To Infinity and Beyond: A Cultural History of the Infinite by Eli Maor (PDF)

Description

Eli Maor examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences. He evokes the profound intellectual impact the infinite has exercised on the human mind–from the “horror infiniti” of the Greeks to the works of M. C. Escher; from the ornamental designs of the Moslems, to the sage Giordano Bruno, whose belief in an infinite universe led to his death at the hands of the Inquisition. But above all, the book describes the mathematician’s fascination with infinity–a fascination mingled with puzzlement. “Maor explores the idea of infinity in mathematics and in art and argues that this is the point of contact between the two, best exemplified by the work of the Dutch artist M. C. Escher, six of whose works are shown here in beautiful color plates.”–Los Angeles Times “[Eli Maor’s] enthusiasm for the topic carries the reader through a rich panorama.”–Choice “Fascinating and enjoyable…. places the ideas of infinity in a cultural context and shows how they have been espoused and molded by mathematics.”–Science

User’s Reviews

Editorial Reviews: Review “Maor explores the idea of infinity in mathematics and in art and argues that this is the point of contact between the two, best exemplified by the work of the Dutch artist M. C. Escher, six of whose works are shown here in beautiful color plates.” ― Los Angeles Times”Fascinating and enjoyable . . . [P]laces the ideas of infinity in a cultural context and shows how they have been espoused and molded by mathematics.” ― Science From the Back Cover ‘Maor explores the idea of infinity in mathematics and in art and argues that this is the point of contact between the two, best exemplified by the work of the Dutch artist M.C. Escher, six of whose works are shown here in beautiful color plates.’ -Los Angeles Times

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book has no rival for its subject. It is especially useful for readers who are not workings in the formal aspects of the areas the book covers. It is a pleasure to read.

⭐Humorous. Well explained math at the foundations of Calculus. Beyond that as well.Highly recommended for anyone interested in modern thought

⭐I bought this book both for its content discussing the infinity in an unusual historical context and for its author Eli Maor who has a fine reputation as a mathematics expositor. The book discusses the infinity from a few different points of view, ranging from mathematical to the aesthetic. He discusses the infinity of positive integers, the concepts of convergence and limits, the intrigue of infinite series (including Zeno’s paradoxes), the strangeness of irrational numbers and more. He also discusses some aesthetic aspects of the infinite including the work of he Dutch artist M.C. Escher which is illustrated using both black and white and color pictures. The appendix supplies additional details for those interested in understanding the topics at a greater depth. Maor’s style of writing is relaxed and his prose is full of historical remarks and lively comments about ideas and the bright people who thought them up. The reader with a with rather negligible mathematical background gets a non-trivial and enjoyable understanding of the infinity from reading this book. This is a more fulfilling read than the average layman level expositions to the topic of infinity that often tend to be too light and airy.

⭐Wow, to look at some of these other reviews, you might think that either I have received a wholly different book than the other reviewers, or maybe the author SURE HAS A LOT OF FRIENDS !!This book should be accessible to middle school children, there is nothing about the subject matter or the proofs in the book that is beyond their mathematical reach. So I bought this book for my kids who are very bright in mathematics. Unfortunately, the writing is horrible. Why would you write a popular science book and target it at readers in the middle of college?I ran the first six paragraphs (1000 words, 6Kb) of the introduction of this book through the AT&T Bell Labs “Writers Workbench” to support my thesis that the writing in this book is needlessly complex. Here is an objective report on the reading grade level, using 4 very-widely accepted formulas for reading grade-level :readability grades: (Kincaid) 13.8 (auto) 14.0 (Coleman-Liau) 10.3 (Flesch) 13.8 (44.9)sentence info: no. sent 36 no. wds 981 av sent leng 27.2 av word leng 4.62 no. questions 2 no. imperatives 0 no. nonfunc wds 537 54.7% av leng 6.11 short sent (<22) 39% (14) long sent (>37) 17% (6) longest sent 76 wds at sent 30; shortest sent 7 wds at sent 16…So by 3 out of 4 measures, the book is appropriate for somebody in 14th grade, i.e. a sophomore in college. What a total waste !!It’s the last time I EVER purchase something from Birkhauser Academic books of Boston, the original publisher. Birkhauser takes all the leftovers that Addison Wesley of Massachusetts won’t publish. The Birkhauser books are usually overly technical for the subject matter they present, whereas Addison Wesley books are a paragon of simplicity. Even though the current edition is published by Princeton University Press, the original version was published by Birkhauser, and that should have been my tip-off that this is not a well-written book.P.S. My doctoral degree is theoretical computer science.

⭐I bought this book just to remind myself a few lessons I had learned about 45- 55 years ago. Now I am ready to answer my grandson’s question, what is infinity and how do I get there?This is a fantastic book for anyone who has had some extensive Math and Calculus training in his/her past. I highly recommend it to anyone who wants to open their mind and learn something beautiful with ease.

⭐I purchased this for a first year seminar college course and thoroughly enjoyed the read. Maor explores the history of infinity through ancient and modern scientists and philosophers. The book covers infinity in art, science, philosophy, mathematics, space, and conceptualization. This book would be a informational read that isn’t too difficult to understand and explains material thoroughly. Will read again in the future.

⭐It’s more cultural than scientific and I am looking for mathematical treatments of infinity.

⭐Maor is thoroughly at home in the realm of mathematics, its history and the frequent detours into the lives of the men who have brought its secrets to light. To Infinity and Beyond is a lighter read than either e, the Story of a Number or Trignometric Delights (his two previous titles). However, this work is infinitely enlightening and exponentially chocked full of “aha’s”. Maor enriches the reader’s understanding not only of mathematics but the culture in which it has flourished. An absorbing read.

⭐It should be noted that this book was written in 1987, several years before Maor’s book: “e- the Story of a Number” – [the computer rendered image on the cover may belie the age of the book]. As I write this I am a second year mathematics undergraduate; I read “To Infinity and Beyond” during the summer. I was first introduced to Cantor’s levels of infinity in this book, (extending countability and uncountability to aliph values, and that in effect bijective functions could map one set to another providing it has the same aliph value. First learning this principle felt like an eery truth of reality of high subtlety and high information. All of the great ideas have the eery convincingness that overcomes initial non-intuitivity… either non-intuitivity or that people before missed all together that which was sprawled in front of them). There was a rewarding explanation of the conception of non-Euclidean geometry, which to my shock but not to my surprise, was yet another fundamental idea that came from the mind of Gauss. Tragedy is touched upon as the tale of the Italian scientist, (he probably would have been called ‘Philosopher’ back then), named Bruno was burnt to the stake for his beatiful imagination in conjecturing that the universe is truly infinite and that there are infinitely many other worlds of creatures like us. The final chapter fills the reader with inspiration as Maor explains our place in the universe and ends with the comment, (not verbatim): “Perhaps the greatest question remaining to human enquiry is whether we are alone.”

⭐This is probably one of Eli Maor’s first. It is good but his other book ‘ e, the story of a number’ goes to greater depth albeit covering, arguably, lesser breadth and is probably his best. These are from a unique genre of math books; their closest parallel that I can think of are Rudy Rucker’s books like ‘ Geometry, Relativity and the 4th dimension ‘. They are not for every Tom, Dick and Harry. If you are well versed in Math you may breeze through courtesy of these excellent authors; else, significant effort is needed to wade through. And if you are up for it, the authors make the journeys worthwhile with many hidden gems in every nook and cranny of the books. Note to American publishers – Print and paper quality can be significantly improved given the price at which you sell books like these.

⭐商品の状態は「良い」とのことでしたが、１９８９年出版の本で非常に古いので、「良い」ことはないだろうと思って購入しました。この商品の中古本を買うのは３度目ですが、他社の表記と比べると経年劣化からして「可」だと思います。それにしても商品がとても煙草臭い。以前の持ち主が喫煙者だったのだと思いますが、匂いまではさすがにクリーニングできないのでしょうか。ビニール袋から取り出した状態で部屋に置いておきたくはないほどです。おそらくそのまま廃棄すると思います。

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