Geometry and Space

"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 laboured upon it."

- Bernhard Riemann (1826 - 1866)

Other Worlds

"Is there anything on earth which would have meaning
and would even change the course of events not only on
earth, but in other worlds?” I asked my teacher.
“There is,” my teacher answered me.
“Well, what is it?” I asked.
“It’s...” began my teacher and suddenly fell silent.

I stood and waited intently for his answer.
But he was silent.
And I stood and was silent.
And he was silent.
And I stood, silent.
And he was silent.
We’re both standing and silent.
Ho-la-la!
We’re both standing and silent.
Ho-le-le!

Yes, yes, we’re both
standing and silent!"

-  Daniil Kharms (1905 - 1942)

Postscript. Daniil Kharms is one of my all-time favorite authors of the "absurd." The best, purest form of absurdist literature - such as its uniquely Russian incarnation (called the Oberiu) in the 1920s and 1930s, which included such luminaries as Alexander Vvedensky, Nikolai Zabolotsky, and  Konstantin Vaginov - shares much with its spiritual cousin, the Zen koan. Its twists of logic, humor, and hallucinatory distortions of babble and reality often - unexpectedly - point to the deepest truths. For those of you who share my affection for these kinds of inner journeys of discovery, a great place to start is with this collection of Kharms' writings: Today I Wrote Nothing, from which the following passage is quoted (from the story, “The Werld”):

"I told myself that I see the world. But the whole world was not accessible to my gaze, and I saw only parts of the world. And everything that I saw I called parts of the world. And I examined the properties of these parts and, examining these properties, I wrought science. I understood that the parts have intelligent properties and that the same parts have unintelligent properties. And there were such parts of the world which could think. And all these parts resembled one another, and I resembled them. And I spoke with these parts. And suddenly I ceased seeing them and, soon after, other parts as well. But then I understood that I do not see parts independently, but I see it all at once. At first I thought that is was NOTHING. But then I understood that this was the world and what I had seen before was NOT the world.

And then I realized
I am the world.
But the world -  is not me.
Although at the same time
I am the world.
But the world's not me.
And I'm the world.
But the world's not me.
And I'm the world.
But the world's not me.
And I'm the world.
And after that
I didn't think anymore more."

Abide in Quietude

"Into the mind of the Exalted One, while he tarried, retired in solitude, came this thought: I have penetrated this deep truth, which is difficult to perceive, and difficult to understand, peace-giving, sublime, which transcends all thought, deeply-significant, which only the wise can grasp. Man moves in an earthly sphere, in an earthly sphere he has his place and finds his enjoyment. For man, who moves in an earthly sphere, and has his place and finds his enjoyment in an earthly sphere, it will be very difficult to grasp this matter, the law of causality, the chain of causes and effects: and this also will be very difficult for him to grasp, the extinction of all conformations, the withdrawal from all that is earthly, the extinction of desire, the cessation of longing, the end, the Nirvana. Should I now preach the Doctrine and mankind not understand me, it would bring me nothing but fatigue, it would cause me nothing but trouble! And there passed unceasingly through the mind of the Exalted One, this voice, which no one had ever before heard. 

Why reveal to the world what I have won by a severe struggle? The truth remains hidden from him whom desire and hate absorb. It is difficult, mysterious, deep, hidden from the coarse mind; He cannot apprehend it, whose mind earthly vocations surround with night. 

"When the Exalted One thought thus, his heart was inclined to abide in quietude and not to proclaim the Doctrine."

- The Mahavagga of the Vinya Pitaka,
The Buddha: His Life, His Doctrine, His Order,
by Herman Oldenberg (1854 - 1920)

Secret from the River

 "Have you also learned that
secret from the river;
that there is no such thing as time?
That the river is everywhere at the same time,
at the source and at the mouth,
at the waterfall, at the ferry,
at the current, in the ocean and
in the mountains, everywhere and that
the present only exists for it,
not the shadow of the past
nor the shadow of the future."

- Hermann Hesse (1877 - 1962)
Siddhartha

Continuous Cloth

 "Time really is one
big continuous cloth, no?
We habitually cut out
pieces of time to fit us,
so we tend to fool ourselves
into thinking that
time is our size,
but it really goes
on and on."

- Haruki Murakami (1949 - )
A Wild Sheep Chase

Light of Skye

 "The light of love, the purity of grace,
The mind, the Music breathing from her face,
The heart whose softness harmonised the whole —
And, oh! that eye was in itself a Soul!"

- Lord Byron (1788 - 1824)

Postscript. As photo-safari opportunities have dwindled (and though I do have a growing backlog of house-studio-facilitated abstracts to work on, as time permits), much of my "photo time" nowadays consists of discovering and reworking old images. This one is from the summer of 2009, captured during the first trip my wife and I took to Scotland; specifically, South Ronaldsay, one of the preternaturally beautiful Orkney Islands off Scotland's northeastern coast. The light there, as in all of Scotland, is not entirely of this world!

Centering

"To have humility is to experience reality, not in relation to ourselves, but in its sacred independence. It is to see, judge, and act from the point of rest in ourselves. Then, how much disappears, and all that remains falls into place. In the point of rest at the center of our being, we encounter a world where all things are at rest in the same way. Then a tree becomes a mystery, a cloud a revelation, each man a cosmos of whose riches we can only catch glimpses. The life of simplicity is simple, but it opens to us a book in which we never get beyond the first syllable."

- Dag Hammarskjöld (1905 - 1961)
Markings 

Living Mirror

 "This interconnection or
accommodation of all
created things to each other,
and each to all the others,
brings it about that each
simple substance has relations
that express all the others,
and consequently, that
each simple substance
is a perpetual,
living mirror of
the universe."

- G.W. Leibniz (1646 - 1716)
Monadology

Waves

 "You are a function of what the whole universe is doing in the same way
that a wave is a function of what the whole ocean is doing."

- Alan Watts (1915 - 1973)

Vibrant Hum

"At a certain point, you say to the woods, to the sea, to the mountains, the world, Now I am ready. Now I will stop and be wholly attentive. You empty yourself and wait, listening. After a time you hear it: there is nothing there. There is nothing but those things only, those created objects, discrete, growing or holding, or swaying, being rained on or raining, held, flooding or ebbing, standing, or spread. You feel the world's word as a tension, a hum, a single chorused note everywhere the same. This is it: this hum is the silence. Nature does utter a peep - just this one. The birds and insects, the meadows and swamps and rivers and stones and mountains and clouds: they all do it; they all don't do it. There is a vibrancy to the silence, a suppression, as if someone were gagging the world. But you wait, you give your life's length to listening, and nothing happens. The ice rolls up, the ice rolls back, and still that single note obtains. The tension, or lack of it, is intolerable. The silence is not actually suppression: instead, it is all there is."

- Annie Dillard (1945 - )
Teaching a Stone to Talk

Subterranean Stream

"The landscape of my days

appears to be composed,

like mountainous regions,

of varied materials

heaped up pell-mell.

There I see my nature,

itself composite,

made up of equal parts

of instinct and training.

Here and there protrude

the granite peaks of

the inevitable, but all

about is rubble from

the landslips of chance.

I strive to retrace my life

to find in it some plan,

following a vein of lead,

or of gold, or the

course of some

subterranean stream,

but such devices

are only tricks

of perspective

in the memory."

- Marguerite Yourcenar (1903 - 1987)
Memoirs of Hadrian

Vibrations

"The infinite vibratory levels,
the dimensions of interconnectedness
are without end.
There is nothing independent.
All beings and things are
residents in your awareness."

- Alex Grey (1953 - )

 

Virtual Delights

"Paul uncovered his eyes, and looked around the room. Away from a few dazzling patches of direct sunshine, everything glowed softly in the diffuse light: the matte white brick walls, the imitation (imitation) mahogany furniture; even the posters — Bosch, Dali, Ernst, and Giger — looked harmless, domesticated. Wherever he turned his gaze (if nowhere else), the simulation was utterly convincing; the spotlight of his attention made it so. Hypothetical light rays were being traced backwards from individual rod and cone cells on his simulated retinas, and projected out into the virtual environment to determine exactly what needed to be computed: a lot of detail near the centre of his vision, much less towards the periphery. Objects out of sight didn’t “vanish” entirely, if they influenced the ambient light, but Paul knew that the calculations would rarely be pursued beyond the crudest first-order approximations: Bosch’s Garden of Earthly Delights reduced to an average reflectance value, a single grey rectangle — because once his back was turned, any more detail would have been wasted. Everything in the room was as finely resolved, at any given moment, as it needed to be to fool him — no more, no less.

...

Paul closed his eyes and turned his face to the sun. In spite of everything, it was hard not to take solace from the warmth flooding onto his skin. He stretched the muscles in his arms, his shoulders, his back -- and it felt like he was reaching out from the "self" in his virtual skull to all his mathematical flesh, imprinting the nebulous data with meaning; binding it all together, staking some kind of claim.

...

Existence was beginning to seduce him. He let himself surrender for a moment to a visceral sense of identity which drowned out all his pale mental images of optical processors, all his abstract reflections on the software's approximations and short-cuts. This body didn't want to evaporate. This body didn't want to bale out. It didn't much care that there was another - "more real" - version of itself elsewhere. It wanted to retain its wholeness. It wanted to endure."

- Greg Egan (1961 - )
Permutation City

An Immense Landscape

 "I picture the vast realm
of the sciences as an
immense landscape scattered
with patches of dark and light.
The goal towards which
we must work is either to
extend the boundaries of
the patches of light, or
to increase their number.
One of these tasks falls
to the creative genius;
the other requires a
sort of sagacity
combined with
perfectionism."

- Denis Diderot (1713 - 1784)
Thoughts on the Interpretation of
Nature and Other Philosophical Works

Stirrings of the Soul

"The sea refreshes our imagination because it does not make us think of human life; yet it rejoices the soul, because, like the soul, it is an infinite and impotent striving, a strength that is ceaselessly broken by falls, an eternal and exquisite lament. The sea thus enchants us like music, which, unlike language, never bears the traces of things, never tells us anything about human beings, but imitates the stirrings of the soul. Sweeping up with the waves of those movements, plunging back with them, the heart thus forgets its own failures and finds solace in an intimate harmony between its own sadness and the sea’s sadness, which merges the sea’s destiny with the destinies of all things."

- Marcel Proust (1871 - 1922)

Middle Ground

"We now know that complexity arises in a middle ground—often at the order–disorder border. Natural systems that evolve with and learn from interaction with their immediate environment exhibit both structural order and dynamical chaos. Order is the foundation of communication between elements at any level of organization, whether that refers to a population of neurons, bees or humans. For an organism order is the distillation of regularities abstracted from observations. An organism’s very form is a functional manifestation of its ancestor’s evolutionary and its own developmental memories.

A completely ordered universe, however, would be dead. Chaos is necessary for life. Behavioural diversity, to take an example, is fundamental to an organism’s survival. No organism can model the environment in its entirety. Approximation becomes essential to any system with finite resources. Chaos, as we now understand it, is the dynamical mechanism by which nature develops constrained and useful randomness. From it follow diversity and the ability to anticipate the uncertain future. 

There is a tendency, whose laws we are beginning to comprehend, for natural systems to balance order and chaos, to move to the interface between predictability and uncertainty. The result is increased structural complexity. This often appears as a change in a system’s intrinsic computational capability. The present state of evolutionary progress indicates that one needs to go even further and postulate a force that drives in time towards successively more sophisticated and qualitatively different intrinsic computation. We can look back to times in which there were no systems that attempted to model themselves, as we do now. This is certainly one of the outstanding puzzles: how can lifeless and disorganized matter exhibit such a drive? The question goes to the heart of many disciplines, ranging from philosophy and cognitive science to evolutionary and developmental biology and particle astrophysics. The dynamics of chaos, the appearance of pattern and organization, and the complexity quantified by computation will be inseparable components in its resolution."

- James P. Crutchfield (1955 - )
Between order and chaos

Imagination

"We know,
but cannot grasp,
that above and below,
beyond the limits of
perception or imagination,
thousands of millions of
simultaneous transformations
are at work,
interlinked like
a musical score by
mathematical counterpoint
...a symphony
...but we lack the
ears to hear it."

- Stanislaw Lem (1921 - 2006)

Plural Realities

"Maybe each human being lives in a unique world, a private world different from those inhabited and experienced by all other humans. . . If reality differs from person to person, can we speak of reality singular, or shouldn't we really be talking about plural realities? And if there are plural realities, are some more true (more real) than others? What about the world of a schizophrenic? Maybe it's as real as our world. Maybe we cannot say that we are in touch with reality and he is not, but should instead say, His reality is so different from ours that he can't explain his to us, and we can't explain ours to him. The problem, then, is that if subjective worlds are experienced too differently, there occurs a breakdown in communication ... and there is the real illness."

- Philip K. Dick (1928 - 1982)

Subliminal Knowledge

 "Can we perceive those
inorganic beings,
don Juan?" I asked.
"We certainly can," he replied.
"Sorcerers do it at will.
Average people do it,
but they don't realize that
they're doing it because
they are not conscious of the
existence of a twin world.
When they think of a twin world,
they enter into all kinds
of mental masturbation,
but it has never occurred
to them that their fantasies
have their origin in a
subliminal knowledge that
all of us have:
that we are not alone."

- Carlos Castaneda (1925 - 1998)
The Active Side of Infinity

Enfoldment

 "The essential feature

in quantum interconnectedness

is that the whole universe

is enfolded in everything,

and that each thing
is enfolded in the whole."

- David Bohm (1917 - 1992)

Lines of Meaning

"The library will endure;

it is the universe.

As for us,
everything has not been written;
we are not turning into phantoms.
We walk the corridors,
searching the shelves
and rearranging them,
looking for lines of meaning
amid leagues of cacophony
and incoherence,
reading the history of
the past and our future,
collecting our thoughts
and collecting the
thoughts of others,
and every so often
glimpsing mirrors,
in which we may recognize
creatures of the information."

- Jorge Luis Borges (1899 - 1986)
The Library of Babel

Dreams and Apparitions

"Dreams, as we all know, are very curious things: certain incidents in them are presented with quite uncanny vividness, each detail executed with the finishing touch of a jeweller, while others you leap across as though entirely unaware of, for instance, space and time. Dreams seem to be induced not by reason but by desire, not by the head but by the heart, and yet what clever tricks my reason has sometimes played on me in dreams!"

- Fyodor Dostoevsky (1821 - 1881)
Notes from Underground

Entropy Curve

"There is no logical necessity
for the existence of a unique
direction of total time;
whether there is only
one time direction,
or whether time
directions alternate,
depends on the shape
of the entropy curve
plotted by the universe."

- Hans Reichenbach (1891 - 1953)
The Direction of Time

 

Forms of Things Unknown

 "More strange than true: I never may believe

These antique fables, nor these fairy toys.
Lovers and madmen have such seething brains,
Such shaping fantasies, that apprehend

More than cool reason ever comprehends.
The lunatic, the lover and the poet

Are of imagination all compact:
One sees more devils than vast hell can hold,
That is, the madman: the lover, all as frantic,
Sees Helen's beauty in a brow of Egypt:
The poet's eye, in fine frenzy rolling,

Doth glance from heaven to earth, from earth to heaven;

...
And as imagination bodies forth
The forms of things unknown, the poet's pen
Turns them to shapes and gives to airy nothing
A local habitation and a name.

...
Such tricks hath strong imagination,
That if it would but apprehend some joy,
It comprehends some bringer of that joy;
Or in the night, imagining some fear,
How easy is a bush supposed a bear!"

- William Shakespeare (1564 - 1616)
Theseus, Act V, Scene I, in A Midsummer Nights Dream

Atmospheric Lights

"Terraforming Mars is a primary goal for the twenty-second century. But scientists are looking beyond Mars as well. The most exciting prospects may be the moons of the gas giants, including Europa, a moon of Jupiter, and Titan, a moon of Saturn. The moons of gas giants were once thought to be barren hunks of rock that were all alike, but they are now seen as unique wonderlands, each with its own array of geysers, oceans, canyons, and atmospheric lights. These moons are now being eyed as future habitats for human life."

- Michio Kaku (1947 - )
The Future of Humanity