Related papers: Tolstoy's Mathematics in "War and Peace"
Climate statistics is of course a very broad field, along with the many connections and impacts for yet other areas, with a history as long as mankind has been recording temperatures, describing drastic weather events, etc. The important…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
The ability to interpret the mental state of another agent based on its behavior, also called Theory of Mind (ToM), is crucial for humans in any kind of social interaction. Artificial systems, such as intelligent assistants, would also…
Understanding how ideas relate to each other is a fundamental question in many domains, ranging from intellectual history to public communication. Because ideas are naturally embedded in texts, we propose the first framework to…
Lewis' theory of counterfactuals is the foundation of many contemporary notions of causality. In this paper, we extend this theory in the temporal direction to enable symbolic counterfactual reasoning on infinite sequences, such as…
In their account of theory change in logic, Aberdein and Read distinguish 'glorious' from 'inglorious' revolutions--only the former preserves all 'the key components of a theory' [1]. A widespread view, expressed in these terms, is that…
The theories of quantum mechanics and relativity dramatically altered our understanding of the universe ushering in the era of modern physics. Quantum theory deals with objects probabilistically at small scales, whereas relativity deals…
This is a brief overview of the role of mathematicians in the so-called "Luzin Case" as well as some analysis of the mathematical and humanitarian roots of the affair.
Computational Logic is the use of computers to establish facts in a logical formalism. Originating in 19th-century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms,…
This article explores the ideas that went into George Boole's development of an algebra for logical inference in his book The Laws of Thought. We explore in particular his wife Mary Boole's claim that he was deeply influenced by Indian…
In the last decades, several objects such as grammars, economical agents, laws of physics... have been defined as algorithms. In particular, after Brouwer, Heyting, and Kolomogorov, mathematical proofs have been defined as algorithms. In…
Philosophers now seem to agree that frequentism is an untenable strategy to explain the meaning of probabilities. Nevertheless, I want to revive frequentism, and I will do so by grounding probabilities on typicality in the same way as the…
Causality is a subject of philosophical debate and a central scientific issue with a long history. In the statistical domain, the study of cause and effect based on the notion of `fairness' in comparisons dates back several hundred years,…
This paper investigates the historical origin and ancestors of typicality, which is now a central concept in Boltzmannian Statistical Mechanics and Bohmian Mechanics. Although Ludwig Boltzmann did not use the word typicality, its main idea,…
In many real-world situations, there is often not enough information to know that a certain strategy will succeed in achieving the goal, but there is a good reason to believe that it will. The paper introduces the term ``doxastic'' for such…
The book A Treatise on Probability was published by John Maynard Keynes in 1921. It contains a critical assessment of the foundations of probability and of the current statistical methodology. As a modern reader, we review here the aspects…
Bunyakovsky's integral inequality (1859) is one of the familiar tools of modern Analysis. We try and understand what Bunyakovsky did, why he did it, why others did not follow the same path, and explore some of the mathematical…
The application of classical methods of statistical mechanics, originally developed by Ludwig Boltzmann in gas dynamics, to the description of social phenomena is a successful story that we try to outline in this paper. On one hand, it is…
This paper is the first in series of four papers that present an analytical approach to war using game theory. We try to explore why is it that "true peace" can't be achieved and all or any efforts we make towards that goal will have huge…
Homotopy type theory is a new branch of mathematics, based on a recently discovered connection between homotopy theory and type theory, which brings new ideas into the very foundation of mathematics. On the one hand, Voevodsky's subtle and…