Unity in Multiplicity

"If we want to know what the mathematicians mean by a continuum, it is useless to appeal to geometry. The geometer is always seeking, more or less, to represent to himself the figures he is studying, but his representations are only instruments to him; he uses space in his geometry just as he uses chalk; and further, too much importance must not be attached to accidents which are often nothing more than the whiteness of the chalk. [...] The continuum thus conceived is no longer a collection of individuals arranged in a certain order, infinite in number, it is true, but external the one to the other. This is not the ordinary conception in which it is supposed that between the elements of the continuum exists an intimate connection making of it one whole, in which the point has no existence previous to the line, but the line does exist previous to the point. Multiplicity alone subsists, unity has disappeared—‘the continuum is unity in multiplicity,’ according to the celebrated formula. [...] Mathematicians do not study objects, but the relations between objects; to them it is a matter of indifference if these objects are replaced by others, provided that the relations do not change. Matter does not engage their attention, they are interested by form alone."

- Henri Poincare (1854 - 1912)

Shadow Physics

"The external world of physics has thus become a world of shadows. In removing our illusions we have removed the substance, for indeed we have seen that substance is one of the greatest of our illusions. Later perhaps we may inquire whether in our zeal to cut out all that is unreal we may not have used the knife too ruthlessly. Perhaps, indeed, reality is a child which cannot survive without its nurse illusion.

But if so, that is of little concern to the scientist, who has good and sufficient reasons for pursuing his investigations in the world of shadows and is content to leave to the philosopher the determination of its exact status in regard to reality. In the world of physics we watch a shadowgraph performance of the drama of familiar life. The shadow of my elbow rests on the shadow table as the shadow ink flows over the shadow paper. It is all symbolic, and as a symbol the physicist leaves it.

Then comes the alchemist Mind who transmutes the symbols. The sparsely spread nuclei of electric force become a tangible solid; their restless agitation becomes the warmth of summer; the octave of aethereal vibrations becomes a gorgeous rainbow."

- Arthur Stanley Eddington (1882 - 1944)
The Nature of the Physical World

Raman Trinity

"And on far-off Earth, Dr. Carlisle Perera had as yet told no one how he had wakened from a restless sleep with the message from his subconscious still echoing in his brain: The Ramans do everything in threes."

- Arthur C. Clarke (1917 - 2008)
Rendezvous with Rama

Eternity in Motion

"He stood there, spellbound, listening to the voice
Of Time itself, the moments hurrying by
For ever irrecoverably. I heard
His very thought. The stones were on their way
To the ocean that had made them; every
note In their wild music was a prophecy
Of continents unborn. When he had seen
Those continents in embryo, beds of sand
And shingle, cumulant on the coastwise plains,
Thousands of feet in thickness, he had doubted
Whether the river of time itself could grind
And pile such masses there. But when he heard
The mountain-torrents rattling, he recalled
How races had been born and passed away,
And night and day, through years unreckonable,
These grinding stones had never ceased to roll
On their steep course. Not even the Cordilleras,
Had they been ribbed with adamant, could withstand
That slow sure waste. Even those majestic heights
Would vanish. Nothing - not the wind that blows
Was more unstable than the crust of the earth."

- Alfred Noyes (1880 - 1958)

Unrevealable Sea

"More than bare mountains ’neath a naked sky,
Or star-enchanted hollows of the night

When clouds are riven, or the most sacred light

Of summer dawns, art thou a mystery

And awe and terror and delight, O sea!

Our Earth is simple-hearted, sad to-day

Beneath the hush of snow, next morning gay

Because west-winds have promised to the lea

Violets and cuckoo-buds; and sweetly these

Live innocent lives, each flower in its green field,

Joying as children in sun, air, and sleep.

But thou art terrible, with the unrevealed

Burden of dim lamentful prophecies,
And thy lone life is passionate and deep.
...

Light ebbs from off the Earth; the fields are strange,

Dusk, trackless, tenantless; now the mute sky

Resigns itself to Night and Memory…"

- Edward Dowden (1843 - 1913)
"Ocean," in Poems

Unknown Shore

"Look about you, Clarke. You see the mountain, and hill following after hill, as wave on wave, you see the woods and orchard, the fields of ripe corn, and the meadows reaching to the reed-beds by the river. You see me standing here beside you, and hear my voice; but I tell you that all these things - yes, from that star that has just shone out in the sky to the solid ground beneath our feet - I say that all these are but dreams and shadows; the shadows that hide the real world from our eyes. There is a real world, but it is beyond this glamour and this vision, beyond these ‘chases in Arras, dreams in a career,’ beyond them all as beyond a veil. I do not know whether any human being has ever lifted that veil; but I do know, Clarke, that you and I shall see it lifted this very night from before another’s eyes. You may think this all strange nonsense; it may be strange, but it is true, and the ancients knew what lifting the veil means. They called it seeing the god Pan.

...

I stood here, and saw before me the unutterable, the unthinkable gulf that yawns profound between two worlds, the world of matter and the world of spirit; I saw the great empty deep stretch dim before me, and in that instant a bridge of light leapt from the earth to the unknown shore, and the abyss was spanned."

- Arthur Machen (1863 - 1947)
The Great God Pan

Cosmic Ether

"One does not seem really to have got out-of-doors till he goes to sea. On the land he is shut in by the hills, or the forests, or more or less housed by the sharp lines of his horizon. But at sea he finds the roof taken off, the walls taken down; he is no longer in the hollow of the earth’s hand, but upon its naked back, with nothing between him and the immensities. He is in the great cosmic out-of-doors, as much so as if voyaging to the moon or to Mars. An astronomic solitude and vacuity surround him; his only guides and landmarks are stellar; the earth has disappeared; the horizon has gone; he has only the sky and its orbs left; this cold, vitreous, blue-black liquid through which the ship plows is not water, but some denser form of the cosmic ether.

...

The world is left behind; all standards of size, of magnitude, of distance, are vanished; there is no size, no form, no perspective; the universe has dwindled to a little circle of crumpled water, that journeys with you day after day, and to which you seem bound by some enchantment."

- John Burroughs (1837 - 1921)
"At Sea" in Fresh Fields

Harmonic Order

"For every mixture, if it is rightly made, as Socrates says, requires these three things, beauty, truth, and symmetry. For neither will any thing base, if it is introduced into the mixture, impart rectitude, since it will be the cause of error, and of inordinate prerogative, nor if truth is at any time separated, will it suffer the mixture to consist of things that are pure, and which are in reality subdued, but it will fill the whole with an image and with non-being. Nor without symmetry will there be a communion of the elements, and an elegant association. Symmetry, therefore, is necessary to the union of the things that are mingled, and to an appropriate communion. But truth is necessary to purity. And beauty to order; which also renders the whole lovely. For when each thing in the mixture has a place adapted to itself, it renders both the elements, and the arrangement resulting from them, beautiful. Here therefore, in the first mixture, these three things are apparent, symmetry, truth, and beauty. And symmetry indeed is the cause to the mixture, that being is one; truth is the cause of the reality of its existence; and beauty is the cause of its being intelligible. Hence it is intelligible and truly being."

- Proclus Lycius (412 – 485)

Note. This remarkable geometry is what meets the gaze of anyone who looks up at the Adolfo Suárez Madrid–Barajas Airport in Spain. We were racing through the airport to get to our flight from Madrid to Galicia last month (to watch the eclipse), my iPhone managed to catch a few vies of the beautiful overhead design in Madrid. Next to the Escher-like ceiling at the international terminal in Auckland, New Zealand, Madrid, this is among my all time favorites.

Weathered Memory

"Now, to return to our immediate subject, it so happens that, in architecture, the superinduced and accidental beauty is most commonly inconsistent with the preservation of original character, and the picturesque is therefore sought in ruin, and supposed to consist in decay. Whereas, even when so sought, it consists in the mere sublimity of the rents, or fractures, or stains, or vegetation, which assimilate the architecture with the work of Nature, and bestow upon it those circumstances of color and form which are universally beloved by the eye of man. So far as this is done, to the extinction of the true characters of the architecture, it is picturesque, and the artist who looks to the stem of the ivy instead of the shaft of the pillar, is carrying out in more daring freedom the debased sculptor's choice of the hair instead of the countenance.

But so far as it can be rendered consistent with the inherent character, the picturesque or extraneous sublimity of architecture has just this of nobler function in it than that of any other object whatsoever, that it is an exponent of age, of that in which, as has been said, the greatest glory of the building consists; and, therefore, the external signs of this glory, having power and purpose greater than any belonging to their mere sensible beauty, may be considered as taking rank among pure and essential characters; so essential to my mind, that I think a building cannot be considered as in its prime until four or five centuries have passed over it; and that the entire choice and arrangement of its details should have reference to their appearance after that period, so that none should be admitted."

- John Ruskin (1819 - 1900)
“The Lamp of Memory” in The Seven Lamps of Architecture

Recursive Gallery

"Zeus himself could not undo the web
of stone closing around me,
I have forgotten the men I was before;
I follow the hated path of monotonous walls
that is my destiny. Severe galleries
which curve in secret circles
to the end of the years. Parapets
cracked by the day’s usury.
In the pale dust I have discerned
signs that frighten me. In the concave
evenings the air has carries a roar

toward me, or the echo of a desolate howl.

I know there is an Other in the shadows,

whose fate it is to wear out the long solitudes

which weave and unweave this Hades

and to long for my blood and devour my death.
Each of us seeks the other.
If only this were the final day of waiting."

- Jorge Luis Borges (1899 - 1986)
"The Labyrinth" in Borges: Selected Poems