Cosmological principle Astronomer William Keel explains: The cosmological principle is usually stated formally as 'Viewed on a sufficiently large scale, the properties of the Universe are the same for all observers.' This amounts to the strongly philosophical statement that the part of the Universe which we can see is a fair sample, and that the same physical laws apply throughout. In essence, this in a sense says that the Universe is knowable and is playing fair with scientists.[1] The cosmological principle contains three implicit qualifications and two testable consequences. The first implicit qualification is that "observers" means any observer at any location in the universe, not simply any human observer at any location on Earth: as Andrew Liddle puts it, "the cosmological principle [means that] the universe looks the same whoever and wherever you are The cosmological principle is first clearly asserted in the Philosophiæ Naturalis Principia Mathematica (1687) of Isaac Newton. Implications[edit]

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]

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]

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]

Cyclic model A cyclic model (or oscillating model) is any of several cosmological models in which the universe follows infinite, or indefinite, self-sustaining cycles. For example, the oscillating universe theory briefly considered by Albert Einstein in 1930 theorized a universe following an eternal series of oscillations, each beginning with a big bang and ending with a big crunch; in the interim, the universe would expand for a period of time before the gravitational attraction of matter causes it to collapse back in and undergo a bounce. Overview[edit] In the 1920s, theoretical physicists, most notably Albert Einstein, considered the possibility of a cyclic model for the universe as an (everlasting) alternative to the model of an expanding universe. However, work by Richard C. One new cyclic model is a brane cosmology model of the creation of the universe, derived from the earlier ekpyrotic model. Other cyclic models include Conformal cyclic cosmology and Loop quantum cosmology. See also[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]

Dyson's eternal intelligence The intelligent beings would begin by storing a finite amount of energy. They then use half (or any fraction) of this energy to power their thought. When the energy gradient created by unleashing this fraction of the stored fuel was exhausted, the beings would enter a state of zero-energy-consumption until the universe cooled. Two recent observations have presented problems for Dyson's scenario. However, even if intelligence cannot continue its own survival indefinitely in an ever-expanding Universe, it may be able to create a `baby universe' via a wormhole in spacetime, add some DNA[original research?] See also[edit] References[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

Ultimate fate of the universe The ultimate fate of the universe is a topic in physical cosmology. Many possible fates are predicted by rival scientific theories, including futures of both finite and infinite duration. Once the notion that the universe started with a rapid inflation nicknamed the Big Bang became accepted by the majority of scientists,[1] the ultimate fate of the universe became a valid cosmological question, one depending upon the physical properties of the mass/energy in the universe, its average density, and the rate of expansion. There is a growing consensus among cosmologists that the universe is flat and will continue to expand forever.[2][3] The ultimate fate of the universe is dependent on the shape of the universe and what role dark energy will play as the universe ages. Emerging scientific basis[edit] Theory[edit] The theoretical scientific exploration of the ultimate fate of the universe became possible with Albert Einstein's 1916 theory of general relativity. Observation[edit] Big Rip[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.

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