Book Description

"The great book of nature," said Galileo, "can be read only by those who know the language in which it was written. And this language is mathematics."

In The Language of Mathematics, award-winning author Keith Devlin reveals the vital role mathematics plays in our eternal quest to understand who we are and the world we live in. More than just the study of numbers, mathematics provides us with the eyes to recognize and describe the hidden patterns of life--patterns that exist in the physical, biological, and social worlds without, and the realm of ideas and thoughts within.

Taking the reader on a wondrous journey through the invisible universe that surrounds us--a universe made visible by mathematics--Devlin shows us what keeps a jumbo jet in the air, explains how we can see and hear a football game on TV, allows us to predict the weather, the behavior of the stock market, and the outcome of elections. Microwave ovens, telephone cables, children's toys, pacemakers, automobiles, and computers--all operate on mathematical principles. Far from a dry and esoteric subject, mathematics is a rich and living part of our culture.

A brilliant exploration of an often woefully misunderstood subject The Language of Mathematics celebrates the simplicity, the precision, the purity, and the elegance of mathematics. ... Read more

Reviews (10)

Step into the shoes of a mathematician
I've always had a like-hate relationship with math; I didn't do well in it in college, but I've long been fascinated by physics. There are many books for the lay person about the cutting edge in physics; books like that are harder to find in the world of mathematics.

But Keith Devlin has done it. He surely captured me near the beginning when he described mathematics as the study of patterns; a wonderful description that starts to get at why mathematics seems to be the language underlying the physical universe.

This was not an easy book for a slightly math-averse person, but Devlin's explanations were always clear, and more importantly, always gave a sense of context of what he was discussing.

Bring it on, baby!
Most people either misunderstand what math is all about, or see it as a collection of rather disjointed areas collected together under a single name. Devlin does an admirable job of re-educating us all, and showing how the different areas of mathematics are linked together, often in rather surprising ways.

This book is simply brilliant. The amount of information Devlin has managed to cram between two covers is amazing. Having spent years studying this stuff, it's rather depressing to see that most of the important things I've learned can fit into a 350 page book, but then this is surely a testament to Devlin's skill.

Although this book makes no formal educational expectations of the reader, I feel that a true beginner would have trouble following a lot of parts, although they would still get the general idea. This would be better then nothing, but I think that this book would be best appreciated by those with some formal math background. I would be curious to see what a high school student would make of this, since I really wish I'd had this book back then. When you see the beautiful ways that mathematics connects the most seemingly disparate ideas, you can't help but want to learn more!

Perceiving patterns.
Devlin: "The particular topics I have chosen are all central themes within mathematics... But the fact is, I could have chosen any collection of seven or eight general areas and told the same story; That mathematics is the science of patterns, and those patterns can be found anywhere you care to look for them, in the physical universe, in the living world, or even in our own minds. And that mathematics serves us by making the invisible visible."
At this writing it has been more than a few years since my last class in mathematics. But I liked math as a student and still do, even at the point that notation and degree of abstraction begins to hurt my head, so to speak, I still like it. There is a solidity and a beauty in mathematics that eclipses the empirical sciences. It is not only the practical applicability, logical purity, and beauty of mathematics that interest me, it is also its very immateriality. As Devlin states, "music exists not on the printed page, but in our minds. The same is true for mathematics; the symbols on a page are just a representation of the mathematics."
This is a wonderful book. Before 1900, mathematics could be wholly categorized within about a dozen subjects. While advances are still being made in some of these older disciplines -- Devlin discusses how developments in number theory are being applied to encryption for such purposes as banking security -- there are now at least 60-70 somewhat distinct disciplines of mathematics. The author reveals the logical foundations, history, and current applications of number theory, mathematical logic, the calculus, relativistic geometry, topology, and probability. Applications of mathematics to such seemingly far-flung fields as linguistics, electrodynamics, and astrophysics are briefly but aptly considered. He introduces us to the patterns and progressions of perceptive minds, from the Pythagoreans, Platonists, and Peripatetics, to Pascal and Penrose, with glances at Galileo, Gauss and Godel. [Okay, enough alliteration ... just having a little fun with patterns; and patterns, as Devlin instructs, is precisely what mathematics is all about.]

Breathtaking
This book is an incredible account into the ideas of mathematics. Devlin presents simple and extremely abstract ideas into a language that just about anyone can understand. Although some previous knowledge of the fields investigated does help, this book serves as a great introduction into such things as perspective geometry, non-Euclidean geometry, network theory, topology and quantum mechanincs. It also provides some great insights into the history and uses of number theory, algebra, geometry and calculus. I've have never read a mathematical/scientific work that was written with such passion and was a complete page turner (I read it straight over the course of 3 days). I am still amazed on how such a work can be under $50 because it is worth much more than that.

Clear and engaging
Keith Devlin is one of the best popular mathematics writers around, and this is one of his best works. The eight chapters cover number theory, set theory, calculus, group theory, topology, probability and the application of mathematics to the physical world. The discussion in each chapter, couched generally in English, not mathematics, is so clear that a math-phobic can understand it. By the end of each chapter a great deal of fascinating mathematics has been described, and in some cases the formal basis is sketched--but the emphasis is always on narration, and a lay reader who doesn't even want to understand mathematics can still read this and get a sense of the dramatic history of mathematics.

Devlin states at the end that he decided to exclude many areas of mathematics in order to focus more effectively on what he did cover. As a result there is little or no coverage of chaos theory, game theory, catastrophe theory, or a long list of other topics. The fact is there will always be holes in a book this size--mathematics has expanded so much in the last hundred years that even a book ten times this size could barely survey it. The decision to focus was a good one, and the subjects chosen are good: the truly exciting stories are here: Archimedes, Fermat, Gauss, Galois, Riemann, Wiles, and many more.

Potential purchasers should note, by the way, that this book was reworked from Devlin's "Mathematics: The Science Of Patterns". In Devlin's words (not from either book): "The Language of Mathematics is a restructuring of Science of Patterns that omits most of the color illustrations (a minus) but has two new chapters covering topics not in Science of Patterns (a plus). If you want lots of color, go for patterns; Language of Mathematics covers more ground." I've read both, and I have to say they're both worth getting. The two new chapters in this book are the ones on probability and the applications of mathematics in science; they're well done and interesting. However, the pictures in Science of Patterns are very high quality.

They're both fine books, and I can strongly recommend each of them. If you have to get one, I'd say get Science of Patterns. Even though Language of Mathematics does have some colour plates, Science of Patterns is really a gorgeous book to read with many good illustrations. I ended up buying both, and you may end up doing that too. ... Read more

Amazon.com

At the very beginning of his book on i, the square root of minus one, Paul Nahin warns his readers: "An Imaginary Tale has a very strong historical component to it, but that does not mean it is a mathematical lightweight. But don't read too much into that either. It is *not* a scholarly tome meant to be read only by some mythical, elite group.... Large chunks of this book can, in fact, be read and understood by a high school senior who has paid attention to his or her teachers in the standard fare of pre-college courses. Still, it will be most accessible to the million or so who each year complete a college course in freshman calculus.... But when I need to do an integral, let me assure you I have not fallen to my knees in dumbstruck horror. And neither should you."

Nahin is a professor of electrical engineering at the University of New Hampshire; he has also written a number of science fiction short stories. His style is far more lively and humane than a mathematics textbook while covering much of the same ground. Readers will end up with a good sense for the mathematics of i and for its applications in physics and engineering. --Mary Ellen Curtin ... Read more

Reviews (29)

A history of "i" for the mathematically initiated!
Nahin's text on the history of i is an exciting, comprehensive look into the origins of i and its elementary theoretical applications. It rightfully has been compared to Eli Maor's wonderful book "e: The Story of A Number", which deserves five stars in its own right. I do have to take issue with some of the other reviews posted here. For instance, a few have said that you have to have a "graduate math" background to fully appreciate this book?!? Who are they kidding? Nahin actually *sacrifices* mathematical rigor in order to improve his exposition. Anyone with a real mathematics background knows that complex analysis gets far more complicated than the basic material Nahin presents in his book. To get an idea, you can peruse Walter Rudin's fine text "Real and Complex Analysis". To be fair, I agree with the reviewer who wrote that Nahin should not have omitted material on Klein groups, Julia and Mandelbrot sets. However, I can understand why he did. It is difficult to write on such subjects as groups and fractals to an audience intended to have a (motivated) high school or freshman calculus background. I read this book, understood it, and loved it, long before I had any idea what groups or fractals were. Nahin gives fair warning in the introduction to his book that it is not a "mathematical lightweight". I do think that a solid background in (single variable) calculus, including power series, is crucial to a true appreciation of the book. In particular, one must know these things to value the genius of Euler and others in the section on "Wizard Mathematics". Nahin does tread lightly into other topics, such as differential equations and (advanced) algebra, but to say these are a prerequisite to reading the book is ridiculous. I think even if the reader has never encountered ideas such as the Fundamental Theorem of Algebra before, they serve to enrich, not detract from, the material. In any case, the reader should be pleased to see a leisurely treatment of something so blown out of proportion as FTA, as an understanding of it is basic to anything beyond calculus. Proofs of it are rich in variety, ranging from topology to geometry to complex variables (using the theorem of Liouville and properties of entire functions). One criticism that is entirely justified is the typographical errors that regrettably plague the book. In particular, the theorem of Green, relating double integrals to single contour integrals, a result that is surprising and illuminating. However, the careful reader can usually spot and correct such errors, and he or she should be delighted in their own astuteness, rather than blame the author. He does a wonderful job explaining the conceptual basis of i, and I think this overrides any of the books minor flaws. The book does seem to end rather abruptly, however, and I hope that if the author chooses to revise his work, he will expand upon the material, in particular, a (brief?) treatment of the Residue Theorem, the crowning jewel of complex integration. Perhaps even a section on conformal mapping? I do realize though that this may place the book too far out of reach of his intended audience.

The bottom line: if you want a storybook, this is not for you. If you like mathematics, and have a historical bent, this book will satisfy you. Those with a mathematical background will realize that Nahin has the perfect background to write this book: electrical engineers have a *much better* idea of what's going on with complex variables in terms of getting their hands dirty than mathematicians themselves. This is because most mathematicians insist on strict formalism and rigor, but engineers think more freely, and in any case they are the ones that discovered half of the applications of complex variables. E.g., imagine Laplace transforms even existing without Oliver Heaviside, who was thought to be a fool by the mathematical community in his day!

For those that are curious, I only have a B.A. in math, and no graduate education, though I do pursue math study in my free time. So I think I am in a position to make the above arguments.

thumbs-up from an EE/physicist - not meant as a textbook
This was an incredible book. I'm an electrical engineer by degree and a physicist by hobby, so I'm pretty familiar with imaginary numbers. While a lot of the concepts were a review to me, the book also introduced me to a lot of new and fascinating territory. But besides the pure math, it also introduced me to a lot of the history and personalities behind it all. Putting it in perspective and historical context helps breathe new life into it.

I must strongly disagree with the reviewers who said that the math was not rigorous enough, and that the presentation was lacking in personality (two opposite viewpoints).

The style had way more personality than any textbook on mathematics. And anyone with a high-school math background can get through most of the book (not all of it - they may need to skip the bits involving calculus). And whoever says the presentation lacks rigor is missing the point entirely, because this is NOT a textbook and was never meant to be. The author never intended to scare away the casual reader with lenghty proofs - he wants to explain in accessible terms, not alienate.

Wish more books like this
Inspiring!
Explaining the true physical meaning of an imaginary real quantity and showing its real imaginary applications.

somewhat dense and no problems to solve by the reader
This book is well written, but, it does feels like the venerable professor took his lecture notes and strung them together, but dear me, he left out problems for the reader; this to me is a cardinal sin when it comes to expository math.

Maybe the professor could create a website with problems + solutions related to the subject matter - give us puzzle people a chance at solving at least a few problems on our own.

The "imaginary" number i is quite real, and very useful.
In high school and college mathematics courses it is generally stated that, since the square root of -1 cannot be expressed as any real number, it must be a so-called imaginary number, usually designated as i. Furthermore, any number multiplied by i, say 2i, is also said to be imaginary. So-called imaginary numbers generally cause even very bright students some discomfiture, as well they should.

But, in fact, i is not an imaginary number (whatever an imaginary number would mean); rather it is something quite real: a 90 degree rotational operator. Mathematical operators -- including rotational operators -- are beyond the average person's knowledge (or interest) of mathematics, but at least they are real. And they are also quite useful, not only in mathematics but in various fields on science and engineering.

In this fascinating book Nahin traces the history of the centuries-long struggles which the concept of negative numbers and, eventually, of their square roots caused both mathematicians and philosophers until an obscure Norwegian surveyor discovered the true meaning of i in 1797.

As a scientist who spent decades using i -- but never really accepted the traditional view that it is an imaginary number -- I was overjoyed when I finally discovered its real meaning.

Clearly this book is not for everyone; but it should be quite interesting to anyone who, like I, never full accepted the concept of an imaginary number. ... Read more

Book Description

The authors, widely known for their contributions to airplane design and development, have captured both the technological progress and the excitement of this important facet of aviation. This updated edition includes new developments in propulsion-controlled aircraft, fly-by-wire technology, redundancy management, applications, and safety. It is profusely illustrated with photographs and figures, and includes brief biographies of noted stability and control figures along with a core bibliography. ... Read more

Reviews (3)

Excellent.
An excellent biography of Godel. Examines his personal life and mathematical work in an integrated manner. Dawson is thorough, well-researched, and shows a command of the mathematics involved. Never sensational or anecdotal, he provides the most accurate picture available of the real Godel. This is not a popular account of Godel's work, so the reader will need an understanding of fundamental mathematical logic and Godel's theorem to appreciate much of the book. But Dawson does provide a lot of history of mathematical logic, including a great chapter on developments up to 1928 that could be read by itself. The appendix provides a chronology, genealogy, and "biographical vignettes" of other important logicians.

The definitive biography of Kurt Godel
Knowing what went on in the mind of Kurt Godel will forever be unattainable. Nonetheless, John Dawson comes as close as possible to understanding what made Godel click.

Having catalogued Godel's works and personal papers, Dawson saw aspects of Godel's life that perhaps no one short of his wife had seen.

The book is a fascinating jaunt through the through the lives of one of the greatest minds of the 20th century. What is also interesting is Godel's interaction with personalities such as Einstein and Van Neumann.

While the mathematics is often abstract, as can be expected, Logical Dilemmas is a mesmerizing read.

By a Mathematician for Mathematicians
Writing a biography of anyone is difficult. How can a writer, no matter how talented, really claim to understand someone well enough to give an overview of his life? When the subject is a genius like Kurt Godel, whose name is known by few and whose work is really understood by even less, the job must be even more difficult. Fortunately, people like Mr. Dawson are will to give it a shot and he succeeds fairly well.

In putting together this biography, Mr. Dawson has the advantage of being mathematician. Additionally, he has the advantage of being the mathematician who catalogued Godel's papers after his death. This gives him a lot of insight into Godel that other writers cannot have and he weaves quotations from these papers into the biography very well. Mr. Dawson's is a well-documented and logical biography that is short on conjecture and long on footnotes. In brief, it is a biography about a mathematician clearly written by a mathematician. This is both its strength and its weakness.

Actually, I like the purely biographical sections of this book very much. The biographical information is clear and informative, though a bit dry in the academic style favored by mathematicians and scientists. Fortunately, having lived and worked among these people, I am comfortable with this style. More importantly, I feel like I have a better idea now of who Godel was and what he was like from reading this book. His focus on his work, his relationship with his family and friends (particularly his wife) and his ultimate decent into mental illness are much more in focus for me now.

On the other hand, the sections that deal with Godel's mathematics are much more difficult to take. The discussion of mathematics in this book goes far beyond what most people are going to be able to handle. I fear the average reader even with a decent math background who comes across this book will drop it as soon as the mathematics starts and that is unfortunate. (I am always looking for books to promote math even among non-mathematicians. This one does not do it.) A reader who can handle the math, however, will find this book revealing. ... Read more

Reviews (1)

A fascinating true adventure tale of the deep sea
This is a gripping, beautifully-told true story about Otis Barton and William Beebe, the first two explorers ever to plumb the deep abyss of the ocean.A tale of daring, ambition and wonder, Descent skillfully weaves together the separate but inextricably linked lives and achievements of these two men, who needed and tolerated one another, but who ended up barely on speaking terms.

Beebe was a renowned naturalist, whose expeditions were followed by an adoring public and whose personal charm and exploits earned him high society standing-but for whom true scientific credibility proved elusive.Barton brought to the partnership the design know-how to craft the Bathysphere, a terrifyingly small steel sphere specially engineered to withstand the pressure of the deep ocean.Technology buffs and novices alike will appreciate the lucid descriptions of how this contraption was created.

But there is nothing technical or "dry" about this marine science history-adventure leaps from every page, as author Brad Matsen engagingly combines meticulous research with a storyteller's talent for suspense and fascination.This is a lively, wonderfully written book-open to any page and your eye is almost sure to land on a beautiful sentence.Engaging and informative-I couldn't put the book down.I also enjoyed learning about some of the smart, intrepid women scientists and artists who worked with Barton and Beebe on their historic dives.Reading between the lines, one gets the sense of plenty of romantic intrigue between Bathysphere descents!

Highly recommended. ... Read more

Book Description

Ioan James introduces and profiles sixty mathematicians from the era when mathematics was freed from its classical origins to develop into its modern form. The subjects, all born between 1700 and 1910, come from a wide range of countries, and all made important contributions to mathematics, through their ideas, their teaching, and their influence. James emphasizes their varied life stories, not the details of their mathematical achievements. The book is organized chronologically into ten chapters, each of which contains biographical sketches of six mathematicians. The men and women James has chosen to portray are representative of the history of mathematics, such that their stories, when read in sequence, convey in human terms something of the way in which mathematics developed.Ioan James is a professor at the Mathematical Institute, University of Oxford.He is the author of Topological Topics (Cambridge, 1983), Fibrewise Topology (Cambridge, 1989), Introduction to Uniform Spaces (Cambridge, 1990), Topological and Uniform Spaces (Springer-Verlag New York, 1999), and co-author with Michael C. Crabb of Fibrewise Homotopy Theory (Springer-Verlag New York, 1998). James is the former editor of the London Mathematical Society Lecture Note Series and volume editor of numerous books. He is the organizer of the Oxford Series of Topology symposia and other conferences, and co-chairman of the Task Force for Mathematical Sciences of Campaign for Oxford. ... Read more

Reviews (4)

Good book
This book is a collection of short biographies of notable mathematicians from Euler to von Neumann. It does a good job of explaining both a mathematicians background and the significance of their contributions to mathematics. Great to read through or as a reference to have on the shelf.

Very good historical account of lives
The only reason that this book doesn't get 5 stars is because of the fact that not enough emphasis is placed on the achievements of the mathematicians in terms of their mathematics.

However, this does not take away from the fact that is is exteremely well researched, laid out and presented. We get a meaningful insight into how these geniuses (genii?) lived and that fact that they were quite ordinary people with the same levels of hardship (and in some cases even more) as the rest of us. Perhaps an improvement could be made on further mathematicians, both past and present.

Still recommended reading.

Learn how mathematicians interacted with each other
When reading about the great ones of mathematics, I always enjoy short biographies rather than long ones. If the biographer is required to fill a large section of a book, then they tend to cover more detail than I really care for. While I do enjoy some details about the personal life of a mathematician, anything more than just a few morsels tends to detract from their accomplishments in mathematics.
James strikes the perfect balance in describing the lives of these great historical figures. Each biographical sketch is less than ten pages and he covers their life from birth to death. One valuable thing that he does is give their complete names, which is often omitted from biographies. In fact, despite all of my reading about the people of mathematics, there were some whose full names I had not known until I read this book.
The emphasis is on the lives of the people, and the general concepts of the mathematics that they created, rather than the specifics. No formulas are used in the explanations. Personal and professional interactions are a large part of the life of nearly all mathematicians, and from these biographies, we learn many of the specifics of how contemporaries reacted to each other. As is always the case, the full range of human foibles are displayed as the lives of the mathematicians unfold.
The lives of these sixty mathematicians are described in chronological order according to their birth years. Given that they all began their mathematically productive lives at different ages, this leads to some degree of overlap in both directions. Nevertheless, it is possible to easily trace the development of the major mathematical ideas as they are nurtured from early germs to towering oaks.
Mathematicians are people who find themselves in a social and political environment that they must cope with and sometimes just survive in. In this book, you will learn about sixty of them who made a major contribution, sometimes starting from a point of privilege, and other times only after great struggle. It is well worth reading for pleasure and can also be used as a resource for a course in mathematical history.

Published in the recreational mathematics e-mail newsletter, reprinted with permission.

Captivating!
Don't miss these captivating tales of the life and the times of mathematicians starting from the period of Tsar Peter the Great of Russia, and right up to recent times, at least up to and including the Cold War. Even if you aren't in math, I think you are likely to be caught up in the drama of the various lives, times, and events. The writing is fast paced and engaging, much like that of Constance Reid's books: "Hilbert", or "Courant"... Over the tumultous historical periods, it has been said that mathematicians have been more likely than others to have been uprooted in the upheavals of history, perhaps because they are concerned with theories and ideas that are more universal. But their lives are still much affected by the times and the events of history: The French Revolution(Galois, Poisson, Fourier...), the Napolionic Wars(Cauchy, Abel...), the period of Bismarck and Nationalism in Europe(Weierstrass, Cantor, Lie...), the Russian Revolution(Alexander, Kolmogorov...), the two World Wars, and the crisis period between WWI and WWII(Banach, Hadamard, Courant, Hilbert...), and the Cold War(von Neumann, Wiener...). The pictures on the cover give you a sample of the profiles in the book: G. Polya, K. Weierstrass, A. N. Kolmogorov, N. Wiener, S. Kovalevskaya, and S.-D. Poisson. Even if you won't get to meet them in person (I was a guest at George Polya's ninetieth birthday!), this book is the next best thing. ... Read more

Book Description

When Dava Sobel's Longitude was published to universal acclaim in 1995, readers voiced only one regret: that it was not illustrated. Now, William Andrewes, the man who organized and hosted the Longitude Symposium that inspired her book, has joined Dava Sobel to create a richly illustrated version of her classic story.

The Illustrated Longitude recounts in words and images the epic quest to solve the thorniest scientific problem of the seventeenth and eighteenth centuries. Throughout the great age of exploration, sailors attempted to navigate the oceans without any means of measuring their longitude: All too often, voyages ended in total disaster when both crew and cargo were captured or lost upon the rocks of an unexpected landfall. Thousands of lives and the fortunes of seafaring nations hung on a resolution.

To encourage a solution, governments established major prizes for anyone whose method or device proved successful. The largest reward of £20,000-truly a king's ransom-was offered by the British Parliament in 1714. The scientific establishment-from Galileo to Sir Isaac Newton-had been certain that a celestial answer would be found and invested untold effort in this pursuit. In stark contrast, one man, John Harrison, imagined and built the unimaginable: a clock that solved the problem by keeping precise time at sea, called today the chronometer. His trials and tribulations to win the prize throughout a forty-year obsession are the culmination of this remarkable story.

The Illustrated Longitude contains the entire original narrative of Longitude, redesigned to accompany 178 images chosen by Will Andrewes: from portraits of every important figure in the story to maps, diagrams, and photographs of scientific instruments, especially John Harrison's remarkable clocks. Andrewes's elegant captions emphasize the scientific and historical events surrounding the images, and they tell their own dramatic story of longitude, paralleling and illuminating Dava Sobel's memorable tale. ... Read more

Reviews (28)

Excellent read that improves on the original
Having bought and read "Longitude", the only lightly illustrated original hardback version, I wanted to know more about how the actual clocks worked, and I wanted to see them, without making a trans-Atlantic pilgrimage to Greenwich.

Hence, when I saw an illustrated version of "Longitude", I had to buy it. This book contains the original text, with no additions, except for the illustrations. The photographs are beautifully done, as is the printing.

My only hesitation in not awarding the book five stars is that I was hoping for one of two things; either an illustrated version of the original, with a couple of pictures of each chronometer, at a reasonable price, or a more detailed illustrated version, with more information on how the chronometers actually work. What we ended up with is a compromise. Beautiful pictures of the chronometers, but little extra detail of Harrison's marvelous inventions.

Still, an improvement on the original, which is an excellent book, one I have read several times. Highly recommended.

By the way, when I purchased this book, I donated my original version to the library.

Highly Recommended!
"The Illustrated Longitude" is an excellent, worthwhile historical account of John Harrison's progression as an instrument maker and legitimate finder of a practical solution to the problem of determining Longitude at Sea.

If you are at all interested in the antecedents of today's accurate timekeeping devices this book is a must. The print quality is very high and the illustrations a wonderful aid to feeling the story unfold. The book does not contain detailed plans of Mr Harrison's chronometers or description of the techniques of celestial navigation, but rather is a brisk, engagingly written account of the origin of the Longitude problem, Mr Harrison's solution and those of his rivals and the political intrigues which delayed full acknowledgement of the merit of the H-1 to H-4 devices.

I bought this book some months after visiting the Old Royal Observatory in Greenwich, England. The ingenious mechanisms at work can keep an observer enthralled for hours. They are also very beautiful. "The Illustrated Longitude" really fills out the significance of the Longitude problem in that era and the career details and challenges overcome by a very clever and self made man.

Great Story, but BEWARE of innaccuracies in this book.
John Harrison completes his first pendulum clock in 1713 before the age of 20. He made the gears for this out of wood which was radical for such a use, but as a carpenter, perhaps not to him---which is a mark of genius, I'd say; to reach beyond accepted norms in this manner. This he did after borrowing a book on math and the laws of motion; which he copied word for word, making his own copy. He incorporated different varieties of wood into his clock for strenth and later invented a bi-metal pendulum to counteract the expansion and compression of various individual metals. He also employed friction-free movements so as to do away with problematic lubricants. When intrigued by the puzzle of time at sea and the issue of longitude he contemplated substituting something not prone to gravity, as a pendulum of course is, to track times passing. In 1737 he creates a cantilevered clock 4 foot square. This the longitude board (which had offered a cash bonus to anyone who could devise a method in which time at sea could be kept) admired. Four years later he returns with an improved model; then starts on a 3rd model, like the previous two, also a fairly large sized clock.But there exists a problem within this book: An artisan freemason by the name of John Jefferys at the Worshipful Company of clockmakers befriends Harrison and then later presents to him a pocket watch in 1753. Then in 1755, while still working on his 3rd model, Harrison says this to the Longitude board: I have..."good reason to think" on the basis of a watch "already executed that such small machines[he's referring to pocketwatches] may be of great service with respect to longitude." He then completes version 3 in 1759. His fourth version appears just a year later, however, and is a 5 inch wide pocketwatch! The obvious inference made by the author is that after he received the pocketwatch from Jeffreys he seemingly put his version #3 on the backburner and soon started on the pocketwatch 4th version. The author does not claim Harrison copied anything from the Jeffreys model, but she certainly phrases this section so as to lend one to believe that this may have been the case; that Jefferys had a hand in the masterstroke invention Harrison eventually produced in version #4. This is not true. Harrison commissioned the watch he received from Jeffreys and was based on Harrison's specifications. It seems that Harrison simply asked Jeffreys to test an idea which he himself hadn't the time to attack just then; as he was still working on his 3rd version of a table-top prototype clock. Hence Harrison's above statement to the board in 1755 whence his ideas were validated by Jeffreys. In addition, the author plays up the part of the Astronomer Royal's part in attempting to impede Harrison from convincing the longitiude board of the efficacy of a time-piece solution to this problem over a celestial answer to this conundrum. The author also jazzes up the issue of whether Harrison received the prize the board promised to pay for a successful solution herein; even though the board supported him for upwards of 20 years as he pursued this quest. It's as if the author intentionally omitted some facts (that the Jefferys was a Harrison commission), and pumped up others (of a rival/foil on the board trying to impede Harrison and the compensation issue; implying that Harrison was jipped) just to make the story more compelling. John Harrison's story, however, is extremely compelling as it is and didn't need this extra spice served up by the author.Do read this (very short) book on how this Mr. Harrison solved the problem of knowing where one is when at sea; and if you're in London, visit the Old Royal Observatory and the Clockmakers museum (in the Guildhall) where you can see Harrison's wonderful creations in person. Enjoy!

The Man who Captured Time so Ships could Navigate Accurately
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Note: This review has been written from a city with the following position on Earth:

LATITUDE: (43 degrees 2 minutes North)
LONGITUDE: (81 degrees 9 minutes West.)

This book contains the original 1995 "Longitude" text by Dava Sobel. In order to understand the significance of this text, the reader has to understand some words in this book's title and subtitle.

"Longitude" along with Latitude are two numbers along with their compass directions that are used to fix the position of anything on the planet Earth (as in the note above). Lines of Latitude are the imaginary, parallel, horizontal lines circling the Earth with the equator (fixed by nature) being the "zero-degree parallel of latitude." Lines of Longitude or "meridians" are the imaginary lines that run top to bottom (north to south), from the Earth's North Pole to its South Pole with the "prime meridian" (established by political means) being the "zero-degree meridian of longitude." (Since the mid-1880s, the prime meridian has passed through Greenwich, England. Before this time, the imaginary line that passed through a ship's home port was usually used as the zero-degree meridian.)

Finding latitude on land or sea is easy and eventually a device was invented to make it even more easier. But finding longitude, especially at sea on a swaying ship is difficult, a difficulty "that stumped the wisest minds of the world for the better part of human history" and was "the greatest scientific problem" of the 1770s. Ways of determining longitude astronomically were devised, but these proved to be impractical when used at sea.

England's parliament recognized that "the longitude problem" had to be solved practically since many ships containing people and valuable cargo were lost at sea as soon as the ship's navigators lost sight of land. Thus, this parliament offered a top monetary prize that's equivalent to many millions of dollars today to anyone who could solve this problem.

Enter "a lone genius" named John Harrison (1693 to 1776). While most thought that the solution to this problem was astronomical, Harrison saw time as the solution.

To calculate the longitude using time on a ship at sea, you have to realize these two facts found in this book:

(i) The Earth takes 24 hours of time to spin 360 degrees on its axis from east to west.
(ii) Noon (12:00 PM) is the highest point the sun seems to "travel" in a day.

To learn one's longitude at sea using time, as the book explains, it's necessary to do the following:

(1) Know the time it is aboard ship. (Local noon was normally used because of fact (ii) above.)
(2) At the very same moment, know the time at a known longitude (such as at Greenwich, England).
(3) The difference in time between (1) and (2) is converted to a longitude reading in degrees and direction (using fact (i) above.)

So Harrison's solution was the determination of time of (2) above by inventing a precise timepiece. It would, in this case, be set to Greenwich time. (Note that, as stated, (1) could be determined using the noon-day sun but this was not always practical. Eventually, another timepiece was used to determine the ship's local noon for a particular day.) It should be realized that this was the "era of pendulum clocks" where, on a deck of a rocking ship, "such clocks would slow down, or speed up, or stop running altogether." Harrison was to capture time by building a marine clock or "timekeeper" (eventually called a "chronometer") that could be used on a ship at sea.

This book tells the "true story" of Harrison and his chronometers. (There were five built over a forty-year period. Harrison's first timekeeping device was known as H-1, his second was H-2, and so on.) Sobel uses accuracy (as evidenced by her many references) and extensive interviews with experts in the historical and marine navigational fields to create an engaging, mostly non-technical narrative to convey a story that's filled with suspense, heroism, perfectionism, and villiany. (She includes some essential technical detail of her description of Harrison's timekeepers.)

The nearly 180 illustrations chosen by William Andrewes compliment and add another dimension to Sobel's text. As Sobel explains: "Images of characters, events, instruments (especially [the exterior and interior] of Harrison's [timekeeping] contrivances), maps,and publications...illuminate the narrative. These pictures, paired with Will's detailed, [informative, and well-referenced] captions, offer up their own version of a swashbuckling, scientific adventure in the context of history and technology."

Finally, there is a good 1999 movie entitled "Longitude" that is based on this book's text. It makes all the illustrations in this book come alive.

In conclusion, this book's text and illustrations document the exciting story of how "a lone genius" solved "the longitude problem." Sobel states this more eloquently: "With his marine clocks, John Harrison tested the waters of space-time. He succeeded, against all odds, in using the fourth...dimension to link points on a three-dimensional globe. He [took] the world's whereabouts from the stars, and locked [or captured] the secret in a...watch."

<=====>

Great If You Can't See Harrison's Clocks in Person.
So as not to repeat myself and try the patience of those customers who have already read "Longitude", I will confine my comments to the additional material in the illustrated version. If you haven't read "Longitude", it's a great little book, and I refer you to reviews by myself and others on that book's page.

"The Illustrated Longitude" contains the entire original text of Dava Sobel's book, "Longitude", along with 178 illustrations provided by William J. H. Andrewes. Mr. Andrewes hosted the Longitude Symposium that inspired Dava Sobel's book and has himself published the annotated proceedings of the Symposium in his book entitled "The Quest for Longitude". The illustrations in this book consist of portraits of people and photographs of documents and instruments which are referenced in the text. The documents include maps, journals, pages of books, and official decrees. Nearly every major player in the Longitude drama is represented with at least one portrait. Most fascinating are the photographs of the time pieces, themselves. I found the illustrations to be only mildly interesting until I got to the discussion of John Harrison's longitude clocks. At this point, I was astonished to see how grand and beautiful H-1 was...and still is, and how small and elegant H-4 is in contrast. I found it difficult to picture Harrison's clocks while reading Dava Sobel's book, and the ability to see them in this illustrated version has left me even more impressed with Mr. Harrison's work. All of Harrison's clocks are represented with large color photographs, and many of the later copies of his works by Larcum Kendall, Thomas Mudge, John Arnold, and Thomas Earnshaw are also pictured. I wish there were more illustrations addressing the workings of Harrison's clocks, but that's probably a subject for another book. I recommend "The Illustrated Longitude" to fans of John Harrison's work and early chronometers who will not have the opportunity to see these incredible instruments in person. ... Read more

Book Description

Reviews (39)

small slice of pi, big helping of Beckmann
This book is more of a chance for Petr Beckmann to give his personal opinions on historical regimes and figures than an exposition of the history of pi. That's not all bad - much of what he has to say is interesting and on target. I really enjoyed his skewering of Aristotle, the Romans, and the Spanish; as well as the homage to his heroes Archimedes, Newton, and Euler. But go in with your eyes open: pi is a sideline, not the main event.

The book also comes across as quite dated in two respects: First, Beckmann has a hard time writing more than a few pages without vehemently slamming the Soviet regime. Unfortunately, these diatribes border on McCarthyism. Second, the section on computer computation of pi is decades out of date.

I found the math somewhat terse and not particularly well explained. Some of the derivations were quite difficult to follow.

All in all, this is an interesting book, but not for anything to do with pi!

A journey through history, science and personalities
This is more than a "book on mathematics". It is an engaging work, chock full of diagrams, charts and illustration, that serve to highlight the witty, erudite text. ALong the way we touch a variety of subjects, numerology, ancient Greece and Rome, professional jealousy, explorers, the Middle Ages and last, but not least, the seeimingly infinite ways in which people have tried to calculate the value of pi.

We start in neolithic times and advance to the Egyptians and Babylonians where he surmises on their attemtps to derive this important number. The book is arranged chronolgically and Beckmann attempts to portray the social and scientific conditions under which a particular theory was conceived. It is also the story of the greats of science, the giants of the mind - Archimedes, Euclid, Newton, Pascal and Euler (and thers).

A leisure read
Buy this book if you are a math lover and are also interested in its history. Although It's not an serious math book that you can learn whole lot of math from, it does contain some mathematical derivations, formulas, proofs which can be skipped without destroying the coherency of the author's presentation.

Diseased Shellfish!
Ugh! Avoid this book like diseased shellfish! Never before have I encountered a more paranoid, chauvinistic, egotistical author. Forget learning anything about Pi. There is nothing in this book that you can't find on a goggle search *and you won't have to sit through at least 50 pages of unrelated, uninteresting garbage* There was plenty of opportunity for the author to discuss related (and for that matter unrelated) historical events concerning mathematics. Instead, you read at least 20-30 pages of Western Culture Bashing. Please, for the sake of all that is right in this world, don't buy this book and destroy every copy you run into at B and N!

How I want a drink, alcoholic of course...
"A History of Pi" is an amusing and informative romp through history with a most unlikely protagonist; a transcendental number that is know by the 16'th letter of the Greek alphabet, pi. Its pages contain historical developments, mathematical formulas, computational methods, and enormously entertaining facts, anecdotes, and trivia. It traces the understanding of this mere number from the ancients, into the dark ages, through the enlightenment, and on into the present, from stone tablet, to abacus, to digital computer. The list of notables whose legacies somehow impinge on 3.14159... include Euclid, Archimedes, Huygens, Pascal, Lambert, Leibniz, Newton, Halley, Euler, Lagrange, and Laplace, to name just a few.

If you haven't even a passing interest in mathematics, then this book will probably be an insufferable bore to you. Similarly, if your interest lies in the mathematics alone, not the surrounding folklore, history, or personalities, then the book will be nearly as insufferable. However, if you have any interest at all in mathematics along with its colorful history, then you will likely find Beckman's book to be an engrossing page-turner. To give you some idea of the range of topics that you will find in this book, here are several excerpts that I particularly enjoyed.

1) Beckman quotes the following episode, which is not directly tied to the number pi, but rather to the astounding calculating prodigies who dot the landscape of mathematics: "Truman Henry Safford (1836-1901) of Royalton, Vermont, could instantly extract the cube root of seven-digit numbers at the age of 10. At the same age, he was examined by the Reverend H. W. Adams, who asked him to square, in his head, the number 365,365,365,365,365,365. Thereupon, reports Dr. Adams, 'He flew around the room like a top, pulled his pantaloons over the tops of his boots, bit his hands, rolled his eyes in their sockets, sometimes smiling and talking, and then seeming to be in agony, until in not more than a minute, said he, 133,491,850,208,566,925,016,658,299,941,583,255!'"

2) Here is what Indiana legislators were up to in 1897: "The Indiana House of Representatives did consider and unanimously pass a bill that attempted to legislate the value of pi (a wrong value)...", which was "the equivalent of pi = 9.2376, ...the biggest overestimate of pi in the history of mathematics."

3) To illustrate the misplaced obsession of those who sought to compute pi to ever-increasing precision, Beckman relates the following quote: "Conceive a sphere constructed with the earth at his center, and imagine its surface to pass through Sirius, which is 8.8 light years distant from the earth [which is roughly 52,000,000,000,000 miles]. Then imagine this enormous sphere to be so packed with microbes that in every cubic millimeter millions of millions of these diminutive animalcula are present. Now conceive these microbes to the unpacked and so distributed singly along a straight line that every two microbes are as far distant from each other as Sirius from us, 8.8 light years. Conceive the long line thus fixed by all the microbes as the diameter of a circle, and imagine its circumference to be calculated by multiplying its diameter by pi to 100 decimal places. Then, in the case of a circle of this enormous magnitude even, the circumference so calculated would not vary from the real circumference by a millionth part of a millimeter. This example will suffice to show that the calculation of pi to 100 or 500 decimal places is wholly useless."

I should point out that the book contains more actual mathematics than I have found in virtually any other book that is intended (largely) for lay consumption. In its pages you will find numerous geometrical constructions, infinite series, calculus, and monstrous-looking continued fractions. Among the more pithy formulas you will find these:

pi / 2 = (2 * 2 * 4 * 4 * 6 * 6 * ...) / (3 * 3 * 5 * 5 * 7 * 7 * ...)

pi / 4 = 1 - 1/3 + 1/5 - 1/7 + ...

But all such formulas can be skipped over, or merely admired for their ingenuity, should the reader be unable, or unwilling, to grasp their entire meaning. I applaud Beckman for including such a panoply of mathematical formulas; it's hard to imagine doing the topic justice without them.

Oh, should you need to memorize pi to 15 significant digits (that is, 3.14159265358979), Beckman provides the following acronym: "How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics!" Enjoy. ... Read more

Book Description

The first edition of this revolutionary look at the scientific discoveries that changed our perception of the world, by the renowned physicist and bestselling author Stephen Hawking, sold over 65,000 copies. Now it's available in a gift-worthy special edition with color photographs and illustrations depicting theoretical models of the planets and their orbits--making Hawking's brilliant insights all the more accessible. This original compilation is based on seven classic works of physics and astronomy which, read in chronological order, trace the evolution of modern science. THE ILLUSTRATED ON THE SHOULDERS OF GIANTS includes selections from On the Revolution of Heavenly Spheres by Nicolaus Copernicus; Principia by Sir Isaac Newton; The Principle of Relativity by Albert Einstein; Dialogues Concerning Two Sciences by Galileo Galilei with Alfonso De Salvio; plus Harmony of the World by Johannes Kepler. It also includes five important critical essays and an original biography of each physicist, written by Hawking himself. ... Read more

Amazon.com

Part history book and part remedial physics text for those who lost interest when the equations started getting unintuitive, In Search of Schr&ouml;dinger's Cat explains quantum physics in a way that's not only clear, but also enjoyable.

Gribbin opens with the subjects that most physics professors have just started to examine at the end of the semester: The mysterious character of light, the valence concept in Nils Bohr's atomic model, radioactive decay, and the physics of life-defining DNA all get clear, comprehensive, and witty coverage. This book reveals the beauty and mystery that underlies everything in the universe.

Does this book claim to explain quantum physics without math? No. Math is too central to physics to be bypassed. But if you can do basic algebra, you can understand the equations in In Search of Schr&ouml;dinger's Cat. Gribbin is the physics teacher everyone should have in high school or college: kind without being a pushover, knowledgeable without being condescending, and clearly expressive without being boring. Gribbin's book belongs on the shelf of every pre-calculus student. It also deserves a place in the library of everyone who was scared away from advanced physics prematurely. ... Read more

Reviews (40)

Irrational reality.
Excellent explanation of the standard Copenhagen interpretation of the quantum world: in this world, events are governed by probabilities. A system (e.g. a photon) can behave as a wave or as a piece of matter. It is the act of observing that photon, that forces it to select one of these options, which then become 'real'. Otherwise, we have absolutely no idea what a photon is doing when we are not looking at it.
Into the bargain, the uncertainty principle of Heisenberg says that we cannot know the present in all its details, for an electron for instance cannot possess both a precise momentum and a precise position. There are only probabilities.
The philosophical impact of these 'facts' cannot be underestimated. Even Einstein could not accept it.
As always with Gribbin, this work is easy to understand, also for the layman. This was absolutely not obvious for that kind of subject. His writing stimulates to read further work about physics and cosmology. It is a real exploratory expedition.

Amazing!
Although "Schroedinger's Cat" is frequently described as quantum physics for the layman, beware! When I first read it, I was only able to handle it because I had recently taken a rather intensive high school chemistry class.

If you're not up-to-date on your chemistry & physics, you might want to try a primer or refresher before you tackle this one. But, believe me, it's well worth it. Once you've got the basics down, "Schoedinger's Cat" gently leads you through mind-blowing concepts your mama never imagined.

And it makes for great conversation! Even your least nerdy friends will be fascinated by your newly-authoritative explanations of How the Universe Really Works.

poor
This book is alright if youd like to hear about what scientist rushed into the other ones office screaming. Or the life of Dr. Planck, and three hours later find out what the planck length is and what it,s used for. i personally want the facts and the information about the interesting subject that they use as their title. Not the history of why a world class scientist killed himself. To sum up it's a great book if you want a biography with the interesting stuff strewn about in many places so you have to search. although if you like a historical book then you may find it interesting.

The Mind Boggles
A friend recommended this book to me...little did I know I was about to embark on a journey to the heart of the atom, and the limits of the known universe.

I am not generally a math person, but John Gribbin makes the ideas and equations of quantum mechanics accessible to non mathematical people in a readable, non patronising yet entertaining way.

More than anything else, this book demonstrated to me the truth of something that Madeleine L'Engle frequently states in her non fiction; scientists are indeed the modern mystics.

Should be required reading for ALL college students
Look! At the photon! It's a particle! No, it's a wave! No, it's a... well, it's BOTH!!! And not only that, but it can interfere with itself, or with other consequential photons!

WHAT?!?!?

Welcome to the wacky world of quantum physics, the science so absurd that even Einstein couldn't believe it (and let's face it, after relativity, he was the MASTER of the absurd-but-true) where statistics are everything, specifics only happen when you're looking for them, and nothing is real at all, anywhere.

Again, WHAT?!?!?

In Schroedinger's Cat, John Gribbin not only explains all this nonsense, but he actually makes it understandable. This amazing book should be required of all college students, as part of a well-rounded education. Engineers and scientists will be amazed and think it's cool, but even "fuzzy majors" (i.e. everything else -- sorry, that's what we arrogant engineers called the denizens of that side of campus) will be able to understand it, and they too will be enlightened by it.

If you have any interest in science, in knowing what theoretical physicists really do, in knowing what a "particle accelerator" is, or even just want to have some idea about how much of Star Trek is based on real science, you MUST read this book. Not only that, but you must read THIS book before reading other books on quantum mechanics.

Ok, enough ranting. I think it takes a certain amount of Zen to grasp all this quantum non-reality particle-wave-duality possible-parallel-universe stuff. Gribbin, then, is the true Zen Master. Gribbin takes that which is not only beyond comprehension but beyond even Einstein's belief, and makes it understandable to the layman. He uses great examples that not only explain key concepts, but also help the non-Zen-Master remember them in such a way that makes one sound like a Guru at cocktail parties.

Pardon my silliness. Just read the book. And then buy it for all your friends, kids, friends' kids, coworkers, and anyone else on your gift list. Yes, it's THAT good. ... Read more

Book Description

"Georges Ifrah is the man. This book, quite simply, rules. . . . It is outstanding . . . a mind-boggling and enriching experience." –The Guardian (London) "Monumental. . . . a fascinating journey taking us through many different cultures."–The Times (London)"Ifrah’s book amazes and fascinates by the scope of its scholarship. It is nothing less than the history of the human race told through figures." –International Herald Tribune Now in paperback, here is Georges Ifrah’s landmark international bestseller–the first complete, universal study of the invention and evolution of numbers the world over. A riveting history of counting and calculating, from the time of the cave dwellers to the twentieth century, this fascinating volume brings numbers to thrilling life, explaining their development in human terms, the intriguing situations that made them necessary, and the brilliant achievements in human thought that they made possible. It takes us through the numbers story from Europe to China, via ancient Greece and Rome, Mesopotamia, Latin America, India, and the Arabiccountries. Exploring the many ways civilizations developed and changed their mathematical systems, Ifrah imparts a unique insight into the nature of human thought–and into how our understanding of numbers and the ways they shape our lives have changed and grown over thousands of years. "Dazzling."–Kirkus Reviews "Sure to transfix readers."–PublishersWeekly ... Read more

Reviews (7)

A great book to browse through
I was intrigued enough by Mr. Peterson's review here to look at the review by Dauben that he mentions. My conclusion is that the Dauben review should be treated with a grain of salt. It's not particularly balanced. In some of the criticism of Ifrah from people with more degrees than he has, one gets just a whiff of jealousy that the reviewers didn't have the endurance to write the book themselves.

If they had, I doubt they would have done any better of a job. Ifrah's book isn't perfect, but one can't expect such a book to be. This book is huge, folks. Ifrah is only one human being who tried to synthesize dozens of fields in none of which he could expect to become an expert. I think he did his best and I find his writing style companionable. Of course he makes errors, but he says a lot more things very well. We should be mindful of the book's limitations. But we also have to be grateful for what Ifrah managed to do.

A deception?
This book is getting raves from intelligent readers who are not
experts in the history of numbers. But it sure isn't getting good reviews from experts. A group of scholars in France was disturbed by the uncritical popularity of the French edition,
and released a report calling the French edition "historically
unacceptable, a deception." [Bulletin de l'Association des
Professeurs de Mathematiques de l'Enseignement Publique 399 June 1995)] (I got this quote from Joseph Dauben's book review.)
More recently, in the January 2002 and February 2002 issues of
the Notices of the American Mathematical Society, Joseph Dauben
of Lehman College at CUNY critiqued the English tranlations of this book and its companion, "The Universal History of Computing." Professor Dauben consulted a number of experts in specialties such as the history of Arabic mathematics, Hindu mathematics, Mesopotamian mathematics, Chinese mathematics, and Mayan mathematics. His review is skeptical.

I'll quote various lines from Dauben's January review:

"...he[Ifrah]either wrote to the wrong experts, was indifferent to their responses, or was not prepared to settle for their inconclusive results and the tentative nature of their research."

"...Ifrah offers nothing but certainties." (when writing about
the Hindu-Arabic number system)

"[James]Ritter simply declares all of this to be false, due to an erroneous conflation of sources. First of all, he takes Ifrah's list to be a contrived amalgamation of names coming from
all epochs." (James Ritter is an Assyriologist at Universite de Paris VIII, the quote is about Ifrah's conclusions about Sumerian numbers.)

Read Professor Dauben's review. Afterwards, George Ifrah's fun-to-read, plausible book won't count for as much.

5000 years in the fascinating story of numbers
One day, the young "devils" in a high school's mathematics class in France, asked some "plain" questions to their teacher: "When the numbers were invented?", "What is the history of the number Zero?", "How the ancients began writing down symbols for the numbers?" and so on... And these questions, changed the life of Georges Ifrah, the mathematics teacher in our story. He began his long voyage in the history of numbers and mathematics, through all mysterious ancient civilizations.

"Universal History of Numbers" is a huge, marvellous, fascinating story which deals with the birth of essential concepts in numbering systems in our distant past. Ifrah chases the clues in ancient sumerians hexagesymal system; the magical hieroglyphes of ancient Egyptians; the mysterious Maya and their counting system; Hebrew, Greek and Roman numbers with the mystics of "gematria"; sacred numerical signs of ancient Indus civilization and China, and much much more.

This is not just a "history of numbers"; Ifrah's work is a brilliant study on the roots of our civilization. While dealing with the numbers, he also presents us a perfect panorama of ancient cultures, such as the Maya calendar, the Vedic philosophy, Ancient Sumerian myths or the stories of Egyptian gods, in a very entertaining style. If you are interested with the roots of civilization and "ancient wisdom", you must read this excellent book - you'll never regret.

Absolutely Astounding
This book is a treasure beyond measure. Truly a history of mankind traced through numbers, starting with the dispersion of mankind at Babel. The dedication of this author is astounding, and his ability to assemble the tremendous amount of research into this work is worthy of some medal or prize of some sort. Surly God gave this man an unusual mind to present to the world such a work. I can't find the words to adequately describe this awesome and monumental work. Well done is not enough. Thank you Georges Ifrah.

Excellent work numbers
Simply the best book on numbers I've read. Many other books on numbers are replete with inaccuracies and exaggerations based on cultural and educational biases. Not here. Ifrah's chapter on the India's contribution to numbers and how the Sanskrit language was used to communicate numbers is simply spectacular. A must read for anyone interested in mathematics. ... Read more

Amazon.com

You probably enjoy eating codfish, but reading about them? Mark Kurlansky has written a fabulous book--well worth your time--about a fish that probably has mattered more in human history than any other. The cod helped inspire the discovery and exploration of North America. It had a profound impact upon the economic development of New England and eastern Canada from the earliest times. Today, however, overfishing is a constant threat. Kurlansky sprinkles his well-written and occasionally humorous history with interesting asides on the possible origin of the word codpiece and dozens of fish recipes.Sometimes a book on an offbeat or neglected subject really makes the grade. This is one of them. ... Read more

Reviews (76)

A bitter ecological tale for our time
This is a fascinating book.

It's also very sad, because it illustrates the ability of modern people to almost unconsciously wipe out the natural resources of our planet. Codfish were once the "buffalo" of the oceans -- big, fat, useful and dumb. As one early explorer wrote, to catch cod all you need do is lower and bucket into the water and haul it back up full of fish. Sorta like buffalo in the days when passengers could shoot them from the windows of passing trains as a harmless sport intended solely to break the boredom of the trip.

Yes, this book is a bitter ecological tale for our time.

It is also a wonderful history of a marvelous fish. Kurlansky obviously had fun writing it, and his love of cod shows in the comfortable style of his writing. He delves into word origins for the different ways used to describe cod, and he plays with the history of a dozen or so nations to illustrate the impact one fish had on entire peoples. Plus, he includes dozens of recipes by which cod was cooked for generations.

But he also explains why such an international treasure has almost vanished.

"Whatever steps are taken, one of the greatest obstacles to restoring cod stocks off Newfoundland is an almost pathological collective denial of what has happened," Kurlansky writes near the end of the book. "Newfoundlanders seem prepared to believe anything other than they have killed off nature's bounty."

What happened? Kurlansky writes that "One Canadian journalist published an article pointing out that the cod disappeared from Newfoundland at about the same time that stocks started rebuilding in Norway.

"Clearly the northern stock had packed up and migrated to Norway," he adds. If this is the Canadian attitude, in one of the self-proclaimed best educated and wealthiest of nations, it's not hard to understand why and how Third World nations have environmental problems. My personal experience with a similar depletion is in the Sea of Cortez, where Mexican fishermen have taken about 20 years to just about exterminate the sharks.

Shrimp boats, based in Puerto Penasco, have likewise decimated the shrimp. Who's to blame? The United States, of course, because the Americans built dams on the Colorado River which prevents the river water from reaching the sea.

There's always someone else to blame.

As I said earlier, it's a sad book. Yet, it is an excellent one and perhaps one of the most appropriate to read in terms of what is fast happening to our marine life. Cod are invisible, not like cute furry little baby seals which so excited Europeans a few years ago when they saw how Canadians clubbed them to death to avoid marking the fur. If the future of our world depends on cute pictures on TV, then our future is truly in deplorable shape.

But, the fact this book exists and is written with elegance, style, wit and great insight, may persuade thick-headed politicians that even "invisible" wildlife deserves protection from our greed and ignorance. If not, and having known many politicians for many years I'm not optimistic, it is a beautiful elegy to a noble fish.

What happens when a native species disappears? Well, two centuries ago the US Southwest had some of the world's finest grasslands. Then came the Russian Thistle, an almost useless weed that choked out the grass. Now we celebrate this import in song, "See them tumbling along . . . . . the tumbling tumbleweeds."

It happens.

hungry for a lost fish
A purse-sized history of the cod fishery, from the Basques & vikings to the fishes' modern decimation by large scale bottom-dragging. The social & historical ramifications spawned (no pun intended) by the international quest for this fish are incredible. Kurlansky's book weaves historical accounts in choronological order with hundreds of years of recipes for preparing cod. Though the book was well-written, concise, and highly interesting, I found it oddly incongruous to read about the vast decimation of this species yet find myself hungry for the very same fish after reading the next page's recipe for it.

Perfect For Detail Junkies
Cod is not for every reader, reflecting as it does the author's deep interest in history, and how individual foods relate to history. What the book gives to thoughtful readers is true context along with its detail. Kurlansky drives home a real point: you cannot separate the fish from the men who risk and lose their lives to extract it from the sea, nor can the food be divorced from the dollars it represents. In culinary terms, I was inspired to start cooking with dried cod; it's the kind of thing you don't notice in your supermarket until something--this book in my case--sticks it into your consciousness with no going back. As a real "foodie" and an incurable history buff, I am thankful that writers like Kurlansky go to the trouble of applying their talents to subjects like this.

Food writer Elliot Essman's other reviews and food articles are available at www.stylegourmet.com

Interesting and informative , but ...
This book is another interesting and informative, but narrow subject history book of the type this author prefers to write. In some sections it poses as a cookbook. I was irritated by the amount of text actually devoted to Codfish recipes, when what I purchased was a historical type book . The author has a very good writing style. The book covers the early history of some cultures that took advantage of this bottom dwelling fish prized for its unique white meat. The Codfish affected these early cultures as it still does today, where regional and national economies are suffering from the impact of worldwide diminishing Codfish stocks in spite of some sporadic conservation measures.
This reader recommends ignoring the all too frequent codfish recipes interspersed with the good historical information. This book makes for a fine compact interesting history of man's relationship with the Codfish. Ignore the historical section and I suppose it would be a passable Codfish cookbook.

A Cod piece
Overall, I thought Cod to be an "ok" read. It's strongest points were the inclusion of historic references to cod, images, and recipes - a novel approach for a non-fiction work. I also found the stories of contemporary cod fishermen (who aren't allowed to fish!) quite compassionate and the history of Basque fishers-of-cod both enlightening and surprising.

However, Kurlansky was often repetitive with his cod anecdotes, and I found his writing style to be a bit cumbersome and slow. I'm a big fan of John McPhee's work, which exemplifies the essay as poetry, and I had hoped that Kurlansky might offer a new, strong voice in the non-fiction, natural history essay. I was a bit disappointed that the central text read much like an undergrad research paper. I do plan to read his recent book Salt because I find the subject premise intriguing.

If you like eating fish or fishing, are interested in how natural and human history intertwine, or are simply a fan of nature writing, I would recommend giving Cod a try. ... Read more

Book Description

Man and Nature in the Renaissance offers an introduction to science and medicine during the earlier phases of the scientific revolution, from the mid-fifteenth century to the mid-seventeenth century. Renaissance science has frequently been approached in terms of the progress of the exact sciences of mathematics and astronomy, to the neglect of the broader intellectual context of the period. Conversely, those authors who have emphasized the latter frequently play down the importance of the technical scientific developments. In this book, Professor Debus amalgamates these approaches: The exact sciences of the period are discussed in detail, but reference is constantly made to religious and philosophical concepts that play little part in the science of our own time. Thus, the renewed interest in mystical texts and the subsequent impact of alchemy, astrology, and natural magic on the development of modern science and medicine are central to the account. Major themes that are followed throughout the book include the effects of humanism, the search for a new method of science, and the dialogue between proponents of the mystical-occult world view and the mathematical-observational approach to nature. ... Read more

Reviews (1)

A chronicle of Science
I almost never read books about man and nature in the renaisance, and this was one of the best ones I have read, if not one of the very best. Read up! ... Read more