathematical concepts such as topology combined with modeling, the book serves as an introduction helping the non-applied reader to see the beauty of mathematical modeling. Second, because Winfree explains the modeling process very thoroughly, instead of just presenting equations, the book can serve as a medium for the medical professional to acquire an understanding of the modeling process. A wonderful accomplishment...I am proud to have this book on my shelf and consider it…a seminal text in mathematical modeling. This is a text that every first year graduate student should look at in some detail." (Mathematical Reviews) "The new edition of The Geometry of Biological Time is a fascinating update of the delightful original. This new edition contains thoughtful commentary on new developments in the field, adding a historical and sociological dimension to the original book's elegant and unifying treatment of biological problems involving processes that repeat themselves regularly, i.e. involve 'rhythmic return through a cycle of change.' The book is an enjoyable page-turner, even for those readers with only a passing interest in biology, and demonstrates well the synergistic effect between biology and mathematics. ... The term 'page-turner' may seem unusual in mathematics; however, it is appropriate here. Not only is the reader continually tantalized by the figures appearing on the ensuing pages, but the new commentary lends a mystery-novel feeling to the book. This second edition was created by inserting new text boxes into the original, mostly intact, edition. This style leads to a fascinating historical picture. For example, the text, '(...In the latter cases the periodicity approximation gets worse closer to the pivot. I wish here to sweep such matters under the rug (in 1978))' is followed by a new text box that begins, 'The bulge under the rug grew and grew...', continuing with a description of developments over the last two decades. The plot continues even now, with descriptions of the last twenty years often followed in the book by descriptions of current puzzles. In summary, the original book is good and the second edition is even better; the historical commentary is fascinating, and there are also a few reorganized and new chapters presenting additonal biological examples." (MAA Online)

Product Details

  • Series: Interdisciplinary Applied Mathematics (Book 12)
  • Hardcover: 803 pages
  • Publisher: Springer; 2nd edition (June 8, 2001)
  • Language: English
  • ISBN-10: 0387989927
  • ISBN-13: 978-0387989921
  • Product Dimensions: 9.5 x 7.4 x 1.7 inches
  • Shipping Weight: 3.6 pounds
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #2,225,790 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews
48 of 52 people found the following review helpful
3.0 out of 5 stars Completely Interdisciplinary Science August 18, 2001
By A Customer
This 2nd edition of a 1980 book is about 50% enlarged. Its readers today will probably be scientists two generations removed from those familiar with the first printing but this review stresses only the new stuff.
The book has two main parts: a first half containing ten chapters mostly about principles and theory, and a second half containing thirteen more about specific experimental systems. It seems curiously hard to decide whether the subject matter is narrow to the point of caricaturing academic specialization, or incredibly broad to the point of suggesting a smorgasbord for science dilettantes. Among the forty thousand academic science journals viable today, not one is devoted to the topic of "biological waves, oscillations, and phase singularities" featured in this book, so it must be too narrow even for such tastes. Yet the literature drawn upon spans an unmatchably wide gamut, ranging from practical medicine to abstract topology, from recent molecular genetics to history of science, from 1836 to 2000. And Science Citations Index shows that the first edition has been cited about a thousand times in widely diverse publications, continuing at about constant rate over the past twenty years. Maybe this is why Springer-Verlag chose to provoke a 2nd edition even after so long.
Updating is usually an opportunity to erase blunders, but this author instead preserves and draws attention to them: how did this mistake happen, and how did the item come to be seen from a different perspective, with different meaning? To avoid giving offense the author preserves mostly his own blunders for such object lessons while going out of his way to credit the innovations of others.
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8 of 9 people found the following review helpful
5.0 out of 5 stars A classic June 9, 2007
Format:Hardcover|Verified Purchase
This book gets better and better with time. The more I know about the topics covered in this book, the more I realize how important the book is and how much is to be learned from it.

For those not familiar with Art Winfree, he was a pioneer in the mathematical and experimental investigation of the temporal and spatial aspects of biological phenomena. I don't know that I would agree with the reviewer who states that the book "transgresses" scientific boundaries. Perhaps a few decades ago this might have been true, but much of what Winfree pioneered is now mainstream science, or at least well-known.

The idea of "transgressing boundaries" implies a certain sense of rebellion and frequently has polticial overtones, and I would best describe Winfree as an explorer, not a rebel. He, along with a few other scietists scattered throughout various disciplines, followed where his interests and results led him. In a way, this is the essence of pure science.

Later in his life Winfree was recognized in many ways, deservedly so, and continued to work on his ideas until his death. By that time, his work was well known to scientists in a variety of areas. As another reviewer stated, Winfree was not concerned so much with his image, as with explaining his ideas and thought processes that he used in trying to "get it right".

If you are new to the work of Art Winfree this book will serve as a valuable part of your education. If you are an old hand, who has not looked at the material in the book in a long time, it is always worth yet another reading. This is a very good book. It is a classic of science.
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