Perceived Geometries #2

"Euclid alone has looked on Beauty bare.

Let all who prate of Beauty hold their peace,

And lay them prone upon the earth and cease

To ponder on themselves, the while they stare

At nothing, intricately drawn nowhere

In shapes of shifting lineage; let geese

Gabble and hiss, but heroes seek release

From dusty bondage into luminous air.

O blinding hour, O holy, terrible day,

When first the shaft into his vision shone

Of light anatomized! Euclid alone

Has looked on Beauty bare. Fortunate they

Who, though once only and then but far away,

Have heard her massive sandal set on stone."

- Edna St. Vincent Millay (1892 - 1950)

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)

Leaves of Forgotten Paths

"On this plank of silent wood, a leaf descends like a stray sentence from a book never written, a fragment of the universe’s lost prose. The droplets cling to it, like memories of rain on the brink of being erased. They are not droplets at all, but miniature worlds, reflecting all that ever was, and all that will never be. Within this moment, time folds itself inward, a palimpsest of lives and stories overlapping in their stillness, as if each droplet were a star trembling on the edge of oblivion.

The leaf, fragile and delicate, is the map to nowhere—a path we will never walk, though it was laid out for us in some forgotten dream. Its veins are threads of infinite labyrinths, spun from the cosmic loom of contingency. Do they lead to Eden or toward the dust? Borges would have marveled at the infinity it holds within the finite, a cipher for the universe itself, decipherable only by those who have forgotten how to read. Its edges fray with the mystery of countless fates untaken.

But look closely—each grain of wood beneath it bears the imprint of time’s invisible steps. Could it be that this scene was destined to be? Or does the leaf choose its resting place, in defiance of all that is written? The universe pauses, just long enough for this image to be both remembered and lost, seen and unseen, a paradox folding in on itself. We are left to wonder if, in the fading moments of the universe, there will be a single leaf left resting on a board, and if we—trapped in Borges’ eternal dream—will finally understand its purpose."

- ChatGPT4o (12 Sep 2024)
Sparks of Artificial General Intelligence

Prompt: "You are a photographer, poet and philosopher, with a penchant for metaphysics and stories by Jorge Luis Borges. You have taken a black and white image of a leaf resting gently on some old wooden boards. Write a prose poem in the style of Borges that describes a mystery imbued in and implied by this image. Limit the number of stanzas to three, with 5 lines each. Be creative."

Tangled Infinity

"The clearest way into the Universe
is through a forest wilderness."

- John Muir (1838 - 1914)

Niagara Concealed

"With cities, it is as with dreams: everything imaginable can be dreamed, but even the most unexpected dream is a rebus that conceals a desire or, its reverse, a fear. Cities, like dreams, are made of desires and fears, even if the thread of their discourse is secret, their rules are absurd, their perspectives deceitful, and everything conceals something else."

- Italo Calvino (1923 - 1985)

Invisible Cities

Forms

"Nature! …

She is ever shaping new forms:

what is, has never yet been;
what has been, comes not again.
Everything is new,
and yet nought but the old."

- Johann Wolfgang von Goethe (1749 - 1832)

Forms Without Substance

"He to whom the portentous conspiracy of night and solitude and silence in the heart of a great forest is not an unknown experience needs not to be told what another world it all is - how even the most commonplace and familiar objects take on another character. The trees group themselves differently; they draw closer together, as if in fear. The very silence has another quality than the silence of the day. And it is full of half-heard whispers, whispers that startle - ghosts of sounds long dead. There are living sounds, too, such as are never heard under other conditions: notes of strange night birds, the cries of small animals in sudden encounters with stealthy foes, or in their dreams, a rustling in the dead leaves - it may be the leap of a wood rat, it may be the footstep of a panther. What caused the breaking of that twig? What the low, alarmed twittering in that bushful of birds? There are sounds without a name, forms without substance, translations in space of objects which have not been seen to move, movements wherein nothing is observed to change its place. Ah, children of the sunlight and the gaslight, how little you know of the world in which you live! "

- Ambrose Bierce (1842 - 1914)
Ghost Stories

The Limitless Aleph

"All language is a set of symbols
whose use among its speakers
assumes a shared past.
How, then, can I translate into
words the limitless Aleph,
which my floundering mind
can scarcely encompass?"

- Jorge Luis Borges (1899 - 1986)

The Source Of All Light

"We are the eyes of the cosmos.
So that in a way, when you look
deeply into somebody's eyes,
you're looking deep into yourself,
and the other person is looking
deeply into the same self.

...

See, the source of all light is in the eye. If there were no eyes in this world, the sun would not be light. So if I hit as hard as I can on a drum which has no skin, it makes no noise. So if a sun shines on a world with no eyes, it's like a hand beating on a skinless drum. No light. YOU evoke light out of the universe, in the same way you, by nature of having a soft skin, evoke hardness out of wood. Wood is only hard in relation to a soft skin. It's your eardrum that evokes noise out of the air. You, by being this organism, call into being this whole universe of light and color and hardness and heaviness and everything.

...

Through our eyes, the universe is perceiving itself.
Through our ears, the universe is listening to its harmonies.
We are the witnesses through which the
universe becomes conscious of
its glory, of its magnificence."

- Alan Watts (1915 - 1973)

Web of Nature

"No pattern is an isolated entity. Each pattern can exist in the world, only to the extent that is supported by other patterns: the larger patterns in which it is embedded, the patterns of the same size that surround it, and the smaller patterns which are embedded in it. This is a fundamental view of the world. It says that when you build a thing you cannot merely build that thing in isolation, but must also repair the world around it, and within it, so that the larger world at that one place becomes more coherent, and more whole; and the thing which you make takes its place in the web of nature, as you make it."

- Christopher Alexander (1936 - 2022)
A Pattern Language