Numerical Harmonies

 "The universe as a giant harpstring,
oscillating in and out of existence!
What note does it play, by the way? 
Passages from the Numerical Harmonies...?"

- Ursula K. Le Guin (1929 - 2018)
The Dispossessed: An Ambiguous Utopia

Inconceivable Dimensions

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

- Mircea Cărtărescu (1956 - )
Solenoid

Elaborate Complexity

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

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

The Fundamental Field

"Since the various aspects of [cymatics] are due to vibration, we are confronted with a spectrum which reveals patterned, figurate formations at one pole and kinetic-dynamic processes at the other, the whole being generated and sustained by its essential periodicity. These aspects however, are not separate entities but are derived from the vibrational phenomenon in which they appear in their "unitariness". Even though one or the other may predominate in this or that phenomenon, we invariably find these three elements present. In other words, the series we have formulated is in reality confluent in homogeneous activity. It is not that we have configuration here and organized pattern there, but that every effect of vibration bears the signature of configuration, movement and a play of forces. We can, so to speak, melt down our spectrum and observe the action of its various categories as a continuous play in one and the same entity. If we wish to describe this single entity, we can say this: there are always figurate and patterned elements in a vibrational process and a vibrational effect, but there are also kinetic and dynamic elements; the whole is of a periodic nature and it is this periodicity which generates and sustains everything. The three fields - the periodic as the fundamental field with the two poles of figure and dynamics - invariably appear as one. They are inconceivable without each other. It is quite out of the question to take away the one or the other; nothing can be abstracted without the whole ceasing to exist."

- Hans Jenny (1904 - 1972)
Cymatics

Beyond the Grasp of The Imagination

"Let us now endeavor to conceive what Matter must be, when, or if, in its absolute extreme of Simplicity. Here the Reason flies at once to Imparticularity - to a particle - to one particle - a particle of one kind of one character - of one nature of one size of one form - a particle, therefore, ‘without form and void’ - a particle positively a particle at all points a particle absolutely unique, individual, undivided, and not indivisible only because He who created it, by dint of his Will, can by an infinitely less energetic exercise of the same Will, as a matter of course, divide it ... Oneness, then, is all that I predicate of the originally created Matter; but I propose to show that this Oneness is a principle abundantly sufficient to account for the constitution, the existing phænomena and the plainly inevitable annihilation of at least the material Universe.

...

By Him, then, existing as Spirit, let us content ourselves, to-night, with supposing to have been created, or made out of Nothing, by dint of his Volition—at some point of Space which we will take as a centre - at some period into which we do not pretend to inquire, but at all events immensely remote - by Him, then again, let us suppose to have been created what? … An intuition altogether irresistible, although inexpressible, forces me to the conclusion that what God originally created - that Matter which, by dint of his Volition, he first made from his Spirit, or from Nihility, could have been nothing but Matter in its utmost conceivable state of Simplicity.

...

Had we discovered, simply, that each atom tended to some one favorite point - to some especially attractive atom - we should still have fallen upon a discovery which, in itself, would have sufficed to overwhelm the mind: but what is it that we are actually called upon to comprehend? That each atom attracts - sympathizes with the most delicate movements of every other atom, and with each and with all at the same time, and forever, and according to a determinate law of which the complexity, even considered by itself solely, is utterly beyond the grasp of the imagination of man."

- Edgar Allan Poe (1809 - 1849)

Eureka: A Prose Poem

A Pattern is a Message

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

...

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

...

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

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

Cymatic Urphänomen

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

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

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

- Henri Bortoft (1938 - 2012)

The Wholeness of Nature

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

Ouroborosian Complexity

"In the end, we self-perceiving, self-inventing, locked-in mirages are little miracles of self-reference. We believe in marbles that disintegrate when we search for them but that are as real as any genuine marble when we’re not looking for them. Our very nature is such as to prevent us from fully understanding its very nature. Poised midway between the unvisualizable cosmic vastness of curved spacetime and the dubious, shadowy flickerings of charged quanta, we human beings, more like rainbows and mirages than like raindrops or boulders, are unpredictable self-writing poems - vague, metaphorical, ambiguous, and sometimes exceedingly beautiful."

 -  Douglas R. Hofstadter (1945 - )
I Am a Strange Loop

A Space-Time Event

"There is nothing mysterious about space-time. Every speck of matter, every idea, is a space-time event. We cannot experience anything or conceive of anything that exists outside of space-time. Just as experience precedes all awareness and creative expression, the visual language of our photographs should ever more strongly express the fourth dimensional structure of the real world.

...

I feel all things as dynamic events, being, changing, and interacting with each other in space and time even as I photograph them.

...

What you see is real - but only on the particular level to which you've developed your sense of seeing. You can expand your reality by developing new ways of perceiving."

- Wynn Bullock (1905 - 1975)

"To be" is to Inter-Be

"If you look deeply, you will see that there is a cloud floating in this sheet of paper. Without a cloud, there will be no rain; without rain, the trees cannot grow; and without trees, we cannot make paper. The cloud is essential for the paper to exist. If the cloud is not here, the sheet of paper cannot be here either. So we can say that the cloud and the paper inter-are. 'Interbeing' is a word that is not in the dictionary yet, but if we combine the prefix 'inter-' with the verb 'to be,' we have a new verb, inter-be.

...

If we look into this sheet of paper even more deeply, we can see the sunshine in it. If the sunshine is not there, the forest cannot grow. In fact, nothing can grow. Even we cannot grow without sunshine. And so, we know the sunshine is also in this sheet of paper. The paper and the sunshine inter-are. And if we continue to look, we can see the logger who cut the tree and brought it to the mill to be transformed into paper. And we see the wheat. We know the logger cannot exist without his daily bread, and therefore the wheat that became his bread is also in this sheet of paper. And the logger’s father and mother are in it too. When we look in this way, we see that without all these things, this sheet of paper cannot exist.

...

Looking even more deeply, we can see we are in it too. This is not difficult to see, because when you look at a sheet of paper, the sheet of paper is part of our perception. Your mind is in here and mine is also. So we can say that everything is in here with this sheet of paper. You cannot point out one thing that is not here – time, space, the earth, the rain, the minerals in the soil, the sunshine, the cloud, the river, the heat. Everything co-exists with this sheet of paper. That is why I think the word inter-be should be in the dictionary. 'To be' is to inter-be. You cannot just be by yourself alone. You have to inter-be with every other thing. This sheet of paper is, because everything else is."

- Thích Nhất Hạnh (1926 - 2022)
The Heart of Understanding

Postscript. As is likely obvious to even casual visitors to my humble blog during the last week, I am currently immersed in the world of cymatics (although my wife thinks of it as more of an obsession). "Cymatics" refers to the study of sound and vibration; specifically, when the two are combined in a way that creates complex patterns in different media such as sand, water, or - what Swiss physician Hans Jenny (who coined the term) liked to use - corn starch in water. For example, if a metal plate is covered with a thin layer of flour or sand and is made to vibrate at specific frequencies, so-called standing-wave Chladni patterns appear in which the flour or sand collects along "nodes" (i.e., lines or points that undergo minimal vibration), while areas that undergo the greatest motion (i.e., the "anti nodes") are effectively left empty as the vibration pushes the flour or sand away. Chladni patterns are named after physicist Ernst Chladni who performed the first such experiments in the late 1700s.

I thank my left-brain/day-job as a physicist for introducing me to cymatics in the late 1990s when I stumbled across this paper describing what (at the time, were never before seriously studied) complex emergent patterns in vibrating layers of small granular media (e.g., cylinders filled with BBs from a toy shotgun). One line from this paper immediately grabbed my attention when I first read it and that still haunts me (both as physicist and photographer): "These excitations [called "oscillons"] have a propensity to assemble into 'molecular' and 'crystalline' structures." I remember musing, Whoa!, pump energy into an otherwise static structureless pile of 'things' and get self-organized geometric patterns?!? It was during my (absurdly slow, pre-Google days) search for related experiments that I discovered Jenny's work on cymatics, the underlying dynamics of which has a far-from-superficial overlap with the physics of oscillons.

So, having known about cymatics for about 25 years - and having even posted about it briefly in 2006 on this same blog! - why has it taken me so long to photograph it? I have no easy answer to that, just as I cannot explain why I never photographed my dad-working-as-an-art-restorer when he was still alive, which is something that - 23 years after his passing - I now profoundly regret (see Postscript 1 in this post from 2010). The creative process and the muse that guides our path are both mysterious and ultimately unknowable, which is as it should be. So, I'll leave it at that. But, whatever the reason(s) for my flurry of recent purchases of frequency generators, vertical vibration generators, lights, and more plates, goblets and petri dishes than any sane photographer has reason to own (and our kitchen cupboards have room for), I am - at the moment (and for the foreseeable future) - completely and utterly "obsessed" with cymatics. The reason is simple enough to state: cymatics is a quintessentially perfect amalgam of all three of my aesthetic and intellectual passions - physics, photography, and mysticism. 

The first two separately play obviously critical roles. The physicist-side of my brain is giddy over the vast phase space waiting to be explored: vibration frequency + medium (type + mix type) + vessel (type + diameter + depth) + ... And the photographer side is not too far behind: light (type + source(s) + directionality) + angle-of-view + f-stop + exposure time + ... But it is the idea of "cymatics as creative bridge" between seen and unseen, between energy and pattern, and between physical and spiritual that I resonate most deeply with, and is most ripe with creative possibilities. (For example, it has not escaped my attention that, in a "mystical" sort of way, the energy that the universe ineffably pumps into an otherwise structureless bag full of 'elemental things' gives rise to an emergent multidimensional dynamic cymatic-like sentient geometry called "Andy")

Since I've only started exploring the cymatics-scape universe, I have no idea what patterns await to be discovered and/or how long the search will keep my interest. But, given that I'm still looking for synesth-scapes after being mesmerized by reflective patterns in my mother-in-law's Nambe-like metal salt and pepper shakers in 2009,  cymatics may take a while 😊

For those still reading this, here is a link to a newly revised version of Hans Jenny's opus, Cymatics: A Study of Wave Phenomenon and Vibration. This version includes both volumes of the original work, as well as new chapters that include a biographical sketch of Hans Jenny, a non-technical primer on the physics of cymatics, and commentaries by researchers, sound therapists, designers, and artists. Indeed, I strongly recommend perusing the entire CymaticSource website, since it is a veritable storehouse of additional information, books and videos. (I am not affiliated with this website in any way. But, having recently purchased the aforementioned reprint of Jenny's revised Cymatics volume, I can personally attest to its quality - it is a stunningly beautiful book.)

Multitudinousness Minds

"Mahamati, since the ignorant and simple-minded, not knowing that the world is only something seen of the mind itself, cling to multitudinousness of external objects, cling to the notions of being and non-being, oneness and otherness, bothness and non-bothness, existence and non-existence, eternity and non-eternity, and think that they have a self-nature of their own, all of which rises from the discriminations of the mind and is perpetuated by habit-energy, and from which they are given over to false imagination. It is all like a mirage in which springs of water are seen as if they were real. "

- Lankavatara Sutra (c.350–400 CE)

Near Symmetry of Nature

"So our problem is to explain where symmetry comes from. Why is nature so nearly symmetrical? No one has any idea why. The only thing we might suggest is something like this: There is a gate in Japan, a gate in Neiko, which is sometimes called by the Japanese the most beautiful gate in all Japan; it was built in a time when there was great influence from Chinese art. This gate is very elaborate, with lots of gables and beautiful carving and lots of columns and dragon heads and princes carved into the pillars, and so on. But when one looks closely he sees that in the elaborate and complex design along one of the pillars, one of the small design elements is carved upside down; otherwise the thing is completely symmetrical. If one asks why this is, the story is that it was carved upside down so that the gods will not be jealous of the perfection of man. So they purposely put an error in there, so that the gods would not be jealous and get angry with human beings. We might like to turn the idea around and think that the true explanation of the near symmetry of nature is this: that God made the laws only nearly symmetrical so that we should not be jealous of His perfection!"

- Richard Feynman (1918 - 1988)

Mycelial Awareness

"Fungi marched onto land more than a billion years ago. Many fungi partnered with plants, which largely lacked these digestive juices. Mycologists believe that this alliance allowed plants to inhabit land around 700 million years ago. Many millions of years later, one evolutionary branch of fungi led to the development of animals.

...

I believe that mycelium is the neurological network of nature. Interlacing mosaics of mycelium infuse habitats with information-sharing membranes. These membranes are aware, react to change, and collectively have the long-term health of the host environment in mind. The mycelium stays in constant molecular communication with its environment, devising diverse enzymatic and chemical responses to complex challenges.

...

If you were a tiny organism in a forest’s soil, you would be enmeshed in a carnival of activity, with mycelium constantly moving through subterranean landscapes like cellular waves, through dancing bacteria and swimming protozoa with nematodes racing like whales through a microcosmic sea of life."

- Paul Stamets (1955 - )
Mycelium Running:
How Mushrooms Can Help Save the World

Silence and Stillness

"When I detect a beauty in any of the recesses of nature, I am reminded, by the serene and retired spirit in which it requires to be contemplated, of the inexpressible privacy of a life - how silent and unambitious it is. The beauty there is in mosses must be considered from the holiest, quietest nook.

...

Silence is the communion of a conscious soul with itself. If the soul attend for a moment to its own infinity, then and there is silence. She is audible to all men, at all times, in all places, and if we will we may always hearken to her admonitions.

...

The gods delight in stillness, they say ’st-’st. My truest - serenest moments are too still for emotion -they have woolen feet. In all our lives we live under the hill, and if we are not gone we live there still."

- Henry David Thoreau (1817 - 1862)

Made of Pattern

"From the systems point of view, the understanding of life begins with the understanding of pattern ... there has been a tension between two perspectives - the study of matter and the study of form - throughout the history of Western science and philosophy. The study of matter begins with the question, 'What is it made of?'; the study of form asks, 'What is its pattern?' Those are two very different approaches, which have been in competition with one another throughout our scientific and philosophical tradition."

- Fritjof Capra (1939 - ) and Pier Luigi Luisi (1938 - )
The Systems View of Life: A Unifying Vision

Self-Creation

"As the spider creates and absorbs...
so this universe proceeds from the immortal."

Commentary: "It was said the immortal is the source of all created things. How it is the source is explained by well-known analogies; as is well-known in the world, the spider without requiring any other cause itself creates, i.e., sends out threads not distinct from its own body and again absorbs them itself, i.e., draws them into itself or makes them part of itself; as medicinal plants, i.e., from the corn plant to the immovable, not distinct from the earth, proceed from the earth, and as from the living person the hairs proceed different in nature from him; as in these illustrations, so here, i.e., in the circle of samsara, all the universe of the same and different nature proceeds from the akshara above described, without requiring any other cause; the statement of many analogies is to facilitate easy understanding of the meaning; universe which proceeds from the Brahman proceeds in this order and not all at once, like the throwing of a handful of apples."

- S. Sitarama Sastri

Upanishads and Sri Sankara's commentary

Postscript. This is a cropped iPhone image of a stylized advertisement for a wedding dress that appears in the window of a local dry-cleaning company appropriately called "Cosmo Cleaners" 😊

Patterns of Organic Energy

"'Wu Li' was more than poetic. It was the best definition of physics that the conference would produce. It caught that certain something, that living quality that we were seeking to express in a book, that thing without which physics becomes sterile. 'Wu' can mean either 'matter' or 'energy.' 'Li' is a richly poetic word. It means 'universal order' or 'universal law.' It also means 'organic patterns.' The grain in a panel of wood is Li. The organic pattern on the surface of a leaf is also Li, and so is the texture of a rose petal. In short, Wu Li, the Chinese word for physics, means 'patterns of organic energy' ('matter/ energy' [Wu] + 'universal order/organic patterns' [Li]). This is remarkable since it reflects a world view which the founders of western science (Galileo and Newton) simply did not comprehend, but toward which virtually every physical theory of import in the twentieth century is pointing!"

-  Gary Zukav (1942 - )
The Dancing Wu Li Masters

An Unknowable Unfolding

"How did the universe get from matter to mattering?

...

Life comes from life," declared Pasteur.
But, if so, whence life in the first place?

...

The biosphere explodes in diversity,
creating more and more cracks in the
floor of Darwin’s nature until the cracks,
ever expanding, become the
very floor of nature,
and nature herself.

...

The ultimate, an unknowable unfolding, slips
its foundational moorings and floats free.

...

Agency introduces meaning into the world!"

- Stuart A. Kauffman (1939 - )
A World Beyond Physics

Ontology of Materialism

"What we observe is not nature itself, but
nature exposed to our method of questioning.

...

The ontology of materialism rested upon
the illusion that the kind of existence,
the direct 'actuality' of the world around us,
can be extrapolated into the atomic range.
This extrapolation, however, is impossible...
Atoms are not things.

...

Whenever we proceed from the known into the unknown
we may hope to understand, but we may have to learn
at the same time a new meaning
of the word 'understanding."

- Werner Heisenberg (1901 - 1976)
Physics and Philosophy

String Theory

"For me, the most beautiful aspects of physics are not the complicated math equations or even the ability of predicting how things will happen. What attracts me to physics is what it teaches us about the bigger picture. The general philosophical lessons that are embedded in physical laws are what excite me. For example, the fact that all particles and forces get unified within string theory teaches us about the unity underlying our universe. The amazingly vast collection of solutions to equations of string theory suggests that there may be many universes besides ours. What happened before the big bang, or was there a time before big bang? The 'duality symmetry' in string theory, which exchanges small spaces with large spaces, suggests that perhaps as we go back in time the universe was effectively getting bigger instead of smaller. This suggests we came from other universes. Physics teaches us deep facts about our universe and our place in it. I hope I can add a little to this beautiful story. That is my goal."

- Cumrun Vafa (1960 - )