Related papers: Tolstoy's Mathematics in "War and Peace"
Just as war is sometimes fallaciously represented as a zero sum game -- when in fact war is a negative sum game - stock market trading, a positive sum game over time, is often erroneously represented as a zero sum game. This is called the…
April 25, 2003, marked the 100th anniversary of the birth of Andrei Nikolaevich Kolmogorov, the twentieth century's foremost contributor to the mathematical and philosophical foundations of probability. The year 2003 was also the 70th…
Topos theory has been suggested by Doring and Isham as an alternative mathematical structure with which to formulate physical theories. In particular it has been used to reformulate standard quantum mechanics in such a way that a novel type…
Mathematical equivalence between statistical mechanics and machine learning theory has been known since the 20th century, and research based on this equivalence has provided novel methodologies in both theoretical physics and statistical…
A sketch of some of the fundamental notions related to the nature of knowledge is offered, with special focus on the role of mathematics and my own opinions. No single idea exposed here is entirely original; indeed, this topic has been…
Some 80-90 years ago, George A. Linhart, unlike A. Einstein, P. Debye, M. Planck and W. Nernst, has managed to derive a very simple, but ultimately general mathematical formula for heat capacity vs. temperature from the fundamental…
We are able to unify various disparate claims and results in the literature, that stand in the way of a unified description and understanding of human conflict. First, we provide a reconciliation of the numerically different exponent values…
We propose an extremely simple mathematical model that is shown to be able to account for more than 99 per cent of all the variation in economic and demographic macrodynamics of the world for almost two millennia of its history. This…
Professor Sir Karl Popper (1902-1994) was one of the most influential philosophers of science of the twentieth century, best known for his doctrine of falsifiability. His axiomatic formulation of probability, however, is unknown to current…
Game theory is an established branch of mathematics that offers a rich set of mathematical tools for multi-person strategic decision making that can be used to model the interactions of decision makers in security problems who compete for…
In this paper, we do three kinds of work. First, we recognize four notions of necessity and two notions of possibility related to time flow, namely strong/weak historical/temporal necessities, as well as historical/temporal possibilities,…
The "War of Attrition" is a classical game theoretic model that was first introduced to mathematically describe certain non-violent animal behavior. The original setup considers two participating players in a one-shot game competing for a…
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
Majorisation, also called rearrangement inequalities, yields a type of stochastic ordering in which two or more distributions can be compared. In this paper we argue that majorisation is a good candidate as a theory for uncertainty. We…
During his brief life, the Polish mathematician and logician Adolf Lindenbaum (1904--1941) contributed to mathematical logic, among other things, by several significant achievements. Some results of Lindenbaum's, which bear his name, were…
The aim of this essay is to propose a conception of mathematics that is fully consonant with naturalism. By that I mean the hypothesis that everything that exists is part of the natural world, which makes up a unitary whole.
Randomisation and time-sharing are some of the oldest methods to achieve fairness. I make a case that applying these approaches to social choice settings constitutes a powerful paradigm that deserves an extensive and thorough examination. I…
This article is devoted to the tactical game theoretical interpretation of dialectics. Dialectical games are considered as abstractly as well as models of the internal dialogue and reflection. The models related to the representation theory…
The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are…
Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to…