Showing posts with label Symmetry. Show all posts
Showing posts with label Symmetry. Show all posts

Monday, November 17, 2025

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

Sunday, November 09, 2025

Electric Universe


"The watcher’s eyes are likely to swivel forward in a sequence of stately turns as the screen’s pixel glows: each quarter-ounce mass of eyeball tugged by six flat muscles, in a glissando slide within the slippery fat lining the orbital cavity. The eye blinks, the widened pupils are in position, and the incoming electromagnetic waves roar in. Ripping through the thin layer of the cornea, they decelerate slightly, with their outermost edges forming a nearly flat plane as they travel inward, carrying the as-yet-undetected signal from the screen deep into the waiting human. The waves continue through the liquid of the aqueous humor and on to the gaping hole of the pupil. The human may have squinted to avoid the glare, but human reflexes work at the rate of slow thousandths of a second and are no match for these racing intruders. The pupil is crossed without obstruction. The stiff lens just below focuses the incoming waves even more, sending them into the inland sea of the jellylike vitreous humor deeper down in the eye. A very few of the incoming electric waves explode against the organic molecules in their way, but most simply whirl through those soft biological barriers and continue straight down, piercing the innermost wrapping of the eyeball, till they reach the end-point of their journey: the fragile, stalklike projection from the living brain known as the retina. And deep inside there, in the dark, barely slowed from their original 670 million mph, the waves splatter into the ancient, moist blood vessels and cell membranes, and something unexpected happens. An electric current switches on."

- David Bodanis, Electric Universe

Friday, November 07, 2025

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

Tuesday, November 04, 2025

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)

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." 

Friday, October 31, 2025

Symphonic Geometry


"The human mind is only capable of absorbing a few things at a time. We see what is taking place in front of us in the here and now, and cannot envisage simultaneously a succession of processes, no matter how integrated and complementary. Our faculties of perception are consequently limited even as regards fairly simple phenomena. The fate of a single man can be rich with significance, that of a few hundred less so, but the history of thousands and millions of men does not mean anything at all, in any adequate sense of the word. The symmetriad is a million—a billion, rather—raised to the power of N: it is incomprehensible. We pass through vast halls, each with a capacity of ten Kronecker units, and creep like so many ants clinging to the folds of breathing vaults and craning to watch the flight of soaring girders, opalescent in the glare of searchlights, and elastic domes which criss-cross and balance each other unerringly, the perfection of a moment, since everything here passes and fades. The essence of this architecture is movement synchronized towards a precise objective. We observe a fraction of the process, like hearing the vibration of a single string in an orchestra of supergiants. We know, but cannot grasp, that above and below, beyond the limits of perception or imagination, thousands and millions of simultaneous transformations are at work, interlinked like a musical score by mathematical counterpoint. It has been described as a symphony in geometry, but we lack the ears to hear it."

Stanislaw Lem (1921 - 2006)

Thursday, October 30, 2025

Experience, Emptiness, and Luminosity


"One of the points in the traditional Buddhist way of viewing the question of what reality is or what truth is, is that in fact we cannot perceive reality, we cannot perceive truth. This is not to say that there is no reality or truth, but rather that whatever we perceive, if we happen to perceive anything, we see in accordance with some particular language or approach, and we color it with our own styles and ways of looking at things.
...
The nonexistence of ego is not a philosophical matter, but simply a matter of perception. Perception is unable to trace back its existence {to an origin}, so it becomes just sheer energy, without a beginner of the perception and without any substance. It is just simple perception. Perception on that level has three aspects.
...
The first is perception as experience. In this case, experience does not refer to the experience of self-confirmation, but to experience in the sense of things as they are. White is white, black is black, and so forth.
...
Then there is {the second aspect}, the perception of emptiness, which is the absence of things as they are. Things have their room; things always come along with a certain sense of room, of space. Even though they may appear within the complexities of the overcrowdedness of experience, they provide their own space within the overcrowdedness. Actually, overcrowdedness and room are the same thing; overcrowdedness is room in some sense. This is because there is movement involved, because there is dance and play involved. At the same time, there is a shifty and intangible quality, and because of that the whole thing is very lucid.
...
There is experience, then space or emptiness, and then the final aspect, which is called luminosity. Luminosity has nothing to do with bright visual light. It is a sense of sharp boundary and clarity. There is no theoretical or intellectual reference point for this, but in terms of ordinary experience, it is a sense of clarity, a sense of things being seen as they are, unmistakably.
...
So there are these three aspects of perception: the sense of experience, the sense of emptiness, and the sense of luminosity. The point is that with that level of perception {that contains the three aspects}, one is able to see all the patterns of one’s life. Whether the patterns of one’s life are regarded as neurotic or enlightened, one is able to see them all clearly. That seems to be the beginning of some glimpse of the mandala perspective, the beginning of a glimpse of the five buddha energies."

- Chogyam Trungpa (1939 - 1987)
Orderly Chaos: The Mandala Principle

Tuesday, October 28, 2025

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

Monday, October 27, 2025

Atomic Poetry


 "We must be clear that when it comes to atoms,
language can be used only as in poetry.
The poet, too, is not nearly so concerned with
describing facts as with creating images
and establishing mental connections."

Niels Bohr (1885 - 1962)

Sunday, October 19, 2025

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)

Friday, September 26, 2025

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

Wednesday, August 27, 2025

Quintessence

 

"In my experience the conscious mind can claim only a relatively central position and must accept the fact that the unconscious psyche transcends and as it were surrounds it on all sides.
...
We can hardly escape the feeling that the unconscious process moves spiral-wise round a centre, gradually getting closer, while the characteristics of the centre grow more and more distinct. Or perhaps we could put it the other way round and say that the centre – itself virtually unknowable – acts like a magnet on the disparate materials and processes of the unconscious and gradually captures them as in a crystal lattice. For this reason the centre is often pictured as a spider in its web.
...
The squaring of the circle breaks down the original chaotic unity into the four elements and then combines them again in a higher unity. Unity is represented by a circle and the four elements by a square. The production of one from four is the result of a process of distillation and sublimation which takes the so-called ‘circular’ form ... so that the ‘soul’ or ‘spirit’ shall be extracted in its purest state. This product is generally called the ‘quintessence."

C. G. Jung (1875-1961)
Psychology and Alchemy

Wednesday, August 06, 2025

Topologically Speaking


"It is as if one hemisphere of your brain is perceiving the world as reflected in a mirror. Through a mirror. See? So left becomes right, and all that that implies. And we don’t know yet what that does imply, to see the world reversed like that. Topologically speaking, a left-hand glove is a right-hand glove pulled through infinity.
...
The bedrock basic stratum of reality is irreality;
the universe is irrational because
it is built not on mere shifting sand –
but on that which is not.
...
Pascal said, 'All history is one immortal
man who continually learns.'"

Philip K. Dick (1928 - 1982)

Tuesday, July 08, 2025

Boundless Ambiguity


Paradox Museum, Miami, Florida

"The writing lies before you and always says the same, if you believe in words. But if you believe in things in whose places only words stand, you never come to the end. And yet you must go an endless road, since life flows not only down a finite path but also an infinite one. But the unbounded makes you anxious since the unbounded is fearful and your humanity rebels against it. Consequently you seek limits and restraints so that you do not lose yourself tumbling into infinity Restraint becomes imperative for you. You cry out for the word which has one meaning and no other, so that you escape boundless ambiguity. The word becomes your God, since it protects you from the countless possibilities of interpretation. The word is protective magic against the daimons of the unending, which tear at your soul and want to scatter you to the winds. You are saved if you can say at last: that is that and only that. You speak the magic word, and the limitless is finally banished. Because of that men seek and make words."

C. G. Jung (1875-1961)
The Red Book: A Reader's Edition

Thursday, May 22, 2025

Photographs-Otherwise-Not-Taken, Taken

Inside of Library, University of Otago, Dunedin, New Zealand

"Nows within this now, rather like snapshots in an album. Each Now is separate and a world unto itself, but the richly structured Nows 'know' about one another because they literally contain one another in certain essential respects. As consciousness surveys many things at once in one Now, it is simultaneously present, at least in part, in other Nows. This awareness of many things in one could well exist in a much more pronounced form in other places in Platonia."

- Julian  Barbour (1937 - )
 The End of Time

Note. The admittedly busy title of this blog post obviously begs an explanation. I'll start by saying that it is inspired by a short email exchange I recently had with a photo buddy of mine (the Zen-master, Paul Cotter). In reply to Paul's kind comments about my recent "travelogue images," I countered with the suggestion that my favorite images from the trip are/may-be those I took with my iPhone and not my 21L-sling-bag's-worth of "pro" gear (the details of which hardly matter)! While I am not (entirely) convinced of the veracity of my claim (and others may differ), I have zero doubt that my iPhone gifted me many images that I will cherish in the years to come precisely because these are photographs I would otherwise have not taken! Some examples - click to see full-size:

View of a wall while waiting to be seated at a restaurant

Footprints on a beach in front of another restaurant


A view from inside the Novotel Auckland Airport
while my wife was busy getting us checked in

Frosted window inside restroom at the
Aoraki/Mount Cook National Park Visitor Centre

View inside a restaurant while being led to our table

Upside down view of one of the ceilings at the
Nadi International Airport in Fiji

Another (upside down) view from inside the library at
the 
University of OtagoDunedin, New Zealand
 
A snapshot view of urban geometry while waiting
for my wife to pay the parking meter


A 5 sec exposure of a part of our boat ride to Milford Sound,
stabilized by my iPhone's computational photography algorithms

I have dozens more of these "Photographs-Otherwise-Not-Taken, Taken" images, all of which share this one salient pattern: had I not used my iPhone to capture them (embarrassingly easily by, literally, framing and tapping, and without any of what my wife describes as "glacier-paced compositional machinations"), they would all have been but fleeting moments doomed to be lost in the mists of memory and time.

Thursday, May 01, 2025

An Escherian Welcome to New Zealand


"It once happened to me on one of my solitary strolls through the woods of Baarn that I suddenly stood still, frozen, caught by a frightening, unreal, and at the same time blissful feeling of standing face to face with the inexplicable. The tree there, before me, was in itself, as an object, as a part of the woods, maybe not exceedingly remarkable, but all of a sudden the distance, the space between it and myself puzzled me. We don’t know space. We don’t see it, we don’t hear it, we don’t feel it. We are in the middle of it, are part of it, but we do not know the slightest thing about it. I might have known the distance between that tree and me, but when I say 'three meters,' the number doesn’t reveal anything of the mystery. I could only see boundaries, demarcations. I could not see space itself. . . . Space remains unfathomable, a miracle."

M. C. Escher (1898 - 1972)
Quoted in Becoming Escher, by Joris Escher

Note. This juxtaposition of image(s) and text could not be more perfect. The main image is of a part of the ceiling of the international terminal of Auckland, New Zealand's airport, through which my wife and I were strolling after arriving in New Zealand a few weeks ago (having just arrived and anticipating a much-much-needed respite from work and front-page politics). While I'd like to believe the ceiling would have caught my attention in any case (given my penchant for abstraction), my eye was seized preternaturally strongly because (when not napping), most of the 15+ hours flight time from Washington, D.C. was devoted to reading a wonderful new biography of one of my favorite artists, M.C. Escher. What an unexpectedly Escherian welcome to a country of wonders, images of which I will be soon sharing as time permits😊

Wednesday, February 12, 2025

A Self-correcting System


"The planet has been through a lot worse than us. Been through earthquakes, volcanoes, plate tectonics, continental drift, solar flares, sun spots, magnetic storms, the magnetic reversal of the poles … hundreds of thousands of years of bombardment by comets and asteroids and meteors, worldwide floods, tidal waves, worldwide fires, erosion, cosmic rays, recurring ice ages … And we think some plastic bags and some aluminum cans are going to make a difference? The planet isn’t going anywhere. WE are!
...
We’re going away. Pack your shit, folks. We’re going away. And we won’t leave much of a trace, either. Maybe a little Styrofoam … The planet’ll be here and we’ll be long gone. Just another failed mutation. Just another closed-end biological mistake. An evolutionary cul-de-sac.
...
The planet’ll shake us off like a bad case of fleas.The planet will be here for a long, long, LONG time after we’re gone, and it will heal itself, it will cleanse itself, ’cause that’s what it does. It’s a self-correcting system. The air and the water will recover, the earth will be renewed. And if it’s true that plastic is not degradable, well, the planet will simply incorporate plastic into a new paradigm: the earth plus plastic. The earth doesn’t share our prejudice toward plastic. Plastic came out of the earth. The earth probably sees plastic as just another one of its children. Could be the only reason the earth allowed us to be spawned from it in the first place. It wanted plastic for itself. Didn’t know how to make it. Needed us. Could be the answer to our age-old egocentric philosophical question, 'Why are we here?'"

- George Carlin (1937 - 2008)

Tuesday, December 10, 2024

Complex Processes


"Like a wave in the physical world, in the infinite ocean of the medium which pervades all, so in the world of organisms, in life, an impulse started proceeds onward, at times, may be, with the speed of light, at times, again, so slowly that for ages and ages it seems to stay, passing through processes of a complexity inconceivable to men, but in all its forms, in all its stages, its energy ever and ever integrally present."

Nikola Tesla (1856 - 1943)

Saturday, November 16, 2024

(Missing) Inhabitants of Impossible Worlds


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

M. C. Escher (1898 - 1972)

Tuesday, September 24, 2024

Perceived Geometries #1


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

- Bernhard Riemann (1826 - 1866)

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

Gregory Bateson (1904 - 1980)

Thursday, July 25, 2024

The Universe is a Single Flower


"The universe is elegant. And there is a harmony in it. We see that the Earth is beautiful, that the beings in it are beautiful. In the Avatamsaka Sutra, the Buddha described the universe to be like one single flower. The cosmos is like a bank of flowers. We we see the planet as a beautiful flower, and each of us is also a beautiful flower. No matter what age we are we are very beautiful. That is the insight of the Buddha in the Avatamsaka sutra. The cosmos is a kind of treasure. Each being on the planet is a flower."

- Thich Nhat Hanh (1926 - 2022)
The Universe is a Single Flower