Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory allows for time machines. The Gödel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin’s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life. This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book’s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. See also: http://www.youtube.com/watch?v=REy9noY5Sg8
This book explores the premise that a physical theory is an interpretation of the analytico–canonical formalism. Throughout the text, the investigation stresses that classical mechanics in its Lagrangian formulation is the formal backbone of theoretical physics. The authors start from a presentation of the analytico–canonical formalism for classical mechanics, and its applications in electromagnetism, Schrödinger's quantum mechanics, and field theories such as general relativity and gauge field theories, up to the Higgs mechanism. The analysis uses the main criterion used by physicists for a theory: to formulate a physical theory we write down a Lagrangian for it. A physical theory is a particular instance of the Lagrangian functional. So, there is already an unified physical theory. One only has to specify the corresponding Lagrangian (or Lagrangian density); the dynamical equations are the associated Euler–Lagrange equations. The theory of Suppes predicates as the main tool in the axiomatization and examples from the usual theories in physics. For applications, a whole plethora of results from logic that lead to interesting, and sometimes unexpected, consequences. This volume looks at where our physics happen and which mathematical universe we require for the description of our concrete physical events. It also explores if we use the constructive universe or if we need set–theoretically generic spacetimes.
Breaching the Bronze Wall deals with the idea that the words of honorable Muslims constitutes proof and that written documents and the words of non-Muslims are of inferior value. Thus, foreign merchants in cities such as Istanbul, Damascus or Alexandria could barely prove any claim, as neither their contracts nor their words were of any value if countered by Muslims. Francisco Apellániz explores how both groups labored to overcome the ‘biases against non-Muslims’ in Mamlūk Egypt’s and Syria’s courts and markets (14th-15th c.) and how the Ottoman conquest (1517) imposed a new, orthodox view on the problem. The book slips into the Middle Eastern archive and the Ottoman Dīvān, and scrutinizes sharīʿa’s intricacies and their handling by consuls, dragomans, qaḍīs and other legal actors.
Francisco Vitoria was the earliest and arguably the most important of the Thomist political philosophers of the Counter-Reformation. Not only did he write important essays on civil and ecclesiastical power, but he became celebrated for his defence of the new world Indians against the imperialism of his own master, the King of Spain. Vitoria's political works are thus of great importance for an understanding both of the rise of modern absolutism, and the debate about the emergent imperialism of the European powers. His works are also unusually accessible, since they survive mainly in the form of 'relectiones', or summaries delivered at the end of his lecture courses on law and theology at the University of Salamanca. Translated here into English for the first time, these texts comprise the core of Vitoria's thought, and will be of interest to specialists in political theory and the history of ideas, ecclesiastical history, and the history of early modern Spain. A comprehensive introduction, a chronology, and a bibliography accompany the texts.
The Lives of Velázquez brings together two seminal early accounts of the great seventeenth-century Spanish painter (ca. 1599–1660). These texts, written by his contemporaries Francisco Pacheco and Antonio Palomino and newly translated for this volume, serve as our main sources of knowledge about this groundbreaking artist. Pacheco’s biography reveals the scale of the challenge to traditional painting presented by Velázquez’s immense talent. Palomino’s text, while precise and detailed in its narrative of the artist’s life, also tackles the aesthetic debate generated by the painter’s choice of subject matter and style. An engaging introduction by art historian Michael Jacobs situates the historical texts in the context of Spain’s Golden Age.
This book constitutes the refereed proceedings of the 11th Iberoamerican Congress on Pattern Recognition, CIARP 2006, held in Cancun, Mexico in November 2006. The 99 revised full papers presented together with three keynote articles were carefully reviewed and selected from 239 submissions. The papers cover ongoing research and mathematical methods.
This coauthored monograph examines how business groups have interacted with state authorities in the three central Andean countries from the mid-twentieth century through the early twenty-first. This time span covers three distinct economic regimes: the period of state-led import substitutive industrialization from the 1950s through the 1970s, the neoliberalism of the 1980s and 1990s, and the post-neoliberal period since the earlier 2000s. These three countries share many similarities but also have important differences that reveal how power is manifested. Peru has had an almost unbroken hegemony of business elites who leverage their power over areas of state activity that affect them. Bolivia, by contrast, shows how strong social movements have challenged business dominance at crucial periods, reflecting a weaker elite class that is less able to exercise influence over decision-making. Ecuador falls in between these two, with business elites being more fragmented than in Peru and social movements being weaker than in Bolivia. The authors analyze the viability of these different regimes and economic models, why they change in specific circumstances, and how they affect the state and its citizens.
This book constitutes the refereed proceedings of the 8th Ibero-American Conference on Artificial Intelligence, IBERAMIA 2002, held in Seville, Spain, in November 2002. The 97 revised full papers presented were carefully reviewed and selected from a total of 345 submissions. The papers are organized in topical sections on knowledge representation and reasoning, machine learning, uncertainty and fuzzy systems, genetic algorithms, neural nets, distributed artificial intelligence and multi-agent systems, natural language processing, intelligent tutoring systems, control and real time, robotics, and computer vision.
Un recorrido por la evolución histórica de la Universidad de Sevilla desde su creación en 1505 hasta 1991. Libro breve y claro, ideal para quien quiera conocer mejor la Universidad Hispalense. Traducido al inglés por Julián Jan Zoltowski.
São Paulo, by far the most populated state in Brazil, has an economy to rival that of Colombia or Venezuela. Its capital city is the fourth largest metropolitan area in the world. How did São Paulo, once a frontier province of little importance, become one of the most vital agricultural and industrial regions of the world? This volume explores the transformation of São Paulo through an economic lens. Francisco Vidal Luna and Herbert S. Klein provide a synthetic overview of the growth of São Paulo from 1850 to 1950, analyzing statistical data on demographics, agriculture, finance, trade, and infrastructure. Quantitative analysis of primary sources, including almanacs, censuses, newspapers, state and ministerial-level government documents, and annual government reports offers granular insight into state building, federalism, the coffee economy, early industrialization, urbanization, and demographic shifts. Luna and Klein compare São Paulo's transformation to other regions from the same period, making this an essential reference for understanding the impact of early periods of economic growth.
A book of writing prompts from the San Francisco Writers’ Grotto, authors of the best-selling 642 Things series Focus on a single aspect of the craft of writing with help from the San Francisco Writers’ Grotto. Writing Sci-Fi and Fantasy starts with a foreword by author Dorothy Hearst, who offers pointers for writing speculative fiction and inventing fantastic new worlds. The rest of the book consists of prompts and space to think, providing opportunities to consider the rules that govern your imagined universe. Among other ideas, you’ll explore the various aspects of world-building by: writing a timeline of the history of your imagined place describing what the inhabitants of your world look like detailing transportation from city to city or planet to planet figuring out who’s in charge and whether or not they should be Take to a café, on vacation, or on your morning commute and practice your creative writing a little bit at a time. Special Features Advice from a published writer, followed by prompts Part of the Lit Start series, a collection of single-subject writing prompt books by the San Francisco Writers’ Grotto Check out the other books in this series: Writing Action, Writing Character, Writing Dialogue, Writing Humor, and Memoir.
Nearly three hundred illustrations and a text reveal the entire range of the Vatican's artistic holdings, replete with priceless masterworks from all periods.
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