Information Theory

"The fundamental problem of communication is that of reproduction at one point either exactly or approximately a message selected at another point. Frequently the messages have meaning; that is, they refer to or are correlated according to some system with certain physical or conceptual entities. These semantic aspects of communication are irrelevant to the engineering problem. The significant aspect is that the actual message is one selected from a set of possible messages."

- Claude Shannon (1916 - 2001)
A Mathematical Theory of Communication

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

Mystic Sea

"The smell of the sea in my nostrils,
The sound of the sea in mine ears;
The touch of the spray on my burning face,
Like the mist of reluctant tears.

The blue of the sky above me,

The green of the waves beneath;

The sun flashing down on a gray-white sail

Like a scimitar from its sheath.

And ever the breaking billows,

And ever the rocks' disdain;

And ever a thrill in mine inmost heart

That my reason cannot explain.

So I say to my heart, ‘Be silent,

The mystery of time is here;

Death's way will be plain when we fathom the main,
And the secret of life be clear."

- Paul Laurence Dunbar (1872 - 1906)
The Mystic Sea

Verdant Spirit

 

"I was utterly alone with the sun and the earth. Lying down on the grass, I spoke in my soul to the earth, the sun, the air, and the distant sea far beyond sight. I thought of the earth’s firmness—I felt it bear me up: through the grassy couch there came an influence as if I could feel the great earth speaking to me. I thought of the wandering air—its pureness, which is its beauty; the air touched me and gave me something of itself. I spoke to the sea: though so far, in my mind I saw it, green at the rim of the earth and blue in deeper ocean; I desired to have its strength, its mystery and glory. Then I addressed the sun, desiring the soul equivalent of his light and brilliance, his endurance and unwearied race. I turned to the blue heaven over, gazing into its depth, inhaling its exquisite colors and sweetness. The rich blue of the unattainable flower of the sky drew my soul towards it, and there it rested, for pure color is rest of heart. By all these I prayed; I felt an emotion of the soul beyond all definition; prayer is a puny thing to it, and the word is a rude sign to the feeling, but I know no other.

...

Touching the crumble of earth, the blade of grass, the thyme flower, breathing the earth-encircling air, thinking of the sea and the sky, holding out my hand for the sunbeams to touch it, prone on the sward in token of deep reverence, thus I prayed that I might touch to the unutterable existence infinitely higher than deity."

- Richard Jefferies (1848 - 1887)
The Story of My Heart

Fathomless Becoming

"As I wend to the shores I know not,
As I list to the dirge, the voices of men and women wreck’d,
As I inhale the impalpable breezes that set in upon me,
As the ocean so mysterious rolls toward me closer and closer,
I too but signify at the utmost a little wash’d-up drift,
A few sands and dead leaves to gather,
Gather, and merge myself as part of the sands and drift.

O baffled, balk’d, bent to the very earth,

Oppress’d with myself that I have dared to open my mouth,

Aware now that amid all that blab whose echoes recoil upon me
I have not once had the least idea who or what I am,

But that before all my arrogant poems the real Me
stands yet untouch’d, untold, altogether unreach’d,

Withdrawn far, mocking me with mock-congratulatory signs and bows,

With peals of distant ironical laughter at every word I have written,

Pointing in silence to these songs, and then to the sand beneath.

I perceive I have not really understood any thing,
not a single object, and that no man ever can,

Nature here in sight of the sea taking advantage of me
to dart upon me and sting me,
Because I have dared to open my mouth to sing at all.
...

Tufts of straw, sands, fragments,

Buoy’d hither from many moods, one contradicting another,

From the storm, the long calm, the darkness, the swell,

Musing, pondering, a breath, a briny tear, a dab of liquid or soil,

Up just as much out of fathomless workings fermented and thrown,

A limp blossom or two, torn, just as much over waves floating, drifted at random,

Just as much for us that sobbing dirge of Nature,

Just as much whence we come that blare of the cloud-trumpets,

We, capricious, brought hither we know not whence, spread out before you,

You up there walking or sitting,

Whoever you are, we
too be in drifts
at your feet."

- Walt Whitman (1819 - 1892)
"As I Ebb’d with the Ocean of Life" in Leaves of Grass

Elemental Exchange

"The mountain range
the stones in the water
all are strange and rare
The beautiful landscape
as we know
belongs to those who are like it
The upper worlds
the lower worlds
originally are one thing
There is not a bit of dust
there is only this still and full
perfect enlightenment.
...
Without a speck of dust being raised,
the mountains tower up;
without a single drop falling,
the streams plunge into the valley."

- Muso Soseki (1275 – 1351)

Indra’s Pool

"In one single mote of dust
Are completely seen all worlds.
If living beings should hear about them,
Their minds would be confused and go insane.

As within a single mote of dust,

So, too, it is in every mote of dust.

All world-systems enter within them.

It is in that way inconceivable.

In every particle of dust

Are Dharmas of the ten directions and three times.

The destinies and kshetras are all limitless,

Yet can be known with all their differences.

In every particle of dust

Are limitless kinds of Buddha kshetras.

Of their various kinds, all limitless,

Not a single one remains unknown.

Everything within the Dharma realm,

With all the varying characteristics

And types of destinies, each having differences,
Can all be discerned and known."

- Indra's Net / Avatamsaka Sutra
(late third or the fourth century CE)

Shared Essence

"The spiritual source shines clear in the light;

the branching streams flow on in the dark.

Grasping at things is surely delusion;

according with sameness is still not enlightenment.

All the objects of the senses

interact and yet do not.

Interacting brings involvement.

Otherwise, each keeps its place.

Sights vary in quality and form,

sounds differ as pleasing or harsh.

Refined and common speech come together in the dark,

clear and murky phrases are distinguished in the light.

The four elements return to their natures

just as a child turns to its mother.

Fire heats, wind moves,

water wets, earth is solid.

Thus with each and every thing,

depending on these roots, the leaves spread forth.

Trunk and branches share the essence;

revered and common, each has its speech.

...

In the light there is darkness,

but don’t take it as darkness;

in the dark there is light,

but don’t see it as light.

Light and dark oppose one another

like front and back foot in walking.

Each of the myriad things has its merit,

expressed according to function and place.

Phenomena exist, like box and lid joining;

principle accords, like arrow points meeting."

- Shitou Xiqian (700–790)

Inward Form

"The whole outward visible World with all its Being is a Signature, or Figure of the inward Spiritual World; whatever is internally, and however its Operation is, likewise it has its Character externally; like as Spirit of each Creature sets forth and manifests the internal Form of its Birth, by its Body, so does the Eternal Being also.

...

The Being of Beings is a wrestling Power; for the Kingdom of God consists in Power, and also the outward World, and it stands especially in seven Properties or Forms, where the one causes and makes the other, and none of them is the first or last, but it is the eternal Band.

...

This Formed world has manifested itself with the motion of all forms with this visible world, as with a visible likeness, so that the Spiritual being might be manifest in a corporeal comprehensive essence; as the desire of the inward forms has made itself external, and the internal being is in the external; the internal holds the external before it as a glass, wherein it beholds itself in the property of the generation of all forms; the external is its signature."

- Jakob Böhme (1575–1624)
The Signature of All Things

Living Pattern

"Thou art confused, my beloved, at seeing the thousandfold union

Shown in this flowery troop over the garden dispersed;

Many a name dost thou hear assigned; one after another

Falls on thy listening ear, with a barbarian sound.

None resembleth another, yet all their forms have a likeness;

Therefore a mystical law is by the chorus proclaimed;

Yes, a sacred enigma! Oh, dearest friend, could I only

Happily teach thee the word, which may the mystery solve!

Closely observe how the plant, by little and little progressing,

Step by step guided on, changeth to blossom and fruit!

...

Here doth Nature close the ring of her forces eternal;

Yet doth a new one, at once, cling to the one gone before,

So that the chain be prolonged for ever through all generations,

And that the whole may have life, e’en as enjoyed by each part.

Now, my beloved one, turn thy gaze on the many-hued thousands

Which, confusing no more, gladden the mind as they wave.

Every plant unto thee proclaimeth the laws everlasting.

Every floweret speaks louder and louder to thee;

But if thou here canst decipher the mystic words of the goddess,

Everywhere will they be seen, e’en though the features are changed."

- Johann Wolfgang von Goethe (1749 - 1832)
 The Metamorphosis of Plants

Woven Becoming

"When we seek definitely to express the relations of events which arise from their spatio-temporal structure, we approximate to simplicity by progressively diminishing the extent (both temporal and spatial) of the events considered. For example, the event which is the life of the chunk of nature which is the Needle during one minute has to the life of nature within a passing barge during the same minute a very complex spatio-temporal relation. But suppose we progressively diminish the time considered to a second, to a hundredth of a second, to a thousandth of a second, and so on. As we pass along such a series we approximate to an ideal simplicity of structural relations of the pairs of events successively considered, which ideal we call the spatial relations of the Needle to the barge at some instant. Even these relations are too complicated for us, and we consider smaller and smaller bits of the Needle and of the barge. Thus we finally reach the ideal of an event so restricted in its extension as to be without extension in space or extension in time. Such an event is a mere spatial point-flash of instantaneous duration. I call such an ideal event an ‘event-particle.’ You must not think of the world as ultimately built up of event-particles. That is to put the cart before the horse. The world we know is a continuous stream of occurrence which we can discriminate into finite events forming by their overlappings and containings of each other and  separations a spatio-temporal structure. We can express the properties of this structure in terms of the ideal limits to routes of approximation, which I have termed event-particles. Accordingly event-particles are abstractions in their relations to the more concrete events. But then by this time you will have comprehended that you cannot analyze concrete nature without abstracting. Also I repeat, the abstractions of science are entities which are truly in nature, though they have no meaning in isolation from nature."

- Alfred North Whitehead (1861 - 1947)
The Concept of Nature

First Distinction

"‘In the beginning,’ my dear, ‘there was that only which is, one only, without a second. Others say, in the beginning there was that only which is not, one only, without a second; and from that which is not, that which is was born.

‘But how could it be thus, my dear?’ the father continued. ‘How could that which is, be born of that which is not? No, my dear, only that which is, was in the beginning, one only, without a second.

‘It thought, may I be many, may I grow forth. It sent forth fire.

‘That fire thought, may I be many, may I grow forth. It sent forth water.

‘Water thought, may I be many, may I grow forth. It sent forth earth.’"

- Chāndogya Upaniṣad (8th to 6th century BCE)
Translated by trans. F. Max Müller, The Upanishads