Recursive Centers

"Let man then contemplate the whole of nature in her full and grand majesty, and turn his vision from the low objects which surround him. Let him gaze on that brilliant light, set like an eternal lamp to illumine the universe; let the earth appear to him a point in comparison with the vast circle described by the sun; and let him wonder at the fact that this vast circle is itself but a very fine point in comparison with that described by the stars in their revolution round the firmament.

But if our view be arrested there, let our imagination pass beyond; it will sooner exhaust the power of conception than nature that of supplying material for conception. The whole visible world is only an imperceptible atom in the ample bosom of nature. No idea approaches it. We may enlarge our conceptions beyond all imaginable space; we only produce atoms in comparison with the reality of things.

It is an infinite sphere, the centre of which is everywhere, the circumference nowhere. In short it is the greatest sensible mark of the almighty power of God, that imagination loses itself in that thought.

...

For after all what is man in nature? A nothing in relation to infinity, all in relation to nothing, a central point between nothing and all and infinitely far from understanding either. The ends of things and their beginnings are impregnably concealed from him in an impenetrable secret. He is equally incapable of seeing the nothingness out of which he was drawn and the infinite in which he is engulfed."

- Blaise Pascal (1623 - 1662)

Information Theory

"The fundamental problem of communication is that of reproduction at one point either exactly or approximately a message selected at another point. Frequently the messages have meaning; that is, they refer to or are correlated according to some system with certain physical or conceptual entities. These semantic aspects of communication are irrelevant to the engineering problem. The significant aspect is that the actual message is one selected from a set of possible messages."

- Claude Shannon (1916 - 2001)
A Mathematical Theory of Communication

Shadow Physics

"The external world of physics has thus become a world of shadows. In removing our illusions we have removed the substance, for indeed we have seen that substance is one of the greatest of our illusions. Later perhaps we may inquire whether in our zeal to cut out all that is unreal we may not have used the knife too ruthlessly. Perhaps, indeed, reality is a child which cannot survive without its nurse illusion.

But if so, that is of little concern to the scientist, who has good and sufficient reasons for pursuing his investigations in the world of shadows and is content to leave to the philosopher the determination of its exact status in regard to reality. In the world of physics we watch a shadowgraph performance of the drama of familiar life. The shadow of my elbow rests on the shadow table as the shadow ink flows over the shadow paper. It is all symbolic, and as a symbol the physicist leaves it.

Then comes the alchemist Mind who transmutes the symbols. The sparsely spread nuclei of electric force become a tangible solid; their restless agitation becomes the warmth of summer; the octave of aethereal vibrations becomes a gorgeous rainbow."

- Arthur Stanley Eddington (1882 - 1944)
The Nature of the Physical World

Unknown Shore

"Look about you, Clarke. You see the mountain, and hill following after hill, as wave on wave, you see the woods and orchard, the fields of ripe corn, and the meadows reaching to the reed-beds by the river. You see me standing here beside you, and hear my voice; but I tell you that all these things - yes, from that star that has just shone out in the sky to the solid ground beneath our feet - I say that all these are but dreams and shadows; the shadows that hide the real world from our eyes. There is a real world, but it is beyond this glamour and this vision, beyond these ‘chases in Arras, dreams in a career,’ beyond them all as beyond a veil. I do not know whether any human being has ever lifted that veil; but I do know, Clarke, that you and I shall see it lifted this very night from before another’s eyes. You may think this all strange nonsense; it may be strange, but it is true, and the ancients knew what lifting the veil means. They called it seeing the god Pan.

...

I stood here, and saw before me the unutterable, the unthinkable gulf that yawns profound between two worlds, the world of matter and the world of spirit; I saw the great empty deep stretch dim before me, and in that instant a bridge of light leapt from the earth to the unknown shore, and the abyss was spanned."

- Arthur Machen (1863 - 1947)
The Great God Pan

Harmonic Order

"For every mixture, if it is rightly made, as Socrates says, requires these three things, beauty, truth, and symmetry. For neither will any thing base, if it is introduced into the mixture, impart rectitude, since it will be the cause of error, and of inordinate prerogative, nor if truth is at any time separated, will it suffer the mixture to consist of things that are pure, and which are in reality subdued, but it will fill the whole with an image and with non-being. Nor without symmetry will there be a communion of the elements, and an elegant association. Symmetry, therefore, is necessary to the union of the things that are mingled, and to an appropriate communion. But truth is necessary to purity. And beauty to order; which also renders the whole lovely. For when each thing in the mixture has a place adapted to itself, it renders both the elements, and the arrangement resulting from them, beautiful. Here therefore, in the first mixture, these three things are apparent, symmetry, truth, and beauty. And symmetry indeed is the cause to the mixture, that being is one; truth is the cause of the reality of its existence; and beauty is the cause of its being intelligible. Hence it is intelligible and truly being."

- Proclus Lycius (412 – 485)

Note. This remarkable geometry is what meets the gaze of anyone who looks up at the Adolfo Suárez Madrid–Barajas Airport in Spain. We were racing through the airport to get to our flight from Madrid to Galicia last month (to watch the eclipse), my iPhone managed to catch a few vies of the beautiful overhead design in Madrid. Next to the Escher-like ceiling at the international terminal in Auckland, New Zealand, Madrid, this is among my all time favorites.

Weathered Memory

"Now, to return to our immediate subject, it so happens that, in architecture, the superinduced and accidental beauty is most commonly inconsistent with the preservation of original character, and the picturesque is therefore sought in ruin, and supposed to consist in decay. Whereas, even when so sought, it consists in the mere sublimity of the rents, or fractures, or stains, or vegetation, which assimilate the architecture with the work of Nature, and bestow upon it those circumstances of color and form which are universally beloved by the eye of man. So far as this is done, to the extinction of the true characters of the architecture, it is picturesque, and the artist who looks to the stem of the ivy instead of the shaft of the pillar, is carrying out in more daring freedom the debased sculptor's choice of the hair instead of the countenance.

But so far as it can be rendered consistent with the inherent character, the picturesque or extraneous sublimity of architecture has just this of nobler function in it than that of any other object whatsoever, that it is an exponent of age, of that in which, as has been said, the greatest glory of the building consists; and, therefore, the external signs of this glory, having power and purpose greater than any belonging to their mere sensible beauty, may be considered as taking rank among pure and essential characters; so essential to my mind, that I think a building cannot be considered as in its prime until four or five centuries have passed over it; and that the entire choice and arrangement of its details should have reference to their appearance after that period, so that none should be admitted."

- John Ruskin (1819 - 1900)
“The Lamp of Memory” in The Seven Lamps of Architecture

Recursive Gallery

"Zeus himself could not undo the web
of stone closing around me,
I have forgotten the men I was before;
I follow the hated path of monotonous walls
that is my destiny. Severe galleries
which curve in secret circles
to the end of the years. Parapets
cracked by the day’s usury.
In the pale dust I have discerned
signs that frighten me. In the concave
evenings the air has carries a roar

toward me, or the echo of a desolate howl.

I know there is an Other in the shadows,

whose fate it is to wear out the long solitudes

which weave and unweave this Hades

and to long for my blood and devour my death.
Each of us seeks the other.
If only this were the final day of waiting."

- Jorge Luis Borges (1899 - 1986)
"The Labyrinth" in Borges: Selected Poems

Amber Apparition

"White in prismatic order is the union or compound light, while the [...] mixture of our material colors becomes the opposite; that is, the destruction of all, or in other words - darkness. Light is therefore color and shadow the privation of it by the removal of those rays of color, or subductions of power; and there are to be found throughout nature [...] the ruling principles of diurnal variations, the grey dawn, the yellow morning sun rise and red departing ray, in ever changing combination; these are the pure combinations of Aerial colors.

...

The ark stood firm on Ararat: th’ returning sun
Exhaled earth’s humid bubbles, and, emulous of light,
Reflected her lost forms, each in prismatic guise,
Hope’s harbinger, ephemeral as the summer fly,
Which rises, flits, expands, and dies."

- J.M.W. Turner (1775 - 1851)

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)

Unreal Things

 "Unreal things have a reality of
their own, in poetry as elsewhere.
We do not hesitate, in poetry,
to yield ourselves to the unreal,
when it is possible to
yield ourselves."

- Wallace Stevens (1879 - 1955)

Photographer's note. There is an amusing story behind this image, which I took with my iPhone yesterday after my wife, our eldest son, and I finished dinner at a local Nepalese restaurant. As we were waiting for the bill to arrive, I was transfixed by what looked like - to my eye, anyway - a mountainous dune-like vista (such as we had recently seen during our visit to Death Valley, CA). In "reality" this is nothing but a three foot section of wall near the ceiling, with the play of light owing itself to some light fixtures on the ceiling itself (which I cropped out of the image you see above). The "amusing" part is that while I was transfixed by the real-but-unreal dunes (and took a few loooong moments, as I usually do, to get the composition just right), our waiter was politely waiting by our table, equally transfixed by my fascination with what - to him - was nothing but peeling paint on a wall that needed repair! Indeed, when I was finished and approached our table to sit back down, I heard the tail end of a conversation that ensued behind my back between our waiter and my wife. My wife was explaining (as she has done countless times before in similar scenarios) that I "see the world a bit differently," even as our waiter kept apologizing for not having yet "fixed" the wall. Light, shadow, texture, reflection, paint, wall in need of repair, or dunes in the desert, ... which of these are "real" and which imagined? And what of the infinite other Borgesian worlds left unperceived and unexplored? Seeing the world differently, indeed 😊

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)

Glittering Universe

"There may be no such thing as the
'glittering central mechanism of the universe'
but magic may be better description
of the treasure that is waiting."

- John Archibald Wheeler (1911 - 2008)

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)

Cloud of Unknowing

 "The universes which are amenable
to the intellect can never satisfy
the instincts of the heart."

- The Cloud of Unknowing

Absence/Presence

 "In perennial Absence you see mystery, and in
perennial Presence you see appearance.
Though the two are one and the same,
once they arise, they differ in name."

- David Hinton
The Four Chinese Classics: Tao Te Ching, Analects, Chuang Tzu, Mencius

Spirits Clad in Veils

"We are spirits clad in veils."

- Christopher P. Cranch (1813 - 1892)

"Live, you say, in the present;
Live only in the present.

But I don’t want the present, I want reality;
I want things that exist, not time that measures them.

What is the present?
It’s something relative to the past and the future.
It’s a thing that exists in virtue of other things existing.
I only want reality, things without the present.

I don’t want to include time in my scheme.
I don’t want to think about things as present;
I don’t want to separate them from themselves,
treating them as present.

I shouldn’t even treat them as real.
I should treat them as nothing.

I should see them, only see them;
See them till I can’t think about them.

See them without time, without space,
To see, dispensing with everything but what you see.
And this is the science of seeing, which isn’t a science."

- Alberto Caeiro (1889 - 1915)
The Collected Poems of Alberto Caeiro

"There are many faiths, but the spirit is one
— in me, and in you, and in him. So that
 if everyone believes himself, all will be united;
everyone be himself and all will be as one."

- Leo Tolstoy (1828 - 1910)
Resurrection

Myriad Worlds of the Universe

"I consider the positions of kings and rulers as that of dust motes. I observe treasure of gold and gems as so many bricks and pebbles. I look upon the finest silken robes as tattered rags. I see myriad worlds of the universe as small seeds of fruit, and the greatest lake in India as a drop of oil on my foot. I perceive the teachings of the world to be the illusion of, magicians. I discern the highest conception of emancipation as golden brocade in a dream, and view the holy path of the illuminated one as flowers appearing in one's eyes. I see meditation as a pillar of a mountain, Nirvana as a nightmare of daytime. I look upon the judgment of right and wrong as the serpentine dance of a dragon, and the rise and fall of beliefs as but traces left by the four seasons."

- Siddhārtha Gautama (c. 563 or 480 BCE)

Geometry Made Visible

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

- Claude F. Bragdon (1866 - 1946)

More Than the Mind Knows

"'Standing in the presence of' must be different than 'spirit taking over.' In the former I photograph my own blocks, veils, abstractions, etc. I know nothing of the latter. ... Be still with yourself. To establish condition - concentration heightened awareness with a still body and active mind ... To stand in the presence of... projection - empathy - to awareness of object and self ... Previsualization. (Become a camera. Let subject generate its own composition or impose, knowingly, yourself. when the subject presents itself as its own photograph.) Subject for what it is. Subject for what else it is ... [Written in upper margin: 'while holding firm to object and self-previsualizing its transformation as a photograph.] ... During a moment of rapport let recognition trigger exposure. Recognition of what? The thing for what it is (surface appearance and let the viewer go on if he wishes). Things for what else they are: A) inner truth or essence B) mirror of self. This means to do this at seeing prior [to] exposure and again at the instant of exposure ... The eye and the camera see more than the mind knows. Photo not understood fully at exposure. Sense of desiring of self and/or of world (by including heart and soul). Beyond verbal and visual, beyond this recognizable image rapport with spirit or depth [of] mind ... (Above delete this because it may become another Canon. Make each photograph a prayer.) ... Once a photo is a mirror of the man and man a mirror of the world, spirit may take over. Make each photo a prayer."

- Minor White (1908 - 1976)
Minor White, Memorable Fancies

Joyfully Reaching the Stream

 "Follow the way of virtue.
Follow the way joyfully
Through this world and on beyond!
...
The fool laughs at generosity.
The miser cannot enter heaven.
But the master finds joy in giving

And happiness is his reward.
...

And more -
For greater than all the joys
Of heaven and of earth,

Greater still than dominion

Over all the worlds,

Is the joy of reaching the stream."

- The Dhammapada