This book examines the ongoing (1655-1680) conflict between Thomas Hobbes and Oxford's Savilian Professor of Mathematics, John Wallis, over the squaring of the circle and related problems of Euclidian geometry. To the end of his long life, Hobbes asserted that he had succeeded in squaring the circle, and Wallis refuted him again and again. This "war" extended beyond mathematics, to, to each man's religious beliefs and politics.
What interested me most immediately was the cast: the people involved and their intellectual and personal relationships. Hobbes' first public involvement with squaring the circle, was his intervention in the dispute between the Danish mathematician Longoburg (Longomontanus) and John Pell. Interestingly, Hobbes demonstrated that Pell was correct in rejecting Longomontanus's claim to having squared the circle. Pell was author of an essay regarding establishment of a library of mathematical books and instruments. That essay was published as an appendix to his friend John Dury's The Reformed Librarian. Pell and Dury were part of the Hartlib circle, as was Theodor Haak, who reported Hobbes' role in the Pell/Longomontanus dispute to John Aubrey. After that we see Henry Oldenburg, secretary of the Royal Society, asking Hobbes to make up a list of mathematical texts. Presumably, the list was for Robert Boyle. In 1658 we find Thomas White and Kenelm Digby carrying communications between Fermat and Fenicle de Bessey in France and Lord Brouncker and Wallis in England. White, a Jesuit, had headed the English College at Douai; he had engaged Hobbes in debate over Galileo's Dialogues; and, at the end of a long life of intellectual distinction, he was caught up in the Popish Plot fabricated by Simon Oates. Etc.
It's worth describing the problem of squaring the circle, because it accounts for so much. Simply put: can a square be constructed that has the same area as a given circle, or vice versa? The key to the answer is in the word "constructed." By means of certain curves, such a square or circle can be defined. But those curves cannot be constructed using the classical instruments: ruler and compasses. Essentially, we're dealing with the transcendental character of pi, something that wasn't proved mathematically until the early 19th century.
Jesseph asks the question: why did Hobbes insist so long, to the end of his life, that he had squared the circle? Wallis refuted him again and again, but Hobbes hung on like a snapping turtle. Answering the question opens a window on the political, philosophical, social, and mathematical developments of the time. To summarize:
Hobbes's materialist philosophy brought him to support Isaac Barrow in Barrow's contention with Wallis over the primacy of geometry over arithmetic. These were the two components of classical mathematics, geometry dealing with continuous quantities and arithmetic with discrete. Barrow held that geometry was primary because it dealt with real physical reality, like distances and area, whereas numbers were abstractions: 1, 2, 3, etc. are concepts drawn from one egg, two brothers, three ships, and the like.
Hobbes' Erastianism--his contention in Leviathan that the king should be ruler over the religion of his subjects--placed him on the side of the Independents (congregationalists) against the Presbyterians in Protectorate religious politics. Hobbes, himself an atheist, felt that the Independents could be more easily be brought to heel by the King than the Presbyterians. Wallis was a Presbyterian, had even been Secretary of the Westminster Assembly.
Hobbes shared with the eduicational reformer John Webster and the Independent preacher William Dell a mistrust of the universities as temples to the scholasticism deriving from Aquinas. Wallis and his friend Seth Ward, Savilian Professor of Astronomy, were both actively involved in defending the universities from these attacks.
Of particular interest is the first of these issues. The debate between geometry and arithmetic came to the fore at this time because the distinction between the two was breaking down. Descartes (1637) and then Viete (1646) had defined analytical geometry. Napier (1620s?) had derived the logarithm from his work on the geometrical problem of the parallax. Cavalieri (1635) developed a "method of indivisibles": parallel slices of a geometric figure which, taken together, define the figure. Where this all is going, it seems to us in Whiggish hindsight, is toward notions of infinity, infinite series, and Newton's calculus.
I'll close by noting that Jesseph responds to Shapin and Schaffer, who, in their Leviathan and the Air-Pump, make "the success or failure of a scientific research program entirely independent of the truth or falsehood of the program's central claims." Jesseph calls their approach Wittgensteinian, but it was recognized when the book came out as post-modernist radicalism: science as pure social construct, without necessary basis in either the physical world or agreed canons of reason and method. The fact that Hobbes persisted so long in his claims is certainly less important than that after 1670 he was no longer taken seriously as a mathematician, except insofar as Wallis took the time and effort to refute him in the Transactions of the Royal Society.

On the surface, this book seems an unlikely candidate for my enthusiasm. It appears to be 500 pages of minutia. In fact, the author starts out by saying it is an expansion of a footnote to an early work on the relatively obscure Calvinist mathematician Wallis. How perfectly academic! If that doesn't put the book out of reach, look forward to reading about 1000 footnotes.

Regardless, I think this a great book. Once I got comfortable with the terms, I realized this might be construed as something much more interesting than the traditional 'discovery' of mathematical truths. I'm still not exactly sure how to characterize it, but I'm having fun thinking it a history of science fiction. After all, 'squaring the circle' is the 17th century equivalent to predicting the winner of the Kentucky Derby or tomorrow's change in the Dow Jones Industrials. I may be stretching a bit here, but there is clearly more on the plate than justifying 17th century mathematic revolutions with apples falling on the head of a reclining Newton.

Rather than placing the subject matter in purely mathematical terms, Jesseph considers his material in a wider context, one that makes room for Restoration style science fiction. Keep in mind that Newton's alchemy was an early form of teleportation and the monads of Leibnitz took advantage of an early warp drive. Despite overtly humiliating Hobbs for his mathematical errors, its clear that Jesseph finds Hobbs the ultimate winner. Hobbs suffers no more from his lapse of academic rigor than any contemporary science fiction author. And like Jules Verne, the spirit of his ideas has won if not his details. The political science advocated by Hobbs in Leviathan is hard to distinguish from contemporary standards. Hobbs advocated severely limiting the legal authority of church bishops, scientific materialism and the notion that good laws could produce a good society. Meanwhile, Wallis would be known as a dogmatic right-wing Christian fundamentalist. Further, most of us are convinced that science has 'solved' the problem of 'squaring the circle' which is all Hobbs was advocating, anyway.

And so, Jesseph does a subtle job of indicting my modern sensibility. Painting Hobbs to be the fool, he is actually pointing a finger at my happy secular humanism. Bravo!

So, why is squaring the circle so tricky?

In short, an attempt to find the circle which is exactly 1 square foot in area forces us to confront conflicting intuitions about how we prove the existence of 'real' objects. Try it out for yourself. It is something you can attempt with pencil and paper, or better... try it with a home computer. One of the great things about this book is that it lays out the mathematical issues clearly enough that anyone with high school algebra and maybe an ability to write an excel spreadsheet, can play the 17th century geometer and mathematician. I had a great time doing a 'quadrature' in Excel. If you are interested, I'll email you the spreadsheet (see users.htcomp.net/markmills).

In summary, I think Jessup's book fits into a broad, ongoing reappraisal of mathematical history. I can identify 3 trends, 'Squaring the circle belonging to the 3rd and most important of them:

1. Bringing non-western mathematics to western readers. The best of this is the ongoing research into ancient Chinese mathematics. See 'Chinese Mathematics: A Concise History', Li Yan, Du Shiran, John N. Crossley, Anthony W.-C. Lun, Shih-Jan Tu or 'Astronomy and Mathematics in Ancient China: The Zhou Bi Suan Jing', Christopher Cullen. In short, most of what the Europeans called 'new' math in the 1500s had been around for 500 years in China.

2. Finding a physiological basis for mathematic intuitions. Check out the cognitive research described by 'Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being', George Lakoff, Rafael E. Nunez, Rafael Nuñez. All you really need to read is the first chapter. The rest is rather speculative.

3. Reappraising the conventional myths about heroic ancient European mathematicians. Unless your ambition is a tenured job teaching the history of math, you will have a great time reading sensible inquiries into pre-modern western math. Take a look at 'Biographies of Scientific Objects , Lorraine Daston (Editor), or Pappus of Alexandria and the Mathematics of Late Antiquity, Serafina Cuomo.

One cannot help wondering why two scholars did engage in such a fiercely dispute for half of their intellectual life. John Wallis, Oxford's Savilian professor of geometry had no trouble in exposing time and again the mathematical short-commings in the preposterous claims of so ill equiped an amateur mathematician as Thomas Hobbes. But why was the battle so intense and why should it cover nearly a quarter of a century, producing hundreds of letters, books and publications? Even more bewildering is the fact that the subject of the debate, squaring the circle, was later proved to be impossible and that neither the claims of Hobbes nor the rebuttals of Wallis contributed anything significant to the field of mathematics. Fortunately, Douglas Jesseph provides adequate answers to these questions in this excellent work on 17th century history of mathematics. A study of these important controversies sheds light on the reform of mathematics in the 17th century and exposes the widely divergent philosophical conceptions of mathematics to which both antagonists adhered.

A first fundamental issue concerned Hobbes' materialistic foundation of mathematics where Wallis reasoned from the traditional account that mathematical facts do not depend on the structure of the material world. A second source of dispute was the completely different concept of ratios: Wallis defended that those ratios could only be applied to homogoneous quantities. Thirdly, the angle of contact between a circle and its tangent was a subject of wilful misunderstanding from the part of Wallis. Finally, the important 17th-century debate on infinitesimal small quantities was heavily criticised by Hobbes and although he did not develop an alternative, his objections to some of the obscurities of Wallis' arithmetic of infinities were well justified. These disputed foundations on the philosophy of mathematics were not the only sources of the irreconcilable conflict. Wallis and Hobbes also held opposing views on methodological issues such as the nature of demonstration and the centuries-old discussion on analytic and synthetic methods. For Hobbes all demonstration must arise from causes and as such he rejected techniques from algebra and analytic geometry in which one starts by assuming the truth of the proposition that is ultimately sought and deduces consequences from that assumption. In doing so he tossed aside the tools that might have helped him in his desperate attempt to make his mark as mathematician. Apart from diverging views on the fundaments of mathematics and methodological issues, religious and political positions play part in explaining the controversy. Wallis fitted neatly into the reformed tradition while Hobbes' religious opinions stood far apart. Hobbes was excluded from the newly established Royal Society for ideological and personal reasons and as such was deprived from a forum to respond to his critics. His political opinions and his vitriolic polemics at universities brought him into conflict with many important people and explain at least some of the vehemence with which the dispute was conducted. However, Jesseph refrains from pursueing sociological reductionist account and spends part of the last chapter convincingly demonstrating the inadequacy of a purely sociological explanation of the dispute. By uncovering the conceptual gulf dividing Hobbes and Wallis, Jesseph succeeds in demonstrating important differences in the philosophy of mathematics in the 17th century and explains why these two men engaged in such ferocious fight. Objectively, Hobbes miserably failed attempt at the solution of classic geometric problems makes him the loser of this dispute. But one can feel in this book also some sympathy for the consequent way in which Hobbes rigorously applied principles of his philosophy to mathematics and ultimately rejected classical geometry to avoid an even worse fate: the refutation of his own philosophy.

MY GREAT GRANDMOTHER WAS IN TOWN WHEN THE BOOTLEGGER WAS SHOT AND KNEW HIM. THIS BOOK SHOWS THE TRUE LIFE AND STRUGGLES OF LIFE NOT JUST IN SMALL TOWNS BUT ACROSS AMERICA. EXCELLENT HISTORY LESSON OF SURVIVAL AND WHAT GENERATIONS BEFORE US DID TO GIVE US WHAT WE HAVE.

This is definitely a page turner--rare in nonfiction. Mr. Hallwas combines the suspense of a murder mystery and the facts of a history lesson and makes it all fascinating! I was born in the area and my family's surnames are mentioned throughout the book. Most of my family members have read the book and have SO enjoyed it! In fact it may have solved a generations-old family mystery of a missing relative! A must read for anyone with family roots in small town America!

This book is excellent. Definitely a "can't put down" book. Hard to imagine the quiet, sleepy town of Colchester was once involved with Al Capone, Shoeless Joe Jackson, bombings of homes of law enforcement agents, and murders, bootlegging and crimes of this nature!

The first book by John T. Noonan, Jr., that I read was his tour de force, Contraception: A History of Its Treatment by the Catholic Theologians and Canonists, which I finished reading on June 5, 1967, finding it an exemplary study of a fascinating subject. On June 16, 1973, I read his Power to Dissolve: Lawyers and Marriages in the Courts of the Roman Curia. Each year I pick a book which I consider the best book I read that year. For the year 1973 I awarded Power to Dissolve the greatest book of the 55 books I read that year. When I saw The Lustre of Our Country I knew I could not go wrong reading it, and I was right. Other reviewers have written well of the book, but even if you do not read the entire book--its chapters are able to stand alone--read Chapter 7, entitled "The Pilgrim's Process." It is a dazzling and devastating critique of the Supreme Court's meanderings in dealing with the religion provisons of the First Amendment. This is an excellent book, and anyone interested in its subject will be rewarded in reading it.

One of the ironies of American Constitutional history is that many of our greatest jurists have never had the opportunity to sit on our highest court. One thinks of such obvious examples as Learned Hand, John Johnston Parker,Arthur Vanderbilt, Roger Traynor, and John Minor Wisdom. John T,. Noonan, currently a senior judge with the Ninth Circuit Court of Appeals, clearly deserves to be ranked in this select company( as does his philosophical antipode, Richard Posner of The seventh circuit). This book, remarkably lucid, remarkably learned and remarkably humane, constitutes the culmination of Noonans historical, legal and philosophical reflection.Other reviewers have already indicated the riches of this fine books contents. I will only note that I learned something new, or encountered a fresh and startling argument, on almost every page. Noonan has thought deeply about democracty and human freedom, not only in America, but in other countries as well. The chapters on France, Japan, and Russia show an understanding of the cultural political, and religous life of those nations which borders on the extraordinary. The chapter on Tocqueville( told through the literary device of an imaginary account of America written by Tocquevilles equallly imaginary sister, Angelique,) is quite brilliant, and opens up new perpectives on Tocqueville. All in all, a great book. One hopes for more from Judge Noonans learned and humane pen.It is truly amazing that mediocrites such as Breyer, Kennedy, Ginsburg and Souter sit on the court, while this deeply patriotic and brilliant man has to preside over the often humdrum cases of the ninth circuit.

This is a very special book. Its subject matter is weighty, its intent serious, its disciplines--law and theology--address issues of grave import. The purpose of this review is to alert potential readers to qualities as to which a more adequate review is likely to leave them unaware. The text of the "Lustre" is not ponderous. Instead navigation of the thicket of ideas which the text presents tends to leave the reader refreshed rather than drained. Eccentric and various in its organization and modes of presentation, this book frees one from captivity to a prescribed routing and invites navigation after one's own bent. Subtle logic combines with a pervasive historical sense. Events permeated with paradox and tragedy are presented with insight and wit. Not an easy read; but rewarding. As in the case of Whitman's Leaves of Grass, a reader of this book touches the life of a very special American.

I used the 23rd edition of Stobo for my internal medicine rotation as a 3rd year medical student and also as a quick reference for several other rotations. I think it is the best mid-size medicine text I have seen. The content is broken down into bite-size chunks that are easy to read in one sitting--the short chapters make it easier to retain the material. Each section begins with an introductory chapter that gives a concise overview of the approach to take when evaluating a problem with a particular organ-system. Each chapter also ends with a list of summary points that are very helpful. Excellent tables are easy to reference. The actual information contained in the book is in more than enough depth for MS3 level, and the text emphasizes pathophysiology in many chapters, which helped me learn to integrate what I had learned in basic sciences and apply it to seeing patients in the clinical setting. The last section also has some good summary chapters for things that fall outside the realm of each organ-system section. This is a truly outstanding book. I highly recommend it, and I can't wait for the next edition.

Easy to read, contains pertinent info in a concise fashion. Great to study from, easily read during a clerkship.

I started my 3rd year medicine rotation with Appleton and Lange's Current Medical Diagnosis and Therapy but soon found this book to be more appropriate. It clearly and concisely explained pathophysiology of disease as well as clinical aspects, such as presentation, diagnosis and treatment. I also really enjoyed how each organ system began with a general approach to the patient. I am now using this books counterpart for my surgery rotation.

The book is an absolutely practical treatise of applied thermodymamics. The explanations of how to use property estimation methods are excellent, but invaluable are the comments on their accuracy and recommendations as to when to use which method.

The book served as my operating manual for the ASPEN software for modeling chemical processes. The book documented nearly every method used by ASPEN.

I was a bit unconfortable when I bought this book since I was suspicious that this one was one of those unreadable thermodynamic books. Fortunately I was wrong. This book provides you with a complete treatment of the properties of gases and liquids in a plain language stressing the understanding of the basic laws governing the behavior of liquids and gases instead of the mathematic that goes with it. The treatment of the topics is very suitable for engineers since it allows quick understanding of the phenomena and provides a wealth of correlations and methods for estimating properties. The appendixes contain all kind of basic information indeed helpful for applying the correlations showed. Without any hesitation, this book is well worth its price.

Lotsa Hotsa Properties...

Ashcroft paints a Proverbs-like portrait of his dad's wisdom. You get the feeling that he wasn't around very much, but had a profound insight in instilling the most important life lessons in his children. It's a wonderful book for fathers who know the importance of the position God has entrusted them with, and I highly recommend it.

As a local sub-commandante for the Albuquerque Operation TIPS unit, I went door to door in my neighborhood trying to give this book away to its various denizens. As I live near a liberal university, I was quickly able to determine who the possible subversives were through each person's response. Thanks to this great book I was able to report over 30 suspected terrorist to the local PPPC (Patriotic Pentacostal Processing Center). And good news, I am told that many of the liberal subversives have now read this book and admitted to their secret tribunals that it is absolutely 100% correct in all its teachings!

In light of his role in the government at this time, it was enlightening and refreshing to read that John Ashcroft had such a great Christian upbringing. The lessons he learned from his father have served him well in public life. This book seems to strive not so much to give an autobiography of John D. Ashcroft, but to show how much his father influenced his life. It is an example to all Christian fathers. Even if the reader might not be a fundamentalist Christian, he or she will learn what an influence one person can be in the life of another. Excellent book!

This book is the best book for young children to actually visually see what money does and what it looks like in different countries. Very good educational book.

I have an older version of this book. The latest has added a section on shared currency. The cover on the older version has more exotic coins such as heart cutouts. However any version of this book shows a lot of colorful pictures of script and coin. There are simple descriptions of the making of and measuring of money. If you are a coin collector the descriptions help enhance the collection by telling what the symbols represent on the coin as well as some tog the history. My only disappointment was the lack of information on porcelain notgeld. This makes you wonder what else may be missing. Well you can not stuff everything in to 64 pages with pictures.

I'm a teacher and I find the Eyewitness books highly educational. I like the way the concepts are presented in a form without backgrounds. This gives clear facts to the reader without over taxing the attention span. The books are highly informative, presenting difficult concepts in comprehendable chunks that stimulate interest. I have almost the whole collection for my own children and they LOVE them!

I found this book to be very helpful in the daily struggles of Positive vs. negative. Nice to be able to find positive input after dealing with the negative people all day. Thanks for the relief.

This book was given to me by a friend, and I've found it to be very helpful as I juggle work and family demands! Its format lets you focus on one or more tips per day, with great suggestions on how to reduce stress in this ever-changing environment. This would be a great gift idea for anyone living with today's challenges!

What a motivator!! Great book that is full of common sense motivators that we all need from time to time. When I feel myself falling back into old habits I pick the book up and read a few pages and can feel the motivation return and I am ready to face any and all tasks be it at the office or at home. I recommend this book to everyone that needs to be motivated toward any task or to manage their time efficiently. It even gets me back on track with my exercise program! And best of all the book is small enough to fit in my briefcase or purse so I can have it with me all of the time (I travel quite a bit).

Very well written, I am so happy I found it!

I've only read Ch 12 - Designing Web Applications and Servlet Patterns, via PDF online at the authors site. It's worth the price alone - I went to my local bookstore to purchase it last night - but alast the isles are full of MS C# and .NET books.

However on to what I learned from Ch 12 - the patterns that are put into action are wonderful! I've used MVC in the past - but adding the 'Command & Controller' to MVC is a real boon! I've not been successful with pattern books in the past, because they typically do not provide code examples, which I find a great learning tool [ I'm a "visual" learner ]. This book includes great code examples, the graphics are very professional, and helpful also.

4 of 5 stars - I've not read the whole book - I've got to reserve total commitment til then.

This is a very good book.
It is a must have for any serious web-application devloper.
It explains well all the subjects you need to know about servlet programming.

Buying this book saves you lot of learning-by-step time.
I really suggest this title.
Finally one book that i'm glad to pay.

This is my forst wrox book but, if all worx books are like this one, for sure not the last.

Hiya All,

I have this book for sometime now, and I think, you can't have a better book to learn Servlets 2.3 API. Specially, the Chap on MVC pattern was very good. I liked the way the book has been written. There are lots of practicle examples in the book. The Patterns have been explained in a very good manner. But my favourite is Chap 8. Its downright interesting that how you can combine a database with a JSP page to create a Web Apps. I had some problems in Running the code and had to take the help of Wrox People, But I managed it with there help. Overall, a dependable book.