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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.
Von der Antike bis in unsere Tage haben sich Wissenschaftler und Philosophen darüber gewundert, dass eine so abstrakte Disziplin wie die Mathematik die Natur derart perfekt erklären kann. Sogar mehr als das: Mathematiker haben oft Voraussagen gemacht, etwa über die Existenz bestimmter Teilchen, die sich später als richtig erwiesen haben. Was ist es, das der Mathematik solch unglaubliche Macht verleiht? Oder, wie Einstein sich einst fragte: „Wie ist es möglich, dass die Mathematik, die doch ein von aller Erfahrung unabhängiges Produkt des menschlichen Denkens ist, auf die Gegenstände der Welt so vortrefflich passt?“ Werden mathematische Erkenntnisse also nicht erfunden, sondern entdeckt? Diese Fragestellung bildet den roten Faden, an dem der Astrophysiker Mario Livio mit großer Lebendigkeit durch die Geistesgeschichte des mathematischen und naturwissenschaftlichen Denkens führt. Zugleich wirft sein Buch einen frischen und unterhaltsamen Blick auf die Lebensgeschichte und die Erkenntnisse großer Denker wie Pythagoras, Platon, Newton und Einstein. „Eine lebendige und faszinierende Lektüre für ein breites Publikum“ – Nature
This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2012 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Robert Lang explains mathematical aspects of origami foldings; Terence Tao discusses the frequency and distribution of the prime numbers; Timothy Gowers and Mario Livio ponder whether mathematics is invented or discovered; Brian Hayes describes what is special about a ball in five dimensions; Mark Colyvan glosses on the mathematics of dating; and much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed mathematician David Mumford and an introduction by the editor Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.
„Max Tegmark, Prophet der Parallelwelten, flirtet mit der Unendlichkeit.“ ULF VON RAUCHHAUPT, FRANKFURTER ALLGEMEINE SONNTAGSZEITUNG WORUM GEHT ES? Max Tegmark entwickelt eine neue Theorie des Kosmos: Das Universum selbst ist reine Mathematik. In diesem Buch geht es um die physikalische Realität des Kosmos, um den Urknall und die „Zeit davor“ und um die Evolution des Weltalls. Welche Rollen spielen wir dabei – die Wesen, die klug genug sind, das alles verstehen zu wollen? Tegmark findet, dieses Terrain sollte nicht länger den Philosophen überlassen bleiben. Denn die Physiker von heute haben die besseren Antworten auf die ewigen Fragen. WAS IST BESONDERS? „Eine hinreißende Expedition, die jenseits des konventionellen Denkens nach der wahren Bedeutung von Realität sucht.“ BBC „Tegmark behandelt die großen Fragen der Kosmologie und der Teilchenphysik weitaus verständlicher als Stephen Hawking.“ THE TIMES WER LIEST? • Jeder, der das Universum verstehen will • Die Leser von Richard Dawkins und Markus Gabriel
Structural realism has rapidly gained in popularity in recent years, but it has splintered into many distinct denominations, often underpinned by diverse motivations. There is, no monolithic position known as ‘structural realism,’ but there is a general convergence on the idea that a central role is to be played by relational aspects over object-based aspects of ontology. What becomes of causality in a world without fundamental objects? In this book, the foremost authorities on structural realism attempt to answer this and related questions: ‘what is structure?’ and ‘what is an object?’ Also featured are the most recent advances in structural realism, including the intersection of mathematical structuralism and structural realism, and the latest treatments of laws and modality in the context of structural realism. The book will be of interest to philosophers of science, philosophers of physics, metaphysicians, and those interested in foundational aspects of science.
The prize-winning essays in this book address the fascinating but sometimes uncomfortable relationship between physics and mathematics. Is mathematics merely another natural science? Or is it the result of human creativity? Does physics simply wear mathematics like a costume, or is math the lifeblood of physical reality? The nineteen wide-ranging, highly imaginative and often entertaining essays are enhanced versions of the prize-winning entries to the FQXi essay competition “Trick or Truth”, which attracted over 200 submissions. The Foundational Questions Institute, FQXi, catalyzes, supports, and disseminates research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality, but unlikely to be supported by conventional funding sources.

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