The Structure of Scientific Revolutions

Chaos theory A double rod pendulum animation showing chaotic behavior. Starting the pendulum from a slightly different initial condition would result in a completely different trajectory. The double rod pendulum is one of the simplest dynamical systems that has chaotic solutions. Chaos: When the present determines the future, but the approximate present does not approximately determine the future. Chaotic behavior can be observed in many natural systems, such as weather and climate.[6][7] This behavior can be studied through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps. Introduction[edit] Chaos theory concerns deterministic systems whose behavior can in principle be predicted. Chaotic dynamics[edit] The map defined by x → 4 x (1 – x) and y → x + y mod 1 displays sensitivity to initial conditions. In common usage, "chaos" means "a state of disorder".[9] However, in chaos theory, the term is defined more precisely. where , and , is: .

The Kingdom of God Is Within You The 1st English edition of The Kingdom of God Is Within You. The Kingdom of God Is Within You (Russian: Царство Божие внутри вас [Tsarstvo Bozhiye vnutri vas]) is the non-fiction magnum opus of Leo Tolstoy. The book was first published in Germany in 1894 after being banned in his home country of Russia.[1] It is the culmination of thirty years of Tolstoy's Christian anarchist thinking, and lays out a new organization for society based on a literal Christian interpretation. Reasoning[edit] The 1st edition of The Kingdom of God Is Within You, 1894. The title of the book is taken from Luke 17:21. “How can you kill people, when it is written in God’s commandment: ‘Thou shalt not murder’?” Tolstoy took the viewpoint that all governments who waged war are an affront to Christian principles. Tolstoy advocated non-violence as a solution to nationalist woes and as a means for seeing the hypocrisy of the church. Tolstoy's relationship with Mohandas Gandhi[edit] Mohandas K. See also[edit]

Phase diagram Overview[edit] Common components of a phase diagram are lines of equilibrium or phase boundaries, which refer to lines that mark conditions under which multiple phases can coexist at equilibrium. Phase transitions occur along lines of equilibrium. Triple points are points on phase diagrams where lines of equilibrium intersect. Types of phase diagrams[edit] 2D phase diagrams[edit] The curves on the phase diagram show the points where the free energy (and other derived properties) becomes non-analytic: their derivatives with respect to the coordinates (temperature and pressure in this example) change discontinuously (abruptly). The existence of the liquid–gas critical point reveals a slight ambiguity in labelling the single phase regions. Other thermodynamic properties In addition to just temperature or pressure, other thermodynamic properties may be graphed in phase diagrams. In a two-dimensional graph, two of the thermodynamic quantities may be shown on the horizontal and vertical axes.

Looking Backward Looking Backward: 2000-1887 is a utopian science fiction novel by Edward Bellamy, a lawyer and writer from Chicopee Falls, Massachusetts; it was first published in 1888. According to Erich Fromm, Looking Backward is "one of the most remarkable books ever published in America".[1] Synopsis[edit] The book tells the story of Julian West, a young American who, towards the end of the 19th century, falls into a deep, hypnosis-induced sleep and wakes up one hundred and thirteen years later. He finds himself in the same location (Boston, Massachusetts), but in a totally changed world: It is the year 2000 and, while he was sleeping, the United States has been transformed into a socialist utopia. The remainder of the book outlines Bellamy's thoughts about improving the future. Although Bellamy's novel did not discuss technology or the economy in detail, commentators frequently compare Looking Backward with actual economic and technological developments. Key excerpts[edit] Precursors[edit]

Phase space Phase space of a dynamic system with focal instability, showing one phase space trajectory A plot of position and momentum variables as a function of time is sometimes called a phase plot or a phase diagram. Phase diagram, however, is more usually reserved in the physical sciences for a diagram showing the various regions of stability of the thermodynamic phases of a chemical system, which consists of pressure, temperature, and composition. In classical mechanics, any choice of generalized coordinates q i for the position (i.e. coordinates on configuration space) defines conjugate generalized momenta pi which together define co-ordinates on phase space. More abstractly, in classical mechanics phase space is the cotangent space of configuration space, and in this interpretation the procedure above expresses that a choice of local coordinates on configuration space induces a choice of natural local Darboux coordinates for the standard symplectic structure on a cotangent space.

News from Nowhere The book explores a number of aspects of this society, including its organisation and the relationships which it engenders between people. Morris cleverly fuses Marxism and the romance tradition when he presents himself as an enchanted figure in a time and place different from Victorian England. As Morris, the romance character, quests for love and fellowship—and through them for a reborn self—he encounters romance archetypes in Marxist guises. In the novel, Morris tackles one of the most common criticisms of socialism; the supposed lack of incentive to work in a communistic society. Looking Backward[edit] Morris reviewed the novel Looking Backward in the Commonweal on 21 June 1889. Morris’s basic antipathy with Bellamy arose chiefly from his disagreement with Bellamy’s social values and aesthetic convictions. More specifically, Morris criticised the limited nature Bellamy's idea of life. Gender in Nowhere[edit] Marriage[edit] Morris offers a Marxian view of marriage and divorce.

Complementarity (physics) In physics, complementarity is a fundamental principle of quantum mechanics, closely associated with the Copenhagen interpretation. It holds that objects governed by quantum mechanics, when measured, give results that depend inherently upon the type of measuring device used, and must necessarily be described in classical mechanical terms. Further, a full description of a particular type of phenomenon can only be achieved through measurements made in each of the various possible bases — which are thus complementary. The complementarity principle was formulated by Niels Bohr, the developer of the Bohr model of the atom, and a leading founder of quantum mechanics.[1] Bohr summarized the principle as follows: ...however far the [quantum physical] phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms. For example, the particle and wave aspects of physical objects are such complementary phenomena. Physicists F.A.M. Dr.

The Great Explosion The Great Explosion is a satirical science fiction novel by Eric Frank Russell, first published in 1962. The story is divided into three sections. The final section is based on Russell's famous 1951 short story "...And Then There Were None." Twenty-three years after the novel was published, it won a Prometheus Hall of Fame Award. Plot[edit] The Blieder drive, a faster-than-light drive system, has permitted the population of Earth to colonize the galaxy. The first planet was a penal colony; it is now many independent kleptocratic despotisms preying on each other. See also[edit] References[edit] Jump up ^ James, Edward (2003). External links[edit]

Wave function collapse When the Copenhagen interpretation was first expressed, Niels Bohr postulated wave function collapse to cut the quantum world from the classical.[5] This tactical move allowed quantum theory to develop without distractions from interpretational worries. Mathematical description[edit] Mathematical background[edit] The quantum state of a physical system is described by a wave function (in turn – an element of a projective Hilbert space). The kets Where represents the Kronecker delta. An observable (i.e. measurable parameter of the system) is associated with each eigenbasis, with each quantum alternative having a specific value or eigenvalue, ei, of the observable. The coefficients c1, c2, c3... are the probability amplitudes corresponding to each basis . For simplicity in the following, all wave functions are assumed to be normalized; the total probability of measuring all possible states is unity: The process of collapse[edit] of that observable. , the wave function collapses from the full . .

A LIST OF BOOKS Quantum nonlocality Quantum nonlocality is the phenomenon by which the measurements made at a microscopic level necessarily refute one or more notions (often referred to as local realism) that are regarded as intuitively true in classical mechanics. Rigorously, quantum nonlocality refers to quantum mechanical predictions of many-system measurement correlations that cannot be simulated by any local hidden variable theory. Many entangled quantum states produce such correlations when measured, as demonstrated by Bell's theorem. Experiments have generally favoured quantum mechanics as a description of nature, over local hidden variable theories.[1][2] Any physical theory that supersedes or replaces quantum theory must make similar experimental predictions and must therefore also be nonlocal in this sense; quantum nonlocality is a property of the universe that is independent of our description of nature. Example[edit] Imagine two experimentalists, Alice and Bob, situated in separate laboratories. and P(b0|A1) = or

Wave function However, complex numbers are not necessarily used in all treatments. Louis de Broglie in his later years proposed a real-valued wave function connected to the complex wave function by a proportionality constant and developed the de Broglie–Bohm theory. The unit of measurement for ψ depends on the system. For one particle in three dimensions, its units are [length]−3/2. These unusual units are required so that an integral of |ψ|2 over a region of three-dimensional space is a unitless probability (the probability that the particle is in that region). For different numbers of particles and/or dimensions, the units may be different and can be found by dimensional analysis.[1] Historical background[edit] In the 1920s and 1930s, quantum mechanics was developed using calculus and linear algebra. Wave functions and function spaces[edit] If the wave function is to change throughout space and time, one would expect the wave function to be a function of the position and time coordinates.