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]]>The post Sleep Paralysis appeared first on UMDA.

]]>Sleep paralysis has been linked to disorders such as narcolepsy, migraines, anxiety disorders, and obstructive sleep apnea; however, it can also occur in isolation. When linked to another disorder, sleep paralysis commonly occurs in association with the neuromuscular disorder narcolepsy.

The two major classifications of sleep paralysis are *isolated sleep paralysis (ISP)* and *recurrent isolated sleep paralysis (RISP).* Of these two types, ISP is much more common than RISP. ISP episodes are infrequent and of short duration, approximately one minute. Sleep paralysis might even only occur once in an individual’s lifetime. As the name suggests, recurrent isolated sleep paralysis is a chronic condition. The individual suffers from frequent episodes throughout their lifetime. One of the major differences between ISP and RISP is duration. RISP episodes can last for up to an hour or longer, and have a much higher occurrence of perceived out of body experiences—while ISP episodes are generally short (usually no longer than one minute) and are typically associated with the intruder and incubus hallucinations. ISP episodes can, however, persist for up to half an hour. With RISP the individual can also suffer back to back episodes of sleep paralysis in the same night while this is unlikely in individuals who suffer from ISP.^{
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It can be difficult to differentiate between cataplexy brought on by narcolepsy and true sleep paralysis, because the two phenomena are physically indistinguishable. The best way to differentiate between the two is to note when the attacks occur most often. Narcolepsy attacks are more common when the individual is falling asleep; ISP and RISP attacks are more common on awakening.^{
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]]>The post Nikola Tesla appeared first on UMDA.

]]>Tesla gained experience in telephony and electrical engineering before emigrating to the United States in 1884 to work for Thomas Edison. He soon struck out on his own with financial backers, setting up laboratories and companies to develop a range of electrical devices. His patented AC induction motor and transformer were licensed by George Westinghouse, who also hired Tesla as a consultant to help develop a power system using alternating current. Tesla is also known for his high-voltage, high-frequency power experiments in New York and Colorado Springs which included patented devices and theoretical work used in the invention of radio communication, for his X-ray experiments, and for his ill-fated attempt at intercontinental wireless transmission in his unfinished Wardenclyffe Tower project.^{
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Tesla’s achievements and his abilities as a showman demonstrating his seemingly miraculous inventions made him world-famous. Although he made a great deal of money from his patents, he spent a lot on numerous experiments. He lived for most of his life in a series of New York hotels although the end of his patent income and eventual bankruptcy led him to live in diminished circumstances. Tesla still continued to invite the press to parties he held on his birthday to announce new inventions he was working and make (sometimes unusual) statements. Because of his pronouncements and the nature of his work over the years, Tesla gained a reputation in popular culture as the archetypal “mad scientist”. He died in room 3327 of the New Yorker Hotel on 7 January 1943.

Tesla’s work fell into relative obscurity after his death, but since the 1990s, his reputation has experienced a comeback in popular culture. His work and reputed inventions are also at the center of many conspiracy theories and have also been used to support variouspseudosciences, UFO theories and New Age occultism. In 1960, in honor of Tesla, the General Conference on Weights and Measures for theInternational System of Units dedicated the term “tesla” to the SI unit measure for magnetic field strength.^{
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]]>The post Leibniz and Newton appeared first on UMDA.

]]>Unoccupied regions are those that *could* have objects in them, and thus spatial relations with other places. For Leibniz, then, space was an idealised abstraction from the relations between individual entities or their possible locations and therefore could not becontinuous but must be discrete.

Space could be thought of in a similar way to the relations between family members. Although people in the family are related to one another, the relations do not exist independently of the people. Leibniz argued that space could not exist independently of objects in the world because that implies a difference between two universes exactly alike except for the location of the material world in each universe. But since there would be no observational way of telling these universes apart then, according to the identity of indiscernibles, there would be no real difference between them. According to the principle of sufficient reason, any theory of space that implied that there could be these two possible universes, must therefore be wrong.^{
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Newton took space to be more than relations between material objects and based his position on observation and experimentation. For a relationist there can be no real difference between inertial motion, in which the object travels with constant velocity, and non-inertial motion, in which the velocity changes with time, since all spatial measurements are relative to other objects and their motions. But Newton argued that since non-inertial motion generates forces, it must be absolute. He used the example of water in a spinning bucket to demonstrate his argument. Water in a bucket is hung from a rope and set to spin, starts with a flat surface. After a while, as the bucket continues to spin, the surface of the water becomes concave. If the bucket’s spinning is stopped then the surface of the water remains concave as it continues to spin.

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]]>Over the following ten years Einstein worked on a general theory of relativity, which is a theory of how gravity interacts with spacetime. Instead of viewing gravity as a force field acting in spacetime, Einstein suggested that it modifies the geometric structure of spacetime itself.^{[19]} According to the general theory, time goes more slowly at places with lower gravitational potentials and rays of light bend in the presence of a gravitational field. Scientists have studied the behaviour of binary pulsars, confirming the predictions of Einstein’s theories and non-Euclidean geometry is usually used to describe spacetime.

In modern mathematics spaces are defined as sets with some added structure. They are frequently described as different types of manifolds, which are spaces that locally approximate to Euclidean space, and where the properties are defined largely on local connectedness of points that lie on the manifold. There are however, many diverse mathematical objects that are called spaces. For example, vector spaces such as function spaces may have infinite numbers of independent dimensions and a notion of distance very different to Euclidean space, and topological spaces replace the concept of distance with a more abstract idea of nearness.

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]]>The post Million-digit prime found appeared first on UMDA.

]]>The number was first reported to the GIMPS server on January 25 from a university computer which had been running 39 days non-stop. However as for any Mersenne prime candidates, the discovery was announced after several people have verified the number using different hardware and software. The three independent verifications took from three to seven days of computation on powerful hardware.

A prime number is a positive integer greater than 1 that can only be evenly divided by 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17 and 19. 77 (for example) is not prime because it is a product of 7 and 11. The newly discovered prime is expressed as 2^{57,885,161} − 1 and has 17,425,170 digits. It is a specific type of prime number called a Mersenne prime, which are of the form 2^{p} − 1. The exponent *p* must be prime for the number to be prime. As of February 2013, there are only 48 known Mersenne primes.

George Woltman developed and founded GIMPS, the longest known continuously running computer project, in 1996. Cooper as a participant had previously discovered two other Mersenne primes, 2^{30,402,457} − 1 in December 2005 and 2^{32,582,657} − 1 in September 2006, with fellow professor Steven Boone. This latest discovery ends an intermission of almost four years; the previous Mersenne prime was found in April 2009.

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