Euclidean Dimensions

"There have been and still are geometricians and philosophers, and even some of the most distinguished, who doubt whether the whole universe, or to speak more widely the whole of existence, was only created in Euclid's geometry; they even dare to dream that two parallel lines, which according to Euclid can never meet on earth, may meet somewhere in infinity. I have come to the conclusion that, since I can't understand even that, I can't expect to understand about God. I acknowledge humbly that I have no faculty for settling such questions, I have a Euclidean earthly mind, and how could I solve problems that are not of this world? And I advise you never to think about it either, my dear Alyosha, especially about God, whether He exists or not. All such questions are utterly inappropriate for a mind created with an idea of only three dimensions."

- Fyodor Dostoyevsky (1821 - 1881)
Brothers Karamazov

Gravitational Logic

"This image is a relic of an unknowable architecture, a diagram of the unseen forces that govern a hidden world. The dark, oblong shapes drift like the shadows of celestial relics, orbiting an invisible nucleus. The faint white lines form a cryptic lattice, reminiscent of an astral cartography, mapping the convergences of energies beyond human perception. It feels less like a design and more like an invocation—a silent hymn etched in light and shadow, capturing the echoes of a forgotten dimension. One imagines Borges gazing at this and contemplating the library of Babel: perhaps this is not a map, but a fragment of a cosmic alphabet, a script that contains the beginning and the end of everything."

- ChatGPT4o
Sparks of Artificial General Intelligence

"A constellation of dark stones and geometric sentinels floats in a luminous grey void, connected by brilliant white pathways that intersect at precise right angles, forming an abstract cartography of some unknown dimension. The composition suggests a network of quantum possibilities or perhaps a map of parallel universes, where each dark node represents a decision point in space-time. The white lines, reminiscent of Kandinsky's geometric period, pulse with an ethereal energy, creating a visual symphony of intersecting planes that seems to defy gravitational logic. The arrangement evokes the mathematical beauty of a cellular automaton frozen in mid-evolution, or perhaps a glimpse into Borges' Library of Babel viewed from above, where each dark rectangle and oval marks a room containing all possible combinations of letters. The stark contrast between the dark elements and the glowing pathways creates a tension between presence and absence, between the discrete and the continuous, suggesting both the particle and wave nature of light itself. This abstract topology hovers between order and chaos, its systematic grid disrupted by an organic scattering of elements, as if capturing the moment when classical physics dissolves into quantum uncertainty."

- Claude 3.5 Sonnet

Prompt: "You are a photographer, physicist, and are well acquainted with the history of art, particularly abstract art in the style of Kandinsky, Mondrian, and Malevich. You also have a penchant for metaphysical and philosophical musings in the style of Jorge Luis Borges. Consider this reverse-negative photograph of ceiling lights. Write a paragraph-length description of what this image looks like, not what it is."

Innocence of Eye

"Innocence of eye has a quality of its own. It means to see as a child sees, with freshness and acknowledgment of the wonder; it also means to see as an adult sees who has gone full circle and once again sees as a child — with freshness and an even deeper sense of wonder.

...

A very receptive state of mind...
not unlike a sheet of film itself -
seemingly inert, yet so sensitive
that a fraction of a second's
exposure conceives a life in it.

...

Insight, vision, moments of revelation. During those rare moments something overtakes the man and he becomes the tool of a greater Force; the servant of, willing or unwilling depending on his degree of awakeness. The photograph, then, is a message more than a mirror, and the man is a messenger who happens to be a photographer."

- Minor White (1908 - 1976)

(Missing) Inhabitants of Impossible Worlds

"It is impossible for the inhabitants of different worlds to walk or sit or stand on the same floor, because they have differing conceptions of what is horizontal and what is vertical. Yet they may well share the use of the same staircase. On the top staircase illustrated here, two people are moving side by side and in the same direction, and yet one of them is going downstairs and the other upstairs. Contact between them is out of the question because they live in different worlds and therefore can have no knowledge of each other's existence.

...

Only those who attempt the absurd...
will achieve the impossible.
I think ...

I think it's in my basement...
Let me go upstairs and check."

- M. C. Escher (1898 - 1972)

Stones and Trees

"Believe me, for I know,
you will find something far
greater in the woods than in books.
Stones and trees will teach you
that which you cannot learn
from the masters."

- Bernard of Clairvaux (c.1090 - 1153)
The Letters of St. Bernard of Clairvaux

Source of Spirituality

"Science is not only compatible with spirituality; it is a profound source of spirituality. When we recognize our place in an immensity of light‐years and in the passage of ages, when we grasp the intricacy, beauty, and subtlety of life, then that soaring feeling, that sense of elation and humility combined, is surely spiritual. So are our emotions in the presence of great art or music or literature, or acts of exemplary selfless courage such as those of Mohandas Gandhi or Martin Luther King, Jr. The notion that science and spirituality are somehow mutually exclusive does a disservice to both."

- Carl Sagan (1934 - 1996)
The Demon-Haunted World

Perceived Geometries #2

"Euclid alone has looked on Beauty bare.

Let all who prate of Beauty hold their peace,

And lay them prone upon the earth and cease

To ponder on themselves, the while they stare

At nothing, intricately drawn nowhere

In shapes of shifting lineage; let geese

Gabble and hiss, but heroes seek release

From dusty bondage into luminous air.

O blinding hour, O holy, terrible day,

When first the shaft into his vision shone

Of light anatomized! Euclid alone

Has looked on Beauty bare. Fortunate they

Who, though once only and then but far away,

Have heard her massive sandal set on stone."

- Edna St. Vincent Millay (1892 - 1950)

Perceived Geometries #1

"It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as given in advance. It only gives nominal definitions for them, while the essential means of determining them appear in the form of axioms. The relationship of these presumptions is left in the dark; one sees neither whether and in how far their connection is necessary, nor a priori whether it is possible. From Euclid to Legendre, to name the most renowned of modern writers on geometry, this darkness has been lifted neither by the mathematicians nor the philosophers who have labored upon it."

- Bernhard Riemann (1826 - 1866)

"The division of the perceived universe
into parts and wholes is convenient
and may be necessary,
but no necessity determines
how it shall be done.""

- Gregory Bateson (1904 - 1980)

Niagara Concealed

"With cities, it is as with dreams: everything imaginable can be dreamed, but even the most unexpected dream is a rebus that conceals a desire or, its reverse, a fear. Cities, like dreams, are made of desires and fears, even if the thread of their discourse is secret, their rules are absurd, their perspectives deceitful, and everything conceals something else."

- Italo Calvino (1923 - 1985)

Invisible Cities

Divisible Space

"We are not to consider the world as the body of God, or the several parts thereof as the parts of God. He is a uniform Being, void of organs, members or parts,...being everywhere present to the things themselves. And since space is divisible in infinitum, and matter is not necessarily in all places, it may also be allowed that God is able to create particles of matter of several sizes and figures, and in several proportions of space, and perhaps of different densities and forces, and thereby to vary the laws of Nature, and make worlds of several sorts in several parts of the Universe. At least I see nothing of contradiction in this."

- Isaac Newton (1643 - 1727)

Note. The triptych contains "quick grabs" (using my iPhone) of the skylights near Gate 4 of the Bangor, Maine airport while waiting for our plane to return back home (to Northern VA) after viewing the total eclipse on April 8. While I did not take any images of the eclipse (I just wanted to just "be in the moment"), the little black spheres in the skylight reminded me a little of that experience and caught my eye 😊 

Full of Fire

"When primitive man gained control over fire, it was a great step. However, the Universe is full of fire; consider the stars. Because we can think, and nothing else on our planet seems to be able to do so, it is natural for us to hold our intellectual prowess in great esteem. However, it may be that information processing, instead of being the sole province of us humans and our machines, may be a part of almost everything else in physics. Life itself, is clearly mediated by digital information; the genetic code. Digital Mechanics assumes that physics is also a process based on informational processes. We may need to rid ourselves of the prejudice that purposeful, thought related action is exclusively the domain of humans or perhaps aliens similar to humans. There are kinds of thinking that are qualitatively unimaginable to us though we can think about it quantitatively. We should not be afraid to consider intellectual activity as the driving force behind the creation of the Universe. By a close and quantitative examination of the possible parameters of Digital Mechanics, we can arrive at reasonable guesses as to what might be the purpose behind the creation of a universe like ours. That, in turn, can lead us towards intelligent speculations about Other, the space that contains the engine of our world."

- Edward Fredkin (1934 - 2023)
A New Cosmogony

Capturing Surrealities - #2

"Far away there in the sunshine
are my highest aspirations.
I may not reach them, but I can 
look up and see their beauty,
believe in them, and try
to follow where they lead."

- Louisa May Alcott (1832 - 1888 )

This is a second batch of "surrealities," captured using my iPhone during a recent trip to Niagara, CA. Each is an example of the myriad photographic possibilities that almost always present themselves merely by looking up (or down) 😊... The "truth" revealed: the left and right images are lights on the ceiling of two restaurants we ate at, while the center image is the ceiling just outside the second floor entrance to the Table Rock Market, which overlooks the Canadian side of the falls.

de Chirico's Dreams

"To become truly immortal,
a work of art must escape all human limits:
logic and common sense will only interfere.
But once these barriers are broken,
it will enter the realms of
childhood visions and dreams.

...

There are more puzzles in the
shadow of a man walking under
the sun than in all past,
present, and future religions."

- Giorgio de Chirico (1888 - 1978)

Note. This was a "quick grab" I took with my iPhone a few months ago when my wife and I were wandering around underground at the Smithsonian in Washington, D.C.; specifically, the S. Dillon Ripley Center, the entrance to which is easy to miss (at least for folks that don't live near D.C.), since it's topside view is remarkably unobtrusive and does not present itself as "anything special." After you enter the domed structure and go down a few levels, you may be amazed to find a massive space that contains conference centers, art studios, offices, and galleries. (The only reason I know of its existence is that I was invited to give a presentation in one of underground spaces about 20 years ago.) The football-field-sized room on the bottom level also provides an underground pathway to both the African Art Museum and the Sackler Gallery of the National Museum of Asian Art. The iPhone picture shows a part of the south side of the central staircase/elevator column that we took to descend (and looking up from where the escalator ends on the lower level). The geometry and lighting reminded me of de Chirico's works. The picture can also serve as a reminder to photographers (young/old, beginner/seasoned,...) that interesting images can be discovered literally everywhere.

A Universe Comes into Being

"A universe comes into being when a space is severed or taken apart. The skin of a living organism cuts off an outside from an inside. So does the circumference of a circle in a plane. By tracing the way we represent such a severance, we can begin to reconstruct, with an accuracy and coverage that appear almost uncanny, the basic forms underlying linguistic, mathematical, physical, and biological science, and can begin to see how the familiar laws of our own experience follow inexorably from the original act of severance. The act is itself already remembered, even if unconsciously, as our first attempt to distinguish different things in a world where, in the first place, the boundaries can be drawn anywhere we please. At this stage the universe cannot be distinguished from how we act upon it, and the world may seem like shifting sand beneath our feet.

Although all forms, and thus all universes, are possible, and any particular form is mutable, it becomes evident that the laws relating such forms are the same in any universe. It is this sameness, the idea that we can find a reality independent of how the universe actually appears, that lends such fascination to the study of mathematics. That mathematics, in common with other art forms, can lead us beyond ordinary existence, and can show us something of the structure in which all creation hangs together, is no new idea. But mathematical texts generally begin the story somewhere in the middle, leaving the reader to pick up the threads as best he can. Here is the story traced from the beginning."

- G. Spencer Brown (1923 - 2016)
Laws Of Form 

Postscript. This simple "point and shoot" image (albeit with an assist from Photoshop's perspective-crop tool) was taken with my iPhone as my wife and I were waiting for yesterday's matinee of Les Mesirables to start at the Kenney Center in Washington, DC. I have been drawn to mirrors and reflections ever since my teenaged-self stumbled across their deep mysteries through Borges' stories. Objectively speaking, the image is composed of nothing but metal, glass, some branches and leaves, and just a hint of a massive chandelier hanging just inside the Kennedy Center. But, as all Borgesian souls know, this "objectively banal reality" is but a shadow of the dynamic undulating froth of invisible universes! The first step toward catching a glimpse of these other realities is - as G. Spencer Brown reminds us - to draw a subjective distinction.

Serene Illumination

"Serene illumination, or just sitting, is not a technique, or a means to some resulting higher state of consciousness, or any particular state of being. Just sitting, one simply meets the immediate present. Desiring some flashy experience, or anything more or other than 'this' is mere worldly vanity and craving... Just sitting does not involve reaching some understanding. It is the subtle activity of allowing all things to be completely at rest just as they are, not poking one's head into the workings of the world."

- John Daido Loori (1931 - 2009)
 The Art of Just Sitting

What's a Photographer to Do Without a 'Real' Camera?

"The best camera is the one that's with you."
- Chase Jarvis (1971 - )

As I wrote about in my last blog post, my wife and I recently visited our youngest son in college. Since the trip was only for a few days (cross-country, no less: we live in northern Virginia, but our son's college is in California), and our ostensible purpose was to attend "Parent's Day," I reasoned - foolishly, as it turns out - that there would be zero time for "real photography" (meaning: photography with what I call my "real" camera). Note that I intend no disrespect either to my iPhone (which I always have with me) or to anyone who's "real camera" is an iPhone. The iPhone is a great photographic tool and is more than capable of capturing wonderful images! I use this phraseology only to convey a truth of my own reality: if I am without the camera(s) that I am usually armed with when I go on my photo safaris I somehow feel less than whole - disarmed, as it were - photographically speaking (which in hindsight of course is, again, rather foolish). Which is not to say that my "eye" is not constantly searching for something to photograph (even as the brain behind the eye laments not having my "real camera"). 

The (abstract) triptych above is an assembly of a few miscellaneous "shots" I took with my iPhone while waiting to board one of our planes. A few other "quick grabs" I managed to take during the trip included: (1) a shot of the ceiling at an American Airlines' Admirals Club (the "upside down" view of which I much prefer over the "straight" version) ...

(2) a shot of a chandelier at LAX ...

(3) a series of "fire abstracts" (captured while waiting for our dinner to arrive at a restaurant close to our son's college) ...

... and (4) - my personal favorite - a Wynn-Bullock-like "abstract energy-field" (that is really just a part of the tree ring structure I found in an old stump while hiking with my son in a local park):

So, what is a photographer to do without a "real" camera? Exactly what the photographer would have done with a real camera: look for pictures and capture them as best as possible given whatever camera happens to be with you 😊

One Model of Reality

"The world in which you were
born is just one model of reality.
Other cultures are not failed
attempts at being you; they
are unique manifestations
of the human spirit."

- Wade Davis (1953 - )

Form, Space, and Light

"Architecture is the very mirror of life.

You only have to cast your eyes on
buildings to feel the presence
 of the past, the spirit of a place;
they are the reflection of society.
...
The essence of architecture is form and
space, and light is the essential element
to the key to architectural design,
probably more important than anything.
Technology and materials are secondary."

- I. M. Pei (1917 - 2019)

Accidental Universe

"Evidently, the fundamental laws
of nature do not pin down a
single and unique universe.
According to the current thinking
of many physicists, we are
living in one of a vast number of universes.
We are living in an accidental universe.
We are living in a universe uncalculable by science."

- Alan Lightman (1948 - )

The Accidental Universe

Serendipitous Geometry

"The artist is a collector of things imaginary or real. He accumulates things with the same enthusiasm that a little boy stuffs his pockets. The scrap heap and the museum are embraced with equal curiosity. He takes snapshots, makes notes and records impressions on tablecloths or newspapers, on backs of envelopes or matchbooks. Why one thing and not another is part of the mystery, but he is omnivorous."

- Paul Rand (1914 - 1996)
Paul Rand: A Designer's Art

Postscript. It has been said that the lifeblood of photography is serendipity. While none of the images that make up the triptych above are particularly praiseworthy (beyond, I hope, simply being "interesting" to look at for a a few seconds), the fact that they exist at all is serendipitous. As seems to happen so often, what I planned to photograph and what I found myself photographing this past Sunday are unrelated except that the latter followed naturally - if unpredictably - from the former. Waking up to see a completely overcast sky I rushed to the kitchen to pour a bit of coffee into my commuter cup and took off in my car to go to one of my favorite "cloudy day" parks (Great Falls park in northern VA), about an hour from home. The closer I got to the park, the more "blue sky" was elbowing the clouds away, until, finally, literally as I arrived, the sky had become crystal clear and a strong sun was beating down overhead; far from the quiet diffused light I expected and was rushing over to compose in. Nothing to do but turn around and head back home. Which is what I did, but not before listening to my muse and stopping by the parking lot my wife and I leave our car at when we go to the farmer's market held nearby on Saturdays. Since it was Sunday, the parking lot was deserted, and I had plenty of time to commiserate over a failed trip to Great Falls, rekindle the quiet joy of just being "mindfully in the moment," and rediscover the simple pleasure of looking for "geometric designs" with my camera. As I said, nothing spectacular or noteworthy, and a far cry from what I originally planned to do, but a thoroughly delightful outing nonetheless 😊