if the universe is a three-torus, one of the distant galaxies. we observe may be our own. The possibility would be hard to verify because the image of our galaxy would be formed from light that left its source billions of years ago and spent the intervening time crossing the universe. What could be seen, given unlimited resolution of the image, would be the Milky Way in its earliest stages of evolution, as it looked when the light was emitted. Such a universe has a finite volume but no boundary of any kind.
What is the spatiotemporal structure of the Universe? Through the looking glass, there is an element of predestination in what is ‘relational’ and an element of free will in what is ‘intrinsic.’ As Julian Barbour conveys the feeling attached to even the most abstract idea, self-determination and predestination apply, I feel, to the story of the Universe. Those relational variables expressed in the intrinsic dynamics of the Universe are dimensionless ratios and their relative infinitesimal variations. When one of them changes, these ratios change collectively. Since the future overlaps the present and the present overlaps the past, the origin of the absence of interactions between particles is tucked deep inside the first sparkle of the Universe’s volitional state. The secret of the temporal topology precedes the reign of matter during which countless degrees of freedom have merged into a three-dimensional reality before our eyes. It is in those first, distant footprints that the Universe, I feel, expresses free will, unleashes free energy, and throws free variables into the mix. Is the ratio of the curvature of space to the curvature of spacetime linked to gravity?
In discourse more sweet,
For eloquence the soul, song charms the sense,
Others apart sat on a hill retired,
In thoughts more elevate, and reasoned high
Of providence, foreknowledge, will, and fate,
Fixed fate, free will, foreknowledge absolute;
And found no end, in wandering mazes lost.
Sitting on the hill around a pot of fundamentals, spirits of dead poets debate at dawn to the song of a mourning dove. Skilled in the art of wishing, their voices send waves floating higher up in space than the ground level chirping of crickets. Direct visualization and abstract representation is what they know best. Edgar Poe speaks of visions of the dark night while John Ashbery calling on the others asks: How about “free will and predestination, to say nothing of self-determination? Just how do they fit together?”(1) . Some stay silent. Others praise the beauty of freedom and wilderness. Walt Whitman speaks of the irresistible Law from which we escape, by a paradox, into true free will.
If to some, free will and predestination apply to two opposite rules, to others, they are closely connected. In spacetime, the present in which we now found ourselves was chosen among countless paths that were otherwise available to us. George Eliot talks about the winding road we walk as if it were “made by the free will of the trees and underwood”(2). Poets for whom sensibility and intuition are the only channel to the Universe (3) see stars and concepts as one and the same.
The fool on the hill who sits next to the ground fire pit joins the dead poets and asks: Can the self escape its predestined identity? Charles Baudelaire, who by now is fully aware of the unidirectionality of time’s arrow, answers from the grave that, for the Law of progress to exist, everyone will have to wish to create it; that is, when all individuals apply themselves to progress, then, and only then, will humanity be in progress. Not only will there be, in progress, an identity between free will and predestination (liberté et fatalité), but this identity has always existed (4).
I read, however, that free will is an illusion ”which arises from our frequent experience of wishing to do something and succeeding in doing so” (5). So where does the wish to create the Law of progress come from then? The source is unknown. Each step forward through the flow of ideas is a balancing act between non-locality and causality. Thomas, who sits in silence and diligently brushes off the continuous rumble of his thoughts, also feels the need for wishing. For him, it is an act of selflessness, when meeting others and wishing them well, when he wishes for the reversal of climate change and for plants and creatures to not go extinct. It is one more element of consciousness that has become embedded in him, he says. His consciousness has no way of knowing what effect the wishes produced “because they spanned time and distances well beyond his physical presence”, similarly to the butterfly effect.
For a start, there is no tree of awakening
And the shiny mirror has no support
Since Buddha’s nature is always pure and immaculate
To what, then, does dust stick?
The mind is the tree of awakening
The body is the support of the shiny mirror
Since the shiny mirror is neat and clean, to begin with
Where, then, is it filthy with dust?
Philosophical concepts step into the physical realm through the intricate lacework of geometry and matter. On the one hand, a free-willed choice can only be a random one. On the other, if a free-willed choice can produce any pattern by mere chance, then such a self-determined pattern, I feel, is predestined. Free will and predestination mingle in a sort of fractal organization of irregularities. Matter and geometry interact usually on equal terms but not in the vicinity of the big bang and in black holes where geometry has the upper hand. Away from the big bang, an ever-changing geometry speaks of infinitely many billiard-like bounces against steep triangular potential walls. Freely falling massive particles follow time-like geodesics whose path is determined by the curvature and causal structure of spacetime around it “not only forwards and backwards in time but also in the three directions of space”. As “neighborhood geodesics can’t feel their shared spatial environment,” Julian Barbour describes, “they can no longer talk to each other”. Beyond the visible, the asymptomatic silence of geodesics echoes in my mind the silence of quantum entanglement.
The Universe appears to be the work of time while our knowledge of it lags behind as if it were on a separate track. Fractals entail scale-invariant patterns and fluctuations. I still entertain the idea, though, that, to some indefinite distance, the Universe is more inhomogeneous and anisotropic than we imagine and that irregularities in the intrinsic ratios will continue to elude our ability to predict.
Relations are multifold. That is why the extent of a relationship is so intangible. Relations are intentional or accidental, quantitative or informational, and, to a poet, they are in the physical and spiritual dimension. Looking at the 0/1 expressions in a different light, the intrinsic angular momentum of a relational Universe “is and forever remains exactly zero” while the rate of change of the curvature of space to the curvature of spacetime is close to one. From zero to one, the momentum of the Universe vanishes in a sequence of events, a chain of relational intricacies.
Dreams carve a path through which providence enters the physical realm. A poet, who struggles to realize a wish, frozen in time, dreams of a chance encounter with the spirit of an old wrinkled face appearing off the veil. She feels the ghostly presence of past, present, and future as those words are whispered in her ear: There are only blended forms, stretching temporally, bubbling spatially, popping symphonically, for the shape of time slips through transparency. Shapes, waves, matter — all point beyond themselves and engage in deep, wordless murmurings across spacetime.
Instead of thinking of expression, think of the relationships of the holistic form…With an artistic mindset, we don’t draw what we can’t see. And because we don’t draw it, we can’t understand it. Drawing transparently lets us see and understand the complete object or enclosure, all at once.
(1) John Ashbery, Flow Chart
(2) George Eliot, Adam Bede
(3) George Kubler, The Shape of Time
(4) Charles Baudelaire, Oeuvres posthumes
(5) Julian Barbour, The Janus Point