Although the description sitting-on ( graph 1 ) is more abstract than the graphic image of a cat sitting on a mat ( picture 1 ), the delineation of abstract things from concrete things is somewhat ambiguous ; this ambiguity or vagueness is characteristic of abstraction.

Although Cantor himself defined the set in a general, abstract way, the most common modern construction is the Cantor ternary set, built by removing the middle thirds of a line segment.

Although many scholars today consider the Treatise to be Hume's most important work and one of the most important books in Western philosophy, the critics in Great Britain at the time did not agree, describing it as " abstract and unintelligible ".

As a result of this method, care must be taken in the interpretation of Ferguson's three factors, as factor analysis will output an abstract ' factor ' whether an objectively real factor exists or not .< reF > SAS ( R ) 3. 11 Users Guide, Multivariate Analysis: Factor Analysis Although replication of the Nationalism factor was inconsistent, the finding of Religionism and Humanitarianism had a number of replications by Ferguson and others.

Although he reserved a distaste for abstract and dogmatic religions founded around personality cults, he was attracted to the type of people he met at the Golden Dawn.

Although these examples offer alternate strategies for achieving the same abstraction, they do not fundamentally alter the need to support abstract nouns in code-all programming relies on an ability to abstract verbs as functions, nouns as data structures, and either as processes.

Although the term " abstract expressionism " was first applied to American art in 1946 by the art critic Robert Coates, it had been first used in Germany in 1919 in the magazine Der Sturm, regarding German Expressionism.

Although it is true that spontaneity or the impression of spontaneity characterized many of the abstract expressionists works, most of these paintings involved careful planning, especially since their large size demanded it.

Although the abstract expressionist school spread quickly throughout the United States, the major centers of this style were New York City and the San Francisco Bay area of California.

Although Hinduism is commonly represented by such anthropomorphic religious icons such as murtis, aniconism is equally represented with such abstract symbols of God such as the Shiva linga and the saligrama.

Although Gurdjieff presents these abstract ideas as preparatory material for an exercise, the exercise itself does not appear in the text, which ends in an ellipsis during an explanation of the peculiarities of air's role in Earth's planetary composition.

Although this seems to contradict our earlier definition, we have to consider that in the abstract world our input can be arbitrarily large.

Although Newman's paintings appear to be purely abstract, and many of them were originally untitled, the names he later gave them hinted at specific subjects being addressed, often with a Jewish theme.

Although computers can play some abstract strategy games better than any human, the best Havannah-playing software to date plays quite weakly compared to human experts.

Although such results are always likely to be controversial, and working intensively with a single animal always incurs the risk of Clever Hans effects, Pepperberg's work has strengthened the argument that humans do not hold the monopoly on the complex or semicomplex use of abstract communication.

Although the algebra exists as a purely abstract construction, it can be most easily visualised in terms of operations on the edges and vertices of a dodecahedron.

Although short-lived, Rayonism was a crucial step in the development of Russian abstract art.

Although these later works have been sometimes called " philosophy ", it has been argued that there is no abstract or theoretical context to justify such a description.

Although a real pair of compasses is used to draft visible illustrations, the ideal compass used in proofs is an abstract creator of perfect circles.

Although this term historically was derived from the notion of a ring ideal of abstract algebra, it has subsequently been generalized to a different notion.

Although Wright occasionally designed art glass using stylized forms from nature, the designs of the Robie House art glass are simply abstract geometric forms.

Although one-sided flux distributions may seem somewhat abstract, they have a surprising number of applications ranging from the refrigerator magnet through industrial applications such as the brushless AC motor and magnetic coupling, to high-tech applications such as wiggler magnets used in particle accelerators and free electron lasers.

Although Hinduism is commonly represented by such anthropomorphic religious murtis, aniconism is equally represented with such abstract symbols of God such as the Shiva linga and the saligrama.

Although the United States and the U.S.S.R. have been arguing whether there shall be four, five or six top assistants, the most important element in the situation is not the number of deputies but the manner in which these deputies are to do their work.

Although players usually use their sticks to move the ball around, they may use any part of their bodies other than their heads, hands or arms and may use their skates in a limited manner.

Although he must have been familiar with the ancient name, Balcia, meaning a supposed island in the Baltic Sea, and although he may have been aware of the Baltic words containing the stem balt -, " white ", as " swamp ", he reports that he followed the local use of balticus from baelt (" belt ") because the sea stretches to the east " in modum baltei " (" in the manner of a belt ").

Although high-end computers may be bought retail in the same manner as the common computer, they are frequently built by their owners.

Although Confucianism is often followed in a religious manner by the Chinese, arguments continue over whether it is a religion.

Although there is agreement on the time and general manner of his death, it is not clear where this happened.

Although these letters are not formally published in the Doctrine and Covenants, they are still deemed to be inspired, and are dealt with in the same manner that revelations are ( that is, they must be deliberated and approved by the voting members of a World Conference ).

Although such material could be worked at low temperatures to produce the striated Damascene pattern of intermixed ferrite and cementite bands in a manner identical to pattern-welded Damascus steel, any heat treatment sufficient to dissolve the carbides would permanently destroy the pattern.

Although many of the descriptions in this book were written in an exaggerated manner or were plainly inventive fiction or 3rd-source misinterpretation, his notes are widely accepted as a useful guide to the cultural aspects and lifestyle of 17th-century Ottoman Empire.

Although he filmed no footage, he made crucial changes to the look of Dorothy by eliminating Judy Garland's blonde wig and adjusting her makeup and costume, encouraging her to act in a more natural manner that greatly contributed to the success of the final film.

Although it says and or by the law of the land, this in no manner can be interpreted as if it were enough to have a positive law, made by the king, to be able to proceed legally against a citizen.

Although small disorganised cells of Central Leadership of Home Resistance ( Ústřední vedení odboje domácího, ÚVOD ) survived, only the communist resistance was able to function in a coordinated manner ( although it also suffered arrests ).

Although not as ideal as " pit stoves ", these allow woks to be used in a manner more suitable for their design and are good enough for most tasks required in home cooking.

Although the concept of information society has been under discussion since the 1930s, in the modern world it is almost always applied to the manner in which information technologies have impacted society and culture.

Although Edward was not a diligent student — his true talents were those of charm, sociability and tact — Benjamin Disraeli described him as informed, intelligent, and of sweet manner.

Although the Union troops put up a furious defense, Pope's army was forced to retreat in a manner similar to the embarrassing Union defeat at First Bull Run, fought on roughly the same battleground.

Although he was voted America ’ s favorite comedian in a 1974 poll and highly sought out for every manner of TV game and variety show, it was the failure of his two series that reportedly exacerbated Lynde ’ s drinking problem, leading to numerous run-ins with the law and frequent arrests for public intoxication.

In the newer continuity, Superman also became aware of his alien heritage only sometime after his debut as a superhero-initially assuming himself to be a human mutated in some manner and launched as part of an Earth space program -, when a holographic program encoded into the craft which brought him to Earth uploaded the information into his brain ( Although Lex Luthor had earlier discovered his alien heritage when his attempts to create a clone of Superman were complicated by the unexpected x-factor of Superman's alien DNA ).

Although all airplanes fly through ground effect at some point, craft that do so in a dedicated manner are designed in such a way that their wings are normally unable to take them into flight out of ground effect ( free flight ).

Although Joyce died shortly after the publication of Finnegans Wake, during the work's composition the author made a number of statements concerning his intentions in writing in such an original manner.

Although this method of measurement is not new, either in theory or in practice, the unique manner in which the techniques were implemented in the MISTRAM system permit measurement of vehicle flight parameters with a degree of precision and accuracy not previously obtainable in other long baseline trajectory measurement systems.

Although some modern commentators claim that Montanus was rejected because he claimed to be a prophet, a careful examination of history shows that the gift of prophecy was still acknowledged during the time of Montanus, and that he was controversial because of the manner in which he prophesied and the doctrines he propagated.

Although the medals of each class were identical, the manner in which each was worn differed.

Although Imagism isolates objects through the use of what Ezra Pound called " luminous details ", Pound's Ideogrammic Method of juxtaposing concrete instances to express an abstraction is similar to Cubism's manner of synthesizing multiple perspectives into a single image.

Although several residents later fell by enemy action, the resolution had failed to specify the manner of death ; so the honor went to Raymond Garland, who died of pneumonia before he ever reached France.