influence signs mathematical reasoning von babbage charles (15 Ergebnisse)

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Taschenbuch. Zustand: Neu. Neuware - A groundbreaking work of mathematical philosophy that explores the role of signs and symbols in the process of reasoning. Babbage's insights paved the way for major developments in computer science and artificial intelligence.

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Buch. Zustand: Neu. Neuware - A groundbreaking work of mathematical philosophy that explores the role of signs and symbols in the process of reasoning. Babbage's insights paved the way for major developments in computer science and artificial intelligence.

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1 p.l., 53 pp. Large 4to, orig. blue wrappers, uncut. London: J. Smith, 1826. A remarkable association copy of this extremely rare offprint, linking two of the greatest scientists of the 19th century, and pre-figuring Babbage's later work on his difference and analytical engines. This copy bears the following inscription on the title-page in Babbage's hand: "To M. Gauss from the Author." Additionally, Babbage has written on the upper wrapper: "M. Gauss. Influence of Signs. 3. Ch. Babbage. On the influence of signs in mathematical reasoning." Babbage here presents his views on the importance of symbolic notation in mathematical reasoning. He argues that algebraic symbolism enables one to express ideas more briefly and precisely than in ordinary language; it enables one to consider problems in great generality, rather than only in special cases; and it often enables one to consider simultaneously different cases of a problem that would otherwise be treated separately. The use of mathematical symbols is more efficient, and less prone to error, than other forms of reasoning, as he emphasized particularly when discussing the superiority of algebraic analysis over geometrical reasoning: "[T]he power which we possess by the aid of symbols in compressing into a small compass the several steps of a chain of reasoning, whilst it contributes greatly to abridge the time which our enquiries would otherwise occupy, in difficult cases influences the accuracy of our conclusions: for from the distance which is sometimes interposed [in geometrical reasoning] between the beginning and the end of a chain of reasoning, although the separate parts are sufficiently clear, the whole is often obscure" (p. 8). Babbage also emphasizes the importance of choosing the correct notation: it should remind the user of the nature of the quantity itself (so use 'v' for velocity, 't' for time, and so on); and related quantities should be denoted by similar symbols (so v, v', v'' etc. for the velocities of different bodies in the same problem, for example). Babbage singles out Lagrange's Mecanique Analitique as a model to be emulated in the correct choice of mathematical symbols. The present paper may be seen as part of a chain of ideas that links not only his mathematical and scientific work, but also his views on politics and industry. While a student at Cambridge, Babbage formed, together with Herschel and Peacock, the "Analytical Society." This society was principally concerned with a matter of mathematical symbolism: its aim was famously to support "the principles of pure D'ism in opposition to the Dot-age of the University." Theological overtones apart, this was a plea to replace what Babbage and the other members of the Society viewed as the outdated and inefficient Newtonian fluxional "dot" notation still used in England with the Leibnizian dy/dx notation which was universally employed on the Continent. "For Herschel and Babbage, however, there was more to analysis than a debate about the appropriate mathematical symbolsThe key to the success of analytical algebra as they saw it was its efficiency. It was a problem-solving technology that could produce answers quickly and without wasting resourcesIt was a way of economizing mental labor. As such it could be used to recognize what the most efficient way of proceeding in other enterprises might be too. It could provide the key, for example, to the most profitable way of deploying resources in order to maximize factory production."Morus, When Physics became King, p. 36. "Babbage's ultimate solution to the problem of how to guarantee efficiency, transparency, and accuracy in reasoning was the same as his solution to the same problem in political economy: replace humans with machinery. Babbage was a firm exponent of the division of labor in factory management and equally enthusiastic for mechanization as the ultimate realization of the principle. His primary concern throughout the 1820s and beyond was to wor.

Leather Bound. Zustand: New. Language: English. This book is available in 5 different Leather color without any extra cost. Explore More Options by Clicking on 'More Images' and Notify Us of Your Choice via Email within 24 hours of placing the order. Presenting an Exquisite Leather-Bound Edition, expertly crafted by the prestigious organization "Rare Biblio" with Original Natural Leather that gracefully adorns the spine and corners. The allure continues with Golden Leaf Printing that adds a touch of elegance, while Hand Embossing on the rounded spine lends an artistic flair. This masterpiece has been meticulously reprinted in 2024, utilizing the invaluable guidance of the original edition published many years ago in 1826. The contents of this book are presented in classic black and white. Its durability is ensured through a meticulous sewing binding technique, enhancing its longevity. Imprinted on top-tier quality paper. A team of professionals has expertly processed each page, delicately preserving its content without alteration. Due to the vintage nature of these books, every page has been manually restored for legibility. However, in certain instances, occasional blurriness, missing segments, or faint black spots might persist. We sincerely hope for your understanding of the challenges we faced with these books. Recognizing their significance for readers seeking insight into our historical treasure, we've diligently restored and reissued them. Our intention is to offer this valuable resource once again. We eagerly await your feedback, hoping that you'll find it appealing and will generously share your thoughts and recommendations. Lang: - English, Pages:- 58, Print on Demand. If it is a multi-volume set, then it is only a single volume. Product Disclaimer: Kindly be informed that, owing to the inherent nature of leather as a natural material, minor discolorations or textural variations may be perceptible. Explore the FOLIO EDITION (12x19 Inches): Available Upon Request. 58.