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13,400 | R's data structures include vectors, arrays, lists, and data frames. Vectors are ordered collections of values and can be mapped to arrays of one or more dimensions in a column major order. That is, given an ordered collection of dimensions, one fills in values along the first dimension first, then fill in one-dimensio... | https://en.wikipedia.org/wiki?curid=376707 |
13,401 | R and its libraries implement various statistical techniques, including linear, generalized linear and nonlinear modeling, classical statistical tests, spatial and time-series analysis, classification, clustering, and others. For computationally intensive tasks, C, C++, and Fortran code can be linked and called at run ... | https://en.wikipedia.org/wiki?curid=376707 |
13,402 | R is an interpreted language; users can access it through a command-line interpreter. If a user types codice_1 at the R command prompt and presses enter, the computer replies with codice_2. | https://en.wikipedia.org/wiki?curid=376707 |
13,403 | R supports procedural programming with functions and, for some functions, object-oriented programming with generic functions. Due to its S heritage, R has stronger object-oriented programming facilities than most statistical computing languages. Extending it is facilitated by its lexical scoping rules, which are derive... | https://en.wikipedia.org/wiki?curid=376707 |
13,404 | Functions are first-class objects and can be manipulated in the same way as data objects, facilitating meta-programming that allows multiple dispatch. Function arguments are passed by value, and are lazy—that is to say, they are only evaluated when they are used, not when the function is called. A generic function acts... | https://en.wikipedia.org/wiki?curid=376707 |
13,405 | R's capabilities are extended through user-created "packages", which offer statistical techniques, graphical devices, import/export, reporting (RMarkdown, knitr, Sweave), etc. These packages and their easy installation and use has been cited as driving the language's widespread adoption in data science. The packaging s... | https://en.wikipedia.org/wiki?curid=376707 |
13,406 | Multiple packages are included with the basic installation. Additional packages are available on CRAN, Bioconductor, R-Forge, Omegahat, GitHub, and other repositories. | https://en.wikipedia.org/wiki?curid=376707 |
13,407 | The "Task Views" on the CRAN website lists packages in fields including Finance, Genetics, High Performance Computing, Machine Learning, Medical Imaging, Meta-Analysis, Social Sciences and Spatial Statistics. R has been identified by the FDA as suitable for interpreting data from clinical research. Microsoft maintains ... | https://en.wikipedia.org/wiki?curid=376707 |
13,408 | Other R package resources include R-Forge, a platform for the collaborative development of R packages. The Bioconductor project provides packages for genomic data analysis, including object-oriented data-handling and analysis tools for data from Affymetrix, cDNA microarray, and next-generation high-throughput sequencin... | https://en.wikipedia.org/wiki?curid=376707 |
13,409 | A group of packages called the Tidyverse, which can be considered a "dialect" of the R language, is increasingly popular among developers. It strives to provide a cohesive collection of functions to deal with common data science tasks, including data import, cleaning, transformation and visualisation (notably with the ... | https://en.wikipedia.org/wiki?curid=376707 |
13,410 | A list of changes in R releases is maintained in various "news" files at CRAN. Some highlights are listed below for several major releases. | https://en.wikipedia.org/wiki?curid=376707 |
13,411 | Early developers preferred to run R via the command line console, succeeded by those who prefer an IDE. IDEs for R include (in alphabetical order) R.app (OSX/macOS only), Rattle GUI, R Commander, RKWard, RStudio, and Tinn-R. R is also supported in multi-purpose IDEs such as Eclipse via the StatET plugin, and Visual Stu... | https://en.wikipedia.org/wiki?curid=376707 |
13,412 | Editors that support R include Emacs, Vim (Nvim-R plugin), Kate, LyX, Notepad++, Visual Studio Code, WinEdt, and Tinn-R. Jupyter Notebook can also be configured to edit and run R code. | https://en.wikipedia.org/wiki?curid=376707 |
13,413 | R functionality is accessible from scripting languages including Python, Perl, Ruby, F#, and Julia. Interfaces to other, high-level programming languages, like Java and .NET C# are available. | https://en.wikipedia.org/wiki?curid=376707 |
13,414 | The main R implementation is written in R, C, and Fortran. Several other implementations aimed at improving speed or increasing extensibility. A closely related implementation is pqR (pretty quick R) by Radford M. Neal with improved memory management and support for automatic multithreading. Renjin and FastR are Java i... | https://en.wikipedia.org/wiki?curid=376707 |
13,415 | TIBCO, who previous sold the commercial implementation S-PLUS, built a runtime engine called TERR, which is part of Spotfire. | https://en.wikipedia.org/wiki?curid=376707 |
13,416 | Microsoft R Open (MRO) is a fully compatible R distribution with modifications for multi-threaded computations. As of 30 June 2021, Microsoft started to phase out MRO in favor of the CRAN distribution. | https://en.wikipedia.org/wiki?curid=376707 |
13,417 | A growing number of R events bring users together, such as conferences (e.g. useR!, WhyR?, conectaR, SatRdays), meetups, as well as R-Ladies groups that promote gender diversity. The R Foundation taskforce focuses on women and other under-represented groups. | https://en.wikipedia.org/wiki?curid=376707 |
13,418 | The official annual gathering of R users is called "useR!". The first such event was useR! 2004 in May 2004, Vienna, Austria. After skipping 2005, the useR! conference has been held annually, usually alternating between locations in Europe and North America. History: | https://en.wikipedia.org/wiki?curid=376707 |
13,419 | "The R Journal" is an open access, refereed journal of the R project. It features short to medium length articles on the use and development of R, including packages, programming tips, CRAN news, and foundation news. | https://en.wikipedia.org/wiki?curid=376707 |
13,420 | R is comparable to popular commercial statistical packages such as SAS, SPSS, and Stata. One difference is that R is available at no charge under a free software license. | https://en.wikipedia.org/wiki?curid=376707 |
13,421 | In January 2009, the "New York Times" ran an article charting the growth of R, the reasons for its popularity among data scientists and the threat it poses to commercial statistical packages such as SAS. In June 2017 data scientist Robert Muenchen published a more in-depth comparison between R and other software packag... | https://en.wikipedia.org/wiki?curid=376707 |
13,422 | R is more procedural than either SAS or SPSS, both of which make heavy use of pre-programmed procedures (called "procs") that are built-in to the language environment and customized by parameters of each call. R generally processes data in-memory, which limits its usefulness in processing larger files. | https://en.wikipedia.org/wiki?curid=376707 |
13,423 | In 2007, Richard Schultz, Martin Schultz, Steve Weston and Kirk Mettler founded Revolution Analytics to provide commercial support for Revolution R, their distribution of R, which includes components developed by the company. Major additional components include: ParallelR, the R Productivity Environment IDE, RevoScaleR... | https://en.wikipedia.org/wiki?curid=376707 |
13,424 | In October 2011, Oracle announced the "Big Data Appliance", which integrates R, Apache Hadoop, Oracle Linux, and a NoSQL database with Exadata hardware. , Oracle R Enterprise became one of two components of the "Oracle Advanced Analytics Option" (alongside Oracle Data Mining). | https://en.wikipedia.org/wiki?curid=376707 |
13,425 | IBM offers support for in-Hadoop execution of R, and provides a programming model for massively parallel in-database analytics in R. | https://en.wikipedia.org/wiki?curid=376707 |
13,426 | Mango Solutions offers a validation package for R, ValidR, to comply with drug approval agencies, such as the FDA. These agencies required the use of validated software, as attested by the vendor or sponsor. | https://en.wikipedia.org/wiki?curid=376707 |
13,427 | The following examples illustrate the basic syntax of the language and use of the command-line interface. (An expanded list of standard language features can be found in the R manual, "An Introduction to R".) | https://en.wikipedia.org/wiki?curid=376707 |
13,428 | In R, the generally preferred assignment operator is an arrow made from two characters codice_5, although codice_6 can be used in some cases. | https://en.wikipedia.org/wiki?curid=376707 |
13,429 | > z_matrix <- matrix(z, nrow=3) # Create a new matrix that turns the vector z into a 3x2 matrix object | https://en.wikipedia.org/wiki?curid=376707 |
13,430 | > 2*t(z_matrix)-2 # Transpose the matrix, multiply every element by 2, subtract 2 from each element in the matrix, and return the results to the terminal. | https://en.wikipedia.org/wiki?curid=376707 |
13,431 | > new_df <- data.frame(t(z_matrix), row.names=c('A','B')) # Create a new data.frame object that contains the data from a transposed z_matrix, with row names 'A' and 'B' | https://en.wikipedia.org/wiki?curid=376707 |
13,432 | > new_df$Z==new_df['Z'] && new_df[3]==new_df$Z # The data.frame column Z can be accessed using $Z, ['Z'], or [3] syntax, and the values are the same. | https://en.wikipedia.org/wiki?curid=376707 |
13,433 | > attributes(new_df)$row.names <- c('one','two') # Access and then change the row.names attribute; can also be done using rownames() | https://en.wikipedia.org/wiki?curid=376707 |
13,434 | One of R's strengths is the ease of creating new functions. Objects in the function body remain local to the function, and any data type may be returned. Example: | https://en.wikipedia.org/wiki?curid=376707 |
13,435 | The R language has built-in support for data modeling and graphics. The following example shows how R can easily generate and plot a linear model with residuals. | https://en.wikipedia.org/wiki?curid=376707 |
13,436 | Short R code calculating Mandelbrot set through the first 20 iterations of equation "z" = "z" + "c" plotted for different complex constants "c". This example demonstrates: | https://en.wikipedia.org/wiki?curid=376707 |
13,437 | The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the universe. According to this theory, space and time emerged together ago, and the universe has b... | https://en.wikipedia.org/wiki?curid=31880 |
13,438 | Some of the earliest cosmological models of the universe were developed by ancient Greek and Indian philosophers and were geocentric, placing Earth at the center. Over the centuries, more precise astronomical observations led Nicolaus Copernicus to develop the heliocentric model with the Sun at the center of the Solar ... | https://en.wikipedia.org/wiki?curid=31880 |
13,439 | Further observational improvements led to the realization that the Sun is one of a few hundred billion stars in the Milky Way, which is one of a few hundred billion galaxies in the universe. Many of the stars in a galaxy have planets. At the largest scale, galaxies are distributed uniformly and the same in all directio... | https://en.wikipedia.org/wiki?curid=31880 |
13,440 | According to the Big Bang theory, the energy and matter initially present have become less dense as the universe expanded. After an initial accelerated expansion called the inflationary epoch at around 10 seconds, and the separation of the four known fundamental forces, the universe gradually cooled and continued to ex... | https://en.wikipedia.org/wiki?curid=31880 |
13,441 | From studying the movement of galaxies, it has been discovered that the universe contains much more matter than is accounted for by visible objects; stars, galaxies, nebulas and interstellar gas. This unseen matter is known as dark matter ("dark" means that there is a wide range of strong indirect evidence that it exis... | https://en.wikipedia.org/wiki?curid=31880 |
13,442 | There are many competing hypotheses about the ultimate fate of the universe and about what, if anything, preceded the Big Bang, while other physicists and philosophers refuse to speculate, doubting that information about prior states will ever be accessible. Some physicists have suggested various multiverse hypotheses,... | https://en.wikipedia.org/wiki?curid=31880 |
13,443 | The physical universe is defined as all of space and time (collectively referred to as spacetime) and their contents. Such contents comprise all of energy in its various forms, including electromagnetic radiation and matter, and therefore planets, moons, stars, galaxies, and the contents of intergalactic space. The uni... | https://en.wikipedia.org/wiki?curid=31880 |
13,444 | The universe is often defined as "the totality of existence", or everything that exists, everything that has existed, and everything that will exist. In fact, some philosophers and scientists support the inclusion of ideas and abstract concepts—such as mathematics and logic—in the definition of the universe. The word "... | https://en.wikipedia.org/wiki?curid=31880 |
13,445 | The word "universe" derives from the Old French word , which in turn derives from the Latin word . The Latin word was used by Cicero and later Latin authors in many of the same senses as the modern English word is used. | https://en.wikipedia.org/wiki?curid=31880 |
13,446 | A term for "universe" among the ancient Greek philosophers from Pythagoras onwards was () 'the all', defined as all matter and all space, and () 'all things', which did not necessarily include the void. Another synonym was () meaning 'the world, the cosmos'. Synonyms are also found in Latin authors (, , ) and survive i... | https://en.wikipedia.org/wiki?curid=31880 |
13,447 | The prevailing model for the evolution of the universe is the Big Bang theory. The Big Bang model states that the earliest state of the universe was an extremely hot and dense one, and that the universe subsequently expanded and cooled. The model is based on general relativity and on simplifying assumptions such as the... | https://en.wikipedia.org/wiki?curid=31880 |
13,448 | The initial hot, dense state is called the Planck epoch, a brief period extending from time zero to one Planck time unit of approximately 10 seconds. During the Planck epoch, all types of matter and all types of energy were concentrated into a dense state, and gravity—currently the weakest by far of the four known forc... | https://en.wikipedia.org/wiki?curid=31880 |
13,449 | Within the first fraction of a second of the universe's existence, the four fundamental forces had separated. As the universe continued to cool down from its inconceivably hot state, various types of subatomic particles were able to form in short periods of time known as the quark epoch, the hadron epoch, and the lepto... | https://en.wikipedia.org/wiki?curid=31880 |
13,450 | After nucleosynthesis ended, the universe entered a period known as the photon epoch. During this period, the universe was still far too hot for matter to form neutral atoms, so it contained a hot, dense, foggy plasma of negatively charged electrons, neutral neutrinos and positive nuclei. After about 377,000 years, the... | https://en.wikipedia.org/wiki?curid=31880 |
13,451 | As the universe expands, the energy density of electromagnetic radiation decreases more quickly than does that of matter because the energy of a photon decreases with its wavelength. At around 47,000 years, the energy density of matter became larger than that of photons and neutrinos, and began to dominate the large sc... | https://en.wikipedia.org/wiki?curid=31880 |
13,452 | In the earliest stages of the universe, tiny fluctuations within the universe's density led to concentrations of dark matter gradually forming. Ordinary matter, attracted to these by gravity, formed large gas clouds and eventually, stars and galaxies, where the dark matter was most dense, and voids where it was least d... | https://en.wikipedia.org/wiki?curid=31880 |
13,453 | Of the four fundamental interactions, gravitation is the dominant at astronomical length scales. Gravity's effects are cumulative; by contrast, the effects of positive and negative charges tend to cancel one another, making electromagnetism relatively insignificant on astronomical length scales. The remaining two inter... | https://en.wikipedia.org/wiki?curid=31880 |
13,454 | The universe appears to have much more matter than antimatter, an asymmetry possibly related to the CP violation. This imbalance between matter and antimatter is partially responsible for the existence of all matter existing today, since matter and antimatter, if equally produced at the Big Bang, would have completely ... | https://en.wikipedia.org/wiki?curid=31880 |
13,455 | According to the general theory of relativity, far regions of space may never interact with ours even in the lifetime of the universe due to the finite speed of light and the ongoing expansion of space. For example, radio messages sent from Earth may never reach some regions of space, even if the universe were to exist... | https://en.wikipedia.org/wiki?curid=31880 |
13,456 | The spatial region that can be observed with telescopes is called the observable universe, which depends on the location of the observer. | https://en.wikipedia.org/wiki?curid=31880 |
13,457 | The proper distance—the distance as would be measured at a specific time, including the present—between Earth and the edge of the observable universe is 46 billion light-years (14 billion parsecs), making the diameter of the observable universe about 93 billion light-years (28 billion parsecs). The distance the light f... | https://en.wikipedia.org/wiki?curid=31880 |
13,458 | Because we cannot observe space beyond the edge of the observable universe, it is unknown whether the size of the universe in its totality is finite or infinite. Estimates suggest that the whole universe, if finite, must be more than 250 times larger than a Hubble sphere. Some disputed estimates for the total size of t... | https://en.wikipedia.org/wiki?curid=31880 |
13,459 | Assuming that the Lambda-CDM model is correct, the measurements of the parameters using a variety of techniques by numerous experiments yield a best value of the age of the universe at 13.799 ± 0.021 billion years, as of 2015. | https://en.wikipedia.org/wiki?curid=31880 |
13,460 | Over time, the universe and its contents have evolved; for example, the relative population of quasars and galaxies has changed and space itself has expanded. Due to this expansion, scientists on Earth can observe the light from a galaxy 30 billion light-years away even though that light has traveled for only 13 billio... | https://en.wikipedia.org/wiki?curid=31880 |
13,461 | The more matter there is in the universe, the stronger the mutual gravitational pull of the matter. If the universe were "too" dense then it would re-collapse into a gravitational singularity. However, if the universe contained too "little" matter then the self-gravity would be too weak for astronomical structures, lik... | https://en.wikipedia.org/wiki?curid=31880 |
13,462 | There are dynamical forces acting on the particles in the universe which affect the expansion rate. Before 1998, it was expected that the expansion rate would be decreasing as time went on due to the influence of gravitational interactions in the universe; and thus there is an additional observable quantity in the univ... | https://en.wikipedia.org/wiki?curid=31880 |
13,463 | Spacetimes are the arenas in which all physical events take place. The basic elements of spacetimes are events. In any given spacetime, an event is defined as a unique position at a unique time. A spacetime is the union of all events (in the same way that a line is the union of all of its points), formally organized in... | https://en.wikipedia.org/wiki?curid=31880 |
13,464 | Events, such as matter and energy, bend spacetime. Curved spacetime, on the other hand, forces matter and energy to behave in a certain way. There is no point in considering one without the other. | https://en.wikipedia.org/wiki?curid=31880 |
13,465 | The universe appears to be a smooth spacetime continuum consisting of three spatial dimensions and one temporal (time) dimension (an event in the spacetime of the physical universe can therefore be identified by a set of four coordinates: ("x", "y", "z", "t"). On average, space is observed to be very nearly flat (with ... | https://en.wikipedia.org/wiki?curid=31880 |
13,466 | Spacetime events are not absolutely defined spatially and temporally but rather are known to be relative to the motion of an observer. Minkowski space approximates the universe without gravity; the pseudo-Riemannian manifolds of general relativity describe spacetime with matter and gravity. | https://en.wikipedia.org/wiki?curid=31880 |
13,467 | General relativity describes how spacetime is curved and bent by mass and energy (gravity). The topology or geometry of the universe includes both local geometry in the observable universe and global geometry. Cosmologists often work with a given space-like slice of spacetime called the comoving coordinates. The sectio... | https://en.wikipedia.org/wiki?curid=31880 |
13,468 | An important parameter determining the future evolution of the universe theory is the density parameter, Omega (Ω), defined as the average matter density of the universe divided by a critical value of that density. This selects one of three possible geometries depending on whether Ω is equal to, less than, or greater t... | https://en.wikipedia.org/wiki?curid=31880 |
13,469 | Observations, including the Cosmic Background Explorer (COBE), Wilkinson Microwave Anisotropy Probe (WMAP), and Planck maps of the CMB, suggest that the universe is infinite in extent with a finite age, as described by the Friedmann–Lemaître–Robertson–Walker (FLRW) models. These FLRW models thus support inflationary mo... | https://en.wikipedia.org/wiki?curid=31880 |
13,470 | The universe may be "fine-tuned"; the Fine-tuned universe hypothesis is the proposition that the conditions that allow the existence of observable life in the universe can only occur when certain universal fundamental physical constants lie within a very narrow range of values, so that if any of several fundamental con... | https://en.wikipedia.org/wiki?curid=31880 |
13,471 | The universe is composed almost completely of dark energy, dark matter, and ordinary matter. Other contents are electromagnetic radiation (estimated to constitute from 0.005% to close to 0.01% of the total mass-energy of the universe) and antimatter. | https://en.wikipedia.org/wiki?curid=31880 |
13,472 | The proportions of all types of matter and energy have changed over the history of the universe. The total amount of electromagnetic radiation generated within the universe has decreased by 1/2 in the past 2 billion years. Today, ordinary matter, which includes atoms, stars, galaxies, and life, accounts for only 4.9% o... | https://en.wikipedia.org/wiki?curid=31880 |
13,473 | Matter, dark matter, and dark energy are distributed homogeneously throughout the universe over length scales longer than 300 million light-years or so. However, over shorter length-scales, matter tends to clump hierarchically; many atoms are condensed into stars, most stars into galaxies, most galaxies into clusters, ... | https://en.wikipedia.org/wiki?curid=31880 |
13,474 | The observable universe is isotropic on scales significantly larger than superclusters, meaning that the statistical properties of the universe are the same in all directions as observed from Earth. The universe is bathed in highly isotropic microwave radiation that corresponds to a thermal equilibrium blackbody spectr... | https://en.wikipedia.org/wiki?curid=31880 |
13,475 | An explanation for why the expansion of the universe is accelerating remains elusive. It is often attributed to "dark energy", an unknown form of energy that is hypothesized to permeate space. On a mass–energy equivalence basis, the density of dark energy (~ 7 × 10 g/cm) is much less than the density of ordinary matter... | https://en.wikipedia.org/wiki?curid=31880 |
13,476 | Two proposed forms for dark energy are the cosmological constant, a "constant" energy density filling space homogeneously, and scalar fields such as quintessence or moduli, "dynamic" quantities whose energy density can vary in time and space. Contributions from scalar fields that are constant in space are usually also ... | https://en.wikipedia.org/wiki?curid=31880 |
13,477 | Dark matter is a hypothetical kind of matter that is invisible to the entire electromagnetic spectrum, but which accounts for most of the matter in the universe. The existence and properties of dark matter are inferred from its gravitational effects on visible matter, radiation, and the large-scale structure of the uni... | https://en.wikipedia.org/wiki?curid=31880 |
13,478 | The remaining 4.9% of the mass–energy of the universe is ordinary matter, that is, atoms, ions, electrons and the objects they form. This matter includes stars, which produce nearly all of the light we see from galaxies, as well as interstellar gas in the interstellar and intergalactic media, planets, and all the objec... | https://en.wikipedia.org/wiki?curid=31880 |
13,479 | Ordinary matter commonly exists in four states (or phases): solid, liquid, gas, and plasma. However, advances in experimental techniques have revealed other previously theoretical phases, such as Bose–Einstein condensates and fermionic condensates. | https://en.wikipedia.org/wiki?curid=31880 |
13,480 | Ordinary matter is composed of two types of elementary particles: quarks and leptons. For example, the proton is formed of two up quarks and one down quark; the neutron is formed of two down quarks and one up quark; and the electron is a kind of lepton. An atom consists of an atomic nucleus, made up of protons and neut... | https://en.wikipedia.org/wiki?curid=31880 |
13,481 | Soon after the Big Bang, primordial protons and neutrons formed from the quark–gluon plasma of the early universe as it cooled below two trillion degrees. A few minutes later, in a process known as Big Bang nucleosynthesis, nuclei formed from the primordial protons and neutrons. This nucleosynthesis formed lighter elem... | https://en.wikipedia.org/wiki?curid=31880 |
13,482 | Ordinary matter and the forces that act on matter can be described in terms of elementary particles. These particles are sometimes described as being fundamental, since they have an unknown substructure, and it is unknown whether or not they are composed of smaller and even more fundamental particles. Of central import... | https://en.wikipedia.org/wiki?curid=31880 |
13,483 | A hadron is a composite particle made of quarks held together by the strong force. Hadrons are categorized into two families: baryons (such as protons and neutrons) made of three quarks, and mesons (such as pions) made of one quark and one antiquark. Of the hadrons, protons are stable, and neutrons bound within atomic ... | https://en.wikipedia.org/wiki?curid=31880 |
13,484 | A lepton is an elementary, half-integer spin particle that does not undergo strong interactions but is subject to the Pauli exclusion principle; no two leptons of the same species can be in exactly the same state at the same time. Two main classes of leptons exist: charged leptons (also known as the "electron-like" lep... | https://en.wikipedia.org/wiki?curid=31880 |
13,485 | The lepton epoch was the period in the evolution of the early universe in which the leptons dominated the mass of the universe. It started roughly 1 second after the Big Bang, after the majority of hadrons and anti-hadrons annihilated each other at the end of the hadron epoch. During the lepton epoch the temperature of... | https://en.wikipedia.org/wiki?curid=31880 |
13,486 | A photon is the quantum of light and all other forms of electromagnetic radiation. It is the force carrier for the electromagnetic force, even when static via virtual photons. The effects of this force are easily observable at the microscopic and at the macroscopic level because the photon has zero rest mass; this allo... | https://en.wikipedia.org/wiki?curid=31880 |
13,487 | The photon epoch started after most leptons and anti-leptons were annihilated at the end of the lepton epoch, about 10 seconds after the Big Bang. Atomic nuclei were created in the process of nucleosynthesis which occurred during the first few minutes of the photon epoch. For the remainder of the photon epoch the unive... | https://en.wikipedia.org/wiki?curid=31880 |
13,488 | General relativity is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics. It is the basis of current cosmological models of the universe. General relativity generalizes special relativity and Newton's law of universal gravitation, provid... | https://en.wikipedia.org/wiki?curid=31880 |
13,489 | With the assumption of the cosmological principle that the universe is homogeneous and isotropic everywhere, a specific solution of the field equations that describes the universe is the metric tensor called the Friedmann–Lemaître–Robertson–Walker metric, | https://en.wikipedia.org/wiki?curid=31880 |
13,490 | where ("r", θ, φ) correspond to a spherical coordinate system. This metric has only two undetermined parameters. An overall dimensionless length scale factor "R" describes the size scale of the universe as a function of time (an increase in "R" is the expansion of the universe), and a curvature index "k" describes the ... | https://en.wikipedia.org/wiki?curid=31880 |
13,491 | The solutions for "R(t)" depend on "k" and "Λ", but some qualitative features of such solutions are general. First and most importantly, the length scale "R" of the universe can remain constant "only" if the universe is perfectly isotropic with positive curvature ("k"=1) and has one precise value of density everywhere,... | https://en.wikipedia.org/wiki?curid=31880 |
13,492 | Second, all solutions suggest that there was a gravitational singularity in the past, when "R" went to zero and matter and energy were infinitely dense. It may seem that this conclusion is uncertain because it is based on the questionable assumptions of perfect homogeneity and isotropy (the cosmological principle) and ... | https://en.wikipedia.org/wiki?curid=31880 |
13,493 | Third, the curvature index "k" determines the sign of the mean spatial curvature of spacetime averaged over sufficiently large length scales (greater than about a billion light-years). If "k"=1, the curvature is positive and the universe has a finite volume. A universe with positive curvature is often visualized as a t... | https://en.wikipedia.org/wiki?curid=31880 |
13,494 | The ultimate fate of the universe is still unknown because it depends critically on the curvature index "k" and the cosmological constant "Λ". If the universe were sufficiently dense, "k" would equal +1, meaning that its average curvature throughout is positive and the universe will eventually recollapse in a Big Crunc... | https://en.wikipedia.org/wiki?curid=31880 |
13,495 | Some speculative theories have proposed that our universe is but one of a set of disconnected universes, collectively denoted as the multiverse, challenging or enhancing more limited definitions of the universe. Scientific multiverse models are distinct from concepts such as alternate planes of consciousness and simula... | https://en.wikipedia.org/wiki?curid=31880 |
13,496 | Max Tegmark developed a four-part classification scheme for the different types of multiverses that scientists have suggested in response to various Physics problems. An example of such multiverses is the one resulting from the chaotic inflation model of the early universe. Another is the multiverse resulting from the ... | https://en.wikipedia.org/wiki?curid=31880 |
13,497 | The least controversial, but still highly disputed, category of multiverse in Tegmark's scheme is . The multiverses of this level are composed by distant spacetime events "in our own universe". Tegmark and others have argued that, if space is infinite, or sufficiently large and uniform, identical instances of the histo... | https://en.wikipedia.org/wiki?curid=31880 |
13,498 | It is possible to conceive of disconnected spacetimes, each existing but unable to interact with one another. An easily visualized metaphor of this concept is a group of separate soap bubbles, in which observers living on one soap bubble cannot interact with those on other soap bubbles, even in principle. According to ... | https://en.wikipedia.org/wiki?curid=31880 |
13,499 | Historically, there have been many ideas of the cosmos (cosmologies) and its origin (cosmogonies). Theories of an impersonal universe governed by physical laws were first proposed by the Greeks and Indians. Ancient Chinese philosophy encompassed the notion of the universe including both all of space and all of time. Ov... | https://en.wikipedia.org/wiki?curid=31880 |
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