Marshall McLuhan quote: “The Greeks encountered the confusion of tongues when numbers invaded Euclidean space.”

“Such ideas as those of matter, force, element, number, space, time, etc., came to us from the ancient Greeks.”

J. R. Partington (1886–1965) British chemist

A Short History of Chemistry (1937)
Context: A great number of our common ideas and ways of looking at the world were really shaped for us by the Greeks of antiquity, and... incorporated into the scientific knowledge of today. Such ideas as those of matter, force, element, number, space, time, etc., came to us from the ancient Greeks.

“…the differential element of non-Euclidean spaces is Euclidean. This fact, however, is analogous to the relations between a straight line and a curve, and cannot lead to an epistemological priority of Euclidean geometry, in contrast to the views of certain authors.”

Hans Reichenbach (1891–1953) American philosopher

The Philosophy of Space and Time (1928, tr. 1957)

“Among the conservative Greek opinion there would be no regrets that Alexander the Greek leader was invading the barbarians.”

Robin Lane Fox (1946) Historian, educator, writer, gardener

Source: Alexander the Great, 1973, p.101

“Euclidean geometry is only one of several congruence geometries… Each of these geometries is characterized by a real number K, which for Euclidean geometry is 0, for the hyperbolic negative, and for the spherical and elliptic geometries, positive. In the case of 2-dimensional congruence spaces… K may be interpreted as the curvature of the surface into the third dimension—whence it derives its name…”

Howard P. Robertson (1903–1961) American mathematician and physicist

Geometry as a Branch of Physics (1949)

“The search for the curvature K indicates that, after making all known corrections, the number N seems to increase faster with d than the third power, which would be expected in a Euclidean space, hence K is positive.”

Howard P. Robertson (1903–1961) American mathematician and physicist

The space implied thereby is therefore bounded, of finite total volume, and of a present "radius of curvature" <math>R = \frac{1}{K^\frac{1}{2}}</math> which is found to be of the order of 500 million light years. Other observations, on the "red shift" of light from these distant objects, enable us to conclude with perhaps more assurance that this radius is increasing...
Geometry as a Branch of Physics (1949)

“The victory over Euclidean space was not achieved by isolated individuals, but by a field of young rebels opposed to all absolutes.”

Marshall McLuhan (1911–1980) Canadian educator, philosopher, and scholar-- a professor of English literature, a literary critic, and a …

Source: 1980s, Laws of Media: The New Science (with Eric McLuhan) (1988), p. 42

“Is the position tenable, that certain phenomena, possible in Euclidean space, would be impossible in non-Euclidean space, so that experience, in establishing these phenomena, would directly contradict the non-Euclidean hypothesis? For my part I think no such question can be put. To my mind it is precisely equivalent to the following, whose absurdity is patent to all eyes: are there lengths expressible in meters and centimeters, but which can not be measured in fathoms, feet, and inches, so that experience, in ascertaining the existence of these lengths, would directly contradict the hypothesis that there are fathoms divided into six feet?”

Henri Poincaré book Science and Hypothesis

Source: Science and Hypothesis (1901), Ch. V: Experiment and Geometry (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead

“The space of early Greek cosmology was structured by logos – resonant utterance or word.”

Marshall McLuhan (1911–1980) Canadian educator, philosopher, and scholar-- a professor of English literature, a literary critic, and a …

Source: 1980s, Laws of Media: The New Science (with Eric McLuhan) (1988), p. 35

“If we wished to relate the space of the [Cubist] painters to geometry, we should have to refer it to the non-Euclidean mathematicians; we should have to study, at some length, certain of Riemann's theorems.”

Jean Metzinger (1883–1956) French painter

Du Cubisme (1912)

“If we wished to relate the space of the [Cubist] painters to geometry, we should have to refer it to the non-Euclidean mathematicians; we should have to study, at some length, certain of Riemann's theorems.”

Albert Gleizes (1881–1953) French painter

1910s, Du Cubisme (1912)

“The Greeks encountered the confusion of tongues when numbers invaded Euclidean space.”

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