Complex Networks

"Thanks to the rapid advances in network theory it appears that we are not far from the next major step: constructing a general theory of complexity. The pressure is enormous. In the twenty-first century, complexity is not a vague science buzzword any longer, but an equally pressing challenge for everything from the economy to cell biology. Yet, most earlier attempts to construct a theory of complexity have overlooked the deep link between it and networks. In most systems, complexity starts where networks turn nontrivial. No matter how puzzled we are by the behavior of an electron or an atom, we rarely call it complex, as quantum mechanics offers us the tools to describe them with remarkable accuracy. The demystification of crystals-highly regular networks of atoms and molecules-is one of the major success stories of twentieth-century physics, resulting in the development of the transistor and the discovery of superconductivity. Yet, we continue to struggle with systems for which the interaction map between the components is less ordered and rigid, hoping to give self-organization a chance."

- Albert-László Barabási (1967 - )
Linked: How Everything Is Connected to Everything Else

Distorted Reality

"Other big questions tackled by ancient cultures are at least as radical. What is real? Is there more to reality than meets the eye? Yes! was Plato's answer over two millennia ago. In his famous cave analogy, he likened us to people who'd lived their entire lives shacked in a a cave, facing a blank wall, watching the shadows cast by things passing behind them, and eventually coming to mistakenly believe that these shadows were the full reality. Plato argued that what we humans call our everyday reality is similarly just a limited and distorted representation of the true reality, and that we must free ourselves from our mental shackles to comprehending it."

- Max Tegmark (1967 - )

Our Mathematical Universe

Dreaming and Seeing

"The diagram in the ashes had two epicenters; one he called “reason,” the other, “will.” “Reason” was interconnected directly with a point he called “talking.” Through “talking,” “reason” was indirectly connected to three other points, “feeling,” “dreaming,” and “seeing.” The other epicenter, “will,” was directly connected to “feeling,” “dreaming,” and “seeing”; but only indirectly to “reason” and “talking.” I remarked that the diagram was different from the one I had recorded years before. “The outer form is of no importance,” he said. “These points represent a human being and can be drawn in any way you want.” “Do they represent the body of a human being?” I asked. “Don’t call it the body” he said. “These are eight points on the fibers of a luminous being. A sorcerer says, as you can see in the diagram, that a human being is, first of all, will, because will is directly connected to three points, feeling, dreaming, and seeing; then next, a human being is reason. This is properly a center that is smaller than will; it is connected only with talking.” “What are the other two points, don Juan?” He looked at me and smiled."

- Carlos Castaneda (1925 - 1998)
Tales of Power

Abstract Forms

“And what is it that experiences our self? Only our self! There is only one substance in experience and it is pervaded by and made out of knowing or awareness. In the classical language of non-duality this is sometimes expressed in phrases such as, ‘Awareness only knows itself’, but this may seem abstract. It is simply an attempt to describe the seamless intimacy of experience in which there is no room for a self, object, other or world; no room to step back from experience and find it happy or unhappy, right or wrong, good or bad; no time in which to step out of the now into an imaginary past or into a future in which we may become, evolve or progress; no possibility of stepping out of the intimacy of love into relationship with an other; no possibility of knowing anything other than knowing, of being anything other than being, of loving anything other than loving; no possibility of a thought arising which would attempt to frame the intimacy of experience in the abstract forms of the mind; no possibility for our self to become a self, a fragment, a part; no possibility for the world to jump outside and for the self to contract inside; no possibility for time, distance or space to appear."

- Rupert Spira (1960 - )
Presence: The Art of Peace and Happiness

Unified Theory

"The mind calls out for a third theory to unify all of physics, and for a simple reason. Nature is in an obvious sense "unified." The universe we find ourselves in is interconnected, in that everything interacts with everything else. There is no way we can have two theories of nature covering different phenomena, as if one had nothing to do with the other. Any claim for a final theory must be a complete theory of nature. It must encompass all we know. Physics has survived a long time without that unified theory. The reason is that, as far as experiment is concerned, we have been able to divide the world into two realms. In the atomic realm, where quantum physics reigns, we can usually ignore gravity. We can treat space and time much as Newton did-as an unchanging background. The other realm is that of gravitation and cosmology. In that world, we can often ignore quantum phenomena. But this cannot be anything other than a temporary, provisional solution. To go beyond it is the first great unsolved problem in theoretical physics."

- Lee Smolin (1955 - )
 The Trouble with Physics

Holiness of the Mountain

"Phædrus wrote a letter from India about a pilgrimage to holy Mount Kailas, the source of the Ganges and the abode of Shiva, high in the Himalayas, in the company of a holy man and his adherents.

He never reached the mountain. After the third day he gave up, exhausted, and the pilgrimage went on without him. He said he had the physical strength but that physical strength wasn’t enough. He had the intellectual motivation but that wasn’t enough either. He didn’t think he had been arrogant but thought that he was undertaking the pilgrimage to broaden his experience, to gain understanding for himself. He was trying to use the mountain for his own purposes and the pilgrimage too. He regarded himself as the fixed entity, not the pilgrimage or the mountain, and thus wasn’t ready for it. He speculated that the other pilgrims, the ones who reached the mountain, probably sensed the holiness of the mountain so intensely that each footstep was an act of devotion, an act of submission to this holiness. The holiness of the mountain infused into their own spirits enabled them to endure far more than anything he, with his greater physical strength, could take."

- Robert M. Pirsig (1928 - )

Zen and the Art of Motorcycle Maintenance

Star-Stuff

"The cosmos is full beyond measure of elegant truths; of exquisite interrelationships; of the awesome machinery of nature. The surface of the Earth is the shore of the cosmic ocean. On this shore we've learned most of what we know. Recently we've waded a little way out, maybe ankle deep, and the water seems inviting. Some part of our being knows this is where we came from. We long to return. And we can. Because the cosmos is also within us. We're made of star-stuff. We are a way for the cosmos to know itself."

- Carl Sagan (1934 - 1996)

Postscript. For those of you wondering what this is "actually" an image of, it is a tight crop - about 1 cm square - of a mildly edited (i.e., basic luminance adjustment, white balance, noise removal, and selective contrast and sharpening) image of an onyx marble stone drink coaster I sometimes use to rest a cup of coffee on while working. Perchance, I happened to catch a glimpse of this phantasmagoric, dreamlike vortex swirling atop a Himalayan mountaintop! I never cease to marvel at the beauty that literally surrounds us throughout our lives; nor at the timeless wisdom contained within the Emerald Tablet of Hermes Trismegistus (purportedly, since no one has actually seen the original tablet):

"As above;
so below.
As within;
so without.
As with the universe;
so with the soul."

Informational Processes

"The greatest flaw of conventional physics is the acceptance of magic that has been forced upon all of us by our ignorance of the science of informational processes. This is particularly true with respect to Newtonian motion. We have no right to complain about the fact that nowhere in all of contemporary physics is there a commonsense model of motion. We haven’t had a way to know better. Newton swept this matter under the rug and Poincare and Einstein convinced us that we must believe that there is nothing under the rug. Intoxicated by all our fantastic accomplishments since Newton, it is human nature to avoid dwelling on dead-end issues. So, as smart as we all are, concepts of motion have remained in a state similar to the vitalistic theories of life that flourished in the past. 'Things move.' 'Mass has inertia.' 'Like begets like.' The idea that physics can get along without a fixed reference frame is utter nonsense from an informational viewpoint. It does not matter how brilliant and convenient the theory of relativity is or how many experiments validate its formulas. It is our collective misfortune that, until recently, no one has ever had any competent idea of what an informational point of view is."

- Edward Fredkin (1934 - )
Introduction to Digital Philosophy

Space

 "We do not know space.
We do not see it,
we do not hear it,
we do not feel it.
We are standing in
the middle of it,
we ourselves are
part of it,
but we know
nothing about it."

- M. C. Escher (1898 - 1972)

Mythology

"That it doesn’t strike us at all when we look around us, move about in space, feel our own bodies, etc. etc., shows how natural these things are to us. We do not notice that we see space perspectivally or that our visual field is in some sense blurred towards the edges. It doesn’t strike us and never can strike us because it is the way we perceive. We never give it a thought and it’s impossible we should, since there is nothing that contrasts with the form of our world.What I wanted to say is it’s strange that those who ascribe reality only to things and not to our ideas move about so unquestioningly in the world as idea and never long to escape from it.

...

An entire mythology is
stored within our language."

- Ludwig Wittgenstein (1889 - 1951)

Temporality #3

 "No permanence is ours;
we are a wave
That flows to fit
whatever form it finds"

- Hermann Hesse (1877 - 1962)
The Glass Bead Game

Postscript. One last "improvisation" on finding ways to render the ephemeral beauty that lives and dwells in flame (as described in Temporality #1) before I move on to other images and musings. The base images in this example are selected from the same set I used for my earlier examples (i.e., roughly 100 or so macros of flame, exposed between 1/2000th and 1/5000th sec). Also, just as in the last example (Temporality #2), each panel of the triptych is effectively an average (in terms of luminance) of three separate images. But this time, I loosened the constraint that individual photographs must retain their original orientation. I've written a short Mathematica program that automates the process of assembling triptychs of luminance-averaged layers, wherein each image either remains "as is" (i.e., in its original upright position), is reflected horizontally or vertically (as in a mirror), or is reflected both horizontally and vertically. Of course, this vastly increases the set of randomly assembled images. Assuming 100 "base" images - i.e., original flame macros - a 3 panel assembly consisting of 3 layered base images, each of which can assume any of four orientations, leads to over 50 million! combinations! But, while this makes it difficult, if not impossible, to sample even a small fraction of the "abstract triptych space," it can also yield striking images that would otherwise likely remain unknown. Of course, there are myriad associated aesthetic, conceptual, and philosophical depths that can be mined here (e.g., "What does the space of all possible 'creative' excursions from a starting set of images even look like?" - echoes of Stuart Kauffman's space of the "Adjacent Possible"), but I best end the discussion here, and let the lone exemplar above speak of what lives in that unimaginably larger universe of latent realities.

Temporality #2

"But what about "time"? After all it is not a bundle in which past, future and present are wrapped up together. Time is not a cage in which the "no longer now," the "not yet now," and the "now" are cooped up together. How do matters stand with "time"? They stand thus: time goes. And it goes in that it passes away. The passing of time is, of course, a coming, but a coming which goes, in passing away. What comes in time never comes to stay, but to go. What comes in time always bears beforehand the mark of going past and passing away. This is why everything temporal is regarded simply as what is transitory."

- Martin Heidegger (1889 - 1976)
What is Called Thinking?

Postscript. A lesson my dad (an artist, who passed away a much too long 19 years ago) implicitly drilled in to me - oh, ever so gently, as it was simply a way of life with him; something he did as instinctually as most people breathe - was the importance of constant play and experimentation (something I've underscored before in another context). As I wrote a few days ago, I am "revisiting" - and rediscovering - the ephemeral beauty that lives and dwells in flame. And so, in the spirit of my dad's freewheeling jazz-like improvisation, I've been toying with alternative ways of "seeing" - after the fact - more deeply into what only my lens can see when the flame I am pointing my camera at is alive. My first stab (as shown in an earlier post) was to use triptychs to emphasize the "dance" within the flame; the preliminary fruits of which have already spawned a small portfolio (with more to follow). An example of an "improvised" second take on this idea is shown above. It is still a triptych, but here each frame merges three separate images, captured in rapid succession during a given sequence (individual images are still exposed between 1/2000th and 1/5000th sec). The implied enfolding makes the flame look even more organic and alive! Perhaps - with a nod to Goethe, who famously described architecture as "frozen music" - I ought to call these ethereal moments frozen fire.

Miniature Universe

"All the matter of the world that surrounds us, the food that we eat, the water that we drink, the air that we breathe, the stones that our houses are built of, our own bodies — everything is permeated by all the matters that exist in the universe. There is no need to study or investigate the sun in order to discover the matter of the solar world; this matter exists in ourselves and is the result of the division of our atoms. In the same way we have in us the matter of all other worlds. Man is, in the full sense of the term, a 'miniature universe'; in him are all the matters of which the universe consists; the same forces, the same laws that govern the life of the universe, operate in him; therefore in studying man we can study the whole world, just as in studying the world we can study man."

- P. D. Ouspensky (1878 - 1947)

Temporality

"The moment is that ambiguity in which time and eternity touch each other, and with this the concept of temporality is posited, whereby time constantly intersects eternity and eternity constantly pervades time. As a result, the above-mentioned division acquires its significance: the present time, the past time, the future time.

...

A moment as such is unique. To be sure, it is short and temporal, as the moment is; it is passing, as the moment is, past, as the moment is in the next moment, and yet it is decisive, and yet it is filled with the eternal. A moment such as this must have a special name. Let us call it: the fullness of time.

...

The fullness of time is the moment as the eternal, and yet this eternal is also the future and the past. If attention is not paid to this, not a single concept can be saved from a heretical and treasonable admixture that annihilates the concept."

- Søren Kierkegaard (1813 -1855)

Postscript. What you are looking at are three closeups of a small flame (less than a few inches in height) captured at about 1/3000th of a sec. While I have toyed with "abstract flames" many years ago (e.g., see here), those earlier experiments used fairly large open flames; such as when my family and I would gather around our backyard firepit after an autumn barbecue. This new series (that I've only just started playing with) is decidedly different. I still use a "firepit," but one that is only 5 inch wide! The beauty of the minimalist "ephemeral sculptures" - that dance so elegantly to and fro - is mesmerizing! Part of the appeal is undeniably philosophical: these sculptures live far too briefly to be visible while "alive"; their presence may be felt only long after they have ceased to be. Testaments to both temporality and the fullness of time.

Beyond One's Reach

"What is frequently appreciated
in many so-called symbols
is exactly their vagueness,
their openness,
their fruitful ineffectiveness
to express a 'final' meaning,
so that with symbols
and by symbols one
indicates what is always
beyond one's reach."

- Umberto Eco (1932 - 2016)
Semiotics and the Philosophy of Language

Imagination Itself

"The tree which moves
some to tears of joy
is in the eyes of others
only a green thing
that stands in the way.
Some see nature all
ridicule and deformity...
and some scarce see
nature at all.
But to the eyes of
the man of imagination,
nature is imagination itself."

- William Blake (1757 - 1827)

Just Sitting

"Thoughts well up in our
mind moment by moment.
But we refrain from doing
anything with our thoughts.
We just let everything come
up freely and go away freely.
We don’t grasp anything.
We don’t try to control anything.
We just sit."

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

Edge of Chaos

"Complex systems have evolved which may have learned to balance divergence and convergence, so that they're poised between chaos and order ... It's precisely those systems that can simultaneously perform the most complex tasks and evolve, in the sense that they can accumulate successive useful variations. The very ability to adapt is itself, I believe, the consequence of evolution. You have to be a certain kind of complex system to adapt, and you have to be a certain kind of complex system to coevolve with other complex systems. We have to understand what it means for complex systems to come to know one another — in the sense that when complex systems coevolve, each sets the conditions of success for the others. I suspect that there are emergent laws about how such complex systems work, so that, in a global, Gaia-like way, complex coevolving systems mutually get themselves to the edge of chaos, where they're poised in a balanced state."

- Stuart Kauffman (1939 - )

Touchstones and Palimpsests

"We’re so caught up in our everyday lives that events of the past, like ancient stars that have burned out, are no longer in orbit around our minds. There are just too many things we have to think about every day, too many new things we have to learn. New styles, new information, new technology, new terminology … But still, no matter how much time passes, no matter what takes place in the interim, there are some things we can never assign to oblivion, memories we can never rub away. They remain with us forever, like a touchstone."

- Haruki Murakami (1949 - )
Kafka on the Shore

The panels of this triptych are "digital double exposures" of images taken at two very different times and places: the foreground consists of photographs of reeds in a pond and a tree basking in a warm sun one autumn day in 2003 at one of my favorite little parks near where my mom used to live on Long Island (before passing away in 2017); the background consists of splotches of paint I found on an old tire that was bobbing up and down in the Port of Piraeus in Athens, Greece in the summer of 2008 as my wife and I were waiting for a boat-ride to Santorini. The fusion of images serves as both touchstone and palimpsest, tinged with melancholy and hope. Melancholy, because ever since my mom's passing, the little park has become less a place to visit, and more a ghostly memory of times past; and the Athenian splotches of paint serve only to strengthen my wife's and my own longing for trips to "faraway places" that - before the pandemic - we used to take for granted. And hope, because though such memories of times and places are indeed ghostly, they also point to happy experiences yet to arrive. Memories fade, but meaning only deepens.   

"It is as if the Caru'ee were able
to perceive an echo of the past,
and unconsciously, as they built
upon a palimpsest of books written
long ago and long forgotten,
chanced to stumble upon an essence
of meaning that could not be lost,
no matter how much
time had passed." 

- Ken Liu (1976 - )
The Paper Menagerie and Other Stories

Silence

“How to be a Poet
(to remind myself)

i

Make a place to sit down.

Sit down. Be quiet.

You must depend upon

affection, reading, knowledge,

skill—more of each

than you have—inspiration

work, growing older, patience,

for patience joins time

to eternity…

ii

Breathe with unconditional breath

the unconditioned air.

Shun electric wire.

Communicate slowly. Live

a three-dimensional life;

stay away from screens.

Stay away from anything

that obscures the place it is in.

There are no unsacred places;

there are only sacred places

and desecrated places.

iii

Accept what comes from silence.

Make the best you can of it.

Of the little words that come

out of the silence, like prayers

prayed back to the one who prays,

make a poem that does not disturb

the silence from which it came.”

- Wendell Berry (1934 - )
 Given

Looking Inward

"He sees the truth as with a jolt. There it is, within his own being, lying deep down but still in his own self. There never was any need to travel anywhere to find it; no need to visit anyone who was supposed to have it already, and sit at his feet; not even to read any book, however sacred or inspired. Nor could another person, place, or writing give it to him; he would have to unveil it for himself in himself. The others could direct him to look inwards, thus saving all the effort of looking elsewhere. But he himself would have to give the needful attention to himself. The discovery must be his own, made within the still center of his being."

- Paul Brunton (1898 - 1981)
Advanced Contemplation: The Peace Within You

Mind at Large

"To make biological survival possible, Mind at Large has to be funnelled through the reducing valve of the brain and nervous system. What comes out at the other end is a measly trickle of the kind of consciousness which will help us to stay alive on the surface of this particular planet. To formulate and express the contents of this reduced awareness, man has invented and endlessly elaborated those symbol-systems and implicit philosophies which we call languages. Every individual is at once the beneficiary and the victim of the linguistic tradition into which he or she has been born -- the beneficiary inasmuch as language gives access to he accumulated records of other people's experience, the victim in so far as it confirms him in the belief that reduced awareness is the only awareness and as it be-devils his sense of reality, so that he is all too apt to take his concepts for data, his words for actual things."

- Aldous Huxley (1894 - 1963)

Life & Entropy

"When things don't change any longer,
that's the end result of entropy,
the heat-death of the universe.
The more things go on moving,
interrelating, conflicting, changing,
the less balance there is -
and the more life."

- Ursula K. Le Guin (1929 - 2018)

The Lathe of Heaven

Agencies of Magic

"A retired English working-man is sitting at his table with his wife and a friend, a returned British sergeant-major from India. The sergeant-major shows his hosts an amulet in the form of a dried, wizened monkey’s paw... [which has] the power of granting three wishes to each of three people... The last [wish of the first owner] was for death... His friend... wishes to test its powers. His first [wish] is for 200 pounds. Shortly thereafter there is a knock at the door, and an official of the company by which his son is employed enters the room. The father learns that his son has been killed in the machinery, but that the company... wishes to pay the father the sum of 200 pounds... The grief-stricken father makes his second wish -that his son may return- and when there is another knock at the door... something appears... the ghost of the son. The final wish is that the ghost should go away. In these stories, the point is that the agencies of magic are literal-minded... The new agencies of the learning machine are also literal minded. If we program a machine... and ask for victory and do not know what we mean by it, we shall find the ghost knocking at our door."

A "updated" fable of the Monkey's Paw,
as quoted in a recent paper on Superintelligence 

Imperceptible Chains

"If man made himself the first object of study, he would see how incapable he is of going further. How can a part know the whole? But he may perhaps aspire to know at least the parts to which he bears some proportion. But the parts of the world are all so related and linked to one another, that I believe it impossible to know one without the other and without the whole.

Man, for instance, is related to all he knows. He needs a place wherein to abide, time through which to live, motion in order to live, elements to compose him, warmth and food to nourish him, air to breathe. He sees light; he feels bodies; in short, he is in a dependent alliance with everything. To know man, then, it is necessary to know how it happens that he needs air to live, and, to know the air, we must know how it is thus related to the life of man, etc. Flame cannot exist without air; therefore to understand the one, we must understand the other.

Since everything then is cause and effect, dependent and supporting, mediate and immediate, and all is held together by a natural though imperceptible chain, which binds together things most distant and most different, I hold it equally impossible to know the parts without knowing the whole, and to know the whole without knowing the parts in detail."

- Blaise Pascal (1623 - 1662)

Musings on the Creative Process: Left-Brain / Right-Brain Blending

 "It's always seemed like

a big mystery how nature,

seemingly so effortlessly,

manages to produce so much

that seems to us so complex.

Well, I think we found its secret.

It's just sampling what's

out there in the

computational universe."

- Stephen Wolfram (1959 - )

I apologize beforehand for what might seem like a long and bizarre excursion away from photography; but please bear with me as the following musings are very much in the vein of exploring the "creative process" of photography (well, at least, a glimpse of the creative process I've recently been immersed in!). Specifically, those aspects of the creative process that lie at the cusp of traditional left/right brain functions. Leaving aside the reality of such a dichotomy (e.g., see this recent paper), let us posit that left-brain processes focus more on logic and analytic thinking, and that right-brain processes focus on art and intuition more. Of course, all of us continually engage both sides throughout our waking hours, albeit with our own unique rhythms of shifting/combining focus and modulating relative emphasis. In my case, I live in two - usually quite separate - worlds, deliberately broken up into "what I do during my work week" (employed, as I am, as a physicist at a federally funded research & development center) and "what I do during essentially all available off hours" (which, among other things, has resulted in this photography blog and more fun with my cameras, lenses, filters, and tripods than I deserve in the 45+ years I've been doing photography). Occasionally, as I'm about to do here, I combine my two sides; though not always for the better - you, kind reader, can judge whether I've strayed a bit too far in this case.

"Working with mental images activates a different mode
of consciousness which is holistic and intuitive." 
- Henri Bortoft (1938 - 2012)

So many ideas come to mind as I ponder this question: Goethe's Holistic Seeing; Bohm's Implicate Order; and Alexander's (opus on fundamental organizing principles of "life forms") Nature of Order, all come to mind. But I will leave the discussion of these approaches for a later entry. For now, these ideas will have to serve merely as backdrops of my explanation of how I've partly fused my "left-brain/right-brain" activities over the last week or so (I promise to keep it short :). 

At its core, my usual "right brain" approach to photography cannot be simpler: I pick up my camera bag and tripod, head out for a walk to a local park (or just go downstairs to a "studio" I've set up for to experiment with color abstracts), and start shooting. If something catches the eye, I shoot. That's about it. And the less ("left-brain") thinking that is involved, the better (though it sometimes leads to thinking about thinking, which I've written about before). The only important - and almost entirely unconscious - action I take is to choose the time I press the shutter (I've assuming that such minutiae as f-stops, exposure times, filters, and the like are "automatic" and add little to the story I'm trying to tell here). OK, so far, so good.

"So the relationship of each moment in the whole to all the others
is implied by its total content: the way in which it
'holds’ all the others enfolded within it." 
- David Bohm (1917 - 1992) 

This is where my several-week-old left-brain machinations come in. While looking over a portfolio of recent abstracts (including those "discovered" in marble and crystals), I ran across a number that fell into the "whole contains other wholes" pictures I described above. I was sitting at the same PC that facilitates both my left-brain (Photoshop) and right-brain (Mathematica) activities, and reflected the same basic type of question I normally reserve for my left-brain: "How can I find the 'best' image?" - meaning one that best satisfies my desire to show "interesting parts" of an image, but in such a way that the whole is still implicitly within sight, "just barely out of reach." I had earlier experimented with breaking up images into thirds and looking for "interesting juxtapositions" (e.g., exchanging the 1st and 2nd panel interchanged, but leaving the 3rd panel fixed). And, while that did lead to some interesting variations, it was also a painstakingly long process. These preliminary experiments were akin to a kind of improvisational play,  wherein I manually dissected each image and created select juxtapositions of interest. Noting that something interesting can actually be found by following this method, my left-brain finally clicked into action.

While the process is still "simple" (relatively speaking), and can - and will - easily be improved upon in coming days and weeks, I wrote a Mathematica function that automatically breaks an image into thirds (i.e., my 3-word alphabet of 'panels' to be used in  constructing new triptychs); applies all possible combinations of (1) leaving the orientation of a given panel unchanged (or as 'original = O'), (2) flipping a panel in the horizontal direction ('HF'), (3) flipping a panel in the vertical direction ('VF'), and (4) rotating a panel 180 deg (i.e., perform a vertical rotation = 'VR'); and assembling the new panels into a triptych with a bit of white space between and on the outside perimeter of the whole image. (90 deg rotations are not allowed, because in order to retain the same aspect ratio, the panels would all need to be square.) The Mathematica function is constrained to not create any triptychs in which the original panel order is left unchanged, since my goal is to find combinations of individually interesting images - in this case, panels - in which the whole, or original image, is only implicit and not directly observable. A bit of counting shows that, with this constraint, there are a total of 320 possible 'panel exchange + rotation/flip' combinations. This is significantly more than I can create by hand, but is easily doable in a few seconds by feeding my Mathematica function a starting image of choice. More specifically (since it is hard to visually digest 320 images at once), I had Mathematica display a smaller array of 16 random triptychs out of the complete set that my right-brain can inspect - and select interesting variants of - "at a glance." 

"No pattern is an isolated entity. Each pattern can exist in the
world only to the extent that is supported by other patterns:
the larger patterns in which it is embedded, the patterns of the
same size that surround it, and the smaller patterns
which are embedded in it."
- Christopher Alexander (1936 - ) 

Two such arrays are displayed at the top of this post, along with - on the right hand side - one of the images I like best. By design, all of the randomly constructed triptychs share the two most important qualities I am searching for: (1) each of the panels is "interesting" (since this cannot be expected to be true of just any image, the starting image must already be specially selected), and (2) the starting image is visible only implicitly, since the viewer is allowed to see only the juxtaposed panels, not in their original order). As for what makes triptych x more/less interesting than triptych y? That's where the right brain jumps back into the process, as it subjectively selects one out of many - just because; though, because of the way my left-brain constructed the samples from which my right-brain is asked to choose (leaving out the "real" image), the right-brain is faced with - what for me, is - an intoxicating aesthetic tension between parts and an implicit whole. Indeed, the pleasure I get from finding and viewing "interesting images" of this sort are a direct analogue of the creative process by which they are spawned. In the same way as (I've just described) my left-brain helps me sort, dissect, operate-on, and create a multiverse of same-but-different sets of images that my right-brain generated the 'starting set' for (by intuitively capturing the original image) - my right-brain now delights in teasing apart the tension between the parts and wholes of images that my left-brain constructed for me (thus revealing "interesting" sets of images otherwise invisible to my own eye). 

Importantly, at least as far as photography - and aesthetics - are concerned, both sides of this creative process are fueled by search, discovery, and selection. That is, a search for a place and time to take a photograph, discovering an image, and selecting how and when to capture it. The only difference between my usual photography and the (admittedly laborious seeming) process described above is the space over which the search, discovery, and selection is conducted: i.e., a meta-space of images constructed out of images already taken vs. the physical world in which an original set of images is captured. The extra delight (I continue to have as I experiment with left-brain / right-brain blending) is that - at least temporarily - both sides of my brains are actively engaged in pursuit of an unchanging goal: to find "interesting images" :)

Here some additional "discoveries" in my left-brain constructed multiverse of meta-images (with more sure to follow)...

Transcendent Other

"...the shaman is the remote ancestor of the poet and artist. Our need to feel part of the world seems to demand that we express ourselves through creative activity. The ultimate wellsprings of this creativity are hidden in the mystery of language. Shamanic ecstasy is an act of surrender that authenticates both the individual self and that which is surrendered to, the mystery of being. Because our maps of reality are determined by our present circumstances, we tend to lose awareness of the larger patterns of time and space. Only by gaining access to the Transcendent Other can those patterns of time and space and our role in them be glimpsed."

-  Terence McKenna (1946 - 2000)
Food of the Gods

"This is a Zen camera"

“After dinner I was distracted
by the dream camera, 

and instead of seriously
reading the Zen anthology

I got from the Louisville Library,

kept seeing curious things to shoot,

especially a window in the

tool room of the woodshed.

The whole place is full of

fantastic and strange subjects––

a mine of Zen photography.”
...
“Marvelous, silent,
vast spaces around
the old buildings.
Cold, pure light, and
some grand trees….
How the blank side of a
frame house can be
so completely beautiful
I cannot imagine.
A completely miraculous
achievement of forms.”

...
“Paradise is all around us
and we do not understand...
'wisdom,' cries the dawn deacon,
but we do not attend.”

- Thomas Merton (1915 - 1968)

Postscript #1. The quote begins with an entry that Merton made in his journal on Sep 22, 1963, which marks the first time he refers to “Zen photography.” Four years would pass before his second entry (made after John Howard Griffin, author of the civil rights classic Black Like Me and photographer loaned Merton a Canon FX): “The camera is the most eager and helpful of beings, all full of happy suggestions: 'Try this! Do it this way!' Reminding me of things I have overlooked, and cooperating in the creation of new worlds. So simply. This is a Zen camera.” 

I had seen a few of Merton's wonderful photographs through the years, but have only recently stumbled on two stupendous collections of his oeuvre, the first being Beholding Paradise, edited by Paul M. Pearson (and, literally, just published). For those of you into "Zen Photography" (which I expect make up a sizeable fraction of my kind readers), I strongly recommend you get this volume. It is replete with insights into how a deeply felt presence of world - of spirit - may be made manifest in visual form. 

It is said that photography, in its purest form, offers a path toward self-discovery, helping reveal how you perceive the world and who you "are" as an observer / participant living in it. But Merton discovered (and immersed himself in) photography only a few short years before his death (he was barely fifty at the time he took his first images, and died a short five years later). His "lens" was therefore immediately pointing outward from within an already well-formed core. Oh, and what a core. Quiet, gentle, and humble pointers to a spirit infused world. 

Merton's approach to photography is eloquently summarized in another fine collection of images, A Hidden Wholeness, edited by Griffin (though affordable copies are hard to come by, as this book is long out of print): “His vision was more often attracted to the movement of wheat in the wind, the textures of snow, paint-spattered cans, stone, crocuses blossoming through weeds – or again, the woods in all their hours, from the first fog of morning, though noonday stillness, to evening quiet. In his photography, he focused on the images of his contemplation, as they were and not as he wanted them to be. He took his camera on his walks and, with his special way of seeing, photographed what moved or excited him – whatsoever responded to that inner orientation. His concept of aesthetic beauty differed from that of most men. Most would pass by dead tree roots in search of a rose. Merton photographed the dead tree root or the texture of wood or whatever crossed his path. In these works, he photographed the natural, unarranged, unpossessed objects of his contemplation, seeking not to alter their life but to preserve it in his emulsions. In a certain sense, then, these photographs do not need to be studied, they need to be contemplated if they are to carry their full impact.”

Postscript #2. I should mention how the triptych of images that appears at the top of this post relates to Merton. The individual photos were all taken during a "meditative retreat" my family and I took back in November (which I wrote about briefly here). We rented a cabin nestled somewhere in the beautiful woodland of southern Virginia (not too far from Natural Bridge State Park); whose babbling-brooks-infused grounds and old storage sheds beckoned quiet walks and contemplation. It may not have been Gethsemani, and I certainly had far less time to ponder - and immerse myself in - our lodge's storehouse of humble riches than did Merton in his Abbey, but it gave me a glimpse of Merton's experience. Less Wagnerian-sized operatic landscapes, and more - much more - simple unassuming delights of everyday miracles and mystery: a vigilant cross protecting a decayed entrance, magic light dancing its way around an "ordinary" bathtub, and a mysterious portal into the ineffable.

Immeasurable Events

 "We are survivors of immeasurable events,

Flung upon some reach of land,

Small, wet miracles without instructions,

Only the imperative of change."

- Rebecca Elson (1960 - 1999)

A Responsibility to Awe

Toward Abstract Gestalts

"If metaphor is a verbal
strategy to evoke images,
then as a photographer
I’m interested in
combining images
to alter associations by
extending the image itself 
... 
It is this act
of transformation,
interactivity between images,
that I find the most challenging."

- Nathan Lyons (1930 - 2016)

Postscript / Slightly-convoluted aside on the creative process. I'm still experimenting with what to do with a storehouse of marble abstracts (from c.2011) that I recently "re-discovered" on an old hard-drive during my almost year-long COVID-19-induced "creative convalescence." While the photographs work by themselves - just as straight images - I've started playing with other ways of displaying them. What got me started was the fact that the best abstracts consist of (or possess) multiple overlapping regions that are just as strong if displayed separately. This aesthetic dilemma is both trivial and deep. It is trivial, because it is really no different from the most basic aesthetic judgement that all exposures depend on; i.e., framing. But it is also deeper, because - tautologically - a completed image can only reveal what the intentional framing allows it to reveal. Ironically, the deepest aesthetic value of an image (whether it is intended by the artist or not) may lie hidden, in latent form, discoverable only by discerning the full inherent richness and complexity of the Gestalt of (the myriad entwined parts of) an image.

What do I mean by this, on a more practical level? I first toyed with deliberately breaking up a selection of my marble abstracts into triptychs, literally breaking the images up into equal thirds. I did this not because I thought the images "looked better" when dissected in this way, but because - for the cases I selected - each individual panel proved to be as strong an image - by itself - as the abstract as a whole. But the whole images proved too intrusive - they made it hard to "see the trees for the forest." I next played with making random triptychs, assembling them from a pool of individual 1/3-sized panels (i.e., a candidate triptych consists of a random panel from a random image X, a random panel from a random image Y, and a random panel from a random image Z, keeping only the ones I "liked”). That exercise proved mostly fruitless. While I found a few stray triptychs mildly interesting, most were - sadly but obviously - "less than the sum of their parts." Then I tinkered with constructing triptychs-of-triptychs, but that soon got unmanageable, and the results (except for a few notable exceptions) were less than stellar. (I also experimented with randomly assembling 3-by-3 blocks of parts of images, but the less said about that effort the better.)

And so, we get to the image you see posted on top, which is but one of a fairly large portfolio I've convinced myself I really like; but which also took me a while to understand why (of course, your taste may differ). First, in the context of the labyrinthine "creative process" I just described, the image represents a rather "simple" excursion from just displaying the whole image. Indeed, the "algorithm" (if that is what I dare call it) is to split an image into three parts as before, and choose the "best" (most pleasing?... most interesting?... in practice, whichever one "holds my gaze longest") among the three possible juxtapositions (i.e., 1st and 2nd panel interchanged, 3rd panel fixed; 1st and 3rd panel interchanged, 2nd one fixed; or 2nd and 3rd panel interchanged, and 1st panel fixed); that's it! What makes it work is that - unlike an image that is just broken up into thirds (wherein you "see" the whole even if any of the individual panels strikes an interest on their own) - the whole in this case is objectively invisible (or visible, but only in latent form) - but is nonetheless implicitly still within sight, "just barely out of reach." The viewer is thus afforded a meditative space in which to quietly view and absorb the individual panels, all the while being gently reminded that none of them is the complete story. Indeed, it comes tantalizingly close to letting one to see - in true Goethian fashion - both the whole and its parts simultaneously. Some of the better examples of this (such as the one at the top of this post) induce a dynamic unresolved tension (in me, at least) between seeing the "whole" and "seeing the parts" (along lines of the infamous Necker cube or Wittgenstein's Duck-Rabbit); and take a step toward enticing the viewer to appreciate an image as "more than the sum of its parts."

"Abstract formal elements are

put together like numbers and

letters to make concrete beings

or abstract things;

in the end a formal cosmos

is achieved so much like

the creation that a mere breath

suffices to transform

religion into art."

- Paul Klee (1879 - 1940)

The Spiritual Eye

"We are easily deluded into assuming that the relationship between a foreign subject and the objects in his world exist on the same spatial and temporal plane as our own relations with the objects in our human world. This fallacy is fed by the belief in the existence of a single world, into which all living creatures are pigeonholed. This gives rise to the widespread conviction that there is only one space and one time for all living things. Only recently have physicists begun to doubt the existence of a universe with a space that is valid for all beings. That such a space cannot exist is evident from the fact that all men live in three distinct spaces, which interpenetrate and complement, but in part also contradict one another."

...

"The mechanists have pieced together the sensory and motor organs of animals, like so many parts of a machine, ignoring their real functions of perceiving and acting, and have even gone on to mechanize man himself. According to the behaviorists, man’s own sensations and will are mere appearance, to be considered, if at all, only as disturbing static. But we who still hold that our sense organs serve our perceptions, and our motor organs our actions, see in animals as well as not only the mechanical structure, but also the operator, who is built into their organs, as we are into our bodies. We no longer regard animals as mere machines, but as subjects whose essential activity consists of perceiving and acting.  We thus unlock the gates that lead to other realms, for all that a subject perceives becomes his perceptual world and all that he does, his effector world. Perceptual and effector worlds together form a closed unit, the Umwelt. These different worlds, which are as manifold as the animals themselves, present to all nature lovers new lands of such wealth and beauty that a walk through them is well worth while, even though they unfold not to the physical but only to the spiritual eye."

- Jakob von Uexküll (1864 - 1944)

Imagining the World

"Sometimes he seemed to be

saying that nothing existed

unless people thought it did,

and the world was really

only there at all because

people kept on imagining it.

But then he seemed to be

saying that there were

lots of worlds, 

all nearly the same and 

all sort of occupying

the same place 

but all separated by the 

thickness of a shadow, 

so that everything that 

ever could happen 

would have somewhere

to happen in."

- Terry Pratchett (1948 - 2015)
Equal Rites

Distant Memory

 "The Cosmos is all

that is or was or ever will be.

Our feeblest contemplations

of the Cosmos stir us -- 

there is a tingling in the spine, 

a catch in the voice, 

a faint sensation, 

as if a distant memory, 

of falling from a height. 

We know we are approaching

the greatest of mysteries."

- Carl Sagan (1934 - 1996)
Cosmos

Broken Symmetry

"Passion for science derives from an aesthetic sensibility, not a practical one. We discover something new about the world, and that lets us better appreciate its beauty. On the surface, the weak interactions are a mess: The force-carrying bosons have different masses and charges, and different interaction strengths for different particles. Then we dig deeper, and an elegant mechanism emerges: a broken symmetry, hidden from our view by a field pervading space. It’s like being able to read poetry in the original language, instead of being stuck with mediocre translations."

-  Sean Carroll (1966 - )
The Particle at the End of the Universe

Eternally Complex Tapestry

"Its substance was known to me. The crawling infinity of colours, the chaos of textures that went into each strand of that eternally complex tapestry…each one resonated under the step of the dancing mad god, vibrating and sending little echoes of bravery, or hunger, or architecture, or argument, or cabbage or murder or concrete across the aether. The weft of starlings’ motivations connected to the thick, sticky strand of a young thief’s laugh. The fibres stretched taut and glued themselves solidly to a third line, its silk made from the angles of seven flying buttresses to a cathedral roof. The plait disappeared into the enormity of possible spaces.

Every intention, interaction, motivation, every colour, every body, every action and reaction, every piece of physical reality and the thoughts that it engendered, every connection made, every nuanced moment of history and potentiality, every toothache and flagstone, every emotion and birth and banknote, every possible thing ever is woven into that limitless, sprawling web.

It is without beginning or end.

It is complex to a degree

that humbles the mind.

It is a work of such beauty

that my soul wept...

..I have danced with the spider. 

I have cut a caper

with the dancing mad god."

- China Miéville (1972 - )
 Perdido Street Station

Wonder about Wonder

"How can a three-pound mass of jelly that you can hold in your palm imagine angels, contemplate the meaning of infinity, and even question its own place in the cosmos? Especially awe inspiring is the fact that any single brain, including yours, is made up of atoms that were forged in the hearts of countless, far-flung stars billions of years ago. These particles drifted for eons and light-years until gravity and change brought them together here, now. These atoms now form a conglomerate- your brain- that can not only ponder the very stars that gave it birth but can also think about its own ability to think and wonder about its own ability to wonder. With the arrival of humans, it has been said, the universe has suddenly become conscious of itself. This, truly, it the greatest mystery of all."

- V. S. Ramachandran (1951 - )
The Tell-Tale Brain