Beyond The Finite

Throughout its long history, and not just as the key aesthetic category for the Romantic Movement, the sublime has created the necessary link between aesthetic and moral judgment, offering the prospect of transcending the limits of measurement, even imagination. The best of science makes genuine claims to the sublime. For in science, as in art, every day brings the entirely new, the extreme, and the unrepresentable. How does one depict negative mass, for example, or the folding of a protein that is contagious? Can one capture emergent phenomena as they emerge? Science is continually faced with describing that which is beyond. This book, through contributions from nine prominent scholars, tackles that challenge. The explorations within Beyond the Finite range from the images taken by the Hubble Telescope to David Bohm's quantum romanticism, from Kant and Burke to a "downward spiraling infinity" of the 21st century sublime, all lucid yet transcendent. Squarely positioned at the interface between science and art, this volume's chapters capture a remarkable variety of perspectives, with neuroscience, chemistry, astronomy, physics, film, painting and music discussed in relation to the sublime experience, topics surely to peak the interest of academics and students studying the sublime in various disciplines.

SHORTLISTED FOR THE 2017 ROYAL SOCIETY SCIENCE BOOK PRIZE Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity. What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough? Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.

From the New York Times bestselling author of Start With Why and Leaders Eat Last, a bold framework for leadership in today’s ever-changing world. How do we win a game that has no end? Finite games, like football or chess, have known players, fixed rules and a clear endpoint. The winners and losers are easily identified. Infinite games, games with no finish line, like business or politics, or life itself, have players who come and go. The rules of an infinite game are changeable while infinite games have no defined endpoint. There are no winners or losers—only ahead and behind. The question is, how do we play to succeed in the game we’re in? In this revelatory new book, Simon Sinek offers a framework for leading with an infinite mindset. On one hand, none of us can resist the fleeting thrills of a promotion earned or a tournament won, yet these rewards fade quickly. In pursuit of a Just Cause, we will commit to a vision of a future world so appealing that we will build it week after week, month after month, year after year. Although we do not know the exact form this world will take, working toward it gives our work and our life meaning. Leaders who embrace an infinite mindset build stronger, more innovative, more inspiring organizations. Ultimately, they are the ones who lead us into the future.

As we attempt to solve engineering problems of ever increasing complexity, so must we develop and learn new methods for doing so. The Finite Difference Method used for centuries eventually gave way to Finite Element Methods (FEM), which better met the demands for flexibility, effectiveness, and accuracy in problems involving complex geometry. Now,

This volume contains the proceedings of the Workshop and 18th International Conference on Representations of Algebras (ICRA 2018) held from August 8–17, 2018, in Prague, Czech Republic. It presents several themes of contemporary representation theory together with some new tools, such as stable ∞ ∞-categories, stable derivators, and contramodules. In the first part, expanded lecture notes of four courses delivered at the workshop are presented, covering the representation theory of finite sets with correspondences, geometric theory of quiver Grassmannians, recent applications of contramodules to tilting theory, as well as symmetries in the representation theory over an abstract stable homotopy theory. The second part consists of six more-advanced papers based on plenary talks of the conference, presenting selected topics from contemporary representation theory: recollements and purity, maximal green sequences, cohomological Hall algebras, Hochschild cohomology of associative algebras, cohomology of local selfinjective algebras, and the higher Auslander–Reiten theory studied via homotopy theory.

Material Falsity and Error in Descartes’s Meditations approaches Descartes’s Meditations as an intellectual journey, wherein Descartes’s views develop and change as he makes new discoveries about self, God and matter. The first book to focus closely on Descartes’s notion of material falsity, it shows how Descartes’s account of material falsity – and correspondingly his account of crucial notions such as truth, falsehood and error – evolves according to the epistemic advances in the Meditations. It also offers important new insights on the crucial role of Descartes’s Third Meditation discussion of material falsity in advancing many subsequent arguments in the Meditations. This book is essential reading for those working on Descartes and early modern philosophy. It presents an independent reading on issues of perennial interest, such as Descartes’s views on error, truth and falsehood. It also makes important contributions to topics that have been the focus of much recent scholarship, such as Descartes’s ethics and his theodicy. Those working on the interface between medieval and modern philosophy will find the discussions on Descartes’s debt to predecessors like Suárez and Augustine invaluable.

Graham Priest presents an expanded edition of his exploration of the nature and limits of thought. Embracing contradiction and challenging traditional logic, he engages with issues across philosophical borders, from the historical to the modern, Eastern to Western, continental to analytic.

This is the first thorough examination of weakly nonlocal solitary waves, which are just as important in applications as their classical counterparts. The book describes a class of waves that radiate away from the core of the disturbance but are nevertheless very long-lived nonlinear disturbances.