Determinism Determinism is the philosophical position that for every event, including human action, there exist conditions that could cause no other event. "There are many determinisms, depending upon what pre-conditions are considered to be determinative of an event."[1] Deterministic theories throughout the history of philosophy have sprung from diverse and sometimes overlapping motives and considerations. Some forms of determinism can be empirically tested with ideas from physics and the philosophy of physics. The opposite of determinism is some kind of indeterminism (otherwise called nondeterminism). Other debates often concern the scope of determined systems, with some maintaining that the entire universe is a single determinate system and others identifying other more limited determinate systems (or multiverse). Varieties[edit] Below appear some of the more common viewpoints meant by, or confused with "determinism". Philosophical connections[edit] With nature/nurture controversy[edit]
Roger Penrose English mathematician, mathematical physicist (born 1931) Sir Roger Penrose OM FRS (born 8 August 1931)[1] is an English mathematician, mathematical physicist, philosopher of science and Nobel Laureate in Physics.[2] He is Emeritus Rouse Ball Professor of Mathematics at the University of Oxford, an emeritus fellow of Wadham College, Oxford, and an honorary fellow of St John's College, Cambridge, and University College London.[3][4][5] Penrose has contributed to the mathematical physics of general relativity and cosmology. He won the Royal Society Science Books Prize for The Emperor's New Mind (1989), which outlines his views on physics and consciousness. He followed it with The Road to Reality (2004), billed as "A Complete Guide to the Laws of the Universe". Early life and education [edit] Born in Colchester, Essex, Roger Penrose is a son of Margaret (née Leathes), a physician, and Lionel Penrose, a psychiatrist and geneticist. As the reviewer Manjit Kumar puts it: Research and career
Boolean algebra Boolean algebra was introduced by George Boole in his first book The Mathematical Analysis of Logic (1847), and set forth more fully in his An Investigation of the Laws of Thought (1854).[1] According to Huntington the term "Boolean algebra" was first suggested by Sheffer in 1913.[2] Boolean algebra has been fundamental in the development of digital electronics, and is provided for in all modern programming languages. It is also used in set theory and statistics.[3] History[edit] In the 1930s, while studying switching circuits, Claude Shannon observed that one could also apply the rules of Boole's algebra in this setting, and he introduced switching algebra as a way to analyze and design circuits by algebraic means in terms of logic gates. Values[edit] As with elementary algebra, the purely equational part of the theory may be developed without considering explicit values for the variables.[12] Operations[edit] Basic operations[edit] The basic operations of Boolean algebra are as follows. J.
Poincaré conjecture Theorem in geometric topology The eventual proof built upon Richard S. Hamilton's program of using the Ricci flow to solve the problem. History[edit] Poincaré's question[edit] Henri Poincaré was working on the foundations of topology—what would later be called combinatorial topology and then algebraic topology. The original phrasing was as follows: Consider a compact 3-dimensional manifold V without boundary. Poincaré never declared whether he believed this additional condition would characterize the 3-sphere, but nonetheless, the statement that it does is known as the Poincaré conjecture. Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere. Solutions[edit] In the 1930s, J. , the prototype of which is now called the Whitehead manifold. In the 1950s and 1960s, other mathematicians attempted proofs of the conjecture only to discover that they contained flaws. Over time, the conjecture gained the reputation of being particularly tricky to tackle. Dimensions[edit] with
Hendrik Lorentz Dutch theoretical physicist (1853–1928) Hendrik Antoon Lorentz[a] (18 July 1853 – 4 February 1928) was a Dutch theoretical physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for their discovery and theoretical explanation of the Zeeman effect.[3] He derived the Lorentz transformation of the special theory of relativity, as well as the Lorentz force, which describes the force acting on a charged particle in an electromagnetic field. He was also responsible for the Lorentz oscillator model, a classical model used to describe the anomalous dispersion observed in dielectric materials when the driving frequency of the electric field was near the resonant frequency of the material, resulting in abnormal refractive indices. Lorentz received many other honors and distinctions, including a term as Chairman of the International Committee on Intellectual Cooperation,[4] the forerunner of UNESCO, from 1925 until his death in 1928. Early life and education [edit] M.
Gravitoelectromagnetism Gravitoelectromagnetism, abbreviated GEM, refers to a set of formal analogies between the equations for electromagnetism and relativistic gravitation; specifically: between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity. Gravitomagnetism is a widely used term referring specifically to the kinetic effects of gravity, in analogy to the magnetic effects of moving electric charge. The most common version of GEM is valid only far from isolated sources, and for slowly moving test particles. The analogy and equations differing only by some small factors were first published in 1893, before general relativity, by Oliver Heaviside as a separate theory expanding Newton's law.[1] Background[edit] ...or equivalently currentI, same field profile, and field generation due to rotation. Physical analogues of fields[2] Indirect validations of gravitomagnetic effects have been derived from analyses of relativistic jets.
Cybernetics Cybernetics is a transdisciplinary[1] approach for exploring regulatory systems, their structures, constraints, and possibilities. Cybernetics is relevant to the study of systems, such as mechanical, physical, biological, cognitive, and social systems. Cybernetics is applicable when a system being analyzed incorporates a closed signaling loop; that is, where action by the system generates some change in its environment and that change is reflected in that system in some manner (feedback) that triggers a system change, originally referred to as a "circular causal" relationship. Concepts studied by cyberneticists (or, as some prefer, cyberneticians) include, but are not limited to: learning, cognition, adaptation, social control, emergence, communication, efficiency, efficacy, and connectivity. Norbert Wiener defined cybernetics in 1948 as "the scientific study of control and communication in the animal and the machine Definitions[edit] Other notable definitions include: Etymology[edit] W.
Ricci flow Partial differential equation In the mathematical fields of differential geometry and geometric analysis, the Ricci flow ( REE-chee, Italian: [ˈrittʃi]), sometimes also referred to as Hamilton's Ricci flow, is a certain partial differential equation for a Riemannian metric. It is often said to be analogous to the diffusion of heat and the heat equation, due to formal similarities in the mathematical structure of the equation. However, it is nonlinear and exhibits many phenomena not present in the study of the heat equation. The Ricci flow, so named for the presence of the Ricci tensor in its definition, was introduced by Richard Hamilton, who used it through the 1980s to prove striking new results in Riemannian geometry. Mathematical definition [edit] On a smooth manifold M, a smooth Riemannian metric g automatically determines the Ricci tensor Ricg. Let k be a nonzero number. Normalized Ricci flow Here R denotes scalar curvature. Existence and uniqueness Let . on , the function where . . If . .
Absolute space and time Theoretical foundation of Newtonian mechanics Absolute space and time is a concept in physics and philosophy about the properties of the universe. In physics, absolute space and time may be a preferred frame. Early concept[edit] A version of the concept of absolute space (in the sense of a preferred frame) can be seen in Aristotelian physics.[1] Robert S. Newton[edit] Originally introduced by Sir Isaac Newton in Philosophiæ Naturalis Principia Mathematica, the concepts of absolute time and space provided a theoretical foundation that facilitated Newtonian mechanics.[3] According to Newton, absolute time and space respectively are independent aspects of objective reality:[4] According to Newton, absolute time exists independently of any perceiver and progresses at a consistent pace throughout the universe. Absolute space, in its own nature, without regard to anything external, remains always similar and immovable. Differing views[edit] Mathematical definitions[edit] Special relativity[edit]
Geodesy The science of the geometric shape, orientation in space, and gravitational field of Earth Definition[edit] The word "geodesy" comes from the Ancient Greek word γεωδαισία geodaisia (literally, "division of Earth"). It is primarily concerned with positioning within the temporally varying gravity field. Geodesy in the German-speaking world is divided into "higher geodesy" ("Erdmessung" or "höhere Geodäsie"), which is concerned with measuring Earth on the global scale, and "practical geodesy" or "engineering geodesy" ("Ingenieurgeodäsie"), which is concerned with measuring specific parts or regions of Earth, and which includes surveying. To a large extent, the shape of Earth is the result of rotation, which causes its equatorial bulge, and the competition of geological processes such as the collision of plates and of volcanism, resisted by Earth's gravity field. History[edit] Geoid and reference ellipsoid[edit] Coordinate systems in space[edit] Coordinate systems in the plane[edit] Heights[edit]