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Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce…

History and Overview · Mathematics 2016-04-04 Noson S. Yanofsky , Mark Zelcer

Symmetry is a fundamental concept in modern physics and other related sciences. Being such a powerful tool, almost all physical theories can be derived from symmetry, and the effectiveness of such an approach is astonishing. Since many…

Popular Physics · Physics 2020-07-15 Ivan Kozic

Symmetry can be used to help solve many problems. For instance, Einstein's famous 1905 paper ("On the Electrodynamics of Moving Bodies") uses symmetry to help derive the laws of special relativity. In artificial intelligence, symmetry has…

Artificial Intelligence · Computer Science 2010-07-06 Toby Walsh

Symmetry, a central concept in understanding the laws of nature, has been used for centuries in physics, mathematics, and chemistry, to help make mathematical models tractable. Yet, despite its power, symmetry has not been used extensively…

Machine Learning · Statistics 2019-09-11 Doron L. Bergman

The general concept of symmetry is realized in manifold ways in different realms of reality, such as plants, animals, minerals, mathematical objects or human artefacts in literature, fine arts and society. In order to arrive at a common…

History and Philosophy of Physics · Physics 2021-07-01 Hartmann Römer

We state the defining characteristic of mathematics as a type of symmetry where one can change the connotation of a mathematical statement in a certain way when the statement's truth value remains the same. This view of mathematics as…

History and Overview · Mathematics 2013-06-19 Noson S. Yanofsky , Mark Zelcer

In contemporary theoretical physics, the powerful notion of symmetry stands for a web of intricate meanings among which I identify four clusters associated with the notion of transformation, comprehension, invariance and projection. While…

History and Philosophy of Physics · Physics 2013-12-23 Amaury Mouchet

Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination…

Quantum Physics · Physics 2019-01-23 Ivan Fernandez-Corbaton

Symmetry is an important feature of many constraint programs. We show that any problem symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each…

Artificial Intelligence · Computer Science 2010-05-31 George Katsirelos , Toby Walsh

Symmetry distills the simplicity of natural laws from the complexity of physical phenomena. The symmetry principle is of vital importance in various aspects of modern physics, including analyzing atomic spectra, determining fundamental…

Strongly Correlated Electrons · Physics 2022-09-14 Congjun Wu

This is the introductive paper to the volume "Symmetries in Physics: Philosophical Reflections", Cambridge University Press, 2003. We begin with a brief description of the historical roots and emergence of the concept of symmetry that is at…

Quantum Physics · Physics 2007-05-23 Katherine Brading , Elena Castellani

The concepts of symmetry and its breakdown are investigated in two different terms according to whether the resulting asymmetry is universal or only obtained for a special configuration: we shall illustrate this by considering in the first…

General Physics · Physics 2022-03-23 Luca Fabbri

The quest for understanding the complex phenomena of the world has led to the development of various fields of science, each with its own methods, models, and assumptions. However, sometimes these fields can intersect and inspire each…

Physics and Society · Physics 2024-02-22 Arnab Kumar Maity

The enterprise of trying to explain different social and economic phenomena using concepts and ideas drawn from physics has a long history. Statistical mechanics, in particular, has been often seen as most likely to provide the means to…

Physics and Society · Physics 2019-06-28 Shakti N. Menon , V. Sasidevan , Sitabhra Sinha

A financial market is a system resulting from the complex interaction between participants in a closed economy. We propose a minimal microscopic model of the financial market economy based on the real economy's symmetry constraint and…

Physics and Society · Physics 2022-06-15 Liu Ziyin , Katsuya Ito , Kentaro Imajo , Kentaro Minami

Symmetry is an important feature of many constraint programs. We show that any symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each symmetry…

Artificial Intelligence · Computer Science 2009-09-18 George Katsirelos , Toby Walsh

Spacetime and internal symmetries can be used to severely restrict the form of the equations for the fundamental laws of physics. The success of this approach in the context of general relativity and particle physics motivates the…

General Relativity and Quantum Cosmology · Physics 2017-02-16 Saurya Das , Gabor Kunstatter

The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…

Statistical Mechanics · Physics 2023-10-04 Roberto C. Alamino

"Symmetry" was one of the most important methodological themes in 20th-century physics and is probably going to play no lesser role in physics of the 21st century. As used today, there are a variety of interpretations of this term, which…

History and Philosophy of Physics · Physics 2015-06-04 Domenico Giulini

Why is ``worthless'' fiat money generally accepted as payment for goods and services? In equilibrium theory, the value of money is generally not determined: the number of equations is one less than the number of unknowns, so only relative…

Statistical Mechanics · Physics 2011-04-12 Per Bak , Simon F. Norrelykke , Martin Shubik
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