The Butterfly In The Quantum World

The Butterfly in the Quantum World

Butterfly in the Quantum World by Indu Satija, with contributions by Douglas Hofstadter, is the first book ever to tell the story of the "Hofstadter butterfly", a beautiful and fascinating graph lying at the heart of the quantum theory of matter. The butterfly came out of a simple-sounding question: What happens if you immerse a crystal in a magnetic field? What energies can the electrons take on? From 1930 onwards, physicists struggled to answer this question, until 1974, when graduate student Douglas Hofstadter discovered that the answer was a graph consisting of nothing but copies of itself nested down infinitely many times. This wild mathematical object caught the physics world totally by surprise, and it continues to mesmerize physicists and mathematicians today. The butterfly plot is intimately related to many other important phenomena in number theory and physics, including Apollonian gaskets, the Foucault pendulum, quasicrystals, the quantum Hall effect, and many more. Its story reflects the magic, the mystery, and the simplicity of the laws of nature, and Indu Satija, in a wonderfully personal style, relates this story, enriching it with a vast number of lively historical anecdotes, many photographs, beautiful visual images, and even poems, making her book a great feast, for the eyes, for the mind and for the soul.

The Butterfly in the Quantum World

The Truly Infinite Universe

The discoveries of general relativity and quantum mechanics in the 20th century provide the perfect opportunity for Hegel's thought to become more topical than it has ever been. By bringing speculative philosophy into conversation with quantum cosmology, this book develops Hegel's metaphysics of true infinitude and Hawking's theory on the origins of spacetime in tandem, providing a compelling rationale for the idea that the universe is a self-generating, self-organizing, self-enclosed whole. Ever sensitive to the complex relationship of scientific, philosophical, and theological issues in theoretical cosmology, the study brings a fresh perspective to the unique brand of metaphysical theology underlying speculative philosophy and offers a new way of conducting transdisciplinary work involving Hegelian thought. This is essential reading for Hegel scholars, Hawking scholars, those interested in philosophical cosmology, the ontology of the quantum void, the realism vs. idealism debate, infinitude, "imaginary��? time, and dialectical materialism, and those compelled by post-classical approaches to theology.