Perfections of models-

The term is used to designate a range of diverse, if often kindred, concepts. These have historically been addressed in a number of discrete disciplines , notably mathematics , physics , chemistry , ethics , aesthetics , ontology , and theology. The form of the word long fluctuated in various languages. The English language had the alternates, "perfection" and the Biblical "perfectness. These expressions in turn come from " perficio " — "to finish", "to bring to an end.

Perfections of models

Perfections of models

Perfections of models

Perfections of models

Taylor lee porn 18th century was the last for which perfection was a principal concept in aesthetics. In the eclectic view of the late Renaissance, Perfections of models in a work would require uniting the talents of many artists. Matthew enjoins: "Be ye therefore perfect, even as your Father which is in heaven is perfect. And if not perfection, then improvement. Others have nurtured kf goals: pluralism, novelty, powerful sensations, faithfulness to truth, self-expression and expression of the world, creativity and originality — all of which may roughly be summarized as "expression. Some artists, schools and epochs have aimed for perfection. New 5,3 degree joiners Pefrections for Pike Perfection and Dynamic!

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The term is used to designate a range of diverse, if often kindred, concepts. These have historically been addressed in a number of discrete disciplines , notably mathematics , physics , chemistry , ethics , aesthetics , ontology , and theology. The form of the word long fluctuated in various languages. The English language had the alternates, "perfection" and the Biblical "perfectness. These expressions in turn come from " perficio " — "to finish", "to bring to an end.

The genealogy of the concept of "perfection" reaches back beyond Latin, to Greek. The Greek equivalent of the Latin " perfectus " was " teleos. Hence the Greek " teleiotes " was not yet so fraught with abstract and superlative associations as would be the Latin " perfectio " or the modern "perfection.

The oldest definition of "perfection", fairly precise and distinguishing the shades of the concept, goes back to Aristotle. In Book Delta of the Metaphysics , he distinguishes three meanings of the term, or rather three shades of one meaning, but in any case three different concepts. That is perfect:. The first of these concepts is fairly well subsumed within the second. Between those two and the third, however, there arises a duality in concept.

This duality was expressed by Thomas Aquinas , in the Summa Theologica , when he distinguished a twofold perfection: when a thing is perfect in itself — as he put it, in its substance ; and when it perfectly serves its purpose. The variants on the concept of perfection would have been quite of a piece for two thousand years, had they not been confused with other, kindred concepts.

The chief of these was the concept of that which is the best: in Latin, " excellentia " "excellence". In antiquity , " excellentia " and " perfectio " made a pair; thus, for example, dignitaries were called " perfectissime ", just as they are now called "excellency. Gottfried Wilhelm Leibniz , who thought much about perfection and held the world to be the best of possible worlds , did not claim that it was perfect.

The parallel existence of two concepts of perfection, one strict "perfection," as such and the other loose "excellence" , has given rise, perhaps since antiquity but certainly since the Renaissance , to a singular paradox : that the greatest perfection is imperfection.

This was formulated by Lucilio Vanini — , who had a precursor in the 16th-century writer Joseph Juste Scaliger , and they in turn referred to the ancient philosopher Empedocles.

Their argument, as given by the first two, was that if the world were perfect, it could not improve and so would lack "true perfection," which depends on progress. To Aristotle , "perfect" meant "complete" "nothing to add or subtract". To Empedocles, according to Vanini, perfection depends on incompleteness " perfectio propter imperfectionem " , since the latter possesses a potential for development and for complementing with new characteristics " perfectio complementii ".

This view relates to the baroque esthetic of Vanini and Marin Mersenne : the perfection of an art work consists in its forcing the recipient to be active—to complement the art work by an effort of mind and imagination. The paradox of perfection—that imperfection is perfect—applies not only to human affairs, but to technology. Thus, irregularity in semiconductor crystals an imperfection, in the form of contaminants is requisite for the production of semiconductors.

The solution to the apparent paradox lies in a distinction between two concepts of "perfection": that of regularity, and that of utility. Imperfection is perfect in technology, in the sense that irregularity is useful. Perfect numbers have been distinguished ever since the ancient Greeks called them " teleioi.

A view that was shared by Plato held that 10 was a perfect number. The number 10 was thought perfect because there are 10 fingers to the two hands. The number 6 was believed perfect for being divisible in a special way: a sixth part of that number constitutes unity; a third is two; a half — three; two-thirds Greek : dimoiron is four; five-sixths pentamoiron is five; six is the perfect whole. The ancients also considered 6 a perfect number because the human foot constituted one-sixth the height of a man, hence the number 6 determined the height of the human body.

Thus both numbers, 6 and 10, were credited with perfection, both on purely mathematical grounds and on grounds of their relevance in nature. The perfection of the number 3 actually became proverbial : " omne trinum perfectum " Latin : all threes are perfect. Another number, 7, found a devotee in the 6th-century Pope Gregory I Gregory the Great , who favored it on grounds similar to those of the Greek mathematicians who had seen 6 as a perfect number, and in addition for some reason he associated the number 7 with the concept of " eternity.

The Middle Ages , however, championed the perfection of 6: Augustine and Alcuin wrote that God had created the world in 6 days because that was the perfect number. The Greek mathematicians had regarded as perfect that number which equals the sum of its divisors that are smaller than itself. It became customary to call such numbers "perfect. Euclid had listed the first four perfect numbers: 6; 28; ; and A manuscript of gave the fifth perfect number: 33,, Gradually mathematicians found further perfect numbers which are very rare.

Despite over 2, years of study, it still is not known whether there exist infinitely many perfect numbers; or whether there are any odd ones. Today the term "perfect number" is merely historic in nature, used for the sake of tradition. These peculiar numbers had received the name on account of their analogy to the construction of man, who was held to be nature 's most perfect creation, and above all on account of their own peculiar regularity.

Thus, they had been so named on the same grounds as perfect objects in nature, and perfectly proportioned edifices and statues created by man; the numbers had come to be called "perfect" in order to emphasize their special regularity. The Greek mathematicians had named these numbers "perfect" in the same sense in which philosophers and artists used the word. Jamblich In Nicomachi arithmeticam , Leipzig, states that the Pythagoreans had called the number 6 "marriage," "health," and "beauty," on account of the harmony and accord of that number.

The perfect numbers early on came to be treated as the measure of other numbers: those in which the sum of the divisors is greater than the number itself, as in 12, have — since as early as Theon of Smyrna , ca. As of 7 December , 51 perfect numbers had been identified. A variety of physical and chemical concepts include, in their names, the word "perfect.

The physicist designates as a perfectly rigid body, one that "is not deformed by forces applied to it. The concept is an ideal construct. A perfectly plastic body is one that is deformed infinitely at a constant load corresponding to the body's limit of plasticity: this is a physical model , not a body observed in nature. A perfectly black body would be one that absorbed completely, radiation falling upon it — that is, a body with a coefficient of absorption equal to unity.

A crystal is perfect when its physically equivalent walls are equally developed; it has a perfect structure when it answers the requirements of spatial symmetry and is free of structural defects, dislocation, lacunae and other flaws. A perfect fluid is one that is incompressible and non-viscous — this, again, is an ideal fluid that does not exist in nature.

A perfect gas is one whose molecules do not interact with each other and which have no volume of their own. Such a gas is fictitious , just as are perfectly solid, perfectly rigid, perfectly plastic and perfectly black bodies.

They are termed "perfect" in the strict non-metaphorical sense of the word. These are all concepts that are necessary in physics, insofar as they are limiting, ideal, fictitious — insofar as they set the extreme which nature may at the most approach. In a looser sense, real things are called "perfect" if they approximate perfection more or less closely, though they be not, strictly speaking, perfect.

The relation of these perfect bodies to real bodies may be illustrated by the relation of a perfect gas to a real one. The equation of state of a perfect gas is a first approximation to a quantum equation of state that results from statistical physics. Thus, the equation of state of a real gas within classical limits assumes the form of the equation of state of a perfect gas. That is, the equation of state of a perfect gas describes an ideal gas comprising points, that is, dimensionless molecules that do not act upon one another.

The perfect gas equation arose from the work of Robert Boyle , Edme Mariotte and Joseph Louis Gay-Lussac , who, in studying the properties of real gases , found formulas applicable not to these but to an ideal, perfect gas.

The ethical question of perfection concerns not whether man is perfect, but whether he should be. And if he should be, then how is this to be attained? Plato seldom actually used the term, "perfection"; but the concept of " good ", central to his philosophy, was tantamount to "perfection.

Soon after, the Stoics introduced the concept of perfection into ethics expressly, describing it as harmony — with nature , reason , man himself. They held that such harmony—such perfection—was attainable for anyone. Plato and the Stoics had made perfection a philosophical watchword.

Soon it would be transformed, in Christianity , into a religious one. The Christian doctrine of perfection is in the Gospels as well as elsewhere in the Bible. Matthew enjoins: "Be ye therefore perfect, even as your Father which is in heaven is perfect. Many of these are collected in a discourse by St. Augustine , De perfectione iustitiae hominis. Elsewhere synonyms for "perfection" are "undefiled", "without rebuke", "without blemish", "blameless", "holy", "righteous", "unblamable", "unreprovable.

Augustine explains that not only that man is properly termed perfect and without blemish who is already perfect, but also he who strives unreservedly after perfection. This is a broader concept, of approximate perfection, resembling that used in the exact sciences.

The first ancient and Christian perfection was not very remote from modern self-perfection. Ambrose in fact wrote about degrees of perfection " gradus piae perfectionis ". Along with the idea of perfection, Holy Scripture conveyed doubt as to whether perfection was attainable for man. According to 1 John , "If we say that we have no sin, we deceive ourselves, and the truth is not in us.

And St. Jerome wrote: " Perfectio vera in coelestibus " — true perfection is to be found only in heaven. As early as the 5th century CE, two distinct views on perfection had arisen within the Church: that it was attainable by man on earth by his own powers; and, that it may come to pass only by special divine grace.

The first view, which was championed by Pelagius , was condemned in CE; the second view, which was championed by St. Augustine, prevailed at the very beginning of the 5th century and became authoritative. Still, the Church did not condemn the writings of the Pseudo-Areopagite , purportedly the first bishop of Athens , voicing a natural possibility for man to rise to perfection, to the contemplation of God.

And so, for centuries, two views contended within the Church. Even as, for the ancient philosophers, the essence of perfection had been harmony , so for the Gospel and the Christian theologians it was charity , or love.

Paul wrote Epistle to the Colossians , : "And above all these things put on charity, which is the bond of perfectness. Gregory wrote that perfection will be realized only after the fulfillment of history — only "then will the world be beautiful and perfect. Discourses in moral theology and asceticism were generous with advice on how this was to be done. The medieval concept of perfection and self-perfection, especially in its mature form, can be natural for modern man.

As formulated by Peter Lombard , this concept implies that perfection is a result of development. And as described by Giles of Rome , perfection has not only personal sources " personalia " but social ones " secundum statum ".

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Perfections of models

Perfections of models

Perfections of models. Helpful Questions for Assessing Perfectionism

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Perfections of models

Perfections of models