|
History Of Randomness
In ancient history, the concepts of chance and randomness were intertwined with that of fate. Many ancient peoples threw dice to determine fate, and this later evolved into games of chance. At the same time, most ancient cultures used various methods of divination to attempt to circumvent randomness and fate. Beyond religion and games of chance, randomness has been attested for sortition since at least ancient Athenian democracy in the form of a kleroterion. The formalization of odds and chance was perhaps earliest done by the Chinese 3,000 years ago. The Greek philosophers discussed randomness at length, but only in non-quantitative forms. It was only in the sixteenth century that Italian mathematicians began to formalize the odds associated with various games of chance. The invention of modern calculus had a positive impact on the formal study of randomness. In the 19th century the concept of entropy was introduced in physics. The early part of the twentieth century saw a rap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pompeii - Osteria Della Via Di Mercurio - Dice Players
Pompeii (, ) was an ancient city located in what is now the ''comune'' of Pompei near Naples in the Campania region of Italy. Pompeii, along with Herculaneum and many villas in the surrounding area (e.g. at Boscoreale, Stabiae), was buried under of volcanic ash and pumice in the Eruption of Mount Vesuvius in 79 AD. Largely preserved under the ash, the excavated city offered a unique snapshot of Roman life, frozen at the moment it was buried, although much of the detailed evidence of the everyday life of its inhabitants was lost in the excavations. It was a wealthy town, with a population of ca. 11,000 in AD 79, enjoying many fine public buildings and luxurious private houses with lavish decorations, furnishings and works of art which were the main attractions for the early excavators. Organic remains, including wooden objects and human bodies, were interred in the ash. Over time, they decayed, leaving voids that archaeologists found could be used as moulds to make plaster ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithmic Randomness
Intuitively, an algorithmically random sequence (or random sequence) is a sequence of binary digits that appears random to any algorithm running on a (prefix-free or not) universal Turing machine. The notion can be applied analogously to sequences on any finite alphabet (e.g. decimal digits). Random sequences are key objects of study in algorithmic information theory. As different types of algorithms are sometimes considered, ranging from algorithms with specific bounds on their running time to algorithms which may ask questions of an oracle machine, there are different notions of randomness. The most common of these is known as Martin-Löf randomness (K-randomness or 1-randomness), but stronger and weaker forms of randomness also exist. When the term "algorithmically random" is used to refer to a particular single (finite or infinite) sequence without clarification, it is usually taken to mean "incompressible" or, in the case the sequence is infinite and prefix algorithmically r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epicurus
Epicurus (; grc-gre, Ἐπίκουρος ; 341–270 BC) was an ancient Greek philosopher and sage who founded Epicureanism, a highly influential school of philosophy. He was born on the Greek island of Samos to Athenian parents. Influenced by Democritus, Aristippus, Pyrrho, and possibly the Cynics, he turned against the Platonism of his day and established his own school, known as "the Garden", in Athens. Epicurus and his followers were known for eating simple meals and discussing a wide range of philosophical subjects. He openly allowed women and slaves to join the school as a matter of policy. Of the over 300 works said to have been written by Epicurus about various subjects, the vast majority have been destroyed. Only three letters written by him—the letters to ''Menoeceus'', ''Pythocles'', and ''Herodotus''—and two collections of quotes—the ''Principal Doctrines'' and the ''Vatican Sayings''—have survived intact, along with a few fragments of his other writing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of philosophy within the Lyceum and the wider Aristotelian tradition. His writings cover many subjects including physics, biology, zoology, metaphysics, logic, ethics, aesthetics, poetry, theatre, music, rhetoric, psychology, linguistics, economics, politics, meteorology, geology, and government. Aristotle provided a complex synthesis of the various philosophies existing prior to him. It was above all from his teachings that the West inherited its intellectual lexicon, as well as problems and methods of inquiry. As a result, his philosophy has exerted a unique influence on almost every form of knowledge in the West and it continues to be a subject of contemporary philosophical discussion. Little is known about his life. Aristotle was born in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Democritus
Democritus (; el, Δημόκριτος, ''Dēmókritos'', meaning "chosen of the people"; – ) was an Ancient Greek pre-Socratic philosopher from Abdera, primarily remembered today for his formulation of an atomic theory of the universe. None of his work has survived. Life Although many anecdotes about Democritus' life survive, their authenticity cannot be verified and modern scholars doubt their accuracy. Democritus was said to be born in the city of Abdera in Thrace, an Ionian colony of Teos,. Ancient accounts of his life have claimed that he lived to a very old age, with some writers claiming that he was over a hundred years old at the time of his death. Philosophy and science states that the relation between Democritus and his predecessor Leucippus is not clear; while earlier ancient sources such as Aristotle and Theophrastus credit Leucippus with the invention of atomism and credit its doctrines to both philosophers, later sources only credit Democritus, making defi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amos Tversky
Amos Nathan Tversky ( he, עמוס טברסקי; March 16, 1937 – June 2, 1996) was an Israeli cognitive and mathematical psychologist and a key figure in the discovery of systematic human cognitive bias and handling of risk. Much of his early work concerned the foundations of measurement. He was co-author of a three-volume treatise, ''Foundations of Measurement''. His early work with Daniel Kahneman focused on the psychology of prediction and probability judgment; later they worked together to develop prospect theory, which aims to explain irrational human economic choices and is considered one of the seminal works of behavioral economics. Six years after Tversky's death, Kahneman received the 2002 Nobel Memorial Prize in Economic Sciences for the work he did in collaboration with Amos Tversky. (The prize is not awarded posthumously.) Kahneman told ''The New York Times'' in an interview soon after receiving the honor: "I feel it is a joint prize. We were twinned for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel Kahneman
Daniel Kahneman (; he, דניאל כהנמן; born March 5, 1934) is an Israeli-American psychologist and economist notable for his work on the psychology of judgment and decision-making, as well as behavioral economics, for which he was awarded the 2002 Nobel Memorial Prize in Economic Sciences (shared with Vernon L. Smith). His empirical findings challenge the assumption of human rationality prevailing in modern economic theory. With Amos Tversky and others, Kahneman established a cognitive basis for common human errors that arise from heuristics and biases, and developed prospect theory. In 2011 he was named by '' Foreign Policy'' magazine in its list of top global thinkers. In the same year his book ''Thinking, Fast and Slow'', which summarizes much of his research, was published and became a best seller. In 2015, ''The Economist'' listed him as the seventh most influential economist in the world. He is professor emeritus of psychology and public affairs at Princeton U ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deborah J
According to the Book of Judges, Deborah ( he, דְּבוֹרָה, ''Dəḇōrā'', "bee") was a prophetess of the God of the Israelites, the fourth Judge of pre-monarchic Israel and the only female judge mentioned in the Bible. Many scholars contend that the phrase, "a woman of Lappidot", as translated from biblical Hebrew in Judges 4:4 denotes her marital status as the wife of Lappidot.Van Wijk-Bos, Johanna WH. ''The End of the Beginning: Joshua and Judges''. Wm. B. Eerdmans Publishing, 2019. Alternatively, "lappid" translates as "torch" or "lightning", therefore the phrase, "woman of Lappidot" could be referencing Deborah as a "fiery woman." Deborah told Barak, an Israelite general from Kedesh in Naphtali, that God commanded him to lead an attack against the forces of Jabin king of Canaan and his military commander Sisera (Judges 4:6–7); the entire narrative is recounted in chapter 4. Judges chapter 5 gives the same story in poetic form. This passage, often called ''The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pascal's Triangle
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in India, Persia, China, Germany, and Italy. The rows of Pascal's triangle are conventionally enumerated starting with row n = 0 at the top (the 0th row). The entries in each row are numbered from the left beginning with k = 0 and are usually staggered relative to the numbers in the adjacent rows. The triangle may be constructed in the following manner: In row 0 (the topmost row), there is a unique nonzero entry 1. Each entry of each subsequent row is constructed by adding the number above and to the left with the number above and to the right, treating blank entries as 0. For example, the initial number of row 1 (or any other row) is 1 (the sum of 0 and 1), whereas the numbers 1 and 3 in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yin And Yang
Yin and yang ( and ) is a Chinese philosophy, Chinese philosophical concept that describes opposite but interconnected forces. In Chinese cosmology, the universe creates itself out of a primary chaos of material energy, organized into the cycles of yin and yang and formed into objects and lives. Yin is the receptive and yang the active principle, seen in all forms of change and difference such as the annual cycle (winter and summer), the landscape (north-facing shade and south-facing brightness), sexual coupling (female and male), the formation of both men and women as characters and sociopolitical history (disorder and order). Taiji (philosophy), Taiji or Tai chi () is a Chinese cosmological term for the "Supreme Ultimate" state of undifferentiated absolute and infinite potential, the oneness before duality, from which yin and yang originate. It can be compared with the old ''Wuji (philosophy), wuji'' (, "without pole"). In the cosmology pertaining to yin and yang, the mate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Book Of Changes
The ''I Ching'' or ''Yi Jing'' (, ), usually translated ''Book of Changes'' or ''Classic of Changes'', is an ancient Chinese divination text that is among the oldest of the Chinese classics. Originally a divination manual in the Western Zhou period (1000750), the ''I Ching'' was transformed over the course of the Warring States period, Warring States and early imperial periods (500200) into a Religious cosmology, cosmological text with a series of philosophical commentaries known as the "Ten Wings". After becoming part of the Five Classics in the 2nd century BC, the ''I Ching'' was the subject of scholarly commentary and the basis for divination practice for centuries across the Far East, and eventually took on an influential role in Western understanding of East Asian philosophical thought. As a divination text, the ''I Ching'' is used for a traditional Chinese form of cleromancy known as I Ching divination, ''I Ching'' divination, in which bundles of yarrow, yarrow stalks a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.svg "Click for more on -> Yin And Yang")
