Ephel Duath

"Far above the Ephel Duath in the West the night-sky was still dim and pale. There, peering among the cloud-wrack above a dark tor high up in the mountains, Sam saw a white star twinkle for a while. The beauty of it smote his heart, as he looked up out of the forsaken land, and hope returned to him. For like a shaft, clear and cold, the thought pierced him that in the end the Shadow was only a small and passing thing: there was light and high beauty for ever beyond its reach."

-  J.R.R. Tolkien (1892 - 1973)
The Return of the King
Sam, Chapter II: The Land of Shadow

Aboriginal Dreaming

"Although The Dreaming conjures up the notion of a sacred, heroic time of the indefinitely remote past, such a time is also, in a sense, still part of the present. One cannot ‘fix’ The Dreaming in time: it was, and is, everywhen. We should be very wrong to try to read into it the idea of a Golden Age, or a Garden of Eden, though it was an Age of Heroes, when the ancestors did marvelous things that men can no longer do [...] Clearly, The Dreaming is many things in one. Among them, a kind of narrative of things that once happened; a kind of charter of things that still happen; and a kind of logos or principle of order transcending everything significant for Aboriginal man. [...] These tales are neither simply illustrative nor simply explanatory, they are fanciful and poetic in content because they are based on visionary and intuitive insights into mysteries; and, if we are ever to understand them, we must always take them in their complex content."

- W.E.H. Stanner (1905 - 1981)

Unconscious Activation

"The creative process, so far as we are able to follow it at all, consists in the unconscious activation of an archetypal image, and in elaborating and shaping this image into the finished work. By giving it shape, the artist translates it into the language of the present, and so makes it possible for us to find our way back to the deepest springs of life."

- C. G. Jung (1875-1961)

Spiritual Harmony

"The more abstract is form, the more clear and direct is its appeal. In any composition the material side may be more or less omitted in proportion as the forms used are more or less material, and for them substituted pure abstractions, or largely dematerialized objects. The more an artist uses these abstracted forms, the deeper and more confidently will he advance into the kingdom of the abstract. And after him will follow the gazer at his pictures, who also will have gradually acquired a greater familiarity with the language of that kingdom.

...

Form alone, even though totally abstract and geometrical, has a power of inner suggestion. A triangle (without the accessory consideration of its being acute- or obtuse-angled or equilateral) has a spiritual value of its own. In connection with other forms, this value may be somewhat modified, but remains in quality the same. The case is similar with a circle, a square, or any conceivable geometrical figure.

...

Every form is as sensitive as a puff of smoke, the slightest breath will alter it completely. This extreme mobility makes it easier to obtain similar harmonies from the use of different forms, than from a repetition of the same one; though of course an exact replica of a spiritual harmony can never be produced. So long as we are susceptible only to the appeal of a whole composition, this fact is of mainly theoretical importance. But when we become more sensitive by a constant use of abstract forms (which have no material interpretation) it will become of great practical significance."

- Wassily Kandinsky (1866 - 1944)

Primordial Ideas

"Colors are primordial ideas,
children of the aboriginal colorless light
and its counterpart, colorless darkness Light,
that first phenomenon of the world, reveals
to us the spirit and the living soul
of the world through colors.

...

Color is life, for a world without color seems dead.
As a flame produces light, light produces color.
As intonation lends color to the spoken word,
color lends spiritually realized sound to a form.
...
Between black and white there throbs the
universe of chromatic phenomena."

- Johannes Itten (1888 - 1967)

Weltanschauung

"That everything is transitory is merely a simile. Everything we see is a proposal, a possibility, an expedient. The real truth, to begin with, remains invisible beneath the surface. The colors that captivate us are not lighting, but light. The graphic universe consists of light and shadow. The diffused clarity of slightly overcast weather is richer in phenomena than a sunny day. A thin stratum of cloud just before the stars break through. It is difficult to catch and represent this, because the moment is so fleeting. It has to penetrate into our soul. The formal has to fuse with the Weltanschauung"

- Paul Klee (1879 - 1940)

Fiery Light

"A fiery light, of the greatest flashing brightness, coming out of a cloudless sky, flooded my entire mind and so inflamed my whole heart and my whole breast like a flame — yet it was not blazing but glowing hot, as the sun makes anything on which its rays fall hot. 

...

And I saw as if in the middle of the southern sky an image, beautiful and wonderful in the mystery of God, like a human in form. Her face was of such beauty and radiance that I could more easily look at the sun than at her; and a great circlet of golden color surrounded her head. [...] And this image spoke: ‘I am the supreme and fiery force, who sets all living sparks alight and breathes forth no mortal things, but judges them as they are. Flying around the circling circlet with my upper wings - with my wisdom - I have ordered all things rightly. But I am also the fiery life of the essence of divinity; I flame above the beauty of the fields, and I shine in the waters, and I burn in the sun, the moon, and the stars. With the airy wind I quicken all things with some invisible life that sustains them all. For the air lives in viridity [i.e., greenness] and in the flowers, the waters flow as if alive, and the sun lives within its own light.

...

The light that I see thus is not spatial, but it is far, far brighter than a cloud that carries the sun. I can measure neither height, nor length, nor breadth in it; and I call it the 'reflection of the living Light.'"

- Hildegard of Bingen (1098 - 1179)

Platonic Forms

"And now look again, and see what will naturally follow if the prisoners are released and disabused of their error. At first, when any of them is liberated and compelled suddenly to stand up and turn his neck round and walk and look towards the light, he will suffer sharp pains; the glare will distress him, and he will be unable to see the realities of which in his former state he had seen the shadows; and then conceive some one saying to him, that what he saw before was an illusion, but that now, when he is approaching nearer to being and his eye is turned towards more real existence, he has a clearer vision. [...] Will he not fancy that the shadows which he formerly saw are truer than the objects which are now shown to him? [...] He will require to grow accustomed to the sight of the upper world. And first he will see the shadows best, next the reflections of men and other objects in the water, and then the objects themselves; then he will gaze upon the light of the moon and the stars and the spangled heaven; and he will see the sky and the stars by night better than the sun or the light of the sun by day. [...] Last of all he will be able to see the sun, and not mere reflections of him in the water, but he will see him in his own proper place, and not in another; and he will contemplate him as he is. [...] This entire allegory you may now append, dear Glaucon, to the previous argument; the prison-house is the world of sight, the light of the fire is the sun, and you will not misapprehend me if you interpret the journey upwards to be the ascent of the soul into the intellectual world according to my poor belief, which, at your desire, I have expressed - whether rightly or wrongly God knows. But, whether true or false, my opinion is that in the world of knowledge the idea of good appears last of all, and is seen only with an effort; and, when seen, is also inferred to be the universal author of all things beautiful and right, parent of light and of the lord of light in this visible world, and the immediate source of reason and truth in the intellectual; and that this is the power upon which he who would act rationally, either in public or private life, must have his eye fixed."

- Plato (c.424 - 348 BC)
"The Allegory of the Cave" (Republic, Book Seven) 

Luminous Forms

"Architecture is the masterly, correct and magnificent play of masses brought together in light. Our eyes are made to see forms in light; light and shade reveal these forms; cubes, cones, spheres, cylinders or pyramids are the great primary forms which light reveals to advantage; the image of these is distinct and tangible within us without ambiguity. It is for this reason that these are beautiful forms, the most beautiful forms. Everybody is agreed to that, the child, the savage and the metaphysician."

- Le Corbusier (1887 - 1965)

Shadow Belongs to Light

"All material in nature, the mountains
and the streams and the air and we,
are made of Light which has been spent, and
this crumpled mass called material casts a shadow,
and the shadow belongs to Light."

- Louis Kahn (1901 - 1974)

Beyond Form

"Thought defines the universe in geometric figures.

...

Those granted the gift of seeing more deeply
can see beyond form, and concentrate
on the wondrous aspect hiding
behind every form, which is
called life.

...

Only for those prepared to leave
their familiar life behind, will life
emerge in a new gown of continually
expanding beauty and perfection.
But in order to attain such a state,
it is necessary to achieve stillness
in both thought and feeling."

- Hilma af Klint (1862 - 1944)

Inconceivable Dimensions

"We are like people drawn inside of a square on a piece of paper. We cannot get out of the black lines, we exhaust ourselves by examining every part of the square, hoping to find a fissure. Until one of us suddenly understands, because he was predestined to understand, that within the plane of the paper escape is impossible. That the exit, simple and open wide, is perpendicular to the paper, in a third dimension that up until that moment was inconceivable."

- Mircea Cărtărescu (1956 - )
Solenoid

Geometry Made Visible

"Architecture is geometry made visible
in the same sense that music
is number made audible."

- Claude F. Bragdon (1866 - 1946)

Elaborate Complexity

"We have a way of discussing the world, when we talk of it at various hierarchies, or levels ... For example, at one end we have the fundamental laws of physics. Then we invent other terms for concepts which are approximate, which have, we believe, their ultimate explanation in terms of the fundamental laws ... if we go higher up from this, in another level we have properties of substances- like "refractive index" ... or "surface tension" ... As we go up in this hierarchy of complexity, we get to things like muscle twitch, or nerve impulse, which is an enormously complicated thing in the physical world, involving an organization of matter in a very elaborate complexity. Then come things like "frog" ... And then ... we come to words and concepts like "man", and "history", or "political expediency", and so forth, a series of concepts which we use to understand things at an ever higher level. And going on, we come to things like evil, and beauty, and hope ... Which end is nearer to God ... beauty and hope, or the fundamental laws? ... I do not think either end is nearer to God. To stand at either end, and to walk off that end of the pier only, hoping that out in that direction is the complete understanding, is a mistake. And to stand with evil and beauty and hope, or to stand with the fundamental laws, hoping that way to get a deep understanding of the whole world, with that aspect alone, is a mistake. ... The great mass of workers in between, connecting one step to another, are improving all the time our understanding of the world, both from working at the ends and working in the middle, and in that way we are gradually understanding this tremendous world of interconnecting hierarchies."

- Richard Feynman (1918 - 1988)
The Character of Physical Law

Intimidated by Logic

"No one is intimidated by logic,
except logicians.

...

All our language is composed of brief little dreams; and the wonderful thing is that we sometimes make of them strangely accurate and marvelously reasonable thoughts. What should we be without the help of that which does not exist? Very little. And our unoccupied minds would languish if fables, mistaken notions, abstractions, beliefs, and monsters, hypotheses, and the so-called problems of metaphysics did not people with beings and objectless images our natural depths and darkness. Myths are the souls of our actions and our loves. We cannot act without moving towards a phantom. We can love only what we create.

...

You can never be too subtle,
and you can never be too simple."

- Paul Valery (1871 - 1945)

Electric Universe

"The watcher’s eyes are likely to swivel forward in a sequence of stately turns as the screen’s pixel glows: each quarter-ounce mass of eyeball tugged by six flat muscles, in a glissando slide within the slippery fat lining the orbital cavity. The eye blinks, the widened pupils are in position, and the incoming electromagnetic waves roar in. Ripping through the thin layer of the cornea, they decelerate slightly, with their outermost edges forming a nearly flat plane as they travel inward, carrying the as-yet-undetected signal from the screen deep into the waiting human. The waves continue through the liquid of the aqueous humor and on to the gaping hole of the pupil. The human may have squinted to avoid the glare, but human reflexes work at the rate of slow thousandths of a second and are no match for these racing intruders. The pupil is crossed without obstruction. The stiff lens just below focuses the incoming waves even more, sending them into the inland sea of the jellylike vitreous humor deeper down in the eye. A very few of the incoming electric waves explode against the organic molecules in their way, but most simply whirl through those soft biological barriers and continue straight down, piercing the innermost wrapping of the eyeball, till they reach the end-point of their journey: the fragile, stalklike projection from the living brain known as the retina. And deep inside there, in the dark, barely slowed from their original 670 million mph, the waves splatter into the ancient, moist blood vessels and cell membranes, and something unexpected happens. An electric current switches on."

- David Bodanis, Electric Universe

A Pattern is a Message

"Organism is opposed to chaos, to disintegration, to death, as message is to noise. To describe an organism, we do not try to specify each molecule in it, and catalogue it bit by bit, but rather to answer certain questions about it which reveal its pattern: a pattern which is more significant and less probable as the organism becomes, so to speak, more fully an organism.

...

We are but whirlpools in a river of ever-flowing water.
We are not stuff that abides, but patterns
that perpetuate themselves.
A pattern is a message...

...

...and may be transmitted as a message. How else do we employ our radio than to transmit patterns of sound, and our television set than to transmit patterns of light? It is amusing as well as instructive to consider what would happen if we were to transmit the whole pattern of the human body, of the human brain with its memories and cross connections, so that a hypothetical receiving instrument could re-embody these messages in appropriate matter."

- Norbert Wiener (1894 - 1964)
The Human Use of Human Beings: Cybernetics and Society

Geometry of Music

 "Music is the arithmetic of sounds
as optics is the geometry of light."

- Claude Debussy (1862 - 1918)

Cymatic Urphänomen

"She [nature] is the sole artist, creating extreme contrast out of the simplest material, the greatest perfection seemingly without effort, the most definite clarity always veiled with a touch of softness. Each of her works has its own being, each of her phenomena its separate idea, and yet all create a single whole."

- Johann Wolfgang von Goethe (1749 - 1832)
 The Metamorphosis of Plants

"The notion of the Urphanomen is an invaluable illustration of the concrete nature of Goethe's way of thinking which dwells in the phenomenon. The primal phenomenon is not to be thought of as a generalization from observations, produced by abstracting from different instances something that is common to them. If this were the case, one would arrive at an abstracted unity with the dead quality of a lowest common denominator. For Goethe, the primal phenomenon was a concrete instance - what he called 'an instance worth a thousand, bearing all within itself.' In a moment of intuitive perception, the universal is seen within the particular, so that the particular instance is seen as a living manifestation of the universal. What is merely particular in one perspective is simultaneously universal in another way of seeing. In other words, the particular becomes symbolic of the universal."

- Henri Bortoft (1938 - 2012)

The Wholeness of Nature

Photographer's note. To help contextualize the relevance of the quotes, I need to point out that the image above contains three (out of a total of about 24) "snapshot" views of a single unfolding cymatic process. Not only does the triptych show only a tiny fraction of what my eye saw through the viewfinder, but the apparent sharpness of the images also belies the frenetic swirling and rhythmic thrashing of the water because my relatively slow 1/40th sec to 1/60th sec exposures smear over finely detailed patterns. But, while we may be unable to "see" the cymatic Urphanomen in its full splendor (and, even if we could, perhaps would understand as little as does Philip K Dick's "electric ant" after it tries seeing all of reality at once), "each of her works has its own being, each of her phenomena its separate idea, and yet all create a single whole." 

Symphonic Geometry

"The human mind is only capable of absorbing a few things at a time. We see what is taking place in front of us in the here and now, and cannot envisage simultaneously a succession of processes, no matter how integrated and complementary. Our faculties of perception are consequently limited even as regards fairly simple phenomena. The fate of a single man can be rich with significance, that of a few hundred less so, but the history of thousands and millions of men does not mean anything at all, in any adequate sense of the word. The symmetriad is a million—a billion, rather—raised to the power of N: it is incomprehensible. We pass through vast halls, each with a capacity of ten Kronecker units, and creep like so many ants clinging to the folds of breathing vaults and craning to watch the flight of soaring girders, opalescent in the glare of searchlights, and elastic domes which criss-cross and balance each other unerringly, the perfection of a moment, since everything here passes and fades. The essence of this architecture is movement synchronized towards a precise objective. We observe a fraction of the process, like hearing the vibration of a single string in an orchestra of supergiants. We know, but cannot grasp, that above and below, beyond the limits of perception or imagination, thousands and millions of simultaneous transformations are at work, interlinked like a musical score by mathematical counterpoint. It has been described as a symphony in geometry, but we lack the ears to hear it."

- Stanislaw Lem (1921 - 2006)

Solaris