Involution- An Odyssey Reconciling Science to God. This book has been called '...a brilliant and profoundly erudite epic...a heroic intellectual tour de force...' (by David Lorimer, the Director of the Scientific and Medical Network) and both 'brave...and totally insightful (by Ervin Laszlo) but the book defies description; it breaks all the rules and is unlike any other. It is so comprehensive in its sweep, original in its writing, and its synthesis, that to isolate any aspect is to misrepresent all the others. Two companions, Reason and Soul, invite the reader to accompany them on a light-hearted poetic journey through the chronology of Western thought to uncover a bold hypothesis: that the evolution of science has been shaped by its gradual and accelerating recovery of memory (involution). That recovery has been led by the inspired maverick genius, moving backwards through time (usually called the past), but which has provided science's future at every moment of new creative thought. Scientific inspiration and its chronology mirrors evolution. This incremental excavation and transfer of memory to intellect implies the pre-human encoding (involution) of consciousness in the structure of matter, and the interconnected consciousness of all life. DNA is the likely encoding and mediating molecule, or resonant coherence of this information, through both time and space. The sweep of history is needed to expose this proposal and its evidence: It requires all the disciplines of science, all the epochs of thought: which only a poetic economy 'woven together with extraordinary subtlety' (Lorimer) could convey. Yet, paradoxically, through involution the collective journey has been lit by individuals, unique in their subjective contributions to the discipline that claims only 'objective' validated truth. The same pattern is mirrored in the congruent history of painting and musical composition. Genius differs only in the languages of expression. This book loosely weaves them all, using familiar material to arrive at an art, a science and divinity behind science. In nine swift Cantos the work travels through pre-human involution, the enfolding of consciousness in matter, and then early man's emergence on the Serengeti. Through the recorded civilizations of Greece, Rome, the Dark Ages, the Renaissance, into the Enlightenment and finally Modernism the success of science progressively obscures the internal story, the story of direct intuition, nous, experience, and the complement to Darwin that this collective involution provides. But there is more to it than merely science; for science is a language through which to follow a deeper journey, Mankind's collective journey inwards, to the nature of himself: which is why the scientific signposts are confined to end-notes to leave the poetic journey unencumbered. They take no scientific knowledge for granted: they are not essential to the poetic narrative but instead caulk the ship from which we view an alternative journey. By adding involution to evolution, mind and matter become two sides of a single coin, only perceived as distinct through the intellect's division from its deeper self, from consciousness, experience, and understanding. The co-creation of God and the universe is what this book restores and is about. It has been called a 'heroic tour de force, a brilliant and erudite epic...' but also 'clearly written and easy to read' It slaughters a few sacred cows, 'brave and a lot of fun.

The book provides a self-contained account of the formal theory of general, i.e. also under- and overdetermined, systems of differential equations which in its central notion of involution combines geometric, algebraic, homological and combinatorial ideas.

This monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. It provides the algebra-theoretic foundations for much of the recent work on linear algebraic groups over arbitrary fields. Involutions are viewed as twisted forms of (hermitian) quadrics, leading to new developments on the model of the algebraic theory of quadratic forms. In addition to classical groups, phenomena related to triality are also discussed, as well as groups of type $F_4$ or $G_2$ arising from exceptional Jordan or composition algebras. Several results and notions appear here for the first time, notably the discriminant algebra of an algebra with unitary involution and the algebra-theoretic counterpart to linear groups of type $D_4$. This volume also contains a Bibliography and Index. Features: original material not in print elsewhere a comprehensive discussion of algebra-theoretic and group-theoretic aspects extensive notes that give historical perspective and a survey on the literature rational methods that allow possible generalization to more general base rings

Agricultural Involution: The Processes of Ecological Change in Indonesia is one of the most famous of the early works of Clifford Geertz. It principal thesis is that many centuries of intensifying wet-rice cultivation in Indonesia had produced greater social complexity without significant technological or political change, a process Geertz terms "involution". Written for a US-funded project on the local developments and following the modernization theory of Walt Whitman Rostow, Geertz examines in this book the agricultural system in Indonesia and its two dominant forms of agriculture, swidden and sawah. In addition to researching its agricultural systems, the book turns to an examination of their historical development. Of particular note is Geertz's discussion of what he famously describes as the process of "agricultural involution" in Java, where both the external economic demands of the Dutch rulers and the internal pressures due to population growth led to intensification rather than change.

This book familiarizes both popular and fundamental notions and techniques from the theory of non-normed topological algebras with involution, demonstrating with examples and basic results the necessity of this perspective. The main body of the book is focussed on the Hilbert-space (bounded) representation theory of topological *-algebras and their topological tensor products, since in our physical world, apart from the majority of the existing unbounded operators, we often meet operators that are forced to be bounded, like in the case of symmetric *-algebras. So, one gets an account of how things behave, when the mathematical structures are far from being algebras endowed with a complete or non-complete algebra norm. In problems related with mathematical physics, such instances are, indeed, quite common.Key features:- Lucid presentation- Smooth in reading- Informative- Illustrated by examples- Familiarizes the reader with the non-normed *-world- Encourages the hesitant- Welcomes new comers.- Well written and lucid presentation.- Informative and illustrated by examples.- Familiarizes the reader with the non-normed *-world.

This book contains the results of work done during the years 1967-1970 on fixed-point-free involutions on manifolds, and is an enlarged version of the author's doctoral dissertation [54J written under the direction of Professor William Browder. The subject of fixed-paint-free involutions, as part of the subject of group actions on manifolds, has been an important source of problems, examples and ideas in topology for the last four decades, and receives renewed attention every time a new technical development suggests new questions and methods ([62, 8, 24, 63J). Here we consider mainly those properties of fixed-point-free involutions that can be best studied using the techniques of surgery on manifolds. This approach to the subject was initiated by Browder and Livesay. Special attention is given here to involutions of homotopy spheres, but even for this particular case, a more general theory is very useful. Two important related topics that we do not touch here are those of involutions with fixed points, and the relationship between fixed-point-free involutions and free Sl-actions. For these topics, the reader is referred to [23J, and to [33J, [61J, [82J, respectively. The two main problems we attack are those of classification of involutions, and the existence and uniqueness of invariant submanifolds with certain properties. As will be seen, these problems are closely related. If (T, l'n) is a fixed-point-free involution of a homotopy sphere l'n, the quotient l'n/Tis called a homotopy projective space.

This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.