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.
Jane McDonnell is Adjunct Research Associate in the Philosophy Department at Monash University, Australia. She has doctorates in both theoretical physics and philosophy and over twenty years' experience applying mathematics in academia and industry. She has authored or co-authored more than eighty technical papers in physics, mathematics, finance and philosophy.
"The present book provides a good overview of the philosophical subject matter concerning the interconnectedness of mathematics and science, in particular physics. The final part on quantum monadology is speculative, albeit thought-inspiring. ... The references throughout the text are useful for more in-depth knowledge on the individual topics and facilitate further research." (Michael M. Tung, Mathematical Reviews, December, 2017)
This book explores the persistence of Pythagorean ideas in theoretical physics. It shows that the Pythagorean position is both philosophically deep and scientifically interesting. However, it does not endorse pure Pythagoreanism; rather, it defends the thesis that mind and mathematical structure are the grounds of reality.
The book begins by examining Wigner's paper on the unreasonable effectiveness of mathematics in the natural sciences. It argues that, whilst many issues surrounding the applicability of mathematics disappear upon examination, there are some core issues to do with the effectiveness of mathematics in fundamental physics which remain. The core issues are the existence of the laws of nature and our minds ability to fathom them, the use of formal mathematics in discovering things about the quantum world, the fact that deep mathematics is needed to describe fundamental physics, and the asymptotic nature of the quest for knowledge. These issues are the focus of the book. The author seeks to explain them within a metaphysical framework that takes mind and mathematical structure as its fundamental principles. The framework - called quantum monadology - combines ideas from Leibnizian monadology, set theory, and consistent histories quantum theory.