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"[W]e think of the analysis of variance as a way of understanding and structuring multilevel models—not as an alternative to regression but as a tool for summarizing complex high-dimensional inferences ..."
For a single factor
The simplest experiment suitable for ANOVA analysis is the completely randomized experiment... | [
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: Welch's heteroscedastic F test, Welch's heteroscedastic F test with trimmed means and Winsorized variances, Brown-Forsythe test, Alexander-Govern test, James second order test and Kruskal-Wallis test, available in onewaytests R
It is useful to represent each data point in the following form, called a statistical mod... | [
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In a 3-way ANOVA with factors x, y and z, the ANOVA model includes terms for the main effects (x, y, z) and terms for interactions (xy, xz, yz, xyz). All terms require hypothesis tests. The proliferation of interaction terms increases the risk that some hypothesis test will produce a false positive by chance. Fortunate... | [
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Associated analysis
Some analysis is required in support of the design of the experiment while other analysis is performed after changes in the factors are formally found to produce statistically significant changes in the responses. Because experimentation is iterative, the results of one experiment alter plans for fo... | [
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Power analysis can assist in study design by determining what sample size would be required in order to have a reasonable chance of rejecting the null hypothesis when the alternative hypothesis is true. Effect size
Several standardized measures of effect have been proposed for ANOVA to summarize the strength of the as... | [
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The follow-up tests may be "simple" pairwise comparisons of individual group means or may be "compound" comparisons (e.g., comparing the mean pooling across groups A, B and C to the mean of group D). Comparisons can also look at tests of trend, such as linear and quadratic relationships, when the independent variable i... | [
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Typically, however, the one-way ANOVA is used to test for differences among at least three groups, since the two-group case can be covered by a t-test. When there are only two means to compare, the t-test and the ANOVA F-test are equivalent; the relation between ANOVA and t is given by . Factorial ANOVA is used when th... | [
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The American Psychological Association (and many other organisations) holds the view that simply reporting statistical significance is insufficient and that reporting confidence bounds is preferred. Generalizations
ANOVA is considered to be a special case of linear regression which in turn is a special case of the gene... | [
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From here, one can use F-statistics or other methods to determine the relevance of the individual factors. Example
We can consider the 2-way interaction example where we assume that the first factor has 2 levels and the second factor has 3 levels. Define if and if , i.e. is the one-hot encoding of the first factor a... | [
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Freedman, David A.; Pisani, Robert; Purves, Roger (2007) Statistics, 4th edition. W.W. Norton & Company
Tabachnick, Barbara G. & Fidell, Linda S. (2007). Using Multivariate Statistics (5th ed.). Boston: Pearson International Edition. External links
SOCR ANOVA Activity
Examples of all ANOVA and ANCOVA models w... | [
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Assistive technology (AT) is a term for assistive, adaptive, and rehabilitative devices for people with disabilities and the elderly. People with disabilities often have difficulty performing activities of daily living (ADLs) independently, or even with assistance. ADLs are self-care activities that include toileting, ... | [
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In other words, assistive technology is any object or system that helps people with disabilities, while adaptive technology is specifically designed for disabled people. Consequently, adaptive technology is a subset of assistive technology. Adaptive technology often refers specifically to electronic and information tec... | [
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The devices come in a number of variations where they can be propelled either by hand or by motors where the occupant uses electrical controls to manage motors and seating control actuators through a joystick, sip-and-puff control, head switches or other input devices. Often there are handles behind the seat for someon... | [
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Highly dependent patients who cannot assist their caregiver in moving them often require a patient lift (a floor or ceiling-suspended sling lift) which though invented in 1955 and in common use since the early 1960s is still considered the state-of-the-art transfer device by OSHA and the American Nursing Association. W... | [
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Other medical devices and aids that can be considered prosthetics include hearing aids, artificial eyes, palatal obturator, gastric bands, and dentures. Prostheses are specifically not orthoses, although given certain circumstances a prosthesis might end up performing some or all of the same functionary benefits as an ... | [
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The exoskeleton supports the shoulder, waist and thigh, and assists movement for lifting and holding heavy items, while lowering back stress. Adaptive seating and positioning
People with balance and motor function challenges often need specialized equipment to sit or stand safely and securely. This equipment is freque... | [
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There are a variety of platforms and applications available for a variety of costs with differing feature sets. Some example of screen readers are Apple VoiceOver, Google TalkBack and Microsoft Narrator. This software is provided free of charge on all Apple devices. Apple VoiceOver includes the option to magnify the sc... | [
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Some braille embossers combine both braille and ink so the documents can be read with either sight or touch. Refreshable braille display
A refreshable braille display or braille terminal is an electro-mechanical device for displaying braille characters, usually by means of round-tipped pins raised through holes in a ... | [
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On the keyboard shown, the round buttons at the top control software which can magnify the screen (zoom in), change the background color of the screen, or make the mouse cursor on the screen larger. The "bump dots" on the keys, installed in this case by the organization using the keyboards, help the user find the right... | [
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Some wearable devices for visual impairment include:
OrCam device
eSight
Brainport
Personal emergency response systems
Personal emergency response systems (PERS), or Telecare (UK term), are a particular sort of assistive technology that use electronic sensors connected to an alarm system to help caregivers manage ... | [
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Hearing impairments
People in the d/Deaf and hard of hearing community have a more difficult time receiving auditory information as compared to hearing individuals. These individuals often rely on visual and tactile mediums for receiving and communicating information. The use of assistive technology and devices provid... | [
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This type of technology allows people with hearing difficulties to focus on a speaker or subject by getting rid of extra background noises and distractions, making places like auditoriums, classrooms, and meetings much easier to participate in. The assistive listening device usually uses a microphone to capture an audi... | [
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They may be as basic as pictures on a board that are used to request food, drink, or other care; or they can be advanced speech generating devices, based on speech synthesis, that are capable of storing hundreds of phrases and words. Cognitive impairments
Assistive Technology for Cognition (ATC) is the use of technolo... | [
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Educational software
Educational software is software that assists people with reading, learning, comprehension, and organizational difficulties. Any accommodation software such as text readers, notetakers, text enlargers, organization tools, word predictions, and talking word processors falls under the category of e... | [
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"Low-tech" devices can include velcro gloves and adaptive bands and tubes. "High-tech" devices can include all-terrain wheelchairs and adaptive bicycles. Accordingly, assistive technology can be found in sports ranging from local community recreation to the elite Paralympic Games. More complex assistive technology devi... | [
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Assistive technology listed is a student's IEP is not only recommended, it is required (Koch, 2017). These devices help students both with and without disabilities access the curriculum in a way they were previously unable to (Koch, 2017). Occupational therapists play an important role in educating students, parents an... | [
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Computer accessibility
One of the largest problems that affect disabled people is discomfort with prostheses. An experiment performed in Massachusetts utilized 20 people with various sensors attached to their arms. The subjects tried different arm exercises, and the sensors recorded their movements. All of the data he... | [
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Eye gaze and head mouse systems can also be used as an alternative mouse navigation. A user may utilize single or multiple switch sites and the process often involves a scanning through items on a screen and activating the switch once the desired object is highlighted. Home automation
The form of home automation called... | [
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Additionally, it has been found to lighten caregiver load. Both family and professional caregivers benefit from assistive technology. Through its use, the time that a family member or friend would need to care for a patient significantly decreases. However, studies show that care time for a professional caregiver incre... | [
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The abacus (plural abaci or abacuses), also called a counting frame, is a calculating tool which has been used since ancient times. It was used in the ancient Near East, Europe, China, and Russia, centuries before the adoption of the Hindu-Arabic numeral system. The exact origin of the abacus has not yet emerged. It co... | [
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Merchants, traders, and clerks in some parts of Eastern Europe, Russia, China, and Africa use abacuses. The abacus remains in common use
as a scoring system in non-electronic table games. Others may use an abacus due to visual impairment that prevents the use of a calculator. Etymology
The word abacus dates to at leas... | [
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Some scholars point to a character in Babylonian cuneiform that may have been derived from a representation of the abacus. It is the belief of Old Babylonian scholars, such as Ettore Carruccio, that Old Babylonians "may have used the abacus for the operations of addition and subtraction; however, this primitive device ... | [
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The Greek abacus was a table of wood or marble, pre-set with small counters in wood or metal for mathematical calculations. This Greek abacus saw use in Achaemenid Persia, the Etruscan civilization, Ancient Rome, and the Western Christian world until the French Revolution. A tablet found on the Greek island Salamis in ... | [
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"calculating tray"), is typically tall and comes in various widths, depending on the operator. It usually has more than seven rods. There are two beads on each rod in the upper deck and five beads each in the bottom one. The beads are usually rounded and made of hardwood. The beads are counted by moving them up or dow... | [
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In the long scroll Along the River During the Qingming Festival painted by Zhang Zeduan during the Song dynasty (960–1297), a suanpan is clearly visible beside an account book and doctor's prescriptions on the counter of an apothecary's (Feibao). The similarity of the Roman abacus to the Chinese one suggests that one c... | [
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Originally pebbles (calculi) were used. Later, and in medieval Europe, jetons were manufactured. Marked lines indicated units, fives, tens, etc. as in the Roman numeral system. This system of 'counter casting' continued into the late Roman empire and in medieval Europe and persisted in limited use into the nineteenth c... | [
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India
The Abhidharmakośabhāṣya of Vasubandhu (316-396), a Sanskrit work on Buddhist philosophy, says that the second-century CE philosopher Vasumitra said that "placing a wick (Sanskrit vartikā) on the number one (ekāṅka) means it is a one while placing the wick on the number hundred means it is called a hundred, and ... | [
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The quotient division is generally used instead of the division method; at the same time, in order to make the multiplication and division digits consistently use the division multiplication. Later, Japan had a 3:5 abacus called 天三算盤, which is now in the Ize Rongji collection of Shansi Village in Yamagata City. Japan a... | [
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The word Nepōhualtzintzin comes from Nahuatl, formed by the roots; Ne – personal -; pōhual or pōhualli – the account -; and tzintzin – small similar elements. Its complete meaning was taken as: counting with small similar elements. Its use was taught in the Calmecac to the temalpouhqueh , who were students dedicated... | [
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When translated into modern computer arithmetic, the Nepōhualtzintzin amounted to the rank from 10 to 18 in floating point, which precisely calculated large and small amounts, although round off was not allowed. The rediscovery of the Nepōhualtzintzin was due to the Mexican engineer David Esparza Hidalgo, who in his tr... | [
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By comparing the form of several yupanas, researchers found that calculations were based using the Fibonacci sequence 1, 1, 2, 3, 5 and powers of 10, 20, and 40 as place values for the different fields in the instrument. Using the Fibonacci sequence would keep the number of grains within any one field at a minimum. Rus... | [
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Some businessmen attempting to import calculators into the Russian Empire were known to leave in despair after watching a skilled abacus operator. Likewise, the mass production of Felix arithmometers since 1924 did not significantly reduce abacus use in the Soviet Union. The Russian abacus began to lose popularity onl... | [
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In the bead frame shown, the gap between the 5th and 6th wire, corresponding to the color change between the 5th and the 6th bead on each wire, suggests the latter use. Teaching multiplication, e.g. 6 times 7, may be represented by shifting 7 beads on 6 wires. The red-and-white abacus is used in contemporary primary sc... | [
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People doing long-term AMC training show higher numerical memory capacity and experience more effectively connected neural pathways. They are able to retrieve memory to deal with complex processes. AMC involves both visuospatial and visuomotor processing that generate the visual abacus and move the imaginary beads. Sin... | [
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The abacus gives these students a tool to compute mathematical problems that equals the speed and mathematical knowledge required by their sighted peers using pencil and paper. Many blind people find this number machine a useful tool throughout life. See also
Chinese Zhusuan
Chisanbop
Logical abacus
Mental abacus
... | [
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The American National Standards Institute (ANSI ) is a private non-profit organization that oversees the development of voluntary consensus standards for products, services, processes, systems, and personnel in the United States. The organization also coordinates U.S. standards with international standards so that Ame... | [
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Prior to 1918, these five founding engineering societies:
American Institute of Electrical Engineers (AIEE, now IEEE)
American Society of Mechanical Engineers (ASME)
American Society of Civil Engineers (ASCE)
American Institute of Mining Engineers (AIME, now American Institute of Mining, Metallurgical, and Petroleu... | [
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ANSI accreditation signifies that the procedures used by standards developing organizations meet the institute's requirements for openness, balance, consensus, and due process. ANSI also designates specific standards as American National Standards, or ANS, when the Institute determines that the standards were developed... | [
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In many instances, U.S. standards are taken forward to ISO and IEC, through ANSI or the USNC, where they are adopted in whole or in part as international standards. Adoption of ISO and IEC standards as American standards increased from 0.2% in 1986 to 15.5% in May 2012. Standards panels
The Institute administers nine s... | [
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The ANSI code standard extended the previously created ASCII seven bit code standard (ASA X3.4-1963), with additional codes for European alphabets (see also Extended Binary Coded Decimal Interchange Code or EBCDIC). In Microsoft Windows, the phrase "ANSI" refers to the Windows ANSI code pages (even though they are not ... | [
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The ANSI/HI (Hydraulic Institute) standards used for pumps. The ANSI for eye protection is Z87.1, which gives a specific impact resistance rating to the eyewear. This standard is commonly used for shop glasses, shooting glasses, and many other examples of protective eyewear. The ANSI paper sizes (ANSI/ASME Y14.1). Othe... | [
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The site currently features content for the United States, China, India, Korea, and Brazil, with additional countries and regions planned for future content. ANSI design standards have also been incorporated into building codes encompassing several specific building sub-sets, such as the ANSI/SPRI ES-1, which pertains ... | [
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The atomic number or proton number (symbol Z) of a chemical element is the number of protons found in the nucleus of every atom of that element. The atomic number uniquely identifies a chemical element. It is identical to the charge number of the nucleus. In an uncharged atom, the atomic number is also equal to the num... | [
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The conventional symbol Z comes from the German word 'number', which, before the modern synthesis of ideas from chemistry and physics, merely denoted an element's numerical place in the periodic table, whose order was then approximately, but not completely, consistent with the order of the elements by atomic weights. ... | [
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Besides the case of iodine and tellurium, later several other pairs of elements (such as argon and potassium, cobalt and nickel) were known to have nearly identical or reversed atomic weights, thus requiring their placement in the periodic table to be determined by their chemical properties. However the gradual identif... | [
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Moseley's 1913 experiment
The experimental position improved dramatically after research by Henry Moseley in 1913. Moseley, after discussions with Bohr who was at the same lab (and who had used Van den Broek's hypothesis in his Bohr model of the atom), decided to test Van den Broek's and Bohr's hypothesis directly, b... | [
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There were seven elements (with Z < 92) which were not found and therefore identified as still undiscovered, corresponding to atomic numbers 43, 61, 72, 75, 85, 87 and 91. From 1918 to 1947, all seven of these missing elements were discovered. By this time, the first four transuranium elements had also been discovered,... | [
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It had been immediately apparent from the work of Moseley that the nuclei of heavy atoms have more than twice as much mass as would be expected from their being made of hydrogen nuclei, and thus there was required a hypothesis for the neutralization of the extra protons presumed present in all heavy nuclei. A helium nu... | [
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Hence, it is the atomic number alone that determines the chemical properties of an element; and it is for this reason that an element can be defined as consisting of any mixture of atoms with a given atomic number. New elements
The quest for new elements is usually described using atomic numbers. As of , all elements w... | [
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Affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement (e.g., "If the lamp were broken, then the room would be dark"), and invalidly inferring its converse ("The room is dark, so the lamp i... | [
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, it is possible to infer P under the condition Q. For example, the statements "It is August 13, so it is my birthday" and "It is my birthday, so it is August 13" are equivalent and both true consequences of the statement "August 13 is my birthday" (an abbreviated form of ). Using one statement to conclude the other ... | [
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Here, it is immediately intuitive that any number of other antecedents ("If an animal is a deer...", "If an animal is an elephant...", "If an animal is a moose...", etc.) can give rise to the consequent ("then it has four legs"), and that it is preposterous to suppose that having four legs must imply that the animal is... | [
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"The author signed his name." "That's my name there." "Then you wrote it. Q.E.D." P in this case is 'The chaplain signs his own name', and Q 'The chaplain's name is written'. The chaplain's name may be written, but he did not necessarily write it, as the colonel falsely concludes.See also
List of fallacies
Abductive... | [
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Ambiguity is a type of meaning in which a phrase, statement or resolution is not explicitly defined, making several interpretations plausible. A common aspect of ambiguity is uncertainty. It is thus an attribute of any idea or statement whose intended meaning cannot be definitively resolved according to a rule or proce... | [
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One could say "I bought herbs from the apothecary". This could mean one actually spoke to the apothecary (pharmacist) or went to the apothecary (pharmacy). The context in which an ambiguous word is used often makes it evident which of the meanings is intended. If, for instance, someone says "I buried $100 in the bank",... | [
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"Good", for example, can mean "useful" or "functional" (That's a good hammer), "exemplary" (She's a good student), "pleasing" (This is good soup), "moral" (a good person versus the lesson to be learned from a story), "righteous", etc. "I have a good daughter" is not clear about which sense is intended. The various ways... | [
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"He ate the cookies on the couch", for example, could mean that he ate those cookies that were on the couch (as opposed to those that were on the table), or it could mean that he was sitting on the couch when he ate the cookies. "To get in, you will need an entrance fee of $10 or your voucher and your drivers' license.... | [
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It is more common that a syntactically unambiguous phrase has a semantic ambiguity; for example, the lexical ambiguity in "Your boss is a funny man" is purely semantic, leading to the response "Funny ha-ha or funny peculiar?" Spoken language can contain many more types of ambiguities which are called phonological ambig... | [
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Some will think they oppose taxes in general because they hinder economic growth. Others may think they oppose only those taxes that they believe will hinder economic growth. In writing, the sentence can be rewritten to reduce possible misinterpretation, either by adding a comma after "taxes" (to convey the first sense... | [
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In calling his work Being and Nothingness an "essay in phenomenological ontology" Jean-Paul Sartre follows Heidegger in defining the human essence as ambiguous, or relating fundamentally to such ambiguity. Simone de Beauvoir tries to base an ethics on Heidegger's and Sartre's writings (The Ethics of Ambiguity), where s... | [
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Following Ernest Becker, he argues that the desire to 'authoritatively disambiguate' the world and existence has led to numerous ideologies and historical events such as genocide. On this basis, he argues that ethics must focus on 'dialectically integrating opposites' and balancing tension, rather than seeking a priori... | [
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Usually, the conversion to another notation requires to scale the argument or the resulting value; sometimes, the same name of the function is used, causing confusions. Examples of such underestablished functions:
Sinc function
Elliptic integral of the third kind; translating elliptic integral form MAPLE to Mathemati... | [
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In most programming languages, the operations of division and multiplication have equal priority and are executed from left to right. Until the last century, many editorials assumed that multiplication is performed first, for example, is interpreted as ; in this case, the insertion of parentheses is required when tran... | [
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Conversely, might seem to mean , as this exponentiation notation usually denotes function iteration: in general, means . However, for trigonometric and hyperbolic functions, this notation conventionally means exponentiation of the result of function application. The expression can be interpreted as meaning ; however... | [
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Just like Ludwig Wittgenstein states in Tractatus Logico-Philosophicus: "...Only in the context of a proposition has a name meaning." A highly confusing term is gain. For example, the sentence "the gain of a system should be doubled", without context, means close to nothing. It may mean that the ratio of the output vol... | [
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Mathematical interpretation of ambiguity
In mathematics and logic, ambiguity can be considered to be an instance of the logical concept of underdetermination—for example, leaves open what the value of X is—while its opposite is a self-contradiction, also called inconsistency, paradoxicalness, or oxymoron, or in math... | [
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Many Christians and Jews endorse Rudolf Otto's description of the sacred as 'mysterium tremendum et fascinans', the awe-inspiring mystery which fascinates humans. The orthodox Catholic writer G. K. Chesterton regularly employed paradox to tease out the meanings in common concepts which he found ambiguous or to reveal m... | [
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High levels of ambiguity in an emergency (e.g. an unconscious man lying on a park bench) make witnesses less likely to offer any sort of assistance, due to the fear that they may have misinterpreted the situation and acted unnecessarily. Alternately, non-ambiguous emergencies (e.g. an injured person verbally asking for... | [
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1 M (where M is ambiguously 1,000,000 or 1,048,576) is less uncertain than the engineering value 1.0e6 (defined to designate the interval 950,000 to 1,050,000). As non-volatile storage devices begin to exceed 1 GB in capacity (where the ambiguity begins to routinely impact the second significant digit), GB and TB almos... | [
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Arthur Schopenhauer ( , ; 22 February 1788 – 21 September 1860) was a German philosopher. He is best known for his 1818 work The World as Will and Representation (expanded in 1844), which characterizes the phenomenal world as the product of a blind noumenal will. Building on the transcendental idealism of Immanuel Kant... | [
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Ducha 47), the son of Johanna Schopenhauer (née Trosiener; 1766–1838) and Heinrich Floris Schopenhauer (1747–1805), both descendants of wealthy German-Dutch patrician families. Neither of them was very religious; both supported the French Revolution, and were republicans, cosmopolitans and Anglophiles. When Danzig beca... | [
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He was also under pressure from his father, who became very critical of his educational results. In 1805, Heinrich drowned in a canal near their home in Hamburg. Although it was possible that his death was accidental, his wife and son believed that it was suicide. He was prone to anxiety and depression; each becoming m... | [
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He left the Gymnasium after writing a satirical poem about one of the schoolmasters. Although Arthur claimed that he left voluntarily, his mother's letter indicates that he may have been expelled. Arthur spent two years as a merchant in honor of his dead father. During this time, he had doubts about being able to start... | [
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He accused his mother of being financially irresponsible, flirtatious and seeking to remarry, which he considered an insult to his father's memory. His mother, while professing her love to him, criticized him sharply for being moody, tactless, and argumentative, and urged him to improve his behavior so that he would no... | [
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In their youthful correspondence Arthur and Anthime were somewhat boastful and competitive about their sexual exploits—but Schopenhauer seemed aware that women usually did not find him very charming or physically attractive, and his desires often remained unfulfilled. He left Weimar to become a student at the Universit... | [
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His friends included Friedrich Gotthilf Osann, Karl Witte, Christian Charles Josias von Bunsen, and William Backhouse Astor Sr. He arrived at the newly founded University of Berlin for the winter semester of 1811–12. At the same time, his mother had just begun her literary career; she published her first book in 1810, ... | [
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Early work
Schopenhauer left Berlin in a rush in 1813, fearing that the city could be attacked and that he could be pressed into military service as Prussia had just joined the war against France. He returned to Weimar but left after less than a month, disgusted by the fact that his mother was now living with her supp... | [
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In a fit of temper Arthur told her that people would read his work long after the "rubbish" she wrote was totally forgotten. In fact, although they considered her novels of dubious quality, the Brockhaus publishing firm held her in high esteem because they consistently sold well. Hans Brockhaus (1888–1965) later claime... | [
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Schopenhauer later admitted that he was greatly hurt by this rejection, but he continued to praise Goethe, and considered his color theory a great introduction to his own. Another important experience during his stay in Weimar was his acquaintance with Friedrich Majer—a historian of religion, orientalist and disciple o... | [
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As the relationship with his mother fell to a new low, in May 1814 he left Weimar and moved to Dresden. He continued his philosophical studies, enjoyed the cultural life, socialized with intellectuals and engaged in sexual affairs. His friends in Dresden were Johann Gottlob von Quandt, Friedrich Laun, Karl Christian Fr... | [
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He enjoyed art, architecture, and ancient ruins, attended plays and operas, and continued his philosophical contemplation and love affairs. One of his affairs supposedly became serious, and for a while he contemplated marriage to a rich Italian noblewoman—but, despite his mentioning this several times, no details are k... | [
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He was especially appalled by Hegel's supposedly poor knowledge of natural sciences and tried to engage him in a quarrel about it already at his test lecture in March 1820. Hegel was also facing political suspicions at the time, when many progressive professors were fired, while Schopenhauer carefully mentioned in his ... | [
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Schopenhauer enjoyed Italy, where he studied art and socialized with Italian and English nobles. It was his last visit to the country. He left for Munich and stayed there for a year, mostly recuperating from various health issues, some of them possibly caused by venereal diseases (the treatment his doctor used suggests... | [
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She had already had numerous lovers and a son out of wedlock, and later gave birth to another son, this time to an unnamed foreign diplomat (she soon had another pregnancy but the child was stillborn). As Schopenhauer was preparing to escape from Berlin in 1831, due to a cholera epidemic, he offered to take her with hi... | [
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Their correspondence remained reserved, and Arthur seemed undisturbed by her death in 1838. His relationship with his sister grew closer and he corresponded with her until she died in 1849. In July 1832 Schopenhauer left Frankfurt for Mannheim but returned in July 1833 to remain there for the rest of his life, except f... | [
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That book was again mostly ignored and the few reviews were mixed or negative. Schopenhauer began to attract some followers, mostly outside academia, among practical professionals (several of them were lawyers) who pursued private philosophical studies. He jokingly referred to them as "evangelists" and "apostles". One ... | [
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He even modified his will, leaving a large part of his property to a Prussian fund that helped soldiers who became invalids while fighting rebellion in 1848 or the families of soldiers who died in battle. As Young Hegelians were advocating change and progress, Schopenhauer claimed that misery is natural for humans and ... | [
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In 1856, the University of Leipzig sponsored an essay contest about Schopenhauer's philosophy, which was won by Rudolf Seydel's very critical essay. Schopenhauer's friend Jules Lunteschütz made the first of his four portraits of him—which Schopenhauer did not particularly like—which was soon sold to a wealthy landowner... | [
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The last friend to visit him was Wilhelm Gwinner; according to him, Schopenhauer was concerned that he would not be able to finish his planned additions to Parerga and Paralipomena but was at peace with dying. He died of pulmonary-respiratory failure on 21 September 1860 while sitting at home on his couch. He died at ... | [
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Nevertheless, these investigations led him to his most important discovery in epistemology: finding a demonstration for the a priori nature of causality. Kant openly admitted that it was Hume's skeptical assault on causality that motivated the critical investigations in his Critique of Pure Reason and gave an elaborate... | [
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