It may be that a throw of dice will never abolish chance, but as soon as the infinite game is on, each time the dice are tossed, it gives a nudge, a direction, builds things to a higher specification. It sets the course like, in the case of the Universe, when constraints are placed upon cosmological parameters. As silence ceases, noise becomes more definite, more in a hurry. After hesitation shown in the first moments, a kind of increased rustling replaces the interval that had disappeared (1).
The Universe starts by preparing and stirring pairs of particles and antiparticles like poets mix ideas in their heads. And then it throws the dice. Within the initial chaos and the intrinsic degrees of freedom, there are potentially the unique Numbers that cannot be others (2) — the necessary fine-tuning of cosmological parameters allowing for the existence of one poet writing the tale of a roll of dice in the midst of a shipwreck.
The Universe resembles a free spirit testing the waters until it finds its way and so, setting the course of its uncharted destiny. Randomly through particles’ interactions, mergers of celestial objects, multiplicity of events, the path upon which it finds itself opens beneath its feet. What sort of a thing the Universe is in its ultimate and simplest nature? Freedom is the essence of its existence. We must recognize, Sartre wrote, that the indispensable and fundamental condition of all action is the freedom (3) of the acting Being. It is the freedom of a diffuse sense of being that spreads through all things.
If, when we speak of being, the hope is to see such a state numerically alone, the multitude of beings, that our common sense leads us to differentiate, become all of a sudden ghosts. Those pretended beings assembled by tribes unite with being and merge within, each of which follows the banner of a particular line of existence.
Against all appearances, it isn’t Mallarmé who brought me to London. It is Longfellow’s soul, whose presence I felt near the Lighthouse of Portland, which guided me to the circle of poets in Westminster Abbey. I passed by where lies what was mortal of Stephen Hawking in the scientists’ corner as I dwelled upon his words about the rolling of dice. Einstein often used that very same expression to convey his idea, that surely, God did not play dice. To him, the Universe is absolutely determined and could not be inherently probabilistic. But as Stephen Hawking pointed out: Not only does God definitely play dice, He sometimes confuses us by throwing them where they can't be seen. The other way to look at it would be to say that our lack of proximity does not allow us to make a proper assessment — possibly because what we can’t see stays below the surface, not in contact with the outside world.
From the surface of a page to the surface of a painting, what is it with shipwrecks in stormy seas that captures the minds of poets and painters alike? Somehow Einstein’s words brought me to Mallarmé’s poem which unfolds like a music composition, a visual representation, a dance choreography. Words scattered on blank pages, like stars in the sky, are debris of a shipwreck swept away, floating on the swinging and rocking waves. Each word and group of words are events spread in timelessness, matter build-up adding texture to the fabric of spacetime.
I pause to meditate upon the uppermost layer of things and how it reflects reality. Gerard ’t Hooft argues that there simply are not more degrees of freedom to talk about than those discrete degrees projected on the surface called boundary. Still, on the oil painting surface, J. M. W. Turner made the Sun rise through vapor. He painted the blurred boundary of skies and waters, the ocean foam, the reflection of clouds in the waves. Art opens to the Infinite. My eyes see the bubbling gathering of the Unveiled whose approach I feel.
Beyond the daily conversation we engage with others, what if our souls could communicate with one another? What if museums were a place for those ghostly encounters? Whatever the artists’ intent is, their artworks trigger something more and bring to the surface what is deep within. The profound meaning isn’t the fragmentary nature of events whose projection on the surface is what we can see. It is that, in the background, events are interlocked, implicated in one another timelessly. Events fit into each other, blending as if they were one and the same. They relate in my mind to the prismatic art of creation. There exists a simultaneity of events: the tossing of dice in a shipwreck.
Life-Boat and Manby Apparatus Going Off to a Stranded Vessel Making Signal (Blue Lights) of Distress, Joseph Mallord William Turner
On the surface, we wonder whether there is such a thing as a sheer coincidence, a supreme conjunction with probability (4). The Universe began its waking day with a Big Bang and will end at the stroke of midnight. One event mirrors the other. A formless existence of an accidental nature — like a brewing storm on a still surface — reveals the hidden process through which what is merely potential frees itself from the fateful suspension of time as if in a landscape painted by Turner.
There are those who believe that there is only one objective reality. It isn’t that the hidden sector is unthinkable, due to information loss. It is that it doesn’t exist, denying therefore the probabilistic properties of the underlying degrees of freedom. Chance, they say, is born out of pretense. And there are those, whom Smolin calls magical realists, who imagine what lies beyond the phantom divide. Chance and fate on a universal scale are so intertwined that we are unable to separate one from the other. We can’t tell which side the Universe is on.
To the magical realists, chance has three properties. It is real, concrete, and eternal (4). How then can chance and variation rise up to the surface? How can it come out from an absence of meaning to get to a state of intended meaning? In short, in an act where chance fulfills its own idea by affirming or denying itself, Mallarmé wrote, in the face of its existence, negation and affirmation fail. It contains the Absurd -- implies it but in a latent state and prevents it from existing: which allows the Infinite to be (4). Chance, whose tangibility manifests itself in the tossing of the dice, is all at once Freedom, Essence, and Existence.
Concepts caught in a circle dance have switched places: Time, Gravity, Space. Freedom, Essence, Existence. If I were to imagine the underpainting of the universal canvas, I would describe how dark energy is diffuse throughout the Universe and would raise the possibility of hidden interactions, through gravity, between the inflationary quintessence and the ordinary matter. Adding another layer to our story, there exists a relation of a particular event — the rolling of dice — to the three Universals of Time, the Quantum Universe, and Nothingness.
Waves Breaking on a Lee Shore at Margate (Study for ‘Rockets and Blue Lights’), Joseph Mallord William Turner
It may be that existence — whether that be of a particle, a wave, or dice — precedes essence. But Nothingness is the origin of their essence. How did the Universe come into being? Infinite interweaves with disorder at the threshold of Nothingness. Sartre, endowed with a sculptor’s mind, visualized the negative space. If negation is the original structure of transcendence, he wrote, what must be the original structure of ‘human reality’ in order for it to be able to transcend (3) the Universe?
Sir Arthur Eddington wrote that the practical measure of the random element which can increase in the Universe but never decrease is called entropy. He added that measuring by entropy is the same as measuring by chance. If God doesn’t play dice, I suppose He knows what entropy means. In any event, I leave Turner behind. My traveling soul is drawn to Cleveland.
- Stéphane Mallarmé, Igitur
- Stéphane Mallarmé, Un coup de dés jamais n'abolira le hasard
- Jean-Paul Sartre, Being and Nothingness
- Quentin Maillassoux, Le Nombre et la sirène
- R. Howard Bloch, One Toss of the dice