“In 1917 Levi-Civita discovered his celebrated parallelism which is an infinitesimal transportation of tangent vectors preserving the scalar product and is the first example of a connection. The salient fact about the Levi-Civita parallelism is the result that it is the parallelism, and not the Riemannian metric, which accounts for most of the properties concerning curvature.”

— Shiing-Shen Chern

[Differential Manifolds (Classroom Notes) Math 352A, Spring 1952, Department of Mathematics, University of Chicago, http://mathunion.org/ICM/ICM1950.2/Main/icm1950.2.0397.0411.ocr.pdf]

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Shiing-Shen Chern 6

mathematician (1911–2004), born in China and later acquirin… 1911–2004

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“It is remarkable that this generalization of plane geometry to surface geometry is identical with that generalization of geometry which originated from the analysis of the axiom of parallels. …the construction of non-Euclidean geometries could have been equally well based upon the elimination of other axioms. It was perhaps due to an intuitive feeling for theoretical fruitfulness that the criticism always centered around the axiom of parallels. For in this way the axiomatic basis was created for that extension of geometry in which the metric appears as an independent variable. Once the significance of the metric as the characteristic feature of the plane has been recognized from the viewpoint of Gauss' plane theory, it is easy to point out, conversely, its connection with the axiom of parallels. The property of the straight line as being the shortest connection between two points can be transferred to curved surfaces, and leads to the concept of straightest line; on the surface of the sphere the great circles play the role of the shortest line of connection… analogous to that of the straight line on the plane. Yet while the great circles as "straight lines" share the most important property with those of the plane, they are distinct from the latter with respect to the axiom of the parallels: all great circles of the sphere intersect and therefore there are no parallels among these "straight lines". …If this idea is carried through, and all axioms are formulated on the understanding that by "straight lines" are meant the great circles of the sphere and by "plane" is meant the surface of the sphere, it turns out that this system of elements satisfies the system of axioms within two dimensions which is nearly identical in all of it statements with the axiomatic system of Euclidean geometry; the only exception is the formulation of the axiom of the parallels.”

Hans Reichenbach (1891–1953) American philosopher

The geometry of the spherical surface can be viewed as the realization of a two-dimensional non-Euclidean geometry: the denial of the axiom of the parallels singles out that generalization of geometry which occurs in the transition from the plane to the curve surface.
The Philosophy of Space and Time (1928, tr. 1957)

“… There's a machine which is called History of Art, which is a structure. And artist fits in this only because he or she is needed for this structure. If for example the History of Art needs some parallel lines, there is an individual who makes parallel lines. And this individual fits into this machine which works by itself; it doesn't care about people or anything else, it just goes by itself.”

Alexander Melamid (1945) Russian artist

Quoted in: Francis Halsall, Systems of Art: Art, History and Systems Theory, (2008) p. 67.
The search for a people's art: painting by the numbers, 1994

“It is well known that in three-dimensional elliptic or spherical geometry the so-called Clifford's parallelism or parataxy has many interesting properties. A group-theoretical reason for the most important of these properties is the fact that the universal covering group of the proper orthogonal group in four variables is the direct product of the universal covering groups of two proper orthogonal groups in three variables. This last-mentioned property has no analogue for orthogonal groups in n (>4) variables. On the other hand, a knowledge of three-dimensional elliptic or spherical geometry is useful for the study of orientable Riemannian manifols of four dimensions, because their tangent spaces possess a geometry of this kind.”

Shiing-Shen Chern (1911–2004) mathematician (1911–2004), born in China and later acquiring U.S. citizenship; made fundamental contributio…

[On Riemannian manifolds of four dimensions, Bulletin of the American Mathematical Society, 51, 12, 1945, 964–971, http://www.ams.org/journals/bull/1945-51-12/S0002-9904-1945-08483-3/S0002-9904-1945-08483-3.pdf]

“If a few people who have come together for the same purpose sit around a table, we can understand them as parallels making up a unity, like the petals of a flower. When we are happy we do not like to hear a discordant voice that disturbs our joy. Proverbially, it is said: Birds of a feather flock together. In all these examples parallelism, or the principle of repetition, can be pointed out. And this parallelism of experience is, in expression, translated into the formal parallelism which we have already discussed.”

Ferdinand Hodler (1853–1918) Swiss artist

from: Die Kunst Ferdinand Hodlers, 1923

“There is no possibility for two people to stay connected and close if they are in different parallel perceptual realities, no matter if their bodies are in the same place. And it is intimacy and attunement that will bridge the gap between these different parallel realities that make us so utterly alone.”

Teal Swan (1984) American spiritual teacher

“For centuries scholars have been forced to grapple with the problem of accounting for the parallels between Greek literature and the Bible.”

Cyrus H. Gordon (1908–2001) American linguist

Did Greece borrow from Israel? Or did Israel borrow from Greece? Can the parallels be accidental, do they obliterate the uniqueness of both Israel and Greece?
Introduction
The Common Background of Greek and Hebrew Civilizations (1965 [1962])

“There are few results of man's activities that so closely parallel man's interests and intellectual capabilities as the map.”

Arthur H. Robinson (1915–2004) American geographer

Robinson (1965) as cited in: Matthew H. Edney (2008) " Putting “Cartography” into the History of Cartography: Arthur H. Robinson, David Woodward, and the Creation of a Discipline https://atrium.lib.uoguelph.ca/xmlui/bitstream/handle/10214/1830/36-Edney.pdf?sequence=1"

“Does not the beauty of the artist's work lie for us in the accuracy with which his symbols resume innumerable facts of our past emotional experience? ... [A]esthetic judgment... how exactly parallel it is to the scientific judgment.”

Karl Pearson book The Grammar of Science

Introductory. Pearson refers the reader to William Wordsworth's preface to the Lyrical Ballads (1815) "General View of Poetry".
The Grammar of Science (1900)

“Even the most distant and exotic place has its parallel in ordinary life.”

Paul Theroux (1941) American travel writer and novelist

Fresh Air Fiend (2000)

“It is always dangerous to draw too precise parallels between one historical period and another; and among the most misleading of such parallels are those which have been drawn between our own age in Europe and North America and the epoch in which the Roman empire declined into the Dark Ages. Nonetheless certain parallels there are. A crucial turning point in that earlier history occurred when men and women of good will turned aside from the task of shoring up the Roman imperium and ceased to identify the continuation of civility and moral community with the maintenance of that imperium.”

Alasdair MacIntyre book After Virtue

What they set themselves to achieve instead - often not recognizing fully what they were doing - was the construction of new forms of community within which the moral life could be sustained so that both morality and civility might survive the coming ages of barbarism and darkness. If my account of our moral condition is correct, we ought also to conclude that for some time now we too have reached that turning point.
Source: After Virtue (1981), p. 263

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Shiing-Shen Chern 6

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