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'When I was sent by the Soviet state to London to further my studies in calculus, knowing I would never become a great mathematician, I strayed instead into the foothills of anthropology ...'It is 1950 and Nikolai Lobachevsky, great-grandson of his illustrious namesake, is surveying a bog in the Irish Midlands, where he studies the locals, the land and their ways. One afternoon, soon after he arrives, he receives a telegram calling him back to Leningrad for a 'special appointment'. Lobachevsky may not be a great genius but he is not foolish: he recognises a death sentence when he sees one and leaves to go into hiding on a small island in the Shannon estuary, where the island families harvest seaweed and struggle to split rocks. Here Lobachevsky must think about death, how to avoid it and whether he will ever see his home again
Dubbed by his fellow Futurists the "King of Time," Velimir Khlebnikov (1885-1922) spent his entire brief life searching for a new poetic language to express his convictions about the rhythm of history, the correspondence between human behavior and the "language of the stars." The result was a vast body of poetry and prose that has been called hermetic, incomprehensible, even deranged. Of all this tragic generation of Russian poets (including Blok, Esenin, and Mayakovsky), Khlebnikov has been perhaps the most praised and the more censured. This first volume of the Collected Works, an edition sponsored by the Dia Art Foundation, will do much to establish the counterimage of Khlebnikov as an honest, serious writer. The 117 letters published here for the first time in English reveal an ebullient, humane, impractical, but deliberate working artist. We read of the continuing involvement with his family throughout his vagabond life (pleas to his smartest sister, Vera, to break out of the mold, pleas to his scholarly father not to condemn and to send a warm overcoat); the naive pleasure he took in being applauded by other artists; his insistence that a young girl's simple verses be included in one of the typically outrageous Futurist publications of the time; his jealous fury at the appearance in Moscow of the Italian Futurist Marinetti; a first draft of his famous zoo poem ("O Garden of Animals!"); his seriocomic but ultimately shattering efforts to be released from army service; his inexhaustibly courageous confrontation with his own disease and excruciating poverty; and always his deadly earnest attempt to make sense of numbers, language, suffering, politics, and the exigencies of publication. The theoretical writings presented here are even more important than the letters to an understanding of Khlebnikov's creative output. In the scientific articles written before 1910, we discern foreshadowings of major patterns of later poetic work. In the pan-Slavic proclamations of 1908-1914, we find explicit connections between cultural roots and linguistic ramifications. In the semantic excursuses beginning in 1915, we can see Khlebnikov's experiments with consonants, nouns, and definitions spelled out in accessible, if arid, form. The essays of 1916-1922 take us into the future of Planet Earth, visions of universal order and accomplishment that no longer seem so farfetched but indeed resonate for modern readers.
At the turn of the 20th century, physics entered into a new world, the invisible silent world of atoms, atomic nuclei and elementary particles. Our twentieth century then produced the theory that has been serving physicists so faithfully for over sixty years -- quantum mechanics. The landscape of the new world is quire unlike our own. So different that phsyicists frequently lack words to describe it. Quantum mechanics had to create new conceptions for the world of the ultrasmall, bizarre conceptions beyond the scope of pictorial imagery. Customary physical laws cease to operate in the new world. Particles lose their dimensions and acquire the properties of waves. Electrons and the other building stones of matter can pass through impenetrable barriers, or they can vanish altogether leaving only photons in their place. Those are the things quantum mechanics dealt with. This book will tell you about the origin and development of quantum mechanics, about its new concepts. It will describe how the new theory deciphered the secrets of the structure of atoms, molecules, crystals, atomic nulei, and how quantum mechanics is dealing with the problem of the most fundamental of all properties of matter --the interaction of particles and the relationships between fields and matter.
This is a volume on the concepts, theories, models and social consequences of creativity. It contains articles by well-known cognitive scientists, economists, mathematicians, philosophers and psychologists.
Lobachevsky wrote Pangeometry in 1855, the year before his death. This memoir is a resume of his work on non-Euclidean geometry and its applications and can be considered his clearest account on the subject. It is also the conclusion of his life's work and the last attempt he made to acquire recognition. The treatise contains basic ideas of hyperbolic geometry, including the trigonometric formulae, the techniques of computation of arc length, of area and of volume, with concrete examples. It also deals with the applications of hyperbolic geometry to the computation of new definite integrals. The techniques are different from those found in most modern books on hyperbolic geometry since they do not use models. Besides its historical importance, Lobachevsky's Pangeometry is a beautiful work, written in a simple and condensed style. The material that it contains is still very alive, and reading this book will be most useful for researchers and for students in geometry and in the history of science. It can be used as a textbook, as a sourcebook, and as a repository of inspiration. The present edition provides the first complete English translation of Pangeometry available in print. It contains facsimiles of both the Russian and the French original versions. The translation is accompanied by notes, followed by a biography of Lobachevky and an extensive commentary.
This volume explores abductive cognition, an important but, at least until the third quarter of the last century, neglected topic in cognition. It aims at increasing knowledge about creative and expert inferences.
Presents the papers of Beltrami, Klein, and Poincare that brought hyperbolic geometry into the mainstream of mathematics.
This book discusses how scientific and other types of cognition make use of models, abduction, and explanatory reasoning in order to produce important and innovative changes in theories and concepts. Gathering revised contributions presented at the international conference on Model-Based Reasoning (MBR18), held on October 24–26 2018 in Seville, Spain, the book is divided into three main parts. The first focuses on models, reasoning, and representation. It highlights key theoretical concepts from an applied perspective, and addresses issues concerning information visualization, experimental methods, and design. The second part goes a step further, examining abduction, problem solving, and reasoning. The respective papers assess different types of reasoning, and discuss various concepts of inference and creativity and their relationship with experimental data. In turn, the third part reports on a number of epistemological and technological issues. By analyzing possible contradictions in modern research and describing representative case studies, this part is intended to foster new discussions and stimulate new ideas. All in all, the book provides researchers and graduate students in the fields of applied philosophy, epistemology, cognitive science, and artificial intelligence alike with an authoritative snapshot of the latest theories and applications of model-based reasoning.