Shape of the Universe The shape of the universe is the local and global geometry of the universe, in terms of both curvature and topology (though, strictly speaking, it goes beyond both). When physicsist describe the universe as being flat or nearly flat, they're talking geometry: how space and time are warped according to general relativity. When they talk about whether it open or closed, they're referring to its topology.[1] Although the shape of the universe is still a matter of debate in physical cosmology, based on the recent Wilkinson Microwave Anisotropy Probe (WMAP) measurements "We now know that the universe is flat with only a 0.4% margin of error", according to NASA scientists. [2] Theorists have been trying to construct a formal mathematical model of the shape of the universe. Two aspects of shape[edit] The local geometry of the universe is determined by whether the density parameter Ω is greater than, less than, or equal to 1. Local geometry (spatial curvature)[edit] Global geometry[edit]

Elbe Day In an arranged photo commemorating the meeting of the Soviet and American armies, 2nd Lt. William Robertson (U.S. Army) and Lt. Alexander Silvashko (Red Army) stand facing one another with hands clasped and arms around each other's shoulders. In the background are two flags and a poster. Elbe Day, April 25, 1945, is the day Soviet and American troops met at the River Elbe, near Torgau in Germany, marking an important step toward the end of World War II in Europe. Elbe Day has never been an official holiday in any country, but in the years after 1945 the memory of this friendly encounter gained new significance in the context of the Cold War between the U.S. and the Soviet Union. History[edit] The first contact between American and Soviet patrols occurred near Strehla, after First Lieutenant Albert Kotzebue, an American soldier, crossed the River Elbe in a boat with three men of an intelligence and reconnaissance platoon. Commemorations[edit] See also[edit] Citations[edit]

Multiverse (religion) In religion a multiverse is the concept of a plurality of universes. Some religious cosmologies propose that the cosmos is not the only one that exists. The concept of infinite worlds is mentioned in the Apannaka Jataka: "Disciples," the Buddha said "nowhere between the lowest of hells below and the highest heaven above, nowhere in all the infinite worlds that stretch right and left, is there the equal, much less the superior, of a Buddha. The concept of multiple universes is mentioned many times in Hindu Puranic literature, such as in the Bhagavata Purana: Every universe is covered by seven layers — earth, water, fire, air, sky, the total energy and false ego — each ten times greater than the previous one. The number of universes seems to be uncountable according to the Puranic literature: Even though over a period of time I might count all the atoms of the universe, I could not count all of My opulences which I manifest within innumerable universes (Bhagavata Purana 11.16.39)

Ultrafinitism In the philosophy of mathematics, ultrafinitism, also known as ultraintuitionism, strict-finitism, actualism, and strong-finitism is a form of finitism. There are various philosophies of mathematics which are called ultrafinitism. A major identifying property common among most of these philosophies is their objections to totality of number theoretic functions like exponentiation over natural numbers. Main ideas[edit] Like other strict finitists, ultrafinitists deny the existence of the infinite set N of natural numbers, on the grounds that it can never be completed. In addition, some ultrafinitists are concerned with acceptance of objects in mathematics which no one can construct in practice because of physical restrictions in constructing large finite mathematical objects. The reason is that nobody has yet calculated what natural number is the floor of this real number, and it may not even be physically possible to do so. times to 0. People associated with ultrafinitism[edit] Notes[edit]

Tesseract A generalization of the cube to dimensions greater than three is called a "hypercube", "n-cube" or "measure polytope".[1] The tesseract is the four-dimensional hypercube, or 4-cube. According to the Oxford English Dictionary, the word tesseract was coined and first used in 1888 by Charles Howard Hinton in his book A New Era of Thought, from the Greek τέσσερεις ακτίνες ("four rays"), referring to the four lines from each vertex to other vertices.[2] In this publication, as well as some of Hinton's later work, the word was occasionally spelled "tessaract." Some people[citation needed] have called the same figure a tetracube, and also simply a hypercube (although a tetracube can also mean a polycube made of four cubes, and the term hypercube is also used with dimensions greater than 4). Geometry[edit] Since each vertex of a tesseract is adjacent to four edges, the vertex figure of the tesseract is a regular tetrahedron. A tesseract is bounded by eight hyperplanes (xi = ±1). See also[edit]

Ergodic hypothesis The ergodic hypothesis is often assumed in the statistical analysis of computational physics. The analyst would assume that the average of a process parameter over time and the average over the statistical ensemble are the same. This assumption that it is as good to simulate a system over a long time as it is to make many independent realizations of the same system is not always correct. (See, for example, the Fermi–Pasta–Ulam experiment of 1953.) Phenomenology[edit] In macroscopic systems, the timescales over which a system can truly explore the entirety of its own phase space can be sufficiently large that the thermodynamic equilibrium state exhibits some form of ergodicity breaking. However, complex disordered systems such as a spin glass show an even more complicated form of ergodicity breaking where the properties of the thermodynamic equilibrium state seen in practice are much more difficult to predict purely by symmetry arguments. Mathematics[edit] See also[edit] Notes[edit]

Infinity The ∞ symbol in several typefaces History[edit] Ancient cultures had various ideas about the nature of infinity. Early Greek[edit] In accordance with the traditional view of Aristotle, the Hellenistic Greeks generally preferred to distinguish the potential infinity from the actual infinity; for example, instead of saying that there are an infinity of primes, Euclid prefers instead to say that there are more prime numbers than contained in any given collection of prime numbers (Elements, Book IX, Proposition 20). However, recent readings of the Archimedes Palimpsest have hinted that Archimedes at least had an intuition about actual infinite quantities. Early Indian[edit] The Indian mathematical text Surya Prajnapti (c. 3rd–4th century BCE) classifies all numbers into three sets: enumerable, innumerable, and infinite. 17th century[edit] European mathematicians started using infinite numbers in a systematic fashion in the 17th century. . 'th power, and infinite products of factors. Calculus[edit]

Japan Japan (Japanese: 日本 Nippon or Nihon; formally 日本国 Nippon-koku or Nihon-koku, "State of Japan") is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south. The Kanji that make up Japan's name mean "sun origin", and Japan is often called "Land of the Rising Sun". Japan is a stratovolcanic archipelago of 6,852 islands. Archaeological research indicates that Japan was inhabited as early as the Upper Paleolithic period. Etymology Main article: Names of Japan The English word Japan derives from the Chinese pronunciation of the Japanese name, 日本 , which in Japanese is pronounced Nippon listen or Nihon listen . From the Meiji Restoration until the end of World War II, the full title of Japan was Dai Nippon Teikoku (大日本帝國?) The English word for Japan came to the West via early trade routes. History Feudal era Modern era Art

Membrane (M-theory) In string theory and related theories, D-branes are an important class of branes that arise when one considers open strings. As an open string propagates through spacetime, its endpoints are required to lie on a D-brane. The letter "D" in D-brane refers to the fact that we impose a certain mathematical condition on the system known as the Dirichlet boundary condition. The study of D-branes has led to important results, such as the anti-de Sitter/conformal field theory correspondence, which has shed light on many problems in quantum field theory. See also[edit] References[edit] Jump up ^ Moore, Gregory (2005).

Infinity (philosophy) The Isha Upanishad of the Yajurveda (c. 4th to 3rd century BC) states that "if you remove a part from infinity or add a part to infinity, still what remains is infinity". The Jain mathematical text Surya Prajnapti (c. 400 BC) classifies all numbers into three sets: enumerable, innumerable, and infinite. Each of these was further subdivided into three orders: Enumerable: lowest, intermediate and highestInnumerable: nearly innumerable, truly innumerable and innumerably innumerableInfinite: nearly infinite, truly infinite, infinitely infinite The Jains were the first to discard the idea that all infinites were the same or equal. They recognized different types of infinities: infinite in length (one dimension), infinite in area (two dimensions), infinite in volume (three dimensions), and infinite perpetually (infinite number of dimensions). According to Singh (1987), Joseph (2000) and Agrawal (2000), the highest enumerable number N of the Jains corresponds to the modern concept of aleph-null

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