“How can art be realized? Out of volumes, motion, spaces bounded by the great space, the universe. Out of different masses, tight, heavy, middling - indicated by variations of size or color - directional line - vectors which represent speeds, velocities, accelerations, forces, etc...”

— Alexander Calder

these directions making between them meaningful angles, and senses, together defining one big conclusion or many. Spaces, volumes, suggested by the smallest means in contrast to their mass, or even including them, juxtaposed, pierced by vectors, crossed by speeds. Nothing at all of this is fixed. Each element able to move, to stir, to oscillate, to come and go in its relationships with the other elements in its universe. It must not be just a fleeting moment but a physical bond between the varying events in life. Not extractions, but abstractions. Abstractions that are like nothing in life except in their manner of reacting.
1930s, How Can Art Be Realized? (1932)

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Alexander Calder 41

American artist 1898–1976

Hans Hofmann (1880–1966) American artist

'Search for the Real in the Visual Arts', p. 44
Search for the Real and Other Essays (1948)

“The universality, invariance, and elegance of principles governing the universe may be reflected in principles of the minds that have evolved in that universe - provided that the mental principles are formulated with respect to the abstract spaces appropriate for the representation of biologically significant objects and their properties. (1) Positions and motions of objects conserve their shapes in the geometrically fullest and simplest way when represented as points and connecting geodesic paths in the six-dimensional manifold jointly determined by the Euclidean group of three· dimensional space and the symmetry group of each object. (2) Colors of objects attain constancy when represented as points in a three-dimensional vector space in which each variation in natural illumination is cancelled by application of its inverse from the three-dimensional linear group of terrestrial transformations of the invariant solar source. (3) Kinds of objects support optimal generalization and categorization when represented, in an evolutionarily shaped space of possible objects, as connected regions with associated weights determined by Bayesian revision of maximum entropy priors”

Roger Shepard (1929) American psychologist

R. N. Shepard, (1994). "Perceptual-cognitive universals as reflections of the world." Psychonomic Bulletin and Review, 1, 2–28.

“Any region of space-time that has no gravitating mass in its vicinity is uncurved, so that the geodesics here are straight lines, which means that particles move in straight courses at uniform speeds (Newton's first law). But the world-lines of planets, comets and terrestrial projectiles are geodesics in a region of space-time which is curved by the proximity of the sun or earth… No force of gravitation is… needed to impress curvature on world-lines; the curvature is inherent in the space…”

James Jeans (1877–1946) British mathematician and astronomer

The Growth of Physical Science (1947)

“In researches in which an infinity of directions of straight lines in space is concerned, it is advantageous to represent these directions by means of those points upon a fixed sphere”

Carl Friedrich Gauss (1777–1855) German mathematician and physical scientist

"Gauss's Abstract of the Disquisitiones Generales circa Superficies Curvas presented to the Royal Society of Gottingen" (1827) Tr. James Caddall Morehead & Adam Miller Hiltebeitel in General Investigations of Curved Surfaces of 1827 and 1825 http://books.google.com/books?id=SYJsAAAAMAAJ& (1902)
Context: In researches in which an infinity of directions of straight lines in space is concerned, it is advantageous to represent these directions by means of those points upon a fixed sphere, which are the end points of the radii drawn parallel to the lines. The centre and the radius of this auxiliary sphere are here quite arbitrary. The radius may be taken equal to unity. This procedure agrees fundamentally with that which is constantly employed in astronomy, where all directions are referred to a fictitious celestial sphere of infinite radius. Spherical trigonometry and certain other theorems, to which the author has added a new one of frequent application, then serve for the solution of the problems which the comparison of the various directions involved can present.

“Arc, amplitude, and curvature sustain a similar relation to each other as time, motion, and velocity, or as volume, mass, and density.”

Carl Friedrich Gauss (1777–1855) German mathematician and physical scientist

“As the pattern of events is unaltered by motion, the mechanism must be the same when the electron is in motion as when it is at rest. But experiment shows that an electron in motion exerts additional forces which are not the same for all directions in space; if we picture this electron as moving head-foremost through space, these forces surround it like a belt around its waist.”

James Jeans (1877–1946) British mathematician and astronomer

Physics and Philosophy (1942)

“Our visual discrimination is far better than our linguistic system at dealing with complex ratios and continuous variations in space, line, shape, and color.”

Jay Lemke (1946) American academic

Source: Textual politics: Discourse and social dynamics, 1995, p. 110

“Poetry is the universal art of the spirit which has become free in itself and which is not tied down for its realization to external sensuous material; instead, it launches out exclusively in the inner space and the inner time of ideas and feelings.”

Georg Wilhelm Friedrich Hegel book Lectures on Aesthetics

As quoted in the Introduction to Aesthetics (1842), translated by T. M. Knox, (1979), p. 89
Lectures on Aesthetics (1835)

“The big will have a different kind of bigness. The network economy encourages the middle space. It supplies technology (which the industrial age could not) to nurture mid-sized wonders.”

Kevin Kelly (1952) American author and editor

Out of Control: The New Biology of Machines, Social Systems and the Economic World (1995), New Rules for the New Economy: 10 Radical Strategies for a Connected World (1999)

“I must now explain what I mean by the quantity of action. A certain action is necessary for the carrying of a body from one point to another: this action depends on the velocity which the body has and the space which it describes; but it is neither the velocity nor the space taken separately. The quantity of action varies directly as the velocity and the length of path described; it is proportional to the sum of the spaces, each being multiplied by the velocity with which the body describes it. It is this quantity of action which is here the true expense (dépense) of nature, and which she economizes as much as possible in the motion of light.”

Pierre Louis Maupertuis (1698–1759) French mathematician, philosopher and man of letters

Histoire de l'Academie (1744) p. 423; Les Oeuvres De Mr. De Maupertuis (1752) vol. iv p. 17; as quoted by Philip Edward Bertrand Jourdain, The Principle of Least Action https://books.google.com/books?id=y3UVAQAAIAAJ (1913) p. 5.

“How can art be realized? Out of volumes, motion, spaces bounded by the great space, the universe. Out of different masses, tight, heavy, middling - indicated by variations of size or color - directional line - vectors which represent speeds, velocities, accelerations, forces, etc...”

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Alexander Calder 41

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