Whirling Light

"Rotating systems often break axisymmetry; were it not so, there would be no hurricanes. There are steadier examples: the skirts of the 'whirling dervish' carry cusped wave patterns which seem to defy gravity and common sense.

...

We consider a rotating, conically symmetric surface made out of a sheet of material that is constrained not to stretch or compress in two dimensions, but is perfectly flexible with respect to bending in the third. The symmetry of the surface permits an additional material flow to be superimposed on the rotation of the surface, leading to Coriolis forces. The equations describing this system yield a three-parameter family of exact solutions, some of which bear a close resemblance to the patterns on a dervish's skirt. We find that the Coriolis terms that arise from the additional flow are crucial for these types of patterns to exist.

...

The results widen our understanding of the dynamics of flexible objects and of pattern formation in rotating systems. They may also shed some light on previously known instabilities of turbine disks and hard disks. Finally, they bring a bit of science into the otherwise nebulous world of the mystic, and address a phenomenon that has been observed with aesthetic pleasure for hundreds of years."

- J. Guven, J. Hanna and M. Müller,
"Whirling skirts and rotating cones,"
New Journal Of Physics (Nov, 2013)

Postscript. The images in the diptych that I took with my iPhone recently (of light reflecting off of cars parked onto the walls of a local garage) reminded me of Rumi's "Whirling Dervishes," about which you can read here and here (in considerably less technical detail than the one you'll find if you follow the link to the physics journal!)

“You are water, whirling water,
Yet still water trapped within,
Come, submerge yourself within us,
We who are the flowing stream.
...
We came whirling out of nothingness,
scattering stars like dust...
The stars made a circle,
and in the middle,
we dance.”

- Rumi (1207 - 1273)

Leaves and Paths

"In a forest of a hundred thousand trees,
no two leaves are alike.
And no two journeys along
the same path are alike."

- Paulo Coelho (1947 - )
Aleph

Between Grief and Geometry

"Geometry is a way to organize our models of the world, its shapes and dynamics. But isn’t this all contingent, balanced on a knife’s edge? Could our models have turned out very differently? If the fractal geometry of Mandelbrot had been discovered before the geometry of Euclid, would manufacture be the same? If you think the question is far-fetched, consider the iterated branching of our pulmonary, circulatory, and nervous systems, or the recursive folding of our DNA, or the large surface area and small volume of our lungs and our digestive tract. Evolution has discovered and uses fractal geometry. If people had looked more closely at the geometry of nature, rather than emulating the 'celestial perfection' imposed by the church’s interpretation of the works of Euclid and Aristotle, our constructions could be very different now.

...

Beauty is a bridge between grief and geometry.

...

Beauty and grief are next-door neighbors, or maybe grief is beauty in a dark mirror… To see beauty is to glimpse something deeper; to grieve is to glimpse a loss whose consequences we will not unpack for years, and maybe never. The beauty of geometry likewise involves great emotional weight, irreversibly alters our perceptions, and is transcendent. For we don’t see all of geometry, only a hint, a shadow of something much deeper."

- Michael Frame (1951 - )
Geometry of Grief

Harmony of Autumnal Colors

"When the eye sees a color it
is immediately excited,
and it is its nature,
spontaneously and of necessity,
at once to produce another,
which with the original colour
comprehends the whole chromatic scale.
A single color excites,
by a specific sensation,
the tendency to universality.
In this resides the fundamental
law of all harmony of colors.
...

Should your glance on mornings lovely

Lift to drink the heaven's blue

Or when sun, vieled by sirocco,

Royal red sinks out of view -

Give to Nature praise and honour.

Blithe of heart and sound of eye,

Knowing for the world of color

Where its broad foundations lie."

- Johann Wolfgang von Goethe (1749 - 1832)

Autumnal Tints

"I am struck by the simplicity of
light in the atmosphere in the autumn,
as if the earth absorbed none,
and out of this profusion of
dazzling light came the
autumnal tints."

- Henry David Thoreau (1817 - 1862)

Serendipitous Geometry

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

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

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

Unobstructed Flow

"The great Tao flows unobstructed in every direction.
All things rely on it to conceive and be born,
and it does not deny even the smallest of creation.
When it has accomplishes great wonders,
it does not claim them for itself.
It nourishes infinite worlds,
yet it doesn't seek to master the smallest creature.
Since it is without wants and desires,
it can be considered humble.
All of creation seeks it for refuge
yet it does not seek to master or control.
Because it does not seek greatness;
it is able to accomplish truly great things. "

- Lao Tzu (6th century – 4th century BCE)
Tao Te Ching, Chapter 34

Light, Shadow, and Geometry

"The phenomenon which I have now briefly mentioned appears to me to partake of the character of the marvelous, almost as much as any fact which physical investigation has yet brought to our knowledge. The most transitory of things, a shadow, the proverbial emblem of all that is fleeting and momentary, may be fettered by the spells of our "natural magic," and may be fixed for ever in the position which it seemed only destined for a single instant to occupy.

This remarkable phenomenon, of whatever value it may turn out in its application to the arts, will at least be accepted as a new proof of the value of the inductive methods of modern science, which by noticing the occurrence of unusual circumstances (which accident perhaps first manifests in some small degree), and by following them up with experiments, and varying the conditions of these until the true law of nature which they express is apprehended, conducts us at length to consequences altogether unexpected, remote from usual experience, and contrary to almost universal belief. Such is the fact, that we may receive on paper the fleeting shadow, arrest it there, and in the space of a single minute fix it there so firmly as to be no more capable of change, even if thrown back into the sunbeam from which it derived its origin."

- Henry Fox Talbot (1800 - 1877)
Some Account of the Art of Photogenic Drawing 

Non-Action

"That which offers no resistance,
Overcomes the hardest substances.
That which offers no resistance
Can enter where there is no space.
Few in the world can comprehend
The teaching without words, or
Understand the value of non-action."

- Lao Tzu (6th century – 4th century BCE)
Tao Te Ching, Chapter 43

Dreams and Mirrors

"I, who have felt the horror of mirrors
Not only in front of the impenetrable crystal
Where there ends and begins, uninhabitable,

An impossible space of reflections,

But of gazing even on water that mimics

The other blue in its depth of sky,

That at times gleams back the illusory flight

Of the inverted bird, or that ripples,

And in front of the silent surface

Of subtle ebony whose polish shows

Like a repeating dream the white

Of something marble or something rose,

Today at the tip of so many and perplexing

Wandering ears under the varying moon,

I ask myself what whim of fate
Made me so fearful of a glancing mirror.

...

It is strange to dream, and to have mirrors

Where the commonplace, worn-out repertory

Of every day may include the illusory

Profound globe that reflections scheme.

God (I keep thinking) has taken pains

To design that ungraspable architecture

Reared by every dawn from the gleam

Of a mirror, by darkness from a dream.

God has created nighttime, which he arms

With dreams, and mirrors, to make clear

To man he is a reflection and a mere

Vanity. Therefore these alarms."

- Jorge Luis Borges (1899 - 1986)
“Mirrors,” in Dreamtigers