Numbers, operators, and degrees of independence facilitate creation and organization of the real environment. The explanation and application of quantum mechanics on atomic and cosmic scales is suggested by the Pythagorean tradition

This book explores precisely how mathematics allows us to model and predict the behaviour of physical systems, to an amazing degree of accuracy. One of the oldest explanations for this is that, in some profound way, the structure of the world is mathematical. The ancient Pythagoreans stated that “everything is number”. However, while exploring the Pythagorean method, this book chooses to add a second principle of the universe: the mind. This work defends the proposition that mind and mathematical structure are the grounds of reality.

This book is a philosophical study of mathematics, pursued by considering and relating two aspects of mathematical thinking and practice, especially in modern mathematics, which, having emerged around 1800, consolidated around 1900 and extends to our own time, while also tracing both aspects to earlier periods, beginning with the ancient Greek mathematics. The first aspect is conceptual, which characterizes mathematics as the invention of and working with concepts, rather than only by its logical nature. The second, Pythagorean, aspect is grounded, first, in the interplay of geometry and algebra in modern mathematics, and secondly, in the epistemologically most radical form of modern mathematics, designated in this study as radical Pythagorean mathematics. This form of mathematics is defined by the role of that which beyond the limits of thought in mathematical thinking, or in ancient Greek terms, used in the book’s title, an alogon in the logos of mathematics. The outcome of this investigation is a new philosophical and historical understanding of the nature of modern mathematics and mathematics in general. The book is addressed to mathematicians, mathematical physicists, and philosophers and historians of mathematics, and graduate students in these fields.

Science is at a cross-roads. For several decades, the Standard Model of particle physics has managed to fit vast amounts of particle scattering data remarkably well, but many questions remain. During those decades, some sophisticated theoretical hypotheses such as string theory, quantum gravity, and quantum cosmology have been proposed and studied intensively, in an effort to break the log-jam of the Standard Model. None of those hypotheses have succeeded to date. Of greater concern is the increasing tendency by some practitioners in those fields to downplay the empirical principles of science.In response, this book is a restatement of those principles, covering numerous aspects of observation. A particular focus is on contextuality versus realism, the two fundamentally contrasting ideologies that underpin modern physics.

This volume gives an overview of the recent representative developments in relativistic and non-relativistic quantum theory, which are related to the application of various mathematical notions of various symmetries. These notions are centered upon groups, algebras and their generalizations, and are applied in interaction with topology, differential geometry, functional analysis and related fields. The emphasis is on results in the following areas: foundation of quantum physics, quantization methods, nonlinear quantum mechanics, algebraic quantum field theory, gauge and string theories, discrete spaces, quantum groups and generalized symmetries.

'If I saw further than others,' said Sir Issac Newton, 'it is because I was standing on the shoulders of giants.''Quantum Leaps' introduces one hundred of these giants and examines their achievements: the men and women who, often in the face of extreme scepticism or worse, have striven and succeeded in pushing back the boundaries of human knowledge. Ranging across the spectrum of scientific endeavour, from the cosmology of Copernicus and Galileo, through the medical revolutions of Hippocrates and Galen, it includes the fields of physics, biology, chemistry and genetics. This is the story of the ideas that have shaped the world today, and the ideas that will shape the future. This is the Popular Reference edition of the fully-illustrated title 'Science', ISBN:9781782120469.

Eurasian Philosophy and Quantum Metaphysics (Theology Reconsidered) By: Juan Valdez The science of our modern age is able to neither address nor solve our current global problems. Author Juan Valdez believes we should study humanity’s ancient wisdom and philosophy texts to develop a new intellectual paradigm that can respond and support our current needs. Eurasian Philosophy and Quantum Metaphysics (Theology Reconsidered) is an in-depth study of the origins and meanings of ancient philosophies before they were fractured into mythology and religions and attacked by modern science. Beginning with creation mythology in Eurasia through the development of philosophical thought, to the Scientific Revolution to our own modern Quantum Era, the progression – and abandonment – of ancient wisdom is carefully studied. Valdez reviews and analyzes the ancient texts themselves to understand what they truly say and not what later historians have said about them. The Indo-Aryan Vedas, the Torah, Rene Descartes’ Discourse on the Method and Principles of Philosophy, Neils Bohr’s Atomic Theory, and more, are all respectfully and critically assessed. As enlightened as we may consider ourselves, Valdez calls attention to how limited modern thought has become. By reviewing past wisdom, we can not only rediscover the roots of modern thought but place Wisdom itself at the top of intellectual pursuits. Eurasian Philosophy and Quantum Metaphysics (Theology Reconsidered) is a rich and nuanced study on how humanity has thought of itself.

"Any reader who aspires to be scientifically literate will find this a good starting place." —Publishers Weekly While we may be familiar with some of science’s greatest equations, we may not know that each and every equation emerged not in "Eureka!" moments but in years of cultural developments and scientific knowledge. With vignettes full of humor, drama, and eccentricity, philosopher and science historian Robert P. Crease shares the stories behind ten of history’s greatest equations, from the "first equation," 1 + 1 = 2, which promises a rational, well-ordered world, to Heisenberg’s uncertainty principle, which reveals the limitations of human knowledge. For every equation, Crease provides a brief account of who discovered it, what dissatisfactions lay behind its discovery, and what the equation says about the nature of our world.

Typically, scientist try to either prove or disprove Scripture, as it relates the Creation story, then write books about their findings. Quantum Phaith is not one of those books. Instead, the author accepts the Word of God, a priori. Quantum Phaith is a journey through elementary quantum mechanics, chaos theory, number theory, and more. This is also a journey through the author's faith and what he has discovered about science through it; his faith has been unshaken by science and mathematics. Quantum Phaith examines the Creation account, using the results to support what scientists have discovered about the universe. Their discoveries were already contained in the Bible! Quantum Phaith portrays God as perfect, His creation perfect in every regard. Imperfection was introduced by the Fall or Man. God is all-powerful, all-knowing, transcends time, space, and our understanding. God is order, and you will find that chaos contains unobservable order! Quantum Phaith will make you think. It may change your life.