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Hermann Weyl (1885-1955) was one of the twentieth century's most important mathematicians, as well as a seminal figure in the development of quantum physics and general relativity. He was also an eloquent writer with a lifelong interest in the philosophical implications of the startling new scientific developments with which he was so involved.Mind and Natureis a collection of Weyl's most important general writings on philosophy, mathematics, and physics, including pieces that have never before been published in any language or translated into English, or that have long been out of print. Complete with Peter Pesic's introduction, notes, and bibliography, these writings reveal an unjustly neglected dimension of a complex and fascinating thinker. In addition, the book includes more than twenty photographs of Weyl and his family and colleagues, many of which are previously unpublished. Included here are Weyl's exposition of his important synthesis of electromagnetism and gravitation, which Einstein at first hailed as \"a first-class stroke of genius\"; two little-known letters by Weyl and Einstein from 1922 that give their contrasting views on the philosophical implications of modern physics; and an essay on time that contains Weyl's argument that the past is never completed and the present is not a point. Also included are two book-length series of lectures,The Open World(1932) andMind and Nature(1934), each a masterly exposition of Weyl's views on a range of topics from modern physics and mathematics. Finally, four retrospective essays from Weyl's last decade give his final thoughts on the interrelations among mathematics, philosophy, and physics, intertwined with reflections on the course of his rich life.

In this magisterial work, Roland Omnès takes us from the academies of ancient Greece to the laboratories of modern science as he seeks to do no less than rebuild the foundations of the philosophy of knowledge. One of the world's leading quantum physicists, Omnès reviews the history and recent development of mathematics, logic, and the physical sciences to show that current work in quantum theory offers new answers to questions that have puzzled philosophers for centuries: Is the world ultimately intelligible? Are all events caused? Do objects have definitive locations? Omnès addresses these profound questions with vigorous arguments and clear, colorful writing, aiming not just to advance scholarship but to enlighten readers with no background in science or philosophy. The book opens with an insightful and sweeping account of the main developments in science and the philosophy of knowledge from the pre-Socratic era to the nineteenth century. Omnès then traces the emergence in modern thought of a fracture between our intuitive, commonsense views of the world and the abstract and--for most people--incomprehensible world portrayed by advanced physics, math, and logic. He argues that the fracture appeared because the insights of Einstein and Bohr, the logical advances of Frege, Russell, and Gödel, and the necessary mathematics of infinity of Cantor and Hilbert cannot be fully expressed by words or images only. Quantum mechanics played an important role in this development, as it seemed to undermine intuitive notions of intelligibility, locality, and causality. However, Omnès argues that common sense and quantum mechanics are not as incompatible as many have thought. In fact, he makes the provocative argument that the \"consistent-histories\" approach to quantum mechanics, developed over the past fifteen years, places common sense (slightly reappraised and circumscribed) on a firm scientific and philosophical footing for the first time. In doing so, it provides what philosophers have sought through the ages: a sure foundation for human knowledge. Quantum Philosophy is a profound work of contemporary science and philosophy and an eloquent history of the long struggle to understand the nature of the world and of knowledge itself.

This chapter contains sections titled: Galilean Transformations and Galilean Invariants A Brief Preliminary: Why Worry? Lorentz Invariance: Collapse Theories Lorentz Invariance: Hyperplane Dependence Lorentz Invariance: Non‐Collapse Theories Choose Your Poison

This book gives a comprehensive and self-contained introduction to the theory of symmetric Markov processes and symmetric quasi-regular Dirichlet forms. In a detailed and accessible manner, Zhen-Qing Chen and Masatoshi Fukushima cover the essential elements and applications of the theory of symmetric Markov processes, including recurrence/transience criteria, probabilistic potential theory, additive functional theory, and time change theory. The authors develop the theory in a general framework of symmetric quasi-regular Dirichlet forms in a unified manner with that of regular Dirichlet forms, emphasizing the role of extended Dirichlet spaces and the rich interplay between the probabilistic and analytic aspects of the theory. Chen and Fukushima then address the latest advances in the theory, presented here for the first time in any book. Topics include the characterization of time-changed Markov processes in terms of Douglas integrals and a systematic account of reflected Dirichlet spaces, and the important roles such advances play in the boundary theory of symmetric Markov processes. This volume is an ideal resource for researchers and practitioners, and can also serve as a textbook for advanced graduate students. It includes examples, appendixes, and exercises with solutions.

This chapter contains sections titled: Causation Fictional Entities Free Will Individuation The Mind/Body Problem Modality and Possible Worlds Persistence Realism and Antirealism about Abstract Entities Space and Time Substance Bibliography

Throughout most of human history, events and phenomena of interest have been characterized using space and time as their major characteristic dimensions, in either absolute or relative conceptualizations. Space-time analysis seeks to understand when and where (and sometimes why) things occur. In the context of several of the most recent and substantial advances in individual movement data analysis (time geography in particular) and spatial panel data analysis, we focus on quantitative space-time analytics. Based on more than 700 articles (from 1949 to 2013) we obtained through a key word search on the Web of Knowledge and through the authors' personal archives, this article provides a synthetic overview about the quantitative methodology for space-time analysis. Particularly, we highlight space-time pattern revelation (e.g., various clustering metrics, path comparison indexes, space-time tests), space-time statistical models (e.g., survival analysis, latent trajectory models), and simulation methods (e.g., cellular automaton, agent-based models) as well as their empirical applications in multiple disciplines. This article systematically presents the strengths and weaknesses of a set of prevalent methods used for space-time analysis and points to the major challenges, new opportunities, and future directions of space-time analysis.

For reasons mostly related to chip shape distortions, global navigation satellite system (GNSS) observations are corrupted by receiver-dependent biases. These are often stable in the long term, though numerically different depending on the signal frequency, satellite system and receiver manufacturer. Based on the mixed-differenced model combining undifferenced pseudorange with epoch-differenced carrier phase observations, we present a multi-GNSS real-time precise clock estimation model considering correction of inter-satellite code biases (ISCBs). Pre-estimated receiver-dependent ISCB corrections are introduced to correct the inter-receiver, inter-satellite and inter-system biases largely. Then the number of estimated parameters is reduced to a manageable level for real-time estimation. Comparisons with post-processed data show that compared to undifferenced, epoch-differenced and non-bias-corrected mixed-differenced models, the proposed bias-corrected model can greatly reduce the precise clock offset systematic biases, especially for GLONASS and BeiDou. The test results show the root mean square data reductions are improved by up to 96% for GLONASS, 78% for BeiDou and 40% for GPS and Galileo.

What are the main findings? * Instrumental Artifact Correction: the study identified and corrected a significant instrumental artifact in the DARA observations. * TSI Composite Reliability: the corrected DARA observations were successfully incorporated into the long-term TSI composite time series. Instrumental Artifact Correction: the study identified and corrected a significant instrumental artifact in the DARA observations. TSI Composite Reliability: the corrected DARA observations were successfully incorporated into the long-term TSI composite time series. What are the implication of the main findings? * Improved Long-Term Climate Records: the study ensures that data from the DARA radiometer can be accurately integrated into the long-term Total Solar Irradiance (TSI) climate data record. * Validation of New Radiometers: the high consistency of the corrected DARA data with the well-established PMOD/WRC composite provides strong validation and confidence in the processing of the observations. Improved Long-Term Climate Records: the study ensures that data from the DARA radiometer can be accurately integrated into the long-term Total Solar Irradiance (TSI) climate data record. Validation of New Radiometers: the high consistency of the corrected DARA data with the well-established PMOD/WRC composite provides strong validation and confidence in the processing of the observations. Since the late 1970s, satellite missions have monitored Total Solar Irradiance (TSI), providing a long-term record of solar variability. The Digital Absolute Radiometer (DARA), onboard the Chinese Fengyun-3E (FY3E) spacecraft since 4 July 2021, contributes to extending this record. In this study, we evaluate the DARA observations in both World Radiometric Reference (WRR) and International System of Units (SI) scales. We compare these records with those from other instruments on different spacecraft (i.e., VIRGO/PMO6, TSIS-1/TIM) and with the co-located Solar Irradiance Absolute Radiometer (SIAR) on FY3E. A key finding is the identification and correction of an instrumental artifact: an issue in the thermal aperture model, linked to annual satellite maneuvers, repetitively introduced an artificial step of 0.15 ± 0.05 Wm[sup.−2] into the TSI measurements. A statistical analysis of the measurements in the SI scale shows that the mean value of the DARA TSI observations is approximately 1359.58 Wm[sup.−2] (6-hourly rate), which is lower than the ones recorded by VIRGO/PMO6 (1.82 Wm[sup.−2]), TSIS-1/TIM (2.90 Wm[sup.−2]), and SIAR (2.54 Wm[sup.−2]). We estimate a degradation of ∼49 ppm over 46 months due to the exposure of the instrument to the (Extreme) Ultraviolet (UV/EUV) radiations. Finally, the corrected DARA observations are incorporated into the long-term TSI composite time series. Comparison with the PMOD/WRC composite shows only marginal differences (less than 0.015 Wm[sup.−2]), confirming the consistency and reliability of including the new TSI product (i.e., JTSIM-DARAv1).

Poleward migration of the latitudinal edge of the tropics of 0.25°–3.0° decade−1has been reported in several recent studies based on satellite and radiosonde data and reanalysis output covering the past ∼30 yr. The goal of this paper is to identify the extent to which this large range of trends can be explained by the use of different data sources, time periods, and edge definitions, as well as how the widening varies as a function of hemisphere and season. Toward this end, a suite of tropical edge latitude diagnostics based on tropopause height, winds, precipitation–evaporation, and outgoing longwave radiation (OLR) are analyzed using several reanalyses and satellite datasets. These diagnostics include both previously used definitions and new definitions designed for more robust detection. The wide range of widening trends is shown to be primarily due to the use of different datasets and edge definitions and only secondarily due to varying start–end dates. This study also shows that the large trends (>∼1° decade−1) previously reported in tropopause and OLR diagnostics are due to the use of subjective definitions based on absolute thresholds. Statistically significant Hadley cell expansion based on the mean meridional streamfunction of 1.0°–1.5° decade−1is found in three of four reanalyses that cover the full time period (1979–2009), whereas other diagnostics yield trends of −0.5°–0.8° decade−1that are mostly insignificant. There are indications of hemispheric and seasonal differences in the trends, but the differences are not statistically significant.