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Klein bottle

Klein bottle
Structure of a three-dimensional Klein bottle In mathematics, the Klein bottle /ˈklaɪn/ is an example of a non-orientable surface; informally, it is a surface (a two-dimensional manifold) in which notions of left and right cannot be consistently defined. Other related non-orientable objects include the Möbius strip and the real projective plane. The Klein bottle was first described in 1882 by the German mathematician Felix Klein. Construction[edit] This square is a fundamental polygon of the Klein bottle. Note that this is an "abstract" gluing in the sense that trying to realize this in three dimensions results in a self-intersecting Klein bottle. By adding a fourth dimension to the three-dimensional space, the self-intersection can be eliminated. This immersion is useful for visualizing many properties of the Klein bottle. A hand-blown Klein Bottle Dissecting the Klein bottle results in Möbius strips. Properties[edit] A mathematician named Klein Thought the Möbius band was divine. Notes[edit] Related:  alan watts

Sunyata (Emptiness) in the Mahayana Context 1. Sunyata (Emptiness) is the profound meaning of the Mahayana Teaching. Two thousand five hundred years ago, the Buddha was able to realise "emptiness" (s. sunyata). By doing so he freed himself from unsatisfactoriness (s. dukkha). From the standpoint of enlightenment, sunyata is the reality of all worldly existences (s. dharma). It is the realisation of Bodhi — Prajna. There are two ways for us to understand this concept of sunyata in the Mahayana context. Mahayana teachings have always considered that the understanding of sunyata is an attainment which is extremely difficult and extraordinarily profound. For example, in the Prajna Sutra it says "That which is profound, has sunyata and non-attachment as its significance. Again in the Dvadasanikaya Sastra (composed by Nagarjuna, translated to Chinese by Kumarajiva A.D. 408) it says: "The greatest wisdom is the so-called sunyata." 2. The sutras often use the word "great void" to explain the significance of sunyata. 3. 4. 5.

Pali Middle Indo-Aryan language native to the Indian subcontinent Burmese Kammavaca manuscript written in Pali in the 'Burmese' script. Pali () is a Middle Indo-Aryan liturgical language native to the Indian subcontinent. Origin and development[edit] Etymology[edit] The word 'Pali' is used as a name for the language of the Theravada canon. The name Pali does not appear in the canonical literature, and in commentary literature is sometimes substituted with tanti, meaning a string or lineage.[3]: 1 This name seems to have emerged in Sri Lanka early in the second millennium CE during a resurgence in the use of Pali as a courtly and literary language.[4][3]: 1 As such, the name of the language has caused some debate among scholars of all ages; the spelling of the name also varies, being found with both long "ā" [ɑː] and short "a" [a], and also with either a retroflex [ɭ] or non-retroflex [l] "l" sound. Geographic origin[edit] Early history[edit] Manuscripts and inscriptions[edit] T. According to K.

Mahayana Mahāyāna (Sanskrit: महायान mahāyāna, literally the "Great Vehicle") is one of two (or three, under some classifications) main existing branches of Buddhism and a term for classification of Buddhist philosophies and practice. The Buddhist tradition of Vajrayana is sometimes classified as a part of Mahayana Buddhism, but some scholars may consider it as a different branch altogether.[1] According to the teachings of Mahāyāna traditions, "Mahāyāna" also refers to the path of the Bodhisattva seeking complete enlightenment for the benefit of all sentient beings, also called "Bodhisattvayāna", or the "Bodhisattva Vehicle The Mahāyāna tradition is the largest major tradition of Buddhism existing today, with 53.2% of practitioners, compared to 35.8% for Theravāda and 5.7% for Vajrayāna in 2010.[3] Etymology[edit] The earliest Mahāyāna texts often use the term Mahāyāna as a synonym for Bodhisattvayāna, but the term Hīnayāna is comparatively rare in the earliest sources. History[edit] Origins[edit]

Śūnyatā Śūnyatā (Sanskrit: शून्यता, translit. śūnyatā; Pali: suññatā) – pronounced ‘shoonyataa’, translated into English most often as emptiness[1] and sometimes voidness[2] – is a Buddhist concept which has multiple meanings depending on its doctrinal context. It is either an ontological feature of reality, a meditative state, or a phenomenological analysis of experience. In Theravada Buddhism, suññatā often refers to the non-self (Pāli: anattā, Sanskrit: anātman)[note 1] nature of the five aggregates of experience and the six sense spheres. In Mahayana, Sunyata refers to the tenet that "all things are empty of intrinsic existence and nature (svabhava)," [4][5] but may also refer to the Buddha-nature teachings and primordial or empty awareness, as in Dzogchen and Shentong. Etymology[edit] "Śūnyatā" (Sanskrit) is usually translated as "devoidness," "emptiness," "hollow, hollowness," "voidness." Development of the concept[edit] Early Buddhism[edit] Pāli Nikāyas[edit] Meditative state[edit] Chán[edit]

History of Computers and Computing, Dreamers, Athanasius Kircher The Llullistic method of Athanasius Kircher The german Athanasius Kircher (1602-1680) (see biography of Athanasius Kircher) was a famous 17th century Jesuit scholar, who published around 40 works, most notably in the fields of oriental studies, geology, medicine and music theory. Kircher's best-known work today is his Oedipus Aegyptiacus (1652–54)—a vast study of Egyptology and comparative religion. His books, written in Latin (which was the common scientific language then), had a wide circulation in the 17th century, and they contributed to the dissemination of scientific information to a broader circle of readers. The name of Kircher is repeatedly mentioned in other articles of this site—e.g. in Napier's Bones, concerning his Organum Mathematicum, as well as in Kircher's automata. Most of his life Kircher lived in Rome (from 1635), where he was to stay, until his death, at the Jesuit Roman College.

The Life and Work of Athanaseus Kircher, S.J. It is difficult to accurately summarize the breadth of activities explored and mastered by the 17th century Jesuit scholar Athanasius Kircher. Inventor, composer, geographer, geologist, Egyptologist, historian, adventurer, philosopher, proprietor of one of the first public museums, physicist, mathematician, naturalist, astronomer, archaeologist, author of more than 40 published works: Kircher was one of the preeminent European intellectuals of the Seventeenth century. A contemporary of Newton, Boyle, Leibniz and Descartes, Kircher's rightful place in the history of science has been shrouded by his attempt to forge a unified world view out of traditional Biblical historicism and the emerging secular scientific theory of knowledge. Born May 2, 1602, the youngest child in a family of lay scholars, Athanasius was sent early on to Jesuit school and to study Hebrew with a rabbi. Then, one night Kircher was awakened by a strange sound. To view this text in German, select this link. Turn Back

Athanasius Kircher German Jesuit scholar and polymath (1602-1680) Athanasius Kircher (2 May 1602 – 27 November 1680)[1] was a German Jesuit scholar and polymath who published around 40 major works, most notably in the fields of comparative religion, geology, and medicine. Kircher has been compared to fellow Jesuit Roger Joseph Boscovich and to Leonardo da Vinci for his enormous range of interests, and has been honoured with the title "Master of a Hundred Arts".[2] He taught for more than 40 years at the Roman College, where he set up a wunderkammer. A resurgence of interest in Kircher has occurred within the scholarly community in recent decades. Kircher claimed to have deciphered the hieroglyphic writing of the ancient Egyptian language, but most of his assumptions and translations in this field were later found to be incorrect. He did, however, correctly establish the link between the ancient Egyptian and the Coptic languages, and some commentators regard him as the founder of Egyptology. Life[edit]

Athanasius Kircher | Biography, Facts, & Contributions Athanasius Kircher, (born May 2, 1601, Geisa, Abbacy of Fulda [Thuringia, Germany]—died November 27, 1680, Rome [Italy]), Jesuit priest and scholar, sometimes called the last Renaissance man, important for his prodigious activity in disseminating knowledge. Kircher learned Greek and Hebrew at the Jesuit school in Fulda, pursued scientific and humanistic studies at Paderborn, Cologne, and Koblenz, and in 1628 was ordained at Mainz. He fled the increasing factional and dynastic fighting in Germany (part of the Thirty Years’ War) and, after occupying various academic positions at Avignon, settled in 1634 in Rome. A renowned polymath, Kircher’s research encompassed a variety of disciplines—including geography, astronomy, mathematics, language, medicine, and music—bringing to each a rigorous scientific curiosity girded in a mystical conception of natural laws and forces.

Agnosia - National Aphasia Association What is Agnosia? Agnosia is a neurological disorder that results in an inability to recognize objects (such as an apple or a key), persons, smells, or sounds despite normally functioning senses (such as visual or auditory). These deficits are not due to memory loss. What causes Agnosia? Agnosia results from brain damage in areas involved in spatial processing, integration of visual and motor information, and attention. How does Agnosia relate to Aphasia? Agnosia is not a speech or language disorder per se. More Agnosia Resources Clinical trialsWhat research is being done – National Institute of Neurological Disorders and StrokeAuditory Agnosia Research – Handbook of Clinical Neurology (2015)

Agnosia Picture of the ventral and dorsal streams. The ventral stream is depicted in purple and the dorsal stream is depicted in green. Types[edit] Visual agnosia[edit] Visual agnosia is a broad category that refers to a deficiency in the ability to recognize visual objects. Visual agnosia can be further subdivided into two different subtypes: apperceptive visual agnosia and associative visual agnosia.[22] Individuals with apperceptive visual agnosia display the ability to see contours and outlines when shown an object, but they experience difficulty if asked to categorize objects. In contrast, individuals with associative visual agnosia experience difficulty when asked to name objects. Speech agnosia[edit] Speech agnosia, or auditory verbal agnosia, refers to "an inability to comprehend spoken words despite intact hearing, speech production and reading ability".[24] Patients report that they do indeed hear sounds being produced, but that the sounds are fundamentally unrecognizable/untranslatable.

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