Toward an Aesthetic Grammar: Part I

A few years ago, I gave an invited presentation at the Smithsonian Institute in Washington, DC, entitled Nature's Way: The Art of Seeing Complexity. My lecture was part of a multiweek workshop sponsored jointly by the Washington Center for Complexity & Public Policy and the Resident Associate Program of the Smithsonian Institution.

The ambitious goal I set out to accomplish with my talk - which, in hindsight I ought to have known would be impossible to achieve in the short time I had to achieve it (about two hours) - was to use the soul-searching inner musings of a physicist as photographer as a springboard toward forging a possible conceptual bridge between art and science; one that is defined by an aesthetic grammar, and hints at an even deeper aesthetic physics (two phrases that I promise to define more carefully below). As I diligently plowed through my slides, and talked through a few I had prepared especially to explain these subtle points, I could tell from the many blank stares and questioning smirks, that my skeletal new art-science "aesthetics theory" was destined to fall far short of my intended goal that day.

"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 (anthropologist, 1904 - 1980)

So, for another, slightly expanded attempt at communicating some soul-searching inner musings of a physicist as photographer...let me begin - in Part I of a multipart series of essays I intend posting in the coming weeks on the same topic as my Smithsonian talk, but retitled Towards an Aesthetic Grammar - by introducing a provocative theorem that I will first make a cautionary meta-claim about: please be forewarned that the theorem I am about to state will likely strike you either as obvious (at best) or idiotically vacuous (at worst). However, I will immediately argue that not only does the truth (of its interpretation) lie nowhere near these two extremes, but that the theorem is deceptively subtle and points to a universal "core truth" that underlies all cognitive, scientific and creative endeavors!

What is this remarkable theorem? It is called the "Ugly-Duck Theorem" (named after the well-known story by Hans Christian Andersen), and was proposed and proven by statistician Satosi Watanabe in 1969 (who was then at the University of Hawaii).

Suppose that the number of predicates that are simultaneously satisfied by two nonidentical objects of a system, A and B, is a fixed constant, P. The Ugly Duck theorem asserts that the number of predicates that are simultaneously satisfied by neither A nor B and the number of predicates that are satisfied by A but not by B are both also equal to P. While this assertion is easy to prove, and certainly appears innocuous at first glance - indeed, you would be forgiven to think it entirely "meaningless" since it is merely restating an obvious combinatorial fact about the set of possible predicates - it has rather significant philosophical and conceptual consequences.

"Thought is creating divisions out of itself and then saying that they are there naturally." - David Bohm

For example, suppose that there are only three objects in the world, arbitrarily labeled (@,@,#). An obvious interpretation is that this describes two kinds of objects: two @s and one #. But there are other ways of partitioning this set. For example, line them up explicitly this way: @ @ #. An implicit new organizing property seems to emerge: the leftmost @ and the rightmost # share the property that they are "not in the middle". We are free to label this property using the symbol @, and the property of being in the middle, #. Now, substituting the new property for each of the original objects, we have @ @ # -> @ # @.

Had we sorted these three objects according to the new property (that discriminates according to spatial position), we would again have two kinds of objects, but in this case they would have been different ones. Obviously, we can play this game repeatedly, since there are endless number of possible properties that can arbitrarily be called @ and #. That is the point. Unless there is an objective measure by which one set of properties can be distinguished from any of the others, there is no objective way to assert that any subset of objects is better than, or different from, any other.

The theorem demonstrates that there is no a priori objective way to ascribe a measure of similarity (or dissimilarity) between any two randomly chosen subsets of a given set. (Or, stated more whimsically, the theorem states that, all things being equal, an ugly duck is just as similar to a swan as two swans are to each other!) More technically speaking, we see that asymmetries within a system (i.e., differences) can be induced only either via some externally imposed “aesthetic” measure, or generated from within.

"Of course" ... you might be saying ... "that is obvious! But why is this important?" It is important because it demonstrates that - fundamentally - all of our perceptions of the world, precisely because they are demonstrably not all uniform, appear as sets of different things interrelated in a myriad of ways because of an internal aesthetic (or internal grammar, or physics!) that we automatically impose on what we perceive (doing so mostly unconsciously). The problem is to find a way to characterize and articulate what such a grammar might actually look like!

We "see" rocks and chairs and people primarily because nature has evolved an immeasurably powerful sensory-cognitive processing mechanism that rapidly "tags" for us (for our "I") the patterns in our environment that we will most likely be interacting with repeatedly throughout our lifetime. These objects are not visible to us (as "things") because the universe has labeled them "objectively meaningful" in a global sense (I doubt whether the universe really cares whether a particular transient pattern of atoms is called a "chair", a "collection of wooden planks" or "an exemplar of post-modern, neo-minimalist drivel"); rather, they appear to us as "meaningful" only because they are meaningful to us locally, in terms of the natural aesthetics we were born with (and evolve for ourselves as we interact with our perceptions and experiences) that determine what objects we can see, and the degree to which we can distinguish one object from another.

Who we are - our "I" - is defined and shaped most strongly by our internal aesthetic; which, I shall argue shortly, does not just describe "what we happen to think is beautiful at the moment" but molds our entire conception of the world, with all of the artistic, scientific, philosophical and spiritual depths that entails.

When I use the phrase "conceptual grammar" (or "aesthetic grammar") I mean - no more and no less - the set of aesthetic-weights we use (mostly unconsciously) to ascribe more or less "thingness" to an object A compared to another object B. According to the Ugly Duck theorem, we would expect the components of this set of weights to all be equal and therefore completely undiscerning in a rigorously objective world. Our conceptual grammar, understood in this way, therefore also constitutes the backbone of a primitive "local physics" we all use to describe our world; where by "physics" I mean a set of "organizing principles" that describe the underlying patterns of what our aesthetics "permit" us to recognize as existing.

Thus, when I write "grammar", I am thinking of primitive building blocks of "things" that (we imagine and/or perceive to) populate our (aesthetically generated asymmetric) local world, and the ways in which things may be "combined" to yield other things. And when I write "physics", I am thinking of the primitive building blocks of "patterns" that connect the things.

"Man tries to make for himself in the fashion that suits him best a simplified and intelligent picture of the world; he then tries to some extent to substitute this cosmos of his for the world of experiences, and thus to overcome it. This is what the painter, the poet, the speculative philosopher, and the natural scientist do, each in his own fashion." - Albert Einstein

I will discuss some important consequences of the Ugly Duck theorem, and suggest how it might be used to generalize what we (think we) know about our "scientific aesthetics" to begin probing what an (objectively artful) "aesthetic grammar" may look like, in Part II (stay tuned....) Speculations on what all of this has to do with complexity, photography, the "art of seeing", and using art to find one's "I", will also appear in forthcoming essays.

Technical Note: The Ugly Duck Theorem complements another well-known theorem called the No Free Lunch theorem, proven by Wolpert and Macready in 1996. The No Free Lunch theorem asserts that the performance of all search algorithms, when averaged over all possible cost functions (i.e., problems), is exactly the same. In other words, no search algorithm is better, or worse, on average than blind guessing. Algorithms must be tailored to specific problems, which therefore effectively serve as the external aesthetic by which certain algorithms are identified as being better than others. Technical proofs of Watanabe's theorem appear in his books Knowing and Guessing and Pattern Recognition (both of which are, sadly, out of print).

Amazing New Resource for Photographers & Students of Photography

Focal Press (i.e., the Media Technology component of Elsevier Publishing) has just published a "book" (a pristine copy of which I have been happily browsing through after it had - literally - landed on my doorstep with a loud THUD!; I put the word "book" in quotes because, as I will describe below, to call this massive cinder-block of a reference work a "book" is roughly equivalent to calling a fresh uneaten loaf of bread a "crumb";-) that has all the tell-tale signs of being a classic scholarly reference for photographers and students of photography for years to come: The Focal Encyclopedia of Photography, Fourth Edition, edited by Michael R. Peres (also available from Amazon).

The encyclopedia is a significant update of its predecessor volumes, with a massive amount of new material. The first edition, a classic in its time when it was published in 1956, has been long out of print and is obviously extremely dated given all of the advances in photographic science, engineering and art that have occurred since then. The third edition (edited by Richard D. Zakia and Leslie Stroebel), which I own and love, is only a decade old but has very little on the burgeoning field of digital photography. However, it still contains a veritable storehouse of useful information and, though it is also out of print, is available in some used book stores (given the hefty price of the new volume, some students on a budget may want to instead consider the third edition).

The new fourth edition has 880 pages in all, over 400 images, covers all major (and minor) areas of photography (ranging from photography and art / society / commerce, museums, the science of photography, galleries, workshops, education, publishing, history, theory, practice, criticism, and short biographies of selected photographers in the 20th Century), and comes with a CD-ROM that contains the entire (and fully searchable) text + images in the book (this one surprising, and most welcome, addition is alone worth the "price of admission").

The book is very handsomely produced, with strong, thick covers and thick, semi-glossy pages that give the volume a "classy feel" and give the overall impression that the editors designed it to be well thumbed and used, and to last a long, long while (which I pray it does since most of my photo books, particularly reference works, tend to become tattered and grow nested dog-ears in no time, as I repeatedly dive in for the shear pleasure of discovering some morsel of photographic delight).

The encyclopedia does have one unfortunate, but arguably unavoidable, drawback: it is so big and heavy that it is impossible to just "whip it out" on your lap and sink into (a flimsy chair) for some leisurely reading; you have to plan on when and where you will be reading this monster! ... and, God forbid, don't even think of taking it to an upstairs room to read in bed: if the staircase doesn't collapse from the weight before you get there, your bed surely will! ;-)

Kudos to Focal Press' editorial board for producing such a fine masterwork. It will likely become the "standard" such reference for all current and future generations of students of photography (and, I suspect, quite a few working professionals as well).

Wonderful Collection of Essays on Photography

Bill Jay is likely familiar to many photographers (and certainly to readers of Lenswork magazine).

Among his many accomplishments, he was the first Director of Photography at the Institute of Contemporary Arts, the first Editor/Director of Creative Camera and Album magazines, and the founder of the Program of Photographic Studies at The University of Arizona, where he has taught for over 25 years. He has published over 400 articles and authored more than 20 books on the history and criticism of photography (see, for example, On Being a Photographer, co-authored with David Hurn, and available either from Lenswork or Amazon). He also writes the delightful Endnotes for Lenswork each month, earmarked with his uniquely witty, and sardonic style.

Mr. Jay has generously posted a rich sampling of his essays and portraits on his website. To suggest that (after you click on the first essay and just start reading) you will be "staying a while" on his site is a profound understatement; plan on spending at least a few hours, and then make time for more later! Thank you Mr. Jay!

Fleeting Glimpse of Uber-Genius

Every once in a while, one runs across a work that is so powerfully moving, so visionary, that it is as though the spiritual cosmos itself has briefly transformed into (or, with a wink to itself, escaped into) corporeal existence; the artist that serves as channel for this wondrous interpenetration of spirit and matter can only be described as an Uber-artist, or more simply, an Uber genius. Allow me to introduce you to a candidate for such an honor...

"...Humanity owes its progress to geniuses...[but] humanity is not want to deal kindly with its geniuses..." (Stanislaw Lem, "Odysseus of Ithaca", Non Servium)

In the April 2007 issue of the fine-art B&W photography magazine (issue #50), I ran across the work of photographer Jerry Wolfe, the front cover of whose extraordinary book - Beginner's Mind - is reproduced at the top of this Blog entry; and was awe-struck by the intensity of spiritual depth captured, and radiated, by his mesmerizing images. The last image of the published series, in particular, titled Cave Detail (page 99, B&W issue #50), triggered a spiritual odyssey - in me - with echoes of visions my youthful self had of what was possible with photography (when in the right eyes and hands) when I first glanced at Minor White's visionary Capitol Reef.

"...First come your run-of-the-mill and middling geniuses, that is of the third order, whose minds are unable to go much beyond the horizon of their times. These, relatively speaking, are threatened the least; they are often recognized and even come into money and fame..." (Stanislaw Lem, "Odysseus of Ithaca", Non Servium)

Mr. Wolfe has been a photographer for over 30 years, gracefully combining his preturnaturally gifted eye for beauty with his lifelong spiritual practice of mindfulness and Buddhist meditation. All of his images are subtlety charged with a quiet grace; as though they are earthly imprints of a mysterious, ethereal spiritual grammar. Their meaning shifts, even as you observe them; and observe them you will, for while, objectively speaking, they are (as are all prints) nothing more than "flat, two-dimensional worlds", they reveal worlds - and worlds of meaning - far beyond the limitations of the page they live on, and sometimes point to even vaster, more mysterious worlds within.

"...The geniuses of the second order are already too difficult for their contemporaries and therefore fare worse...recognition awaits the geniuses of the second order, in the form of a triumph beyond the grave..." (Stanislaw Lem, "Odysseus of Ithaca", Non Servium)

Mr. Wolfe's Beginner's Mind is an extraordinary work of art, with an emphasis on extra-ordinary, for it transcends even (otherwise conventionally) symbolic levels of meaning, achieving visual/spiritual tones rarely attained by even the most "gifted" of artists. How does he do this? I have no idea, nor could I, except to embrace the idea that all of us are humble channels for nature's own creative powers.

"...The intermediate types [beyond second but below first order] are discovered either by the succeeding generation or by some later one..." (Stanislaw Lem, "Odysseus of Ithaca", Non Servium)

Condider just one small part of Mr. Wolfe's Opus, his Buddhist Expressions Series (#1 - #12, pages 20-43 in Beginner's Mind), which Mr. Wolfe (humbly, poetically and very appropriately) opens with ...

Each Moment
Fresh and original.
Where's the "I"
Experiencing this?

To which, after seeing these wondrous prints, I can only say that they are among the finest abstracts I have ever seen. Not because they are merely "beautiful abstracts" (which they surely are), but because they embody the core Kandinsky-like essence of what a true "abstract" represents: a portal to other, higher, worlds and realities.

"...the geniuses of the first order are never known - not by anyone, not in life, not after death. For they are creators of truth so unprecedented, purveyors of proposals so revolutionary, that not a soul is capable of making head or tail of them..." (Stanislaw Lem, "Odysseus of Ithaca", Non Servium)

Mr. Wolfe is certainly not threatened by obscurity, for he is already a well known artist, teacher and author. But he represents a small class of profoundly gifted visionaries that - for whatever reason (perhaps simply the vagaries of life's currents) - are not much better known than they are!

I urge all fine-art photographers, particularly those with a penchant for using their art for spiritual exploration, to experience Mr. Wolfe's Beginner's Mind for themselves (you can also order it from Amazon). Who knows what paths a simple click of a mouse might take you?

Transitory Impermanence

The Merriam-Webster on-line dictionary informs us that the word "transitory" comes from the Middle English word transitorie (and from Anglo-French, from Late Latin transitorius; from Latin, of or allowing passage, from transire); and means tending to pass away; not persistent (or of brief duration). Yet, as with most things (and particularly processes) in this world, even this seemingly iron-clad "definition" is not without some ambiguity and a sense of mystery.

At first sight, what we see here is the very epitome of transitory reality: water, flowing over monolithic rock. The effervescent fluid is full of life and energy, and is demonstrably and obviously impermanent. The boulders are classic symbols of stability and permanence. But is either element really such a stalwart exemplar of the class of being that it purports to be?


Are not the rocks, if viewed in their natural context, more of an impermanent reality than the water, as they slowly, but inevitably, succumb to the rushing water's punishing power? Is not the flow of water (rather than its substance), in fact, a much longer living entity; one destined to outlive even the strongest of rocks? How many years had the "rocks" that are no longer part of the Grand Canyon withstood the inexorable onslaught of the Colorado River's persistent flow?...


...and what is the analog, I wonder, of the "rushing water" to our seemingly permanent (but, in truth, merely transitory) "reality" as living, sentient, and soulful creatures? How many years will go by before life itself becomes a distant memory? ...before it turns into an organically eroded gorge, carved into oblivion by the methodical, uncaring flow of time?

This existence of ours is as transient as autumn clouds
To watch the birth and death of beings is like looking at the movements of a dance.
A lifetime is like a flash of lightning in the sky,
Rushing by, like a torrent down a steep mountain. - Buddha

Rejuvenating Metapatterns

It has been quite some time since I've posted any new images; indeed, it has been quite some time since I've captured any. While an unqualified virtue of being a devout "amateur" photographer is that I am (for the most part) able to focus my attention on the kind of photographs I like to take (rather than shoot for clients and cater to their needs); the downside is that my "day job" always has priority; and the past few months have been particularly busy.


So, what does this amateur photographer do when he finally finds a few precious moments to prowl around with his camera? He ventures off in search of the primitive metapatterns (identified a few years ago by my then 6yo son as forming the core of his dad's "eye"): rocks, leaves and water.


Of course, these metapatterns both arise and persist mostly due to happenstance as I can travel only so far from home for my "safaris" and usually wind up taking short nature walks at local parks. On the other hand, these metapatterns are also almost always (as noted by my son) those that I turn to first after a long period of relative inactivity. I have learned from experience that these simple, timeless, themes rejuvenate my soul, and refocus my mind from equations, computer code and technical reports to more artful pursuits.


What is fascinating to me is how much "rust" I always find in the artful part of my brain, even after what (objectively speaking) is only a relatively short time "away" from the camera. Photographers (likely all artists!) know precisely what I mean by this. It is not that I have forgotten the technical aspects of my craft (f-stops and such); it is simply that what is usually an effortless act of unconscious composition, is, for a time at least, anything but effortless. I feel the process, as though my eye/I is moving through molasses. The same is true for any craft, of course (even physics: though I find that I must be away from that for a considerably longer time to feel the same degree of "rust"). But there is something subjectively different about art; in that the artist's rust seems to appear virtually simultaneously with the artist losing his/her engagement and total immersion.


A less convoluted way of saying the same thing, I suppose, is that our muse simply wanders off when we lose attention. Hardly a surprise in hindsight, and something I always relearn as I try to reconnect with my muse.

The Four-Dimensional Photographer

Stephen Shore, the well known photographer (and teacher; who, among other things, was the first living photographer to have a one-man show at the Metropolitan Museum of Art in NY) has recently updated his classic meditation on the Nature of Photographs. Recommended to all aspiring (and working) photographers, the beauty of this book is the density of its distilled wisdom.

You will not find anything here on f-stops, film speeds and lenses, nothing on the darkroom (analog or digital), nothing on the raging "debate" whether to pick up an 8 megapixel DSLR or a 10, and no instructions - at least explicit ones - on how to take "better" pictures. What you will find is the crystalline essence of Shore's lifetime's worth of thinking about the nature of the photograph. His short, Zen-like prose-poem musings pierce the proverbial bullseye like an archer's arrow; and leave the reader both enchanted and haunted by their eloquence and wisdom.

Shore reminds us that amidst the infinity of potential images, both real and imagined, the photographer has four - and only four - formal tools for defining a picture's content and organization: vantage point, frame, focus and time. Stop and think about that for a moment. With all the wonderful technology underneath our thumb as we prepare to press the shutter, with all the different ways in which we can image ourselves "taking" a shot, and all the different images that can conceivably exist, the photographer really only has these four fundamental "creative dimensions" with which to work, and no more! Where do I position myself; what do I put in the picture and what do I leave out; where should I focus my attention; and how much of a slice of time do I want to include?

Every picture that has ever been taken, and every photograph yet to be captured - from Adams' shots of Yosemite, to Cartier-Bresson's visual etudes on the "Decisive Moment," to visual realities created by some future technologies - is "reality" as aesthetically transformed by the four-dimensional human creative filter!

Yet somehow, miraculously even, this suffices to provide (however brief) glimpses of an infinite dimensional world of meaning and beauty. That is the magic of photography!