De verdad, te enseña a aquilatarte en lo que vales y te DEMUESTRA QUE VALES MUCHISIMO..
Sin auto estima, no llega uno a ninguna parte...Y este te la aumenta ESCANDALOSAMENTE !
Because it gives us good reasons to cerify that WE ARE PURE GOLD !
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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.
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.
It was an exciting and perilous time, as the book is set against the background of the English Civil War, as men struggled to stay on the right side of first the monarchy, then Cromwell's protectorate, and then the monarchy again. This gives Jesseph's book a deep and rich texture, and adds drama to what could have been -- in a less capable writer's hands -- a dry discussion.
The last chapter brings in yet another aspect, as the author uses the Hobbes - Wallis debate to reflect into one of today's academic battles: Whether the results of science and mathematics are relative, that is, a product of sociological factors -- or if they have a standing that is independent of those factors. Jesseph's point of view is well-argued, and, for this reviewer, comes to the correct conclusion.
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Amber Laughton proves that the more you keep secrets the more embroiled your life becomes. But hey, what a great character she turned out to be.
Gideon has a story behind him and he turns out to be a great friend to Derek even though they had just met 300 miles before the story starts.
Even with the vagueness of the scene where Derek gets shot, I am surprised he stayed in the saddle long enough to make it home let alone up to his bedroom. Wonderful care-giving action and emotions with Derek's healing.
Beau does need a lady friend to heal his heart and soul. Was really glad to hear that Nathan showed up. Loved the shoot-out with the KKK.
Great story - GREATLY RECOMMENDED --M -- good addition to your library.
I'm not sure if a sequel is planned, but I heartily hope the powers that be will let Ms. Douglas write a book for Gideon, Nathan and Beau. These guys are as HOT as Derek!
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Cuando terminas de leerlo, TE SIENTES ORO PURO...Y la verdad, es que todos los somos, solo hay que pulirlo con un buen libro como este