“There is no art more akin to mysticism than architecture. Abstract, geometrical, musical and yet dumb, passionless, it depends entirely upon symbolism, form and suggestion. Simple lies, and the harmonious combination and numerical relations between these, present something mysterious and at the same time incomplete.”

— Alexander Herzen , book My Past and Thoughts

My Past and Thoughts(1852-1870)

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Alexander Herzen 9

Russian author 1812–1870

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“I strive to make my art bear the same relation to painting that polyphony bears to music. Illustrative music is a thing of the past: it has become abstract and purely aesthetic, dependent for its effect upon rhythm and form.”

Stanton Macdonald-Wright (1890–1973) American artist

Quoted in Bryant American Pictures And Their Painters (1917), p. 302

“At the moment there is a great tendency in painting to discover the 'new' harmony by constructive means whereby the rhythmic is built on an almost geometric form... I am certain that our own modern harmony is not to be found in the 'geometric' way, but rather in the anti-geometric, anti-logical way. And this way is that of 'dissonance in art', in painting, therefore, just as much as in music. And 'today's' dissonance in painting and music is merely the consonance of 'tomorrow.”

Wassily Kandinsky (1866–1944) Russian painter

Quote in Kandinsky's letter to Arnold Schönberg, 18 Jan. 1911; as cited in Schonberg and Kandinsky: An Historic Encounter, by Klaus Kropfinger; edited by Konrad Boehmer; published by Routledge (imprint of Taylor & Francis, an informal company), 2003, p. 9
1910 - 1915

“Measure-relations can only be studied in abstract notions of quantity, and their dependence on one another can only be represented by formulæ. On certain assumptions, however, they are decomposable into relations which, taken separately, are capable of geometric representation; and thus it becomes possible to express geometrically the calculated results. In this way, to come to solid ground, we cannot, it is true, avoid abstract considerations in our formulæ, but at least the results of calculation may subsequently be presented in a geometric form. The foundations of these two parts of the question are established in the celebrated memoir of Gauss, Disqusitiones generales circa superficies curvas.”

Bernhard Riemann (1826–1866) German mathematician

On the Hypotheses which lie at the Bases of Geometry (1873)

“That play of black upon white, white upon black, has the intent and takes the form of creative art. It has in it a flow of the spirit and a harmony of music.”

Yasunari Kawabata book The Master of Go

Source: The Master of Go (1951), Ch. 38, p. 164.
Context: That play of black upon white, white upon black, has the intent and takes the form of creative art. It has in it a flow of the spirit and a harmony of music. Everything is lost when suddenly a false note is struck, or one party in a duet suddenly launches forth on an eccentric flight of his own. A masterpiece of a game can be ruined by insensitivity to the feelings of an adversary.

“My interest in working sites is linked to an investigation of what is behind the extravagant forms and perfect lines of Hadid’s Architecture; it is an interest in the relation between the elegance of her gesture and her radical way of making a building. Something very primordial and out of time is present in those situations. I think of this as a process of forming.”

Hélène Binet (1959) Swiss photographer

In: Hélène Binet’s ‘Forming | Portrait – Architecture of Zaha Hadid’ @ Gabrielle Ammann // Gallery http://sandsof.com/2012/11/24/helene-binets-forming-portrait-architecture-of-zaha-hadid-gabrielle-ammann-gallery/, sandsof.com, 24 November 2012
Binet has photographed the finished building as well as the project during construction of Zaha Hadid's buildings since mid-1980s.

“There is no such thing as abstract art, or else all art is abstract, which amounts to the same thing. Abstract art no more exists than does curved art yellow art or green art.”

Jean Dubuffet book Prospectus et tous écrits suivants

Source: 1960-70's, Prospectus et tous écrits suivants, 1967, p. 206

“THEY who are acquainted with the present state of the theory of Symbolical Algebra, are aware, that the validity of the processes of analysis does not depend upon the interpretation of the symbols which are employed, but solely upon the laws of their combination. Every system of interpretation which does not affect the truth of the relations supposed, is equally admissible, and it is thus that the same process may, under one scheme of interpretation, represent the solution of a question on the properties of numbers, under another, that of a geometrical problem, and under a third, that of a problem of dynamics or optics. This principle is indeed of fundamental importance; and it may with safety be affirmed, that the recent advances of pure analysis have been much assisted by the influence which it has exerted in directing the current of investigation.”

George Boole (1815–1864) English mathematician, philosopher and logician

Source: 1840s, The Mathematical Analysis of Logic, 1847, p. ii: Lead paragraph of the Introduction

“Neo-Plasticism has its roots in Cubism. It could just as easy be called the Painting of Real Abstraction. Since the abstract can be expressed by a plastic reality... It achieves what all painting has tried to achieve but has been able to express only in a veiled manner. By their position and their dimension as well as by the importance of given to colour, the coloured planes express in a plastic way only relations and not forms. Neo-Plasticism imparts to these relations an aesthetic balance and thereby expresses universal harmony... For the moment what art had discovered must still be limited to art itself. Our environment cannot yet be realized as a creation of pure harmony. Art today is at the very point formerly occupied by religion. In its deepest meaning art was the transposition of the natural [into another plane]; in practice it always sought to achieve harmony between man and untransposed nature. Generally speaking, so do Theosophy and Anthroposophy, although these already possessed the original symbol of balance. And this is why they never were able to achieve equivalent relations, that is to say true harmony.”

Piet Mondrian (1872–1944) Peintre Néerlandais

Quote in Mondrian's letter to Rudolf Steiner, c. 1921-23; as cited in Abstract Painting, Michel Seuphor, Dell Publishing Co 1964, p. 83-85
1920's

“When, in architecture, one uses a fixed unit and combinations of it, to produce harmony, the effect should be most striking and apparent… as it is in music by the measured beat and in poetry by the cadence and rhythm.”

Ernest Flagg (1857–1947) American architect

Small Houses: Their Economic Design and Construction (1922)
Context: When, in architecture, one uses a fixed unit and combinations of it, to produce harmony, the effect should be most striking and apparent... as it is in music by the measured beat and in poetry by the cadence and rhythm.<!--Ch. II

“Every solution to every problem is simple. It's the distance between the two where the mystery lies.”

Derek Landy Skulduggery Pleasant

Source: Skulduggery Pleasant

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Alexander Herzen 9

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