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Probability theory

The revolutions that Gregory Chaitin brought within the fields of science are well known. From his discovery of algorithmic information complexity to his work on Gödel's theorem, he has contributed deeply and expansively to such diverse fields. This book attempts to bring together a collection of articles written by his colleagues, collaborators and friends to celebrate his work in a festschrift. It encompasses various aspects of the scientific work that Chaitin has accomplished over the years. Topics range from philosophy to biology, from foundations of mathematics to physics, from logic to computer science, and all other areas Chaitin has worked on. It also includes sketches of his personality with the help of biographical accounts in some unconventional articles that will provide a rare glimpse into the personal life and nature of Chaitin. Compared to the other books that exist along a similar vein, this book stands out primarily due to its highly interdisciplinary nature and its scope that will attract readers into Chaitin's world

This book combines detailed scientific historical research with characteristic philosophic breadth and verve.

This Element has two main aims. The first one (sections 1-7) is an historically informed review of the philosophy of probability. It describes recent historiography, lays out the distinction between subjective and objective notions, and concludes by applying the historical lessons to the main interpretations of probability. The second aim (sections 8-13) focuses entirely on objective probability, and advances a number of novel theses regarding its role in scientific practice. A distinction is drawn between traditional attempts to interpret chance, and a novel methodological study of its application. A radical form of pluralism is then introduced, advocating a tripartite distinction between propensities, probabilities and frequencies. Finally, a distinction is drawn between two different applications of chance in statistical modelling which, it is argued, vindicates the overall methodological approach. The ensuing conception of objective probability in practice is the 'complex nexus of chance'.

Pierre-Simon Laplace (1749-1827) is remembered amoung probabilitists today particularly for his "Theorie analytique des probabilites", published in 1812. The "Essai philosophique dur les probabilites" is his introduction for the second edition of this work. Here Laplace provided a popular exposition on his "Theorie". The "Essai", based on a lecture on probability given by Laplace in 1794, underwent sweeping changes, almost doubling in size, in the various editions published during Laplace's lifetime. Translations of various editions in different languages have apeared over the years. The only English translation of 1902 reads awkwardly today. This is a thorough and modern translation based on the recent re-issue, with its voluminous notes, of the fifth edition of 1826, with preface by Rene Thom and postscript by Bernard Bru. In the second part of the book, the reader is provided with an extensive commentary by the translator including valuable histographical and mathematical remarks and various proofs.

The advancements in society are intertwined with the advancements in science. To understand how changes in society occurred, and will continue to change, one has to have a basic understanding of the laws of physics and chemistry. Physical Chemistry: Multidisciplinary Applications in Society examines how the laws of physics and chemistry (physical chemistry) explain the dynamic nature of the Universe and events on Earth, and how these events affect the evolution of society (multidisciplinary applications). The ordering of the chapters reflects the natural flow of events in an evolving Universe: Philosophy of Science, the basis of the view that natural events have natural causes - Cosmology, the origin of everything from the Big Bang to the current state of the Universe - Geoscience, the physics and chemistry behind the evolution of the planet Earth from its birth to the present - Life Science, the molecules and mechanisms of life on Earth - Ecology, the interdependence of all components within the Ecosphere and the Universe - Information Content, emphasis on how words and phrases and framing of issues affect opinions, reliability of sources, and the limitations of knowledge. - Addresses the four Ws of science: Why scientists believe Nature works the way it does, Who helped develop the fields of science, What theories of natural processes tell us about the nature of Nature, and Where our scientific knowledge is taking us into the future - Gives a historical review of the evolution of science, and the accompanying changes in the philosophy of how science views the nature of the Universe - Explores the physics and chemistry of Nature with minimal reliance on mathematics - Examines the structure and dynamics of the Universe and our Home Planet Earth - Provides a detailed analysis of how humans, as members of the Ecosphere, have influenced, and are continuing to influence, the dynamics of events on the paludarium called Earth - Presents underlying science of current political issues that shape the future of humankind - Emphasizes how words and phrases and framing of issues can influence the opinions of members of society - Makes extensive use of metaphors and everyday experiences to illustrate principles in science and social interactions