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Infinitely Divisible Probability Distributions
Infinite divisibility arises in different ways in philosophy, physics, economics, order theory (a branch of mathematics), and probability theory (also a branch of mathematics). One may speak of infinite divisibility, or the lack thereof, of matter, space, time, money, or abstract mathematical objects such as the continuum. In philosophy The origin of the idea in the Western tradition can be traced to the 5th century BCE starting with the Ancient Greek pre-Socratic philosopher Democritus and his teacher Leucippus, who theorized matter's divisibility beyond what can be perceived by the senses until ultimately ending at an indivisible atom. The Indian philosopher, Maharshi Kanada also proposed an atomistic theory, however there is ambiguity around when this philosopher lived, ranging from sometime between the 6th century to 2nd century BCE. Around 500 BC, he postulated that if we go on dividing matter ('' padarth''), we shall get smaller and smaller particles. Ultimately, a time ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy
Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational and critical inquiry that reflects on its methods and assumptions. Historically, many of the individual sciences, such as physics and psychology, formed part of philosophy. However, they are considered separate academic disciplines in the modern sense of the term. Influential traditions in the history of philosophy include Western philosophy, Western, Islamic philosophy, Arabic–Persian, Indian philosophy, Indian, and Chinese philosophy. Western philosophy originated in Ancient Greece and covers a wide area of philosophical subfields. A central topic in Arabic–Persian philosophy is the relation between reason and revelation. Indian philosophy combines the Spirituality, spiritual problem of how to reach Enlightenment in Buddhism, enlighten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Timaeus (dialogue)
''Timaeus'' (; , ) is one of Plato's dialogues, mostly in the form of long monologues given by Critias and Timaeus, written 360 BC. The work puts forward reasoning on the possible nature of the physical world and human beings and is followed by the dialogue '' Critias''. Participants in the dialogue include Socrates, Timaeus, Hermocrates, and Critias. Some scholars believe that it is not the Critias of the Thirty Tyrants who appears in this dialogue, but his grandfather, also named Critias. At the beginning of the dialogue, the absence of another, unknown dialogue participant, present on the day before, is bemoaned. It has been suggested from some traditions— Diogenes Laertius (VIII 85) from Hermippus of Smyrna (3rd century BC) and Timon of Phlius ( 320 – 235 BC)—that ''Timaeus'' was influenced by a book about Pythagoras, written by Philolaus, although this assertion is generally considered false. Introduction The dialogue takes place the day after Socrates de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quark
A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nucleus, atomic nuclei. All commonly observable matter is composed of up quarks, down quarks and electrons. Owing to a phenomenon known as ''color confinement'', quarks are never found in isolation; they can be found only within hadrons, which include baryons (such as protons and neutrons) and mesons, or in quark–gluon plasmas. There is also the theoretical possibility of #Other_phases_of_quark_matter, more exotic phases of quark matter. For this reason, much of what is known about quarks has been drawn from observations of hadrons. Quarks have various Intrinsic and extrinsic properties, intrinsic physical property, properties, including electric charge, mass, color charge, and Spin (physics), spin. They are the only elementary particles in the Standard Mode ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Model
The Standard Model of particle physics is the Scientific theory, theory describing three of the four known fundamental forces (electromagnetism, electromagnetic, weak interaction, weak and strong interactions – excluding gravity) in the universe and classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century, through the work of many scientists worldwide, with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then, proof of the top quark (1995), the tau neutrino (2000), and the Higgs boson (2012) have added further credence to the Standard Model. In addition, the Standard Model has predicted various properties of weak neutral currents and the W and Z bosons with great accuracy. Although the Standard Model is believed to be theoretically self-consistent and has demonstrated some success in providing experimental predictions, it leaves some physics be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partition Of A Set
In mathematics, a partition of a set is a grouping of its elements into Empty set, non-empty subsets, in such a way that every element is included in exactly one subset. Every equivalence relation on a Set (mathematics), set defines a partition of this set, and every partition defines an equivalence relation. A set equipped with an equivalence relation or a partition is sometimes called a setoid, typically in type theory and proof theory. Definition and notation A partition of a set ''X'' is a set of non-empty subsets of ''X'' such that every element ''x'' in ''X'' is in exactly one of these subsets (i.e., the subsets are nonempty mutually disjoint sets). Equivalently, a family of sets ''P'' is a partition of ''X'' if and only if all of the following conditions hold: *The family ''P'' does not contain the empty set (that is \emptyset \notin P). *The union (set theory), union of the sets in ''P'' is equal to ''X'' (that is \textstyle\bigcup_ A = X). The sets in ''P'' are said ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ad Infinitum
''Ad infinitum'' is a Latin phrase meaning "to infinity" or "forevermore". Description In context, it usually means "continue forever, without limit" and this can be used to describe a non-terminating process, a non-terminating ''repeating'' process, or a set of instructions to be repeated "forever," among other uses. It may also be used in a manner similar to the Latin phrase '' et cetera'' to denote written words or a concept that continues for a lengthy period beyond what is shown. Examples include: * "The sequence 1, 2, 3, ... continues ''ad infinitum''." * "The perimeter of a fractal may be iteratively drawn ''ad infinitum''." The 17th-century writer Jonathan Swift incorporated the idea of self-similarity in the following lines from his satirical poem ''On Poetry: a Rhapsody'' (1733): The vermin only teaze and pinch Their foes superior by an inch. So, naturalists observe, a flea Has smaller fleas that on him prey; And these have smaller still to bite 'em, And so proceed ''a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot. Classical physics can describe many aspects of nature at an ordinary (macroscopic and Microscopic scale, (optical) microscopic) scale, but is not sufficient for describing them at very small submicroscopic (atomic and subatomic) scales. Classical mechanics can be derived from quantum mechanics as an approximation that is valid at ordinary scales. Quantum systems have Bound state, bound states that are Quantization (physics), quantized to Discrete mathematics, discrete values of energy, momentum, angular momentum, and ot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Process And Reality
''Process and Reality'' is a book by Alfred North Whitehead, in which the author propounds a philosophy of organism, also called process philosophy. The book, published in 1929, is a revision of the Gifford Lectures he gave in 1927–28. Whitehead's ''Process and Reality'' Whitehead's background was an unusual one for a speculative philosopher. Educated as a mathematician, he became, through his co-authorship with his student and disciple Bertrand Russell and publication in 1913 of ''Principia Mathematica'', a major logician. Later he wrote extensively on physics and its philosophy, proposing a theory of gravity in Minkowski space as a logically possible alternative to Einstein's general theory of relativity. Whitehead's ''Process and Reality''Whitehead, A.N. (1929). ''Process and Reality. An Essay in Cosmology. Gifford Lectures Delivered in the University of Edinburgh During the Session 1927–1928'', Macmillan, New York, Cambridge University Press, Cambridge UK. is perhap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfred North Whitehead
Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher. He created the philosophical school known as process philosophy, which has been applied in a wide variety of disciplines, including ecology, theology, education, physics, biology, economics, and psychology. In his early career Whitehead wrote primarily on mathematics, logic, and physics. He wrote the three-volume ''Principia Mathematica'' (1910–1913), with his former student Bertrand Russell. ''Principia Mathematica'' is considered one of the twentieth century's most important works in mathematical logic, and placed 23rd in a list of the top 100 English-language nonfiction books of the twentieth century by Modern Library."The Modern Library ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zeno's Paradoxes
Zeno's paradoxes are a series of philosophical arguments presented by the ancient Greek philosopher Zeno of Elea (c. 490–430 BC), primarily known through the works of Plato, Aristotle, and later commentators like Simplicius of Cilicia. Zeno devised these paradoxes to support his teacher Parmenides's philosophy of monism, which posits that despite people's sensory experiences, reality is singular and unchanging. The paradoxes famously challenge the notions of plurality (the existence of many things), motion, space, and time by suggesting they lead to logical contradictions. Zeno's work, primarily known from second-hand accounts since his original texts are lost, comprises forty "paradoxes of plurality," which argue against the coherence of believing in multiple existences, and several arguments against motion and change. Of these, only a few are definitively known today, including the renowned "Achilles Paradox", which illustrates the problematic concept of infinite divisibi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extended Item
Extension, extend or extended may refer to: Mathematics Logic or set theory * Axiom of extensionality * Extensible cardinal * Extension (model theory) * Extension (proof theory) * Extension (predicate logic), the set of tuples of values that satisfy the predicate * Extension (semantics), the set of things to which a property applies * Extension (simplicial set) * Extension by definitions * Extensional definition, a definition that enumerates every individual a term applies to * Extensionality Other uses * Extension of a function, defined on a larger domain * Extension of a polyhedron, in geometry * Extension of a line segment (finite) into an infinite line (e.g., extended base) * Exterior algebra, Grassmann's theory of extension, in geometry * Field extension, in Galois theory * Group extension, in abstract algebra and homological algebra * Homotopy extension property, in topology * Kolmogorov extension theorem, in probability theory * Linear extension, in order the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
