Modal realism. The term possible world[edit] The term goes back to Leibniz's theory of possible worlds, used to analyse necessity, possibility, and similar modal notions. In short: the actual world is regarded as merely one among an infinite set of logically possible worlds, some "nearer" to the actual world and some more remote. A proposition is necessary if it is true in all possible worlds, and possible if it is true in at least one. Main tenets of modal realism[edit] At the heart of David Lewis's modal realism are six central doctrines about possible worlds: Reasons given by Lewis[edit] Lewis believes that the concept of alethic modality can be reduced to talk of real possible worlds. Taking this latter point one step further, Lewis argues that modality cannot be made sense of without such a reduction. Details and alternatives[edit] How many [possible worlds] are there? Criticisms[edit] Lewis's own critique[edit] Here are some of the major categories of objection: Stalnaker's response[edit] See also[edit]
Parallel universe (fiction) A parallel universe is a hypothetical self-contained separate reality co-existing with one's own. A specific group of parallel universes is called a "multiverse", although this term can also be used to describe the possible parallel universes that constitute reality. While the terms "parallel universe" and "alternative reality" are generally synonymous and can be used interchangeably in most cases, there is sometimes an additional connotation implied with the term "alternative reality" that implies that the reality is a variant of our own. The term "parallel universe" is more general, without any connotations implying a relationship, or lack of relationship, with our own universe.
A universe where the very laws of nature are different – for example, one in which there are no Laws of Motion – would in general count as a parallel universe but not an alternative reality and a concept between both fantasy world and earth. In 1884, Edwin A. In 1895, The Time Machine by H. 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. Informally, the term is often used to describe a counter-intuitive result. 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] List of fiction employing parallel universes. Infinity. The ∞ symbol in several typefaces History[edit] Ancient cultures had various ideas about the nature of infinity. The ancient Indians and Greeks did not define infinity in precise formalism as does modern mathematics, and instead approached infinity as a philosophical concept.
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. . Factors. and. 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. 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] Multiverse. Omniverse. 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] 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).
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] 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] Eternal inflation. Eternal inflation is predicted by many different models of cosmic inflation.
MIT professor Alan H. Guth proposed an inflation model involving a "false vacuum" phase with positive vacuum energy. Parts of the Universe in that phase inflate, and only occasionally decay to lower-energy, non-inflating phases or the ground state. In chaotic inflation, proposed by physicist Andrei Linde, the peaks in the evolution of a scalar field (determining the energy of the vacuum) correspond to regions of rapid inflation which dominate.
Alan Guth's 2007 paper, "Eternal inflation and its implications",[1] details what is now known on the subject, and demonstrates that this particular flavor of inflationary universe theory is relatively current, or is still considered viable, more than 20 years after its inception.[2] [3][4] Inflation and the multiverse[edit] Both Linde and Guth believe that inflationary models of the early universe most likely lead to a multiverse but more proof is required. History[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.
Incalculable is the excellence which springs from obeying the Precepts and from other virtuous conduct. " - Apannaka Jataka 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: Analogies to describe multiple universes also exist in the Puranic literature: 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] 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. Once the universe had cooled sufficiently, half of the remaining half (one quarter of the original energy) of the intelligent beings' fuel reserves would once again be released, powering a brief period of thought once more.
This would continue, with smaller and smaller amounts of energy being released. As the universe cooled, the thoughts would be slower and slower, but there would still be an infinite number of them. The idea was published in a scientific paper[1] and in a popular book[2] by Freeman Dyson. Two recent observations have presented problems for Dyson's scenario. See also[edit] References[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]
Buddhist cosmology. Hindu cosmology. Hindu cycle of the universe. The All. Shape of the Universe. Cosmological principle. Ultimate fate of the universe. Ekpyrotic universe. Fine-tuned Universe.