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]
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]
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]
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
Eternal return Eternal return (also known as "eternal recurrence") is a concept that the universe has been recurring, and will continue to recur, in a self-similar form an infinite number of times across infinite time or space. The concept is found in Indian philosophy and in ancient Egypt and was subsequently taken up by the Pythagoreans and Stoics. With the decline of antiquity and the spread of Christianity, the concept fell into disuse in the Western world, with the exception of Friedrich Nietzsche, who connected the thought to many of his other concepts, including amor fati. In addition, the philosophical concept of eternal recurrence was addressed by Arthur Schopenhauer. It is a purely physical concept, involving no supernatural reincarnation, but the return of beings in the same bodies. Premise[edit] The basic premise proceeds from the assumption that the probability of a world coming into existence exactly like our own is greater than zero (we know this because our world exists). Judaism[edit]
List of paradoxes This is a list of paradoxes, grouped thematically. The grouping is approximate, as paradoxes may fit into more than one category. Because of varying definitions of the term paradox, some of the following are not considered to be paradoxes by everyone. This list collects only scenarios that have been called a paradox by at least one source and have their own article. Although considered paradoxes, some of these are based on fallacious reasoning, or incomplete/faulty analysis. Logic[edit] Self-reference[edit] These paradoxes have in common a contradiction arising from self-reference. Barber paradox: A barber (who is a man) shaves all and only those men who do not shave themselves. Vagueness[edit] Ship of Theseus (a.k.a. Mathematics[edit] Statistics[edit] Probability[edit] Infinity and infinitesimals[edit] Geometry and topology[edit] The Banach–Tarski paradox: A ball can be decomposed and reassembled into two balls the same size as the original.
Philosophy of space and time Philosophy of space and time is the branch of philosophy concerned with the issues surrounding the ontology, epistemology, and character of space and time. While such ideas have been central to philosophy from its inception, the philosophy of space and time was both an inspiration for and a central aspect of early analytic philosophy. The subject focuses on a number of basic issues, including whether or not time and space exist independently of the mind, whether they exist independently of one another, what accounts for time's apparently unidirectional flow, whether times other than the present moment exist, and questions about the nature of identity (particularly the nature of identity over time). Ancient and medieval views[edit] The earliest recorded Western philosophy of time was expounded by the ancient Egyptian thinker Ptahhotep (c. 2650–2600 BC), who said, "Do not lessen the time of following desire, for the wasting of time is an abomination to the spirit." Leibniz and Newton[edit]
Metaverse The Metaverse is a collective virtual shared space, created by the convergence of virtually enhanced physical reality and physically persistent virtual space,[1] including the sum of all virtual worlds, augmented reality, and the internet. The word metaverse is a portmanteau of the prefix "meta" (meaning "beyond") and "universe" and is typically used to describe the concept of a future iteration of the internet, made up of persistent, shared, 3D virtual spaces linked into a perceived virtual universe.[2] Developing technical standards for the Metaverse[edit] Conceptually, the Metaverse describes a future internet of persistent, shared, 3D virtual spaces linked into a perceived virtual universe,[2] but common standards, interfaces, and communication protocols between and among virtual environment systems are still in development. Many of these working groups are still in the process of publishing drafts and determining open standards for interoperability. [edit] [edit] 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]
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).