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6,200 | where "t" and are the "p"th quantiles of the "t"- and "χ"-distributions respectively. These confidence intervals are of the "confidence level" , meaning that the true values "μ" and "σ" fall outside of these intervals with probability (or significance level) "α". In practice people usually take , resulting in the 95% confidence intervals. | https://en.wikipedia.org/wiki?curid=21462 |
6,201 | The approximate formulas become valid for large values of "n", and are more convenient for the manual calculation since the standard normal quantiles "z" do not depend on "n". In particular, the most popular value of , results in . | https://en.wikipedia.org/wiki?curid=21462 |
6,202 | Normality tests assess the likelihood that the given data set {"x", ..., "x"} comes from a normal distribution. Typically the null hypothesis "H" is that the observations are distributed normally with unspecified mean "μ" and variance "σ", versus the alternative "H" that the distribution is arbitrary. Many tests (over 40) have been devised for this problem. The more prominent of them are outlined below: | https://en.wikipedia.org/wiki?curid=21462 |
6,203 | Diagnostic plots are more intuitively appealing but subjective at the same time, as they rely on informal human judgement to accept or reject the null hypothesis. | https://en.wikipedia.org/wiki?curid=21462 |
6,204 | Bayesian analysis of normally distributed data is complicated by the many different possibilities that may be considered: | https://en.wikipedia.org/wiki?curid=21462 |
6,205 | The following auxiliary formula is useful for simplifying the posterior update equations, which otherwise become fairly tedious. | https://en.wikipedia.org/wiki?curid=21462 |
6,206 | This equation rewrites the sum of two quadratics in "x" by expanding the squares, grouping the terms in "x", and completing the square. Note the following about the complex constant factors attached to some of the terms: | https://en.wikipedia.org/wiki?curid=21462 |
6,207 | A similar formula can be written for the sum of two vector quadratics: If x, y, z are vectors of length "k", and A and B are symmetric, invertible matrices of size formula_427, then | https://en.wikipedia.org/wiki?curid=21462 |
6,208 | In other words, it sums up all possible combinations of products of pairs of elements from x, with a separate coefficient for each. In addition, since formula_431, only the sum formula_432 matters for any off-diagonal elements of A, and there is no loss of generality in assuming that A is symmetric. Furthermore, if A is symmetric, then the form formula_433 | https://en.wikipedia.org/wiki?curid=21462 |
6,209 | For a set of i.i.d. normally distributed data points X of size "n" where each individual point "x" follows formula_436 with known variance σ, the conjugate prior distribution is also normally distributed. | https://en.wikipedia.org/wiki?curid=21462 |
6,210 | This can be shown more easily by rewriting the variance as the precision, i.e. using τ = 1/σ. Then if formula_437 and formula_438 we proceed as follows. | https://en.wikipedia.org/wiki?curid=21462 |
6,211 | First, the likelihood function is (using the formula above for the sum of differences from the mean): | https://en.wikipedia.org/wiki?curid=21462 |
6,212 | In the above derivation, we used the formula above for the sum of two quadratics and eliminated all constant factors not involving "μ". The result is the kernel of a normal distribution, with mean formula_441 and precision formula_442, i.e. | https://en.wikipedia.org/wiki?curid=21462 |
6,213 | This can be written as a set of Bayesian update equations for the posterior parameters in terms of the prior parameters: | https://en.wikipedia.org/wiki?curid=21462 |
6,214 | That is, to combine "n" data points with total precision of "nτ" (or equivalently, total variance of "n"/"σ") and mean of values formula_445, derive a new total precision simply by adding the total precision of the data to the prior total precision, and form a new mean through a "precision-weighted average", i.e. a weighted average of the data mean and the prior mean, each weighted by the associated total precision. This makes logical sense if the precision is thought of as indicating the certainty of the observations: In the distribution of the posterior mean, each of the input components is weighted by its certainty, and the certainty of this distribution is the sum of the individual certainties. (For the intuition of this, compare the expression "the whole is (or is not) greater than the sum of its parts". In addition, consider that the knowledge of the posterior comes from a combination of the knowledge of the prior and likelihood, so it makes sense that we are more certain of it than of either of its components.) | https://en.wikipedia.org/wiki?curid=21462 |
6,215 | The above formula reveals why it is more convenient to do Bayesian analysis of conjugate priors for the normal distribution in terms of the precision. The posterior precision is simply the sum of the prior and likelihood precisions, and the posterior mean is computed through a precision-weighted average, as described above. The same formulas can be written in terms of variance by reciprocating all the precisions, yielding the more ugly formulas | https://en.wikipedia.org/wiki?curid=21462 |
6,216 | For a set of i.i.d. normally distributed data points X of size "n" where each individual point "x" follows formula_436 with known mean μ, the conjugate prior of the variance has an inverse gamma distribution or a scaled inverse chi-squared distribution. The two are equivalent except for having different parameterizations. Although the inverse gamma is more commonly used, we use the scaled inverse chi-squared for the sake of convenience. The prior for σ is as follows: | https://en.wikipedia.org/wiki?curid=21462 |
6,217 | For a set of i.i.d. normally distributed data points X of size "n" where each individual point "x" follows formula_436 with unknown mean μ and unknown variance σ, a combined (multivariate) conjugate prior is placed over the mean and variance, consisting of a normal-inverse-gamma distribution. | https://en.wikipedia.org/wiki?curid=21462 |
6,218 | The respective numbers of pseudo-observations add the number of actual observations to them. The new mean hyperparameter is once again a weighted average, this time weighted by the relative numbers of observations. Finally, the update for formula_458 is similar to the case with known mean, but in this case the sum of squared deviations is taken with respect to the observed data mean rather than the true mean, and as a result a new "interaction term" needs to be added to take care of the additional error source stemming from the deviation between prior and data mean. | https://en.wikipedia.org/wiki?curid=21462 |
6,219 | &= \frac{(\sigma_0^2\nu_0/2)^{\nu_0/2}}{\Gamma(\nu_0/2)}~\frac{\exp\left[ \frac{-\nu_0 \sigma_0^2}{2 \sigma^2}\right]}{(\sigma^2)^{1+\nu_0/2}} \\ | https://en.wikipedia.org/wiki?curid=21462 |
6,220 | In other words, the posterior distribution has the form of a product of a normal distribution over "p"("μ" | "σ") times an inverse gamma distribution over "p"(σ), with parameters that are the same as the update equations above. | https://en.wikipedia.org/wiki?curid=21462 |
6,221 | The occurrence of normal distribution in practical problems can be loosely classified into four categories: | https://en.wikipedia.org/wiki?curid=21462 |
6,222 | Certain quantities in physics are distributed normally, as was first demonstrated by James Clerk Maxwell. Examples of such quantities are: | https://en.wikipedia.org/wiki?curid=21462 |
6,223 | "Approximately" normal distributions occur in many situations, as explained by the central limit theorem. When the outcome is produced by many small effects acting "additively and independently", its distribution will be close to normal. The normal approximation will not be valid if the effects act multiplicatively (instead of additively), or if there is a single external influence that has a considerably larger magnitude than the rest of the effects. | https://en.wikipedia.org/wiki?curid=21462 |
6,224 | There are statistical methods to empirically test that assumption; see the above Normality tests section. | https://en.wikipedia.org/wiki?curid=21462 |
6,225 | John Ioannidis argues that using normally distributed standard deviations as standards for validating research findings leave falsifiable predictions about phenomena that are not normally distributed untested. This includes, for example, phenomena that only appear when all necessary conditions are present and one cannot be a substitute for another in an addition-like way and phenomena that are not randomly distributed. Ioannidis argues that standard deviation-centered validation gives a false appearance of validity to hypotheses and theories where some but not all falsifiable predictions are normally distributed since the portion of falsifiable predictions that there is evidence against may and in some cases are in the non-normally distributed parts of the range of falsifiable predictions, as well as baselessly dismissing hypotheses for which none of the falsifiable predictions are normally distributed as if were they unfalsifiable when in fact they do make falsifiable predictions. It is argued by Ioannidis that many cases of mutually exclusive theories being accepted as "validated" by research journals are caused by failure of the journals to take in empirical falsifications of non-normally distributed predictions, and not because mutually exclusive theories are true, which they cannot be, although two mutually exclusive theories can both be wrong and a third one correct. | https://en.wikipedia.org/wiki?curid=21462 |
6,226 | In computer simulations, especially in applications of the Monte-Carlo method, it is often desirable to generate values that are normally distributed. The algorithms listed below all generate the standard normal deviates, since a can be generated as , where "Z" is standard normal. All these algorithms rely on the availability of a random number generator "U" capable of producing uniform random variates. | https://en.wikipedia.org/wiki?curid=21462 |
6,227 | The values Φ("x") may be approximated very accurately by a variety of methods, such as numerical integration, Taylor series, asymptotic series and continued fractions. Different approximations are used depending on the desired level of accuracy. | https://en.wikipedia.org/wiki?curid=21462 |
6,228 | Shore (1982) introduced simple approximations that may be incorporated in stochastic optimization models of engineering and operations research, like reliability engineering and inventory analysis. Denoting , the simplest approximation for the quantile function is: | https://en.wikipedia.org/wiki?curid=21462 |
6,229 | This approximation delivers for "z" a maximum absolute error of 0.026 (for , corresponding to ). For replace "p" by and change sign. Another approximation, somewhat less accurate, is the single-parameter approximation: | https://en.wikipedia.org/wiki?curid=21462 |
6,230 | The latter had served to derive a simple approximation for the loss integral of the normal distribution, defined by | https://en.wikipedia.org/wiki?curid=21462 |
6,231 | This approximation is particularly accurate for the right far-tail (maximum error of 10 for z≥1.4). Highly accurate approximations for the CDF, based on Response Modeling Methodology (RMM, Shore, 2011, 2012), are shown in Shore (2005). | https://en.wikipedia.org/wiki?curid=21462 |
6,232 | Some more approximations can be found at: Error function#Approximation with elementary functions. In particular, small "relative" error on the whole domain for the CDF formula_68 and the quantile function formula_474 as well, is achieved via an explicitly invertible formula by Sergei Winitzki in 2008. | https://en.wikipedia.org/wiki?curid=21462 |
6,233 | Some authors attribute the credit for the discovery of the normal distribution to de Moivre, who in 1738 published in the second edition of his ""The Doctrine of Chances"" the study of the coefficients in the binomial expansion of . De Moivre proved that the middle term in this expansion has the approximate magnitude of formula_475, and that "If "m" or "n" be a Quantity infinitely great, then the Logarithm of the Ratio, which a Term distant from the middle by the Interval "ℓ", has to the middle Term, is formula_476." Although this theorem can be interpreted as the first obscure expression for the normal probability law, Stigler points out that de Moivre himself did not interpret his results as anything more than the approximate rule for the binomial coefficients, and in particular de Moivre lacked the concept of the probability density function. | https://en.wikipedia.org/wiki?curid=21462 |
6,234 | In 1823 Gauss published his monograph ""Theoria combinationis observationum erroribus minimis obnoxiae"" where among other things he introduces several important statistical concepts, such as the method of least squares, the method of maximum likelihood, and the "normal distribution". Gauss used "M", , to denote the measurements of some unknown quantity "V", and sought the "most probable" estimator of that quantity: the one that maximizes the probability of obtaining the observed experimental results. In his notation φΔ is the probability density function of the measurement errors of magnitude Δ. Not knowing what the function "φ" is, Gauss requires that his method should reduce to the well-known answer: the arithmetic mean of the measured values. Starting from these principles, Gauss demonstrates that the only law that rationalizes the choice of arithmetic mean as an estimator of the location parameter, is the normal law of errors: | https://en.wikipedia.org/wiki?curid=21462 |
6,235 | where "h" is "the measure of the precision of the observations". Using this normal law as a generic model for errors in the experiments, Gauss formulates what is now known as the non-linear weighted least squares method. | https://en.wikipedia.org/wiki?curid=21462 |
6,236 | Although Gauss was the first to suggest the normal distribution law, Laplace made significant contributions. It was Laplace who first posed the problem of aggregating several observations in 1774, although his own solution led to the Laplacian distribution. It was Laplace who first calculated the value of the integral in 1782, providing the normalization constant for the normal distribution. Finally, it was Laplace who in 1810 proved and presented to the Academy the fundamental central limit theorem, which emphasized the theoretical importance of the normal distribution. | https://en.wikipedia.org/wiki?curid=21462 |
6,237 | It is of interest to note that in 1809 an Irish-American mathematician Robert Adrain published two insightful but flawed derivations of the normal probability law, simultaneously and independently from Gauss. His works remained largely unnoticed by the scientific community, until in 1871 they were exhumed by Abbe. | https://en.wikipedia.org/wiki?curid=21462 |
6,238 | In the middle of the 19th century Maxwell demonstrated that the normal distribution is not just a convenient mathematical tool, but may also occur in natural phenomena: "The number of particles whose velocity, resolved in a certain direction, lies between "x" and "x" + "dx" is | https://en.wikipedia.org/wiki?curid=21462 |
6,239 | Today, the concept is usually known in English as the normal distribution or Gaussian distribution. Other less common names include Gauss distribution, Laplace-Gauss distribution, the law of error, the law of facility of errors, Laplace's second law, Gaussian law. | https://en.wikipedia.org/wiki?curid=21462 |
6,240 | Gauss himself apparently coined the term with reference to the "normal equations" involved in its applications, with normal having its technical meaning of orthogonal rather than "usual". However, by the end of the 19th century some authors had started using the name "normal distribution", where the word "normal" was used as an adjective – the term now being seen as a reflection of the fact that this distribution was seen as typical, common – and thus "normal". Peirce (one of those authors) once defined "normal" thus: "...the 'normal' is not the average (or any other kind of mean) of what actually occurs, but of what "would", in the long run, occur under certain circumstances." Around the turn of the 20th century Pearson popularized the term "normal" as a designation for this distribution. | https://en.wikipedia.org/wiki?curid=21462 |
6,241 | Also, it was Pearson who first wrote the distribution in terms of the standard deviation "σ" as in modern notation. Soon after this, in year 1915, Fisher added the location parameter to the formula for normal distribution, expressing it in the way it is written nowadays: | https://en.wikipedia.org/wiki?curid=21462 |
6,242 | The term "standard normal", which denotes the normal distribution with zero mean and unit variance came into general use around the 1950s, appearing in the popular textbooks by P. G. Hoel (1947) ""Introduction to mathematical statistics"" and A. M. Mood (1950) ""Introduction to the theory of statistics"". | https://en.wikipedia.org/wiki?curid=21462 |
6,243 | Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the Roman Republic it became the dominant language in the Italian region and subsequently throughout the Roman Empire. Even after the fall of Western Rome, Latin remained the common language of international communication, science, scholarship and academia in Europe until well into the 18th century, when other regional vernaculars (including its own descendants, the Romance languages) supplanted it in common academic and political usage, and it eventually became a dead language in the modern linguistic definition. | https://en.wikipedia.org/wiki?curid=17730 |
6,244 | Latin is a highly inflected language, with three distinct genders (masculine, feminine, and neuter), six or seven noun cases (nominative, accusative, genitive, dative, ablative, and vocative), five declensions, four verb conjugations, six tenses (present, imperfect, future, perfect, pluperfect, and future perfect), three persons, three moods, two voices (passive and active), two or three aspects, and two numbers (singular and plural). The Latin alphabet is directly derived from the Etruscan and Greek alphabets. | https://en.wikipedia.org/wiki?curid=17730 |
6,245 | By the late Roman Republic (75 BC), Old Latin had been standardized into Classical Latin used by educated elites. Vulgar Latin was the colloquial form spoken at that time among lower-class commoners and attested in inscriptions and the works of comic playwrights Plautus and Terence and author Petronius. Late Latin is the written language from the 3rd century, and its various Vulgar Latin dialects developed in the 6th to 9th centuries into the modern Romance languages. Medieval Latin was used during the Middle Ages as a literary language from the 9th century to the Renaissance, which then used Renaissance Latin. Later, New Latin evolved during the early modern era to eventually become various forms of rarely spoken Contemporary Latin, one of which, Ecclesiastical Latin, remains the official language of the Holy See and the Roman Rite of the Catholic Church at Vatican City. | https://en.wikipedia.org/wiki?curid=17730 |
6,246 | Latin has also greatly influenced the English language and historically contributed many words to the English lexicon after the Christianization of Anglo-Saxons and the Norman conquest. In particular, Latin (and Ancient Greek) roots are still used in English descriptions of theology, science disciplines (especially anatomy and taxonomy), medicine, and law. | https://en.wikipedia.org/wiki?curid=17730 |
6,247 | A number of historical phases of the language have been recognized, each distinguished by subtle differences in vocabulary, usage, spelling, morphology, and syntax. There are no hard and fast rules of classification; different scholars emphasize different features. As a result, the list has variants, as well as alternative names. | https://en.wikipedia.org/wiki?curid=17730 |
6,248 | In addition to the historical phases, Ecclesiastical Latin refers to the styles used by the writers of the Roman Catholic Church from late antiquity onward, as well as by Protestant scholars. | https://en.wikipedia.org/wiki?curid=17730 |
6,249 | After the Western Roman Empire fell in 476 and Germanic kingdoms took its place, the Germanic people adopted Latin as a language more suitable for legal and other, more formal uses. | https://en.wikipedia.org/wiki?curid=17730 |
6,250 | The earliest known form of Latin is Old Latin, which was spoken from the Roman Kingdom to the later part of the Roman Republic period. It is attested both in inscriptions and in some of the earliest extant Latin literary works, such as the comedies of Plautus and Terence. The Latin alphabet was devised from the Etruscan alphabet. The writing later changed from what was initially either a right-to-left or a boustrophedon script to what ultimately became a strictly left-to-right script. | https://en.wikipedia.org/wiki?curid=17730 |
6,251 | During the late republic and into the first years of the empire, a new Classical Latin arose, a conscious creation of the orators, poets, historians and other literate men, who wrote the great works of classical literature, which were taught in grammar and rhetoric schools. Today's instructional grammars trace their roots to such schools, which served as a sort of informal language academy dedicated to maintaining and perpetuating educated speech. | https://en.wikipedia.org/wiki?curid=17730 |
6,252 | Philological analysis of Archaic Latin works, such as those of Plautus, which contain fragments of everyday speech, indicates that a spoken language, Vulgar Latin (termed , "the speech of the masses", by Cicero), existed concurrently with literate Classical Latin. The informal language was rarely written, so philologists have been left with only individual words and phrases cited by classical authors and those found as graffiti. | https://en.wikipedia.org/wiki?curid=17730 |
6,253 | As it was free to develop on its own, there is no reason to suppose that the speech was uniform either diachronically or geographically. On the contrary, Romanised European populations developed their own dialects of the language, which eventually led to the differentiation of Romance languages. | https://en.wikipedia.org/wiki?curid=17730 |
6,254 | The Romance languages descend from Vulgar Latin and were originally the popular and informal dialects spoken by various layers of the Latin-speaking population. These dialects were distinct from the classical form of the language spoken by the Roman upper classes, the form in which Romans generally wrote. | https://en.wikipedia.org/wiki?curid=17730 |
6,255 | The decline of the Roman Empire meant a deterioration in educational standards that brought about Late Latin, a postclassical stage of the language seen in Christian writings of the time. It was more in line with everyday speech, not only because of a decline in education but also because of a desire to spread the word to the masses. | https://en.wikipedia.org/wiki?curid=17730 |
6,256 | Currently, the five most widely spoken Romance languages by number of native speakers are Spanish, Portuguese, French, Italian and Romanian. Despite dialectal variation, which is found in any widespread language, the languages of Spain, France, Portugal, and Italy have retained a remarkable unity in phonological forms and developments, bolstered by the stabilising influence of their common Christian (Roman Catholic) culture. It was not until the Muslim conquest of Spain in 711, cutting off communications between the major Romance regions, that the languages began to diverge seriously. The Vulgar Latin dialect that would later become Romanian diverged somewhat more from the other varieties, as it was largely separated from the unifying influences in the western part of the Empire. | https://en.wikipedia.org/wiki?curid=17730 |
6,257 | One key marker of whether a given Romance feature was found in Vulgar Latin is to compare it with its parallel in Classical Latin. If it was not preferred in Classical Latin, then it most likely came from the undocumented contemporaneous Vulgar Latin. For example, the Romance for "horse" (Italian , French , Spanish , Portuguese and Romanian ) came from Latin . However, Classical Latin used . Therefore, was most likely the spoken form. | https://en.wikipedia.org/wiki?curid=17730 |
6,258 | Vulgar Latin began to diverge into distinct languages by the 9th century at the latest, when the earliest extant Romance writings begin to appear. They were, throughout the period, confined to everyday speech, as Medieval Latin was used for writing. | https://en.wikipedia.org/wiki?curid=17730 |
6,259 | Medieval Latin is the written Latin in use during that portion of the postclassical period when no corresponding Latin vernacular existed. The spoken language had developed into the various incipient Romance languages; however, in the educated and official world, Latin continued without its natural spoken base. Moreover, this Latin spread into lands that had never spoken Latin, such as the Germanic and Slavic nations. It became useful for international communication between the member states of the Holy Roman Empire and its allies. | https://en.wikipedia.org/wiki?curid=17730 |
6,260 | Without the institutions of the Roman Empire that had supported its uniformity, medieval Latin lost its linguistic cohesion: for example, in classical Latin and are used as auxiliary verbs in the perfect and pluperfect passive, which are compound tenses. Medieval Latin might use and instead. Furthermore, the meanings of many words have been changed and new vocabularies have been introduced from the vernacular. Identifiable individual styles of classically incorrect Latin prevail. | https://en.wikipedia.org/wiki?curid=17730 |
6,261 | The Renaissance briefly reinforced the position of Latin as a spoken language by its adoption by the Renaissance Humanists. Often led by members of the clergy, they were shocked by the accelerated dismantling of the vestiges of the classical world and the rapid loss of its literature. They strove to preserve what they could and restore Latin to what it had been and introduced the practice of producing revised editions of the literary works that remained by comparing surviving manuscripts. By no later than the 15th century they had replaced Medieval Latin with versions supported by the scholars of the rising universities, who attempted, by scholarship, to discover what the classical language had been. | https://en.wikipedia.org/wiki?curid=17730 |
6,262 | During the Early Modern Age, Latin still was the most important language of culture in Europe. Therefore, until the end of the 17th century, the majority of books and almost all diplomatic documents were written in Latin. Afterwards, most diplomatic documents were written in French (a Romance language) and later native or other languages. | https://en.wikipedia.org/wiki?curid=17730 |
6,263 | Despite having no native speakers, Latin is still used for a variety of purposes in the contemporary world. | https://en.wikipedia.org/wiki?curid=17730 |
6,264 | The largest organisation that retains Latin in official and quasi-official contexts is the Catholic Church. The Catholic Church required that Mass be carried out in Latin until the Second Vatican Council of 1962–1965, which permitted the use of the vernacular. Latin remains the language of the Roman Rite. The Tridentine Mass (also known as the Extraordinary Form or Traditional Latin Mass) is celebrated in Latin. Although the Mass of Paul VI (also known as the Ordinary Form or the Novus Ordo) is usually celebrated in the local vernacular language, it can be and often is said in Latin, in part or in whole, especially at multilingual gatherings. It is the official language of the Holy See, the primary language of its public journal, the , and the working language of the Roman Rota. Vatican City is also home to the world's only automatic teller machine that gives instructions in Latin. In the pontifical universities postgraduate courses of Canon law are taught in Latin, and papers are written in the same language. | https://en.wikipedia.org/wiki?curid=17730 |
6,265 | In the Anglican Church, after the publication of the "Book of Common Prayer" of 1559, a Latin edition was published in 1560 for use in universities such as Oxford and the leading "public schools" (English private academies), where the liturgy was still permitted to be conducted in Latin. There have been several Latin translations since, including a Latin edition of the 1979 USA Anglican Book of Common Prayer. | https://en.wikipedia.org/wiki?curid=17730 |
6,266 | In the Philippines and in the Western world, many organizations, governments and schools use Latin for their mottos due to its association with formality, tradition, and the roots of Western culture. | https://en.wikipedia.org/wiki?curid=17730 |
6,267 | Canada's motto ("from sea to sea") and most provincial mottos are also in Latin. The Canadian Victoria Cross is modelled after the British Victoria Cross which has the inscription "For Valour". Because Canada is officially bilingual, the Canadian medal has replaced the English inscription with the Latin . | https://en.wikipedia.org/wiki?curid=17730 |
6,268 | Spain's motto "Plus ultra", meaning "even further", or figuratively "Further!", is also Latin in origin. It is taken from the personal motto of Charles V, Holy Roman Emperor and King of Spain (as Charles I), and is a reversal of the original phrase ("No land further beyond", "No further!"). According to legend, this phrase was inscribed as a warning on the Pillars of Hercules, the rocks on both sides of the Strait of Gibraltar and the western end of the known, Mediterranean world. Charles adopted the motto following the discovery of the New World by Columbus, and it also has metaphorical suggestions of taking risks and striving for excellence. | https://en.wikipedia.org/wiki?curid=17730 |
6,269 | In the United States the unofficial national motto until 1956 was "E pluribus unum" meaning "Out of many, one". The motto continues to be featured on the Great Seal, it also appears on the flags and seals of both houses of congress and the flags of the states of Michigan, North Dakota, New York, and Wisconsin. The mottos 13 letters symbolically represent the original Thirteen Colonies which revolted from the British Crown. The motto is featured on all presently minted coinage and has been featured in most coinage throughout the nation's history. | https://en.wikipedia.org/wiki?curid=17730 |
6,270 | Some colleges and universities have adopted Latin mottos, for example Harvard University's motto is ("truth"). Veritas was the goddess of truth, a daughter of Saturn, and the mother of Virtue. | https://en.wikipedia.org/wiki?curid=17730 |
6,271 | Switzerland has adopted the country's Latin short name on coins and stamps, since there is no room to use all of the nation's four official languages. For a similar reason, it adopted the international vehicle and internet code "CH", which stands for , the country's full Latin name. | https://en.wikipedia.org/wiki?curid=17730 |
6,272 | Some films of ancient settings, such as "Sebastiane" and "The Passion of the Christ", have been made with dialogue in Latin for the sake of realism. Occasionally, Latin dialogue is used because of its association with religion or philosophy, in such film/television series as "The Exorcist" and "Lost" ("Jughead"). Subtitles are usually shown for the benefit of those who do not understand Latin. There are also songs written with Latin lyrics. The libretto for the opera-oratorio by Igor Stravinsky is in Latin. | https://en.wikipedia.org/wiki?curid=17730 |
6,273 | The continued instruction of Latin is often seen as a highly valuable component of a liberal arts education. Latin is taught at many high schools, especially in Europe and the Americas. It is most common in British public schools and grammar schools, the Italian and , the German and the Dutch . | https://en.wikipedia.org/wiki?curid=17730 |
6,274 | A variety of organisations, as well as informal Latin 'circuli' ('circles'), have been founded in more recent times to support the use of spoken Latin. Moreover, a number of university classics departments have begun incorporating communicative pedagogies in their Latin courses. These include the University of Kentucky, the University of Oxford and also Princeton University. | https://en.wikipedia.org/wiki?curid=17730 |
6,275 | There are many websites and forums maintained in Latin by enthusiasts. The Latin Wikipedia has more than 130,000 articles. | https://en.wikipedia.org/wiki?curid=17730 |
6,276 | Urdaneta City's motto ("It is enough for the people to serve God") the Latin motto can be read in the old seal of this Philippine city. | https://en.wikipedia.org/wiki?curid=17730 |
6,277 | Italian, French, Portuguese, Spanish, Romanian, Catalan, Romansh and other Romance languages are direct descendants of Latin. There are also many Latin borrowings in English and Albanian, as well as a few in German, Dutch, Norwegian, Danish and Swedish. Latin is still spoken in Vatican City, a city-state situated in Rome that is the seat of the Catholic Church. | https://en.wikipedia.org/wiki?curid=17730 |
6,278 | Some inscriptions have been published in an internationally agreed, monumental, multivolume series, the (CIL). Authors and publishers vary, but the format is about the same: volumes detailing inscriptions with a critical apparatus stating the provenance and relevant information. The reading and interpretation of these inscriptions is the subject matter of the field of epigraphy. About 270,000 inscriptions are known. | https://en.wikipedia.org/wiki?curid=17730 |
6,279 | The works of several hundred ancient authors who wrote in Latin have survived in whole or in part, in substantial works or in fragments to be analyzed in philology. They are in part the subject matter of the field of classics. Their works were published in manuscript form before the invention of printing and are now published in carefully annotated printed editions, such as the Loeb Classical Library, published by Harvard University Press, or the Oxford Classical Texts, published by Oxford University Press. | https://en.wikipedia.org/wiki?curid=17730 |
6,280 | Latin translations of modern literature such as: "The Hobbit", "Treasure Island", "Robinson Crusoe", "Paddington Bear", "Winnie the Pooh", "The Adventures of Tintin", "Asterix", "Harry Potter", , "Max and Moritz", "How the Grinch Stole Christmas!", "The Cat in the Hat", and a book of fairy tales, "", are intended to garner popular interest in the language. Additional resources include phrasebooks and resources for rendering everyday phrases and concepts into Latin, such as Meissner's Latin Phrasebook. | https://en.wikipedia.org/wiki?curid=17730 |
6,281 | The Latin influence in English has been significant at all stages of its insular development. In the Middle Ages, borrowing from Latin occurred from ecclesiastical usage established by Saint Augustine of Canterbury in the 6th century or indirectly after the Norman Conquest, through the Anglo-Norman language. From the 16th to the 18th centuries, English writers cobbled together huge numbers of new words from Latin and Greek words, dubbed "inkhorn terms", as if they had spilled from a pot of ink. Many of these words were used once by the author and then forgotten, but some useful ones survived, such as 'imbibe' and 'extrapolate'. Many of the most common polysyllabic English words are of Latin origin through the medium of Old French. Romance words make respectively 59%, 20% and 14% of English, German and Dutch vocabularies. Those figures can rise dramatically when only non-compound and non-derived words are included. | https://en.wikipedia.org/wiki?curid=17730 |
6,282 | The influence of Roman governance and Roman technology on the less-developed nations under Roman dominion led to the adoption of Latin phraseology in some specialized areas, such as science, technology, medicine, and law. For example, the Linnaean system of plant and animal classification was heavily influenced by "Historia Naturalis", an encyclopedia of people, places, plants, animals, and things published by Pliny the Elder. Roman medicine, recorded in the works of such physicians as Galen, established that today's medical terminology would be primarily derived from Latin and Greek words, the Greek being filtered through the Latin. Roman engineering had the same effect on scientific terminology as a whole. Latin law principles have survived partly in a long list of Latin legal terms. | https://en.wikipedia.org/wiki?curid=17730 |
6,283 | A few international auxiliary languages have been heavily influenced by Latin. Interlingua is sometimes considered a simplified, modern version of the language. Latino sine Flexione, popular in the early 20th century, is Latin with its inflections stripped away, among other grammatical changes. | https://en.wikipedia.org/wiki?curid=17730 |
6,284 | Throughout European history, an education in the classics was considered crucial for those who wished to join literate circles. This also was true in the United States where many of the nation's Founders obtained a classically-based education in grammar schools or from tutors. Admission to Harvard in the Colonial era required that the applicant "Can readily make and speak or write true Latin prose and has skill in making verse . . ." Latin Study and the classics were emphasized in American secondary schools and colleges well into the Antebellum era. | https://en.wikipedia.org/wiki?curid=17730 |
6,285 | Instruction in Latin is an essential aspect. In today's world, a large number of Latin students in the US learn from "Wheelock's Latin: The Classic Introductory Latin Course, Based on Ancient Authors". This book, first published in 1956, was written by Frederic M. Wheelock, who received a PhD from Harvard University. "Wheelock's Latin" has become the standard text for many American introductory Latin courses. | https://en.wikipedia.org/wiki?curid=17730 |
6,286 | The Living Latin movement attempts to teach Latin in the same way that living languages are taught, as a means of both spoken and written communication. It is available in Vatican City and at some institutions in the US, such as the University of Kentucky and Iowa State University. The British Cambridge University Press is a major supplier of Latin textbooks for all levels, such as the Cambridge Latin Course series. It has also published a subseries of children's texts in Latin by Bell & Forte, which recounts the adventures of a mouse called Minimus. | https://en.wikipedia.org/wiki?curid=17730 |
6,287 | In the United Kingdom, the Classical Association encourages the study of antiquity through various means, such as publications and grants. The University of Cambridge, the Open University, a number of prestigious independent schools, for example Eton, Harrow, Haberdashers' Aske's Boys' School, Merchant Taylors' School, and Rugby, and The Latin Programme/Via Facilis, a London-based charity, run Latin courses. In the United States and in Canada, the American Classical League supports every effort to further the study of classics. Its subsidiaries include the National Junior Classical League (with more than 50,000 members), which encourages high school students to pursue the study of Latin, and the National Senior Classical League, which encourages students to continue their study of the classics into college. The league also sponsors the National Latin Exam. Classicist Mary Beard wrote in "The Times Literary Supplement" in 2006 that the reason for learning Latin is because of what was written in it. | https://en.wikipedia.org/wiki?curid=17730 |
6,288 | The ancient pronunciation of Latin has been reconstructed; among the data used for reconstruction are explicit statements about pronunciation by ancient authors, misspellings, puns, ancient etymologies, the spelling of Latin loanwords in other languages, and the historical development of Romance languages. | https://en.wikipedia.org/wiki?curid=17730 |
6,289 | In Old and Classical Latin, the Latin alphabet had no distinction between uppercase and lowercase, and the letters did not exist. In place of , were used, respectively; represented both vowels and consonants. Most of the letterforms were similar to modern uppercase, as can be seen in the inscription from the Colosseum shown at the top of the article. | https://en.wikipedia.org/wiki?curid=17730 |
6,290 | The spelling systems used in Latin dictionaries and modern editions of Latin texts, however, normally use in place of Classical-era . Some systems use for the consonant sounds except in the combinations for which is never used. | https://en.wikipedia.org/wiki?curid=17730 |
6,291 | In Classical Latin, as in modern Italian, double consonant letters were pronounced as long consonant sounds distinct from short versions of the same consonants. Thus the "nn" in Classical Latin "year" (and in Italian ) is pronounced as a doubled as in English "unnamed". (In English, distinctive consonant length or doubling occurs only at the boundary between two words or morphemes, as in that example.) | https://en.wikipedia.org/wiki?curid=17730 |
6,292 | In Classical Latin, did not exist as a letter distinct from V; the written form was used to represent both a vowel and a consonant. was adopted to represent upsilon in loanwords from Greek, but it was pronounced like and by some speakers. It was also used in native Latin words by confusion with Greek words of similar meaning, such as and . | https://en.wikipedia.org/wiki?curid=17730 |
6,293 | Classical Latin distinguished between long and short vowels. Then, long vowels, except for , were frequently marked using the apex, which was sometimes similar to an acute accent . Long was written using a taller version of , called "long I": . In modern texts, long vowels are often indicated by a macron , and short vowels are usually unmarked except when it is necessary to distinguish between words, when they are marked with a breve . However, they would also signify a long vowel by writing the vowel larger than other letters in a word or by repeating the vowel twice in a row. The acute accent, when it is used in modern Latin texts, indicates stress, as in Spanish, rather than length. | https://en.wikipedia.org/wiki?curid=17730 |
6,294 | Long vowels in Classical Latin are, technically, pronounced as entirely different from short vowels. The difference is described in the table below: | https://en.wikipedia.org/wiki?curid=17730 |
6,295 | This difference in quality is posited by W. Sidney Allen in his book "Vox Latina". However, Andrea Calabrese has disputed that short vowels differed in quality from long vowels during the classical period, based in part upon the observation that in Sardinian and some Lucanian dialects, each long and short vowel pair was merged. This is distinguished from the typical Italo-Western romance vowel system in which short /i/ and /u/ merge with long /eː/ and /oː/. Thus, Latin 'siccus' becomes 'secco' in Italian and 'siccu' in Sardinian. | https://en.wikipedia.org/wiki?curid=17730 |
6,296 | A vowel letter followed by at the end of a word, or a vowel letter followed by before or , represented a short nasal vowel, as in . | https://en.wikipedia.org/wiki?curid=17730 |
6,297 | Classical Latin had several diphthongs. The two most common were . was fairly rare, and were very rare, at least in native Latin words. There has also been debate over whether is truly a diphthong in Classical Latin, due to its rarity, absence in works of Roman grammarians, and the roots of Classical Latin words (i.e. to , to , etc.) not matching or being similar to the pronunciation of classical words if were to be considered a diphthong. | https://en.wikipedia.org/wiki?curid=17730 |
6,298 | The sequences sometimes did not represent diphthongs. and also represented a sequence of two vowels in different syllables in "of bronze" and "began", and represented sequences of two vowels or of a vowel and one of the semivowels , in "beware!", "whose", "I warned", "I released", "I destroyed", "his", and "new". | https://en.wikipedia.org/wiki?curid=17730 |
6,299 | Old Latin had more diphthongs, but most of them changed into long vowels in Classical Latin. The Old Latin diphthong and the sequence became Classical . Old Latin and changed to Classical , except in a few words whose became Classical . These two developments sometimes occurred in different words from the same root: for instance, Classical "punishment" and "to punish". Early Old Latin usually changed to Classical . | https://en.wikipedia.org/wiki?curid=17730 |
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