Introduction to Deep Beauty

No scientic theory has caused more puzzlement and confusion than quantum theory. Beginning in 1900, the theory developed in ts and starts, and only found a consistent mathematical framing when in 1932, John von Neumann published hisMathematische Grundlagen der Quantenmechanik. But even today, we struggle to understand the world as pictured by quantum theory. Physics is supposed to help us to understand the world, and yet quantum theory makes it seem a very strange place. Onemight be tempted to push aside our puzzlement as resulting fromour clinging to a primitive worldview. But our puzzlement is not merely a psychological obstacle; it is also an obstacle to the development of physics itself. is obstacle is encountered primarily in our attempts to unify quantum theory and the general theory of relativity. As argued persuasively by Chris Isham, Lee Smolin, and others, the primary obstacle between us and future physics is our own failure to understand the conceptual foundations of current physical theories. How then are we to make conceptual progress? What is the process by which we nd a new perspective, a perspective in which previously puzzling phenomena nd a place in an intelligible — and perhaps beautiful — structure? We do not wish here tomake prescriptions, or to claim that conceptual progress can be achieved in only one way. But this book begins with the Ansatz that conceptual progress might be achieved through free creations of the human intellect. And where are we to nd this free creative activity? According to a distinguished tradition, beginning with the philosopher Immanuel Kant and running through the philosopher-mathematicians Gottlob Frege and L.E.J. Brouwer, the mathematical sciences are in the business of constructing new and “fruitful” concepts. us, this book begins from the assumption that creative developments in mathematics might catalyze the conceptual advances that enable us to understand our current physical theories (in particular, quantum theory), and thereby to promote future advances in physics. Since the guiding theme of this book is methodological, rather than thematic, its chapters are naturally written fromdiverse perspectives—unied only by the attempt to introduce new concepts that will aid our understanding of current physics, and the growth of future physics. Some of our authors are mathematicians (Conway, de Groote, Kochen), some mathematical physicists (Baez, Coecke, Döring, Isham, Landsman, Lauda, Summers), some theoretical physicists (Brukner, Dakić, Hardy), and some philosophers (e.g. Bub, Redei). But regardless of their professional a›liations, each author takes an interdisciplinary approach that combines methods and ideas from physics, mathematics, and philosophy. In the remainder of this introduction, we will briežy overview the various chapters and their contribution to the ongoing task of making sense of the physical world.