The impact of Gödel's theorem on twentieth-century thought is on par with that of Einstein's theory of relativity, Heisenberg's uncertainty principle, or Keynesian economics. These previously unpublished intimate and informal conversations, however, bring to light and amplify Gödel's other major contributions to logic and philosophy. They reveal that there is much more in Gödel's philosophy of mathematics than is commonly believed, and more in his philosophy than his philosophy of mathematics.
Wang writes that "it is even possible that his quite informal and loosely structured conversations with me, which I am freely using in this book, will turn out to be the fullest existing expression of the diverse components of his inadequately articulated general philosophy."
The first two chapters are devoted to Gödel's life and mental development. In the chapters that follow, Wang illustrates the quest for overarching solutions and grand unifications of knowledge and action in Gödel's written speculations on God and an afterlife. He gives the background and a chronological summary of the conversations, considers Gödel's comments on philosophies and philosophers (his support of Husserl's phenomenology and his digressions on Kant and Wittgenstein), and his attempt to demonstrate the superiority of the mind's power over brains and machines. Three chapters are tied together by what Wang perceives to be Gödel's governing ideal of philosophy: an exact theory in which mathematics and Newtonian physics serve as a model for philosophy or metaphysics. Finally, in an epilog Wang sketches his own approach to philosophy in contrast to his interpretation of Gödel's outlook.
In the context of subtractive manufacturing, ultra-precision diamond turning is based on the pillars of materials science, machine tools, modeling and simulation technologies, etc., making the study of such machining processes intrinsically interdisciplinary. However, in contrast to the substantial advances that have been achieved in machine design, laser metrology and control systems, relatively little research has been conducted on the material behavior and its effects on surface finish, such as the material anisotropy of crystalline materials. The feature of the significantly reduced depth of cut on the order of a few micrometers or less, which is much smaller than the average grain size of work-piece materials, unavoidably means that conventional metal cutting theories can only be of limited value in the investigation of the mechanisms at work in micro-cutting processes in ultra-precision diamond turning.
This book studies the classical stochastic volatility and deterministic volatility models. For the former, the classical Heston model is integrated with volatility term structure. The correlation of Heston model is considered to be variable. For the latter, the local volatility model is improved from experience of financial practice. The improved local volatility surface is then used for price forecasting. VaR and CVaR are employed as standard criterions for risk management. The options trading strategies are also designed combining different types of options and they have been proven to be profitable in real market.
This book is a combination of theory and practice. Users will find the applications of these financial models in real market to be effective and efficient.