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An essential and timely collection of wise and compelling essays from one of the longtime leaders of the sustainable agriculture movement in America. Wes Jackson, “a well–known and admired advocate for sustainability especially as it relates to agriculture, has the rare ability to transform his convictions into captivating prose . . . Jackson’s thoughts are still as significant and profound as they were nearly 20 years ago” (Publishers Weekly) and can teach us many things about the land, soil, and conservation, but what most resonates is this: The ecosphere is self–regulating, and as often as we attempt to understand it, we are not its builders, and our manuals will often be faulty. The only responsible way to learn the nuances of the land is to study the soil and vegetation in their natural state and pass this knowledge on to future generations. “[A] small book rich in ideas” (The New York Times Book Review), Nature as Measure collects Jackson’s essays from Altars of Unhewn Stone and Becoming Native to This Place, presenting ideas of land conservation and education that are written from the point of view of a man who has practiced what he’s preached and proven that it is possible to partially restore much of the land that we’ve ravaged. Wes Jackson lays the foundation for a new farming economy, grounded in nature’s principles and located in dying small towns and rural communities. Exploding the tenets of industrial agriculture, Jackson seeks to integrate food production with nature in a way that sustains both. His longtime friend Wendell Berry provides an informative, contextual Introduction. “For those concerned about what will be left and how many billion will be starving in twenty years, this is a must read.” —Register of the Kentucky Historical Society “A good introduction to a thinker whose ideas on agriculture are radical both in their technical approach to food production as well as in terms of the economic, social, and cultural context within which it is practiced.” —Review of Radical Political Economics
Weights and measures form an essential part of our ingrained view of the world. It is just about impossible to function effectively without some internalized system of measurement. In this volume, I outline a history of the science of measurement, and the
This book argues for the place of capacities within an grounds of meaning, not method. Yet it is questions of method that should concern the modern empiricist: can capacities be measured? Cartwright argues that they are measured if anything is. Stanford University's Gravity-Probe-B will measure capacities in a cryogenic dewar deep in space. More mundanely, we use probabilities to measure capacities, and the assumptions required to ensure that probabilities are a reliable instrument are investigated in the opening chapters of this book, where the early methods of econometrics set a model. The last chapter applies lessons about probabilities and capacities to quantum mechanics and the Bell inequalities. The central thesis throughout is that capacities not only can be admitted by empiricists, but indeed must be - otherwise the empirical methods of modern science will make no sense.
Instruments of the True Measure charts the coordinates and intersections of land, history, and culture. Lyrical passages map the parallel lives of ancestral figures and connect dispossessions of the past to lived experiences of the present. Shawnee history informs the collection, and Da’s fascination with uncovering and recovering brings the reader deeper into the narrative of Shawnee homeland. Images of forced removal and frontier violence reveal the wrenching loss and reconfiguration of the Shawnee as a people. The body and history become lands that are measured and plotted with precise instruments. Surveying and geography underpin the collection, but even as Da’ investigates these signifiers of measurement, she pushes the reader to interrogate their function within the stark atrocities of American history. Da’ laments this harsh dichotomy, observing that America’s mathematical point of beginning is located in the heart of her tribe’s homeland: “I do not have the Shawnee words to describe this place; the notation that is available to me is 40°38 ́32.61 ́ ́ N 80°31 ́9.76 ́ ́ W.”
This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online. For errata and updates, visit https://measure.axler.net/