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Author: David I. Spivak
Publisher: MIT Press
ISBN: 0262320533
Category : Mathematics
Languages : en
Pages : 495
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Book Description
An introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences. Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines. Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs—categories in disguise. After explaining the “big three” concepts of category theory—categories, functors, and natural transformations—the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with solutions. Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.
Author: David I. Spivak
Publisher: MIT Press
ISBN: 0262320533
Category : Mathematics
Languages : en
Pages : 495
Get Book Here
Book Description
An introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences. Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines. Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs—categories in disguise. After explaining the “big three” concepts of category theory—categories, functors, and natural transformations—the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with solutions. Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.
Author: Herbert Alexander Simon
Publisher: MIT Press (MA)
ISBN:
Category : Science
Languages : en
Pages : 156
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Book Description
The Sciences of the Artificialreveals the design of an intellectual structure aimed at accommodating those empirical phenomena that are "artificial" rather than "natural." The goal is to show how empirical sciences of artificial systems are possible, even in the face of the contingent and teleological character of the phenomena, their attributes of choice and purpose. Developing in some detail two specific examples—human psychology and engineering design—Professor Simon describes the shape of these sciences as they are emerging from developments of the past 25 years. "Artificial" is used here in a very specific sense: to denote systems that have a given form and behavior only because they adapt (or are adapted), in reference to goals or purposes, to their environment. Thus, both man-made artifacts and man himself, in terms of his behavior, are artificial. Simon characterizes an artificial system as an interface between two environments—inner and outer. These environments lie in the province of "natural science," but the interface, linking them, is the realm of "artificial science." When an artificial system adapts successfully, its behavior shows mostly the shape of the outer environment and reveals little of the structure or mechanisms of the inner. The inner environment becomes significant for behavior only when a system reaches the limits of its rationality and adaptability, and contingency degenerates into necessity.
Author: David Cahan
Publisher: University of Chicago Press
ISBN: 9780226089270
Category : History
Languages : en
Pages : 480
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Book Description
During the 19th century, much of the modern scientific enterprise took shape: scientific disciplines were formed, institutions and communities were founded and unprecedented applications to and interactions with other aspects of society and culture occurred. taught us about this exciting time and identify issues that remain unexamined or require reconsideration. They treat scientific disciplines - biology, physics, chemistry, the earth sciences, mathematics and the social sciences - in their specific intellectual and sociocultural contexts as well as the broader topics of science and medicine; science and religion; scientific institutions and communities; and science, technology and industry. From Natural Philosophy to the Sciences should be valuable for historians of science, but also of great interest to scholars of all aspects of 19th-century life and culture.
Author: F. S. C. Northrop
Publisher:
ISBN:
Category :
Languages : en
Pages : 402
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Book Description
Author: Phyllis McKay Illari
Publisher: Oxford University Press
ISBN: 0199574138
Category : Mathematics
Languages : en
Pages : 953
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Book Description
Why do ideas of how mechanisms relate to causality and probability differ so much across the sciences? Can progress in understanding the tools of causal inference in some sciences lead to progress in others? This book tackles these questions and others concerning the use of causality in the sciences.
Author: Geoffrey C. Bowker
Publisher: MIT Press
ISBN: 0262524899
Category : Science
Languages : en
Pages : 275
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Book Description
How the way we hold knowledge about the past—in books, in file folders, in databases—affects the kind of stories we tell about the past. The way we record knowledge, and the web of technical, formal, and social practices that surrounds it, inevitably affects the knowledge that we record. The ways we hold knowledge about the past—in handwritten manuscripts, in printed books, in file folders, in databases—shape the kind of stories we tell about that past. In this lively and erudite look at the relation of our information infrastructures to our information, Geoffrey Bowker examines how, over the past two hundred years, information technology has converged with the nature and production of scientific knowledge. His story weaves a path between the social and political work of creating an explicit, indexical memory for science—the making of infrastructures—and the variety of ways we continually reconfigure, lose, and regain the past. At a time when memory is so cheap and its recording is so protean, Bowker reminds us of the centrality of what and how we choose to forget. In Memory Practices in the Sciences he looks at three "memory epochs" of the nineteenth, twentieth, and twenty-first centuries and their particular reconstructions and reconfigurations of scientific knowledge. The nineteenth century's central science, geology, mapped both the social and the natural world into a single time package (despite apparent discontinuities), as, in a different way, did mid-twentieth-century cybernetics. Both, Bowker argues, packaged time in ways indexed by their information technologies to permit traffic between the social and natural worlds. Today's sciences of biodiversity, meanwhile, "database the world" in a way that excludes certain spaces, entities, and times. We use the tools of the present to look at the past, says Bowker; we project onto nature our modes of organizing our own affairs.
Author: Jean-Henri Fabre
Publisher:
ISBN:
Category : Natural history
Languages : en
Pages : 426
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Book Description
A book about metals, plants, animals, and planets.
Author: Robert S. Cohen
Publisher: Springer Science & Business Media
ISBN: 9400962339
Category : Science
Languages : en
Pages : 475
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Book Description
To the scientists and philosophers of our time, Hegel has been either a ne glected or a provocative thinker, a source of irrelevant dark metaphysics or of complex but insightful analysis. His influence upon the work of natural scientists has seemed minimal, in the main; and his stimulus to the nascent sciences of society and to psychology has seemed to be as often an obstacle as an encouragement. Nevertheless his philosophical analysis of knowledge and the knowing process, of concepts and their evolutionary formation, of rationality in its forms and histories, of the stages of empirical awareness and human practice, all set within his endless inquiries into cultural formations from the entire sweep of human experience, must, we believe, be confronted by anyone who wants to understand the scientific consciousness. Indeed, we may wish to situate the changing theories of nature, and of humankind in nature, within a philosophical account of men and women as social practi tioners and as sensing, thinking, feeling centers of privacy; and then we will see the work of Hegel as a major effort to mediate between the purest of epistemological investigations and the most practical of the political and the religious. This book, long delayed to our deep regret, derives from a Symposium on Hegel and the Sciences which was sponsored jointly by the Hegel Society of America and the Boston University Center for Philosophy and History of Science a decade ago.
Author: Michela Massimi
Publisher: Routledge
ISBN: 1317664450
Category : Philosophy
Languages : en
Pages : 165
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Book Description
What is the origin of our universe? What are dark matter and dark energy? What is our role in the universe as human beings capable of knowledge? What makes us intelligent cognitive agents seemingly endowed with consciousness? Scientific research across both the physical and cognitive sciences raises fascinating philosophical questions. Philosophy and the Sciences For Everyone introduces these questions and more. It begins by asking what good is philosophy for the sciences before examining the following questions: The origin of our universe Dark matter and dark energy Anthropic reasoning in philosophy and cosmology Evolutionary theory and the human mind What is consciousness? Intelligent machines and the human brain Embodied Cognition. Each chapter includes an introduction, summary and study questions and there is a glossary of technical terms. Designed to be used on the corresponding Philosophy and the Sciences online course offered by the University of Edinburgh this book is also a superb introduction to central topics in philosophy of science and popular science.
Author: Claudio Calosi
Publisher: Springer
ISBN: 3319053566
Category : Philosophy
Languages : en
Pages : 389
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Book Description
This volume is the first systematic and thorough attempt to investigate the relation and the possible applications of mereology to contemporary science. It gathers contributions from leading scholars in the field and covers a wide range of scientific theories and practices such as physics, mathematics, chemistry, biology, computer science and engineering. Throughout the volume, a variety of foundational issues are investigated both from the formal and the empirical point of view. The first section looks at the topic as it applies to physics. The section addresses questions of persistence and composition within quantum and relativistic physics and concludes by scrutinizing the possibility to capture continuity of motion as described by our best physical theories within gunky space times. The second part tackles mathematics and shows how to provide a foundation for point-free geometry of space switching to fuzzy-logic. The relation between mereological sums and set-theoretic suprema is investigated and issues about different mereological perspectives such as classical and natural Mereology are thoroughly discussed. The third section in the volume looks at natural science. Several questions from biology, medicine and chemistry are investigated. From the perspective of biology, there is an attempt to provide axioms for inferring statements about part hood between two biological entities from statements about their spatial relation. From the perspective of chemistry, it is argued that classical mereological frameworks are not adequate to capture the practices of chemistry in that they consider neither temporal nor modal parameters. The final part introduces computer science and engineering. A new formal mereological framework in which an indeterminate relation of part hood is taken as a primitive notion is constructed and then applied to a wide variety of disciplines from robotics to knowledge engineering. A formal framework for discrete mereotopology and its applications is developed and finally, the importance of mereology for the relatively new science of domain engineering is also discussed.
