Taming Infinity

Published on by Catherine Toulsaly



Some flowers shy away from light, hidden at the ground level under the thick leaves of the mayapples. Others at the tip of the stems compete in their rush to rise above all. The mind, on its toes, steps into every breach. It crawls through every tunneling hole and sneaks in through every gap, hoping for a fateful encounter with nothingness. 

Gulf Branch Nature Center & Park

Gulf Branch Nature Center & Park

The Universe, as I see it,  has revealed itself by expressing itself. “How did the Universe come into being?” At the core, it is ultimately and simply conceptual in nature. There is ‘order’ in the way self-feeding bits of information have built growing connections within the one general conceptual framework. The further the human mind attempts to cut through the thick fog of concepts and look at relations between all objects, the more intuition and visualization sharpen. The Universe’s generated form is a structural reality that follows visible and invisible lines, like the rotational symmetry of a plane around a point. 

David Hockney, The Arrival of Spring in Woldgate, East Yorkshire in 2011 (twenty eleven)

David Hockney, The Arrival of Spring in Woldgate, East Yorkshire in 2011 (twenty eleven)

Taming infinity brings up the image of a long walk along a winding road around puddles that stretches away from the observer’s eye to disappear over the horizon. It creates in one’s mind the picture of a river that begins upstream, flows in meanders, through lakes, and down waterfalls to irrigate the Earth. How can an infinite line, a road carved out of thin air, proceed from past to future? If time is something added to space, it is an infinite loop space. From particles to astronomical objects, wherever we go, there is circularity and roundness. Although particles’ circularity may be easier to determine than their sphericity, a “near-perfect sphericity” is the origin of all structure in the Universe, Julian Barbour argues. Clusters of particles or matter have formed circular patches. Taming infinity means taming the flow of time and all the things within, one shape at a time. 

Something could be round even if it were the only in the universe, unaccompanied by anything from itself.

Rae Langton and David Lewis

David Hockney, The Arrival of Spring in Woldgate, East Yorkshire in 2011 (twenty eleven)

David Hockney, The Arrival of Spring in Woldgate, East Yorkshire in 2011 (twenty eleven)

The emotion of time arises through the organized manifestation of the life of feelings. It may be possible to tame infinity if we consider spacetime as a relational space. Events are necessarily relational on an abstract entity like a quantum field or a dynamical hyperspace like the observable Universe. All the way through, shape appears to be a fundamental property of all objects. Nothingness is what precedes the creation measure. Julian Barbour labels it as the most important number in the Universe. It defines the “proportion of the total kinetic energy that is in change of shape and therefore changing — indeed, increasing — the amount of structure in the universe.” Numbers are said to show two faces. One is algebraic; the other is topological.  If a near-perfect sphericity describes the topologically related space initially,  the creation measure is its algebraically related image.

A relational perspective is highlighted in Lee Smolin’s causal theory of views. He proposes that the Universe is constituted of views of events which comprise information about energy and momentum transferred to an event from its causal past. In a particle formulation, he writes, the view of an event is the set of incoming energy-momentum vectors which coincide or interact at the event. His theory takes me back to Whitehead and the existence of feeling-like phenomena within an intrinsically experiential Universe in which every bit of experience holds its particular point of view. Events involving the interactions of particles with their nearest neighbors have created the view held by Julian Barbour of a shape sphere. From a shape sphere to the sphericity of Earth and Sun, is the Universe, too, a sphere rubbing against others that inches its way through a multiverse? But then the Universe, we’re told, is flat. How things snap into place and to what extent they interlock is a matter of perspective. We can only observe outcomes, whether they are spherical, ellipsoidal, or any other n-shaped objects.


Constanza Rojas-Molina

Constanza Rojas-Molina


Van der Waerden is quoted to have said that Emmy Noether “only worked with concepts”*, noting the principle of detachment that characterizes her work. Her life contribution marks a shift from particular mathematical objects to more general conceptual connections. She explained in her 1918 paper on Invariant Variational Problems that by a ‘group of transformation’ is meant a system of transformations such that for each transformation, there exists an inverse contained in the system, and such that the composition of any two transformations of the system, in turn, belongs to the system. In other terms, every invariance or symmetry property of the laws of nature or a proposed theory there corresponds a conservation law and vice versa. It means, I gather, the relative invariance of properties, the existence of a codependency between the shape of objects and the space they cover even when shapes become distorted. Scale invariance points to an absence of scale, a dimensionless aspect of the Universe. Christof Wetterich proposes that a fundamental quantum field theory does not involve any intrinsic parameter with dimension, mass, or length. This is the meaning of fundamental scale invariance. But then, when I hear the word invariance, somehow it rhymes with the word convergence


The efforts of most human beings are consumed in the struggle for their daily bread but most of those who are, either through fortune or some special gift, relieved of this struggle are largely absorbed in further improving their worldly lot. Beneath the effort directed toward the accumulation of worldly goods lies all too frequently the illusion that this is the most substantial and desirable end to be achieved; but there is, fortunately, a minority composed of those who recognize early in their lives that the most beautiful and satisfying experiences open to humankind are not derived from the outside, but are bound up with the development of the individual’s own feeling, thinking and acting. Genuine artists, investigators, and thinkers have always been persons of this kind. However inconspicuously the life of these individuals runs its course, nonetheless, the fruits of their endeavors are the most valuable contributions which one generation can make to its successors.

Albert Einstein in a letter to the New York Times on the passing of Emmy Noether


How that which is variational fits with that which is invariant emphasizes events over objects. If, at the onset, an impulse out of nothingness has set off the outbound of bits of energy, we still wonder not just what nothingness is but whether objects arise prior to any relational structure. Philip Morison, for his part, writes that the chief indiscernability is the fact that the Universe is modular, with its smallest denominator being a particle or quantum. Objects have dispositional properties within the confines of their internal degrees of freedom and within the bounds of their external degrees of freedom. It may be why shape dynamics takes a relational approach towards objects. Like with the orbit of the Moon, the revolution of the Earth, the clumping of molecular clouds, the expansion of the Universe, a spatial and temporal relationism has been initiated and sustained from the start. It may be of a spherical nature.

Indications from quantum gravity suggest that there is a more fundamental level of description in which there is causal structure but no space. Instead, space emerges as a low energy description of nature, and with it emerges locality

Lee Smolin, The dynamics of difference

In a maze of abstractions, is time something added to space or space, something added to time? Beyond transformation and differentiation, what is left of the identity of things? Invariance, more commonly known as constancy, is the will of the timeless flow. It defines spacetime uniformity, homogeneity, and isotropy. Invariance belongs to the category of events. It stresses that there subsists an enduring relationship. It is reminiscent of the concept of doing nothing, remaining inactive, a principle of willful detachment, in Taoist philosophy, from any outcome. “The Tao always remains inactive, yet it acts upon everything in the world.” If the Universe is ultimately and simply conceptual in nature, can nothingness be treated as a standalone property that allows objects to connect? Science might give to this last bastion which has yet to be conquered the name of dark energy. In essence, nothingness is the state of relations without relata.

In the primordial state of Constancy, there is no material existence. There is simplicity, stillness, and emptiness. Simplicity is Great Simplicity; stillness is Great Stillness; emptiness is Great Emptiness. It fulfills itself without repressing itself. 恒先無有,樸,靜,虛。樸,大樸;靜,大靜;虛,大虛。自厭,不自忍。
Space arises. Once there is space, there is qi; once there is qi, there is material existence; once there is material existence, there is a beginning; once there is a beginning, there is the passage of time. 域作。有域,焉有氣;有氣,焉有有;有有,焉有始;有始,焉有往者。

Erica F. Brindley & Paul R. Goldin & Esther S. Klein, A Philosophical Translation of the "Heng Xian"

*David E. Rowe & Mechthild Koreuber, Proving it her way

Philip Morison “Broken Symmetries” in Judith Wechsler, ed. On Aesthetics in Science, 1981

Julian Barbour, The Janus Point

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Published on by Catherine Toulsaly

Chamaeleon I molecular cloud viewed by Herschel and Planck (ESA/Herschel/Planck; J. D. Soler, MPIA)

Chamaeleon I molecular cloud viewed by Herschel and Planck (ESA/Herschel/Planck; J. D. Soler, MPIA)

This blog flows like a river. Posts are waterfalls where words get caught upstream while others go over. The best way to conceive expansion of the Universe, Julian Barbour writes, is subtle. His use of the term “subtle” echoes Wing Tsit-Chan’s translated words, that non-being defines the subtlety of all things and being is the outcome. Nothing is neither space, time, nor matter. It precedes and vanishes. Its number is zero, a circle that dives into eternity, a well that plunges into infinity, the daily exercise of Ensō


Which of zero or one pertains to unity? Zero is nothingness, and one is wholeness. Both could imply unity, but the former, concealed, is unity in darkness; the latter is unity brought to light. Within one system, one Universe, there occurs a unitary evolution. Unity refers to an invariant variational upon which “energy is conserved because time is uniform; momentum is conserved  because space is the same everywhere  — it is homogeneous; angular momentum is conserved because space looks the same in every direction — it is isotropic.”It isn’t the stars rustling that I hear but the muffled sound of nothingness. 

There appear to be conceptual objects too subtle to differentiate, subtleties that call for candid recognition. One is the gate of all subtleties. In our pursuit of nothingness, we find ourselves at the Janus point where no direction is distinguished.  Stephen Hawkins is quoted to have said that asking what came before the Big Bang is meaningless. It is like asking, “what lies south of the South Pole?”. It would be like sliding down the celestial Sphere from the imaginary point of the celestial South Pole beyond the dark clouds of the Chamaeleon complex and the South Pole Wall. Is it where lies the elusive birth of time? 


DI Cha in the Chamaeleon I dark cloud (ESA/Hubble & NASA, Acknowledgement: Judy Schmidt)

DI Cha in the Chamaeleon I dark cloud (ESA/Hubble & NASA, Acknowledgement: Judy Schmidt)

If we could go back in time to near the presumed start of the Universe, Barbour writes, we would find that indeed time becomes space. “Since a beginning of the Universe presupposes time, this would mean the Universe did not in fact have any singular beginning.” It would imply that time may not have preceded everything else, that it is space from which all things emerge. Could a timeless quantum-size geometrical object, suspended by itself like a lost memory, be the origin of everything? Is that all what time is about: something added to space?

 Space-time picture of the causal relationship between the events (Nima Arkani-Hamed, Paolo Benincasa, Alexander Postnikov)

Space-time picture of the causal relationship between the events (Nima Arkani-Hamed, Paolo Benincasa, Alexander Postnikov)

Determining the geometry of the Universe implies measuring spatial correlations between cosmological structures. In their attempt to trace the cosmic web, cosmologists chase discreet geometrical patterns in the sky, one cosmological polytope at a time. They infer angles from not readily seen tetrahedrons,  double square pyramids, and amplituhedron, hoping for all the lines to be drawn, the pieces to fit into a larger geometry so that the puzzle of the Universe is complete. Over time because of scattering amplitudes contained within, spatial correlations grow and expand, giving a history of time itself. Faces of polytopes speak a more familiar language as if they originate from a distant memory. Geometrical figures are symbols used in the conversation between the Universe and Consciousness. They project a big picture on the universal screen, an overview of a process that takes us from nothingness through the quantum state into a classical view of the observable Universe. 


The bootstrap method is different—instead of asking “what is the answer for the correlator?” it asks, “what is the question to which the correlator is the unique answer?”

Nima Arkani-Hamed, Daniel Baumann, Hayden Lee, and Guilherme L. Pimentel

In Thoughtland, there are mathematical spaces — deSitter Space, Swampland, and String Landscape. Sean Carroll, for his part, proposes that the fundamental ontology of the world consists of a vector in Hilbert space evolving according to the Schrödinger equation. The phase space is a space in which the set of all possible states is represented. Julian Barbour poetically describes it as a “prison in which a Nietzschean eternal-recurrence nightmare gives sleepers no respite.” His words echo those engraved in my memory of Baudelaire’s immense trails of rain spreading like the bars of a vast prison. But the girl in sandals, Barbour adds, can  “walk in an infinite sandpit, and streams need not, like the River Jordan, end in the Dead Sea. They can and often do reach ‘great Neptune’s ocean.”


Take Hilbert space, a realm of infinite dimensions swarming with arrow-shaped abstractions called vectors. Pondering Hilbert space makes me feel like a lump of dumb, decrepit flesh trapped in a squalid, 3-D prison. 

John Horgan

Chamaeleon II molecular cloud viewed by Herschel and Planck (ESA/Herschel/Planck; J. D. Soler, MPIA)

Chamaeleon II molecular cloud viewed by Herschel and Planck (ESA/Herschel/Planck; J. D. Soler, MPIA)

While the thermodynamic arrow coincides with time direction, shapes of the Universe hold  inconspicuous clues about the nature of time. Is it the causal structure of spacetime that provides a rationale for having intersections of lines in the sky? Or will the true shape of the Universe be revealed once the scale falls from one’s inner eye? The Universe is moving along a path chosen out of all possibles that appear to have been otherwise available from the initial state, pulled by unknown attractors. Barbour sees that path not only devoid of scale but apart from time itself. “Everything that is essential is kept; everything that is not is eliminated. That included not only scale but also time”.  The philosopher Mariam Thalos depicts in her book on the Scale Freedom of the Universe a figure of reductionist ontology that brings me back to the collapsing circles of concepts


Without hierarchy: The Scale Freedom of the Universe (Mariam Thalos)

Without hierarchy: The Scale Freedom of the Universe (Mariam Thalos)

Cosmology is a historical science that knows neither its end nor its beginning. How can the endgame be without a scale if attractors lead us to it? How can an expanding universe be a finite one? It is hard to fathom a finite universe with a closed geometry that appears out of nowhere. In order to discuss the initial state, spacetime needs to be quantized. The main idea is to find an underlying first-principle mathematical structure which the wavefunction of the Universe arises from. As we struggle to spell out how nothing creates something, it is replaced by something akin to a quantum tunneling effect. The wavefunction of the Universe represents a probability distribution that presupposes the necessary condition of our existence. While probabilities are said to be an operational concept, they unveil shadowy figures and hidden patterns that silently wait for their turn before taking a particular path among all possibles. Is the whole Universe a lark mirror, made up of looking glass that sparkles in the light for our eyes only and causes us to build bottomless castles on the sandy shores of our dreams?


The iconic representation of a no-boundary saddle point in the absence of matter other than a cosmological constant. The geometry is regular and Euclidean near the south pole and evolves across a matching surface into an expanding de Sitter universe (J. J. Halliwell, J. B. Hartle, and T. Hertog)

The iconic representation of a no-boundary saddle point in the absence of matter other than a cosmological constant. The geometry is regular and Euclidean near the south pole and evolves across a matching surface into an expanding de Sitter universe (J. J. Halliwell, J. B. Hartle, and T. Hertog)

5W Infographics for Quanta Magazine

5W Infographics for Quanta Magazine

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Thought forms and shapes of the Universe

Published on by Catherine Toulsaly

Thought forms and shapes of the Universe

Philosophy is the vernacular form of all objects, physical and conceptual. We find ourselves on a life mission to identify every single one of the shadows surrounding us. Knowledge is perspectival. It colors our expectations of what remains out of reach. Even a void-centered conception of reality would still attach a form to an object. The French philosopher Tristan Garcia writes that nothingness is “the negative form of something in the absence of that something. Nothingness is not the opposite of something, but rather the opposite of something added to the absence of something.” This realization was highlighted in the past by Taoist philosophers and Zen Buddhism masters. 

The Tao that can be told of is not the eternal Tao; The name that can be named is not the eternal name.The Nameless is the origin of Heaven and Earth; The Named is the mother of all things.Therefore let there always be non-being, so we may see their subtlety, And let there always be being, so we may see their outcome.The two are the same, But after they are produced, they have different names. They both may be called deep and profound. Deeper and more profound, The door to all subtleties!

The Tao Te Ching by Lao Tzu, section 1, translated by Wing-Tsit Chan, 1963

Objects leave their footprints in the fabric of spacetime and form a multidimensional physical complexity like a spiderweb in which we are trapped. We wonder what lies outside the observable Universe. As soon as we try to catch nothingness in the act, it becomes an object, maybe a hypothetical particle or a cosmic string. What we have found so far are layers upon layers of infinitesimally small-mass objects. I wish to visualize the revolving door of particles, their dance moves, what physicists would describe as their coupling and decoupling.  


Among the vanishingly small particles crossing the four-dimensional reality and swimming in higher dimensions, neutrinos play a fundamental role. They affect the structure and evolution of the Universe by the constraints they impose on the formation of galaxies. Although their emission may be attributed to gamma-ray burst jets in supernovas, hadronic collisions and nuclear reactions in stars like the Sun, neutrinos form a larger fraction of the matter density in voids than in denser regions. The free-streaming length of neutrinos is comparable to the size of voids. At scales below their free-streaming length, they suppress the growth of structures. A 2019 study aimed to explore the effects of massive neutrinos on dark matter haloes in galaxies within voids concluded that, for both all halos and void halos, increasing the neutrino mass leads to a decrease in the number of massive halos, but more importantly, this effect is more pronounced in the void halo population. Could the neutrino mass mechanism explain why the Universe is expanding faster than expected? But, then, if we live in a large underdensity named Keenan–Barger–Cowie Void, does it imply that our local patch inflated more rapidly than denser parts of the Universe, sufficiently for life to arise?


Cosmic neutrinos pass through us every second. What’s unsettling is that it’s happening without us realizing it as our visible Universe overlaps an invisible realm of particles like an intricate set of multidimensional universes from the infinitely small to the infinitely large placed in and out of each other. Neutrinos may be more abundant than any other type of particle, perhaps with the exception of photons. Once produced, they are hard to destroy. We wonder then about their lifetime. Our understanding of processes involved in the finite yet tiny neutrino masses could help us gain more ground and push further into retreat the concept of nothingness. Decay processes and relational dynamics are the subject of a great number of studies,  prompting particle physicists to imagine all sorts of scenarios to explain how neutrinos get their tiny masses.


Zooming out, from a philosophical standpoint that dominates the forest of theories, shapeless nothingness waits behind the curtains of a cosmic neutrino background or a gravitational field. The Universe is filled with forms and shapes constantly changing and moving. From the initial singularity, the rate of expansion measures the speed at which individual bodies travel from each other and how large their change of position is relative to the changes in position of other bodies in the Universe, with — as I understand it — degrees of freedom of particles such as neutrinos opening up new dimensions. But, on the quantum level, what is changing isn’t the positions of particles, Steven Weinberg argues, but something called the state vector, which I would read like a concept, a metaphysical idea that brings me back to the two-state vector formalism

A particle is simply a physical system that has no continuous degrees of freedom except for its total momentum.

Steven Weinberg, Third Thoughts, p.75

What is the role of the shape-shifting neutrino in all of this? With electrons, muons, and taus, neutrinos form a set of particles called leptons. They are left-handed, prompting the search for right-handed neutrinos such as the hypothetical particles referred to as sterile neutrinos. Among other hypothetical particles, majorons — through their interaction with neutrinos — and sterile neutrinos are introduced as possible dark matter candidates in the goal to elucidate the observed asymmetry between matter and antimatter and the expansion history of the Universe. Researchers investigate as well whether neutrinos are their own antiparticles. Could the so-called ghost particles shed light on the phantom window between matter and antimatter? 

The shapes of the Universe influence the forms of our thoughts: that is what defines consciousness in a broader sense. There exists a language, a relationship between them like a reflection of one action on the other in an endless succession of events except that like with a mirror, the shapes appear in reverse, as an outcome whose whereabouts need to be retraced. The Universe is composed of shifting conceptual components. The faint form of a geometrical object with concepts as coordinate axes emerges. Circles become elliptical or spherical. Is the Universe shaped like the Sun, the Earth, or a flat galaxy? Or is it something else with a more irregular form like a walking brain? 














The above relational framework creates in my head a new image of three inverted pyramids. It conveys the notion that there is no agency without space, no sentience without time, no consciousness without gravity. Of course, this preliminary list of fundamental concepts isn’t exhaustive and can be looked at not only horizontally, vertically, but any other way it pleases. In the end, there isn’t anything wrong with being wrong. At least the recognition of a mistake opens the door to the unexpected. Uncertainties affect the forms of our thoughts and the shapes of the Universe. The hardest part is the state of confusion that precedes a spark in the dark. Perhaps, “there is no underlying theory, that all we will ever have is a number of approximate theories, each valid under different circumstances, and agreeing with each other where the circumstances overlap.” * Theoretical studies and intellectual models are what we do when we dare to reach beyond what we can directly test on Earth. Approximative theories are cobblestones used for paving the way to a theory of everything that appears to be in constant evolution.





Tristan Garcia, Forme et Objet

Julian Barbour, The Janus Point

* Steven Weinberg, Third Thoughts

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Published on by Catherine Toulsaly


Never fear shadows. They simply mean that there is a light shining somewhere nearby.

Ruth E. Renkel

Ruth Renkel was a deaf writer from Elyria, Ohio, who died at the age of 68 in December 1983. In June 1973,  the Elyria Chronicle Telegram published a piece about her. At that time, she was already a selling writer for 25 years and even wrote hundreds of gags for cartoons. It’s fascinating how words have a life of their own. They resonate inside us and leave breadcrumbs along the way. In my case, the word ‘shadows’ haunts me. Writers fill the role of soulkeepers. They feed on sounds, emotions, flashes of light, dreams piling up on each other so much so that they no longer know where reality lies.


Specters from another life
Will haunt in spite of how I've tried to let this lie
And leave the past behind
But the past will never go
For the things we never show
For what we cannot atone


When we close our eyes on a starry night, we feel the presence of shadows as we listen to stars rustling. Fleeting shadows whispering echoes curve the fabric of spacetime and hint at the faraway presence of unidentified mass as they propagate from their source. There is a game of hide-and-seek between lights and shadows. On the one hand, our expectation of light shining nearby stems from our need to infer light from shadows. On the other, we infer the shadowy afterglow of a disk from the photon region orbiting just outside of an infinite throat.

Black holes are really spectacular creatures
They’ve got some extremely peculiar features
Their gravity’s strong, of course. So strong, in fact
That objects nearby just can not stay intact

A doll floating by would be stretched to spaghetti
As gravity pulls on the legs poor Betty
The name of this process: spaghettification!
The noodles are wrapped up in rapid rotation

A disk is created from torn-apart shreds
Most of the time it’s from stars (not doll heads).
These disks are quite common and often quite bright
They’re kind of like signposts for black holiest night

Sean Raymond, Black holes, Stars, Earth and Mars, 2020

In every phenomenon, there is a part that is manifest and a part hidden from us. When three galaxies collide, what happens to black holes at their center and their dark matter haloes? Will microscopic black holes splash across the resulting object? A study released in December analyzed seven nearby triple galaxy mergers and found one with a single growing supermassive black hole, five with double growing supermassive black holes, and one that is a triple. But on the microscopic level, I still wonder how they behave.  A 2019 paper observes that novel information about the microstructure of black holes could be obtained from a geometric viewpoint. Is everything only geometry, or, more precisely, is everything multidimensional gravity written in geometrical patterns? How do black holes evaporate anyway? Their gravitational collapse offers the picture of their irremediable decay — a thermodynamically irreversible process — although some may just be wormholes in disguise.


Mathematics responds to our need to see the Universe as a structural reality. We draw abstract representations out of the hat of physical structures and peel mathematical layers off physical quantities. Theories keep insiders in and outsiders out. How moonshine study is related to string theory isn’t something that I can wrap my head around,  neither is the difference between versions of superstring theories. Where, then, do we go from here if our paths pull us apart? Geometrical representations, though, captivate me. In my world, there are shadows of wormholes and blackholes in the far end, light beings piercing through tree branches nearby, and the early morning call of white-throated sparrows outside my window.


Stereographic projection in 3D

Words transpose themselves from one field to the next. They swap their cultural or philosophical coat for a mathematical varnish. A faithful representation of a finite group refers to something more abstract than an artistic composition. A shadow function in mathematics isn’t a shadow function in psychology. I wish anyway to form a mental image of algebraic structures and visualize how exactly finite groups and modular objects are related via physical structures. But then it would require me to figure out the complex mathematics of modular functions. 


Among the five fundamental operations of arithmetic, if I can relate to addition, subtraction, division, and multiplication, modular forms appear mysterious as they satisfy a number of internal symmetries. Modular forms, Barry Mazur said, are “functions on the complex plane that are inordinately symmetric… their mere existence seems like accidents. But they do exist.” Shadows of modular forms create a connection in my mind with the spatiotemporal image of every footstep in a lifetime at home and on neighborhood walks, every distance traveled in the air, on the sea, underground, and around the globe to form a web-like monster structure with real-life events as spacetime points. 


Neighborhood graph of Niemeier lattices

In the world of numbers, the classification of finite simple groups was achieved. Mathematicians determined 18 infinite families and 26 sporadic groups, the largest of which is the Fischer–Griess Monster group M whose smallest dimension is 196883.  The Monster contains 20 of the 26 sporadic groups as its subgroups, and these 20, including the five Mathieu groups and the Thompson group, are said to form three generations of a happy family by Robert Griess. It was suggested that the Monster group M has its origin in a gravity theory in 26 + 1 dimensions. The other six sporadic groups are called the pariahs, including the O’Nan group discovered in 1976.


Lucy Reading-Ikkanda, Quanta Magazine

Lucy Reading-Ikkanda, Quanta Magazine

When we say that the Universe is a mathematical structure, I am unsure whether this is based on scientific observation or the unique way we have to connect with it or whether that’s what it is intrinsically. Our brain may be the one with a hierarchy problem. It yearns for structure, naturally numbers, classifies, and hierarchizes. Theories form a labyrinth of nesting boxes through which it appears impossible to find one’s way. Each topic is a box-in-a-box. Each subject slides from thermodynamics to information geometry. Each concept becomes representational. It is transposed, translated, and conjugated to another. Moonshine correspondences are striking because of internal symmetries revealed. The vast numbers involved in the monstrous moonshine make all the more difficult for it to be described as a mere coincidence.


Is “the theory of everything” merely the ultimate ensemble theory? Max Tegmark, 1998

Is “the theory of everything” merely the ultimate ensemble theory? Max Tegmark, 1998

In Thoughtland, where all space-like or time-like dimensions exist beyond our immediate awareness, shadows hint at hidden symmetries and the translational quality of fractals. We are not conscious of extra dimensions because they rule the infinitely small and the infinitely large. For a century, Steven Weinberg writes, physicists have speculated that our familiar four-dimensional spacetime may really be embedded in a higher dimensional continuum. Pockets of inertial frames provide observational proof of an intimate connection between inertia and gravitation. On that same starry night, our eyes wide open, we spin around. Stars rotate with us in a synchronous dance. In that inertial frame of reference in the midst of which we stand, our arms irresistibly draw upward. We feel the immateriality of shadows beyond the four-dimensional realm. 


Realists are wary of the translational aspect of symbols in their search for rigorous proof. Idealists find meaning in bridges between concepts. On the one hand, we could define a ‘dimension’ as nothing more than another coordinate axis, another degree of freedom, a purely symbolic concept. On the other, a dimension may indeed encompass a higher state, open a gate to a whole new Universe. Our four-dimensional spacetime is the tip of the iceberg that conceals beneath extra small dimensions which contract and compactify through traceless routes into our observable reality. The Quantum Universe might give us access to the infinitely small, while fractals of the infinitely large display infinite-dimensional representations on the other end of the spectrum. Beyond the four dimensions, the Kaluza-Klein theory adds a dilaton field. In 2017, Stephane Collion and Michel Vaugon proposed a new approach to the Kaluza-Klein idea and showed that a unified geometrical frame could be set for gravitation and electromagnetism.


Cross section of the quintic Calabi–Yau manifold. Produced using the methods described in Hanson (1994), "A construction for computer visualization of certain complex curves", Notices of the Amer.Math.Soc. 41(9): 1156–1163.

Cross section of the quintic Calabi–Yau manifold. Produced using the methods described in Hanson (1994), "A construction for computer visualization of certain complex curves", Notices of the Amer.Math.Soc. 41(9): 1156–1163.

The investigation into the infinitely small has resulted in the discovery of 59 new hadrons and counting over the past 10 years by the Large Hadron Collider. I imagine higher dimensional theories filled with massless particles. Finding evidence of such particles could be key to understanding how a Universe with 10, 11, 24, 26, and more dimensions operates. Reality, as it stands external to us, isn’t just mathematical but conceptual. Each concept in the four reference circles that define the essence of information could be seen as a whole new dimension.


Edwin Abbott Abbott, Flatland: A Romance of Many Dimensions


Family tree of theories (Tegmark, 2007)

Family tree of theories (Tegmark, 2007)

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Philosophical Interlude

Published on by Catherine Toulsaly

Eye in the Sky (ESA/Hubble & NASA, J. Lee and the PHANGS-HST Team; CC BY 4.0 Acknowledgement: Judy Schmidt)

Eye in the Sky (ESA/Hubble & NASA, J. Lee and the PHANGS-HST Team; CC BY 4.0 Acknowledgement: Judy Schmidt)

Theoreticians are idealists who fight each other with their dreams. Do we believe that our brain holds the key to that which unites the infinitely large and the infinitely small? While some puzzles are better left to state-of-the-art computations, tucked away in a mathematical code, locked in geometrical patterns, poets attempt to keep a record of vanishing thoughts and translate the beat of those dreams with an eye to find a common purpose. The abyss, Lucien Braun writes, between the expression of what is and what is left unexpressed commands the “awkwardness” of thought. Beyond stating similarities and identifying connections, we hardly grasp all the nuances of meaning in one single concept. There exists a struggle in our brain with the verb to make it say the unspeakable. 


It would seem easier to transpose philosophical ideas into the field of science than the other way around. A “crucial part of developing scientific theories,” James Owen Weatherall writes, “is to take basic concepts and make them precise enough to support scientific inquiry. But this process of adapting our intuitive ideas to the more rigorous demands of science can result in radical changes to our conception of reality.” If space and time can be curved even when there is nothing, can it be called nothingness


Voids appear to be the most dark energy dominated regions in the cosmic web. If they are filled with that sort of vacuum energy free to interact with dark matter, shouldn’t it be part of the solution to find the beginning of time?  Time is born in a void, lost in a black hole. Whether there exist patches of antimatter, dark energy puppeteers, shadows of dark matter halos, gushing white holes, and gobbling black holes, these are theories that may help one day to make sense of time.


…the most likely scenario is that at present we have understood neither the full matter-energy content of the Universe nor the law of gravity that governs it

Elena Asencio, Indranil Banik and Pavel Kroupa

I struggle to imagine what it is like to be a space devoid of matter. Stillness, silence, and invisibility are its attributes. It is inconsistent, in my mind, with black holes drawing matter in and voids clearing it out. That which unites the infinitely large and the infinitely small emerges and builds up over time out of intemporal voids whose bodies shrink and expand. We don’t just live on the outside limit of the Local Void, but inside the perimeter of a large underdensity around the Local Group, known as the Keenan–Barger–Cowie Void. It implies the necessity for a radical change in our conception of reality, a void-centered view of our neck of the woods, a revolution in our frame of reference.


I pause and dwell a moment on the nature of light, the soul of the Universe, and the earthly things. Light passes towards our eyes through the air and other transparent bodies in the same way, Descartes writes, that the movement or the resistance of bodies, which a blind man meets, passes towards his hand, through his staff. Light, Maxwell argues, is an “electromagnetic phenomenon the laws of which can be deduced from those of electricity and magnetism, on the theory that all these phenomena are affections of one and the same medium.” We have privileged all along a substance named luminiferous aether that is the energy distribution of photons in cosmic lights. 


Shuttle Discovery With Moon (NASA/Bill Ingalls)

Shuttle Discovery With Moon (NASA/Bill Ingalls)

We see farther by standing on the shoulders of those who came before us, by climbing invisible steps up into space and pulling strings attached to spacecrafts as far away as interstellar space. One must bear in mind the possibility, however, “that it might be the presence of a gravitational field that takes the description of a physical system out of the realm of pure quantum physics,” Roger Penrose writes. We have learned that astronomical bodies exert a gravitational force on one another and affect one another by changing the geometrical structure of space and time. Nothingness is the background of the gravitational field in which a photon-graviton conversion may occur through strong primordial magnetic fields.


Not only do we believe that primordial magnetic fields were generated through magnetogenesis during inflation and post-inflation,  but it is suggested that quantum magnetic monopoles were created during preinflation. Barbour writes that those magnetic monopoles might be today so widely spread out through the Universe that we cannot reasonably expect to observe any. Suppose they played a role as dark matter candidates through their connection with (hidden) dark sectors. In that case, I wonder how the study of dark matter and the investigation into the properties of primordial magnetic fields are related.


Mission drift describes the path taken by my wandering mind. In the search for an absolute vacuum, a perfect void, we are left to accept Descartes’ definition of an extension as the necessary existence of a substance. We realize that even voids and black holes have shapes and magnetic fields. While the essence of information on the origin, nature, and existence of matter travels at the speed of light, such a thing as nothingness is nowhere to be found in our four-dimensional reality. 


The unspeakable is what occurs behind a veil of darkness. Voids in our heads mirror voids in space. The elusive quality of timelessness creates images of a time void from which countless subjective experiences arise. If the Universe is a mismatch of past and future subsystems, the rear end of the arrow is born out of a nothingness hidden in the heart of a time void behind the moving walls of a void in space. 


Philosophical Interlude

Poets use images like walking sticks to help ease their mental and physical journey. Words are multidimensional. They change forms and transpose themselves from one field to the next. They are like point particles in which internal strings vibrate. How far can we reach collectively and individually? Our existence woven into the fabric of time conceals aspects we have yet to discover.

Philosophical Interlude

Lucien Braun, Paracelse

James Owen Weatherall, Void: The Strange Physics of Nothing

Descartes, Principes de la philosophie

The scientific papers of James Clerk Maxwell 

Barbour, The Janus Point

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Published on by Catherine Toulsaly

Cinnamon in the Sun

Cinnamon in the Sun


The hypothesis that the Big Bang came out of a quantum fluctuation from a very specific prior state opens the door to more questions. If timelessness involves an infinite timeline or an endless bouncing process, why does our brain only make sense of boundaries? Mine feels the reach of its own limit and hesitates to jump ahead. A system may be symmetric to the extent that it is made of one part moving forward, the other going backward. What remains confusing to me is whether a time divide lies inside the box crisscrossed by circles or lines of past and future subsystems or outside in a larger timeless state. New pocket universes are brought into being while chains of events happen both to the past and the future, either in a multiverse or a subsystems-made universe.


When it comes to time’s arrow, we tend to look for answers “into the box and not out into the Universe.” We know its shape and its age, but what we know of its size is limited to what we are able to observe: 46.5 billion light-years in radius, which is 93 billion light-years in diameter.  While knowledge increases with time and new technical capabilities, the Universe will continue its expansion as if to stay out of our reach. Unable to explore its boundaries, we assume its existence to be unaffected by ‘exterior’ influence. In the realm of analogies, the brain is an entryway between what is and what is not in a similar way, I feel, that the Big Bang is a phase through which the universe passes


This past October, I asked to be corrected when I wrote that “our present is as much part of the past as it is part of the future for the observer who would look out into space from the other side of the Universe”. As far as they can determine, both observers think of each other as living in the “past.” Today, we have detected the most distant quasar yet known J0313-1806 as it would have appeared more than 13 billion years ago. Its collapsed structure contains a  supermassive black hole that came into being just 670 million years after the Big Bang. We have also discovered the protocluster LAGER-z7OD1when the Universe was only 770 million years old.


Let’s imagine a second that an observer stargazes from their end in their own future— whether it be a disembodied brain or a celestial object endowed with a soul. They would see what was anterior to the Earth, three billion years before Gaia-Enceladus dwarf galaxy and the progenitor of our Milky Way collided. They would catch a glimpse of the reign of bubbles during cosmic reionization. 


The epoch of reionization is a bridge between the cosmology that we can theoretically calculate from first principles and the astrophysics we observe today and try to understand.

Aaron Parsons

By the end of the year, the James Webb Spatial Telescope, our latest time-machine,  will finally be launched. It will be operational by mid-2022. In our mind, a clear milestone in the macroscopic nature of spacetime is the unveiling of the first lights. If there is a Janus Point, the universe on the other side isn’t an “exact mirror reflection,” Barbour stresses.  There is a single past for two distinct futures emerging from it. We live in a universe that is time-symmetric on ultra-large scales. What we see in those early structures is a mirroring image of ourselves, a fractal memory.  Quasars and dwarf galaxies played an essential role in the build-up of massive galaxies and the reionization process. The initial conditions surrounding the formation of the first celestial objects bring back in my mind the image of dwarf galaxies that have been observed to be moving out of the Local Void.


If inflation is to play a role in explaining the initial conditions of the universe, we need to understand how it arises from some specific condition, rather than simply appealing to randomness.

Sean M. Carroll and Jennifer Chen

But then, if the Big Bang isn't a unique event, how to reconcile eternal inflation or bounce cosmology with a reversed arrow of time? The Universe hasn’t followed a path of unitary evolution. I suppose it is unlikely that it could recollapse into the exact shape of its initial conditions. Janus-point systems may not be subject to recurrence — they are not in a ‘box’. The arrows exist “not because of statistical fluctuations but because of dynamical necessity.”


Information flows drip by drip into my brain as I attempt to reach the far edges of the unknown. I thought I would roam between stars. I swapped them for concepts instead. On the outskirts of the solar system, a planetoid labeled 2018 AG37 stands four times farther away from the Sun than Pluto. Its nickname Farfarout appears to be coming out of the Shrek Universe. Although it depends on its one-thousand-year orbit, which takes it from time to time closer than Neptune to the Sun, it has become the last frontier of the solar system along the rim of nothingness. Spotted for the first time in 2018, it unseats Farout, aka 2018 VG18. 



I wish nicknames to convey a poetic, historical or cultural message. I hope for names like Oumuamua and Arrokoth and wonder whether the next minor planet will be dubbed Farfarfarout. If indeed, as Kepler suggested, there exists a bond of sympathy between heavenly and earthy things, Farfarout might know best how the Earth feels about the relentless environmental degradation that its two-legged tenants impose on the planet.


Holding my notebook in which I write a neverending list of whys, I wish to ask an alien lifeform on an interstellar spacecraft passing nearby. I would not refrain from reading aloud my latest rant on infinite ways to explain hows. I would take a leap of faith, drawn by eerie sounds of resonance orbits from the faraway system TOI-178 in the Sculptor constellation. Could human anguish be caused by our greatly elongated form stretching even more over the spatial-temporal grid? 



Stars and galaxies are seen as exaptations – structures that have found a use other than that for which they were originally developed by evolution.

Sean M. Carroll and Jennifer Chen

The word 'conundrum' isn't music in my ear, but it describes how I feel as I move forward. Crawling through Barbour’s book, I circle back into the intricacy of entropy. Within the observable patch, what is measured as the entropy is dominated by photons and neutrinos. An increase in the entropy, I gather, relates to photons and neutrinos energy distribution. Barbour explains that “the direction of entropy increase is the direction of time.” They are one and the same.  “A single direction had been mistaken for two.”


Cinnamon in the Sun

Cinnamon in the Sun

Julian Barbour, The Janus Point

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Boltzmann Brains

Published on by Catherine Toulsaly



As for the poet, she only sees the Universe as a symphony of lights and sounds played on the keyboard of time.

Prologue to all the possibles

Along with the Universe, we, too, are gifted with an emotional keyboard, but we don't play it the same way. Concepts, words, and emotions blend together. They, too, have a life of their own. Reading about the genetic diversity among sequoias created in my mind the visual metaphor of a forest of walking brains. The unsettling concept of disembodied brains has taken me back to that analogy. ‘Boltzmann brains’ are observers stripped to an absolute bare minimum — their consciousness.  


What is a brain anyway? A tool conceptually and causally integrated into a physical state with the ability to sense and adapt, an entryway between what is and what is not. I have another image in my head: that of cephalopod-like giant brains propelling their appendages bestowed with a sense of beauty and complexity. Boltzmann brains may be pair-produced from photons and gravitons, provided that the existence of an elementary graviton particle is verified.


A Boltzmann Brain is a configuration of matter that is (along with its local environment) as close as possible to thermal equilibrium, while still qualifying as an intelligent observer

Sean Carroll

If we understand processes to be going forward and backward in time, Boltzmann brains could reach consciousness both ways and experience the flow of time when it goes forward and when it is reversed. To bring them to life, we would only need local subsystems to behave ergodically, not the universe as a whole. Sean Carroll wrote the following dialogue between two scientists on why Boltzmann brains are bad:

W : I am worried that our best cosmological model predicts that typical observers are Boltzmann Brains. 

S: Why? Sure, there may be a huge number of BBs in this universe, but I’m not one of them, so what do I care? 

W : How do you know you’re not a Boltzmann Brain? 

S: I don’t seem very brain-like. I have arms, legs, etc. The environment around me seems pretty dramatically far from equilibrium. 

W : Fine. But in a large, randomly-fluctuating universe, even if you are not a minimal-fluctuation observer (a BB), it’s overwhelmingly likely that you are in a state that represents the minimum possible fluctuation away from equilibrium, conditioned on whatever features your local environment has. Call these “Boltzmann Observers” (BOs). Even granting that you have arms and legs and are sitting in an office, it’s still overwhelmingly likely that all of that has randomly fluctuated into existence out of equilibrium. How do you know you’re not a Boltzmann Observer? 

S: Because I can see that I’m not! I can go out and, for example, observe the cosmic microwave background, which is evidence that the universe was in a much lower-entropy state several billion years ago, which isn’t what I would expect if I were a BO. 

W : But even if you are observing the microwave background, you’re not necessarily seeing the leftover photons from the Big Bang. You’re seeing a radiation field entering your telescope right here in your nearby environment. In a fluctuating-universe scenario, it’s certainly possible to see such photons, but it’s overwhelmingly likely that they randomly fluctuated into existence, without any connection to an earlier low-entropy state. 

S: Well, that scenario makes a very reliable prediction, as Feynman basically pointed out: all I have to do is look in my radio telescope again, and see whether 16 or not the background radiation is still there. If what I observed already is just a random fluctuation, there’s no reason for it to persist over time; in fact it’s incredibly unlikely. So let me wait a second before checking again and... Nope. There’s the microwave background. I still seem to be in a thermodynamically sensible environment. I am not a BO. 

W : You don’t have the right to conclude that. In a randomly-fluctuating universe, just as almost all observers are minimal-fluctuation BBs, and almost all observers with arms and legs and microwave backgrounds are minimal-fluctuation BOs subject to those macroscopic constraints, it’s also the case that almost all of the observers with arms etc. who believe they have just waited a few seconds and failed to observe any evidence of the surrounding equilibrium are also random fluctuations with just those properties. You can conditionalize on any macroscopic information you like: in a randomly-fluctuating universe, it remains overwhelmingly likely that you are at a local minimum of entropy that evolved by chance out of equilibrium. 

S: But everything I know and feel and think about the world is what I would expect if I were an ordinary observer who has arisen in the aftermath of a low-entropy Big Bang, and nothing that I perceive is what I would expect if I were a random fluctuation. 

W : And in a randomly-fluctuating universe, the overwhelming majority of people who would say exactly that are, as a matter of fact, random fluctuations. That’s why those kinds of cosmological models are bad. 


Although the existence of Boltzmann brains may be vastly improbable, it doesn’t make it impossible. They may inhabit one part of the Universe while we, walking brains, live in another. There may be other scenarios. Could the extremely rare occurrence of random fluctuations have resulted in the formation of only one Boltzmann brain that has given shape to all matter? 


If ultimately, the sort of thing that the Universe holds within is a brain with furrows and ridges where signals ricochet, one might also ask where the rest of the body is. If even the most abstract idea has a sort of feeling attached to it, and without it, an idea has no resonance, no meaning, the organized manifestation of the life of feelings might as well have resulted in the shaping of a Boltzmann heart. 


Are we, ourselves, part of a simulated reality or born out of a Boltzmann fluctuation? We would then expect not just Boltzmann brains, Boltzmann hearts, Boltzmann galaxies, and, who knows, Boltzmann universes to eventually fluctuate into existence. Such a suggestion would put us on even shakier ground. Therefore it should be rejected, Sean Carroll argues, because it is cognitively unstable. 

The nightmare in the most extreme case envisaged is that exactly what you firmly believe yourself to be doing now, in this very instant and in every last detail, is being replicated infinitely many times by infinitely many identical avatars of yourself scattered around the infinite multiverse, every one of them believing themselves to be the one and only true you. What is more, each of them including almost certainly you, consists of nothing more than a disembodied brain that exists fleetingly in what is otherwise fluctuating chaos.

Julian Barbour, The Janus Point, p.77

This is not much different from the uneasiness felt by philosophers in the past. Long ago, the Chinese philosopher Zhuang Zi dreamt that he was a fluttering butterfly (needless to say that a butterfly strikes me as a better alternative than a disembodied brain). When he woke up, he felt suddenly lost. He no longer knew if he had dreamt that he was a butterfly, or a butterfly dreamt that it was he. For all that we know, we could be frogs in a meditative state, dreaming that they are humans, looking for ways to jump out and escape their unavoidable environment.


All this flow of time that we experience and these various bodies that we feel, these different thoughts that agitate us, are perhaps only illusions. We believe we see spaces, figures, movements in our dreams. Who knows if this other half of life where we think we are awake, the French philosopher Blaise Pascal wrote, is not another sleep a little different from the first, from which we wake up when we feel we are sleeping?


If we are allowed to dream that we are butterflies and live our waking lives as human beings, I feel there is more to us than our physicality. The stuff that we are made of is a kinetically nonlocal energy that transcends dreams and reality. In the end, we are left to wonder whether stars, galaxies, filaments are pictorial representations of a Boltzmann brain or physical manifestations that do not presuppose the existence of a brain. At the basis of it all lies the fundamental question of quantum ontology. It appears more likely that our thoughts randomly fluctuate in our heads. We are quantum-theoretical beings, not randomly-fluctuated physical observers.


My brain keeps hidden, in its folds, metapatterns, circles, and lines moving poetically, enigmas that do not lend themselves to reason, leaps forward and beyond. Circles contract and expand. They regulate the flow of my thoughts, forming snakes eating tails, drawing the start and end of Wheeler’s Universe. Inside circles, the snow falls into eternity, making the Universe quieter. Wells, too, are circles opening their mouth into the bowels of the Earth. What’s an idea whose time has come? Ensō. 

(Quote by Thich Nhat Hank)

(Quote by Thich Nhat Hank)

Humankind is not a circle with a single center but an ellipse with two focal points: facts are one, and ideas are the other.

Victor Hugo

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All the many layers

Published on by Catherine Toulsaly

Titan's many layers (NASA/JPL/Space Science Institute)

Titan's many layers (NASA/JPL/Space Science Institute)

Very well, you may smile at this; but you must admit that the model of the world developed here is at least a possible one… It also gives an incentive, not only to speculation but also to experiments…

Ludwig Boltzmann, Lectures on Gas theory

I have felt before that imagination is a double-edged sword, lighting up the path to reality and distorting it at the same time. While we may feel mesmerized by the imaginative power of others, we know our own to be involved in a tug-of-war with reason.

The back-and-forth between attractors and repellers in the three circles of dance left in my mind the image of individual streams of time, each with their own sense of being. While we follow a time path toward the Great Attractor, those in the zone of influence of the Dipole Repeller, who feel the repulsion of the Cold Spot Repeller, may be embarked in a time channel flowing in the opposite direction. Ludwig Boltzmann alluded briefly to a scenario in which processes would go in the opposite direction and living beings separated from us by aeons of time and spatial distances would feel the passing of time differently from us. 


Hans Reichenbach contemplated in more detail the possibility that after “reaching a high-entropy state and staying in it for a long time," during which “living organisms cannot exist," the Universe would enter a “long downgrade of the entropy curve, then, for this section, time would have the opposite direction.” He defined supertime in a similar way as Kerri Welch writes about timelessness. It has no direction, “only an order, whereas it contains individual sections that have a direction, though these directions alternate from section to section.” It would forever be unknown to the inhabitants caught in individual sections that their direction is different from ours. For all that we know, we could be unaware that such fated circumstances occurred before us. That no living organisms had existed in the time gap prior to our existence would explain the memory loss of a time in the opposite direction, wiped out from the conscious realm. 


Full moon

Full moon

Time, a recurrent subject in the dialogue between Consciousness and the Universe, is deeply embedded in our intuition. If the concept of existence cannot be applied to the quantum Universe where there is no “either-or,” I can’t imagine time being part of the picture either. If we could perceive nonclassical superpositions, we would see that any quantum state is a correlation of another. Timelessness and nonlocality paint in words the quantum Universe. Probabilities are the currency in which information circulates.

Frozen pond

Frozen pond

At the intersection of the quantum world and the macroscopic Universe is the field of statistics.  If we look at the essence of life, it is a statistical improbability on a colossal scale.“The true explanation for the existence of life,” Richard Dawkins writes, “must embody the very antithesis of chance.” It doesn’t mean that we need to look for answers in the realm of the improbable,  but to ‘tame’ chance means to break down the very improbable into less improbable small components. Peter Hertel argues, “There are no hidden variables”. The more we break down the very improbable, the more we mate quantum events to respect certain probabilities. When we say that quantum processes are ruled by probability, there appears to be a probability scale or distribution that we are made aware of. But if such a scale or distribution exists, it may be all about our own expectations.

Calculating expectation values is the task of quantum theory, not more, not less.

Peter Hertel, Quantum Theory and Statistical Thermodynamics

While probability, I recall, is said to be an operational concept, a philosophical category, decoherence and collapse represent, on the other hand, a technical approach more than a philosophical point of view. They are key concepts in the quantum-to-classical transition. Decoherence serves as a human tool that allows the conscious mind to determine how and when the quantum probability distributions approach the classically expected distributions. I will come back to the concept of collapse at some point in the future. But for the time being, I’ll focus on what decoherence means.


Wojciech H. Zurek, Decoherence and the Transition from Quantum to Classical—Revisited

Wojciech H. Zurek, Decoherence and the Transition from Quantum to Classical—Revisited

Decoherence, Dieter Zeh writes, is the dynamical dislocalization of quantum mechanical superpositions — of what is “somehow all at once” — through the formation of entanglement of any system with its unavoidable environment. It describes, Maximilian Schlosshauer adds, how entangling interactions with the environment influence the statistics of results of future measurements on the system. However, entanglement isn’t just a statistical correlation between local objects. It becomes reality itself. 

It is generally understood that a measurement involves an amplification of a microscopic superposition into the macroscopic realm by means of entanglement, followed by decoherence by the environment…

The Two-Time Interpretation and Macroscopic Time-Reversibility

Environmental interferences bind together time and phenomena. Because quantum systems are never completely isolated from their environment, Schlosshauer explains, when a quantum system interacts with it, what it becomes entangled with is a large number of environmental degrees of freedom. This entanglement influences what we can locally observe upon measuring the system. In the interactions with the unavoidable environment, not just matter and the conscious mind exist, but the information channel — part of past and present information on which path was taken — is also known.


Bits of time perspectives tenaciously endure. If it were not for the second law of thermodynamics under which the Universe operates and without causality, will time still slip away in the macroscopic Universe? The term coarse-graining was introduced by Boltzmann in 1872 in the context of thermodynamics. While quantum phenomena provide a source of entropy — defined as entanglement entropy — it is distinct from the classical one generated by coarse-graining. Any particular event may be an instance of a lot of different coarse-grained events, Antony Eagle argues. Carlo Rovelli uses the concept of coarse-graining to highlight how interactions within the Universe creates the perspectival aspect of time. 


Arrows of perspectival time derive from the quantum Universe. Superpositions, though, do not cease to exist, even though they are not there anymore. From neither-nor, coherence and decoherence take turns in harmony. My mind wanders as it visualizes layers of time and space, all at different decay times. In the kinematically nonlocal Universe where time-dependent scenarios emerge, the collective kinetic energy bounces around and back.  




Hans Reichenbach, The Direction of Time 

Julian Barbour, The Janus Point 

Richard Dawkins, The Blind Watchmaker

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The Essence of Information

Published on by Catherine Toulsaly

Complex, Nelleke Beltjens

Complex, Nelleke Beltjens

Do processes like fractals mirror each other from one end of the Universe to the other? Stars springing out of darkness is a metaphor for ourselves. Complexity tells the continued story of a behavioral trait that spreads from the Big Bang to the fabric of our societies. It appears, though, impossible to predict based on its main build blocks alone the observable clustering properties of the Universe. How small variations on the set of cosmological parameters could produce a more complex evolution of large-scale structures remains one of the main issues for astrophysicists like Franco Vazza.


…any physical phenomenon can be regarded as an information processing device, whose evolution produces a sequence of outputs (e.g. energy states), which can be analysed through symbolic analysis.

Franco Vazza


For scientists like Julian Barbour, stars are fossil-like objects. For me, they are living things. I cannot look at the night sky and think it is an archeological field. Barbour asserts that entropy is better defined as a measure of complexity rather than of disorder. One does not exclude the other, I suppose. “This is perfectly true at the microscopic level,” explains Barbour, but not at macroscopic scale. Complexity appears messy, chaotic at first as an evolving system enters a new threshold. Its complexity grows inwards and outwards. 


Guided by a thread of hope on the outside and a sense of harmony within, I wrestle with the words ‘darkness’ and ‘complexity’ as if they ought to say something more. Darkness is sadness that’s slowly sinking in once anger and uproar have settled. “Violence, ” writes Martin Luther King, “is the antithesis of creativity and wholeness.” We are blind moles weighted down by the burden of ignorance, hoping to see in the mirror that stands at the Janus point the reflection of our wings. Within darkness and complexity lies the essence of information, a path to differentiate all aspects of reality.


I had a dream, which was not all a dream.

The bright sun was extinguish'd, and the stars

Did wander darkling in the eternal space,

Rayless, and pathless, and the icy earth

Swung blind and blackening in the moonless air;

Morn came and went—and came, and brought no day,

And men forgot their passions in the dread

Of this their desolation; and all hearts

Were chill'd into a selfish prayer for light:

And they did live by watchfires—and the thrones,

The palaces of crowned kings—the huts,

The habitations of all things which dwell,

Were burnt for beacons; cities were consum'd,

And men were gather'd round their blazing homes

To look once more into each other's face;

Happy were those who dwelt within the eye

Of the volcanos, and their mountain-torch:

A fearful hope was all the world contain'd;

Forests were set on fire—but hour by hour

They fell and faded—and the crackling trunks

Extinguish'd with a crash—and all was black.

The brows of men by the despairing light

Wore an unearthly aspect, as by fits

The flashes fell upon them; some lay down

And hid their eyes and wept; and some did rest

Their chins upon their clenched hands, and smil'd;

And others hurried to and fro, and fed

Their funeral piles with fuel, and look'd up

With mad disquietude on the dull sky,

The pall of a past world; and then again

With curses cast them down upon the dust,

And gnash'd their teeth and howl'd: the wild birds shriek'd

And, terrified, did flutter on the ground,

And flap their useless wings; the wildest brutes

Came tame and tremulous; and vipers crawl'd

And twin'd themselves among the multitude,

Hissing, but stingless—they were slain for food.

And War, which for a moment was no more,

Did glut himself again: a meal was bought

With blood, and each sate sullenly apart

Gorging himself in gloom: no love was left;

All earth was but one thought—and that was death

Immediate and inglorious; and the pang

Of famine fed upon all entrails—men

Died, and their bones were tombless as their flesh;

The meagre by the meagre were devour'd,

Even dogs assail'd their masters, all save one,

And he was faithful to a corse, and kept

The birds and beasts and famish'd men at bay,

Till hunger clung them, or the dropping dead

Lur'd their lank jaws; himself sought out no food,

But with a piteous and perpetual moan,

And a quick desolate cry, licking the hand

Which answer'd not with a caress—he died.

The crowd was famish'd by degrees; but two

Of an enormous city did survive,

And they were enemies: they met beside

The dying embers of an altar-place

Where had been heap'd a mass of holy things

For an unholy usage; they rak'd up,

And shivering scrap'd with their cold skeleton hands

The feeble ashes, and their feeble breath

Blew for a little life, and made a flame

Which was a mockery; then they lifted up

Their eyes as it grew lighter, and beheld

Each other's aspects—saw, and shriek'd, and died—

Even of their mutual hideousness they died,

Unknowing who he was upon whose brow

Famine had written Fiend. The world was void,

The populous and the powerful was a lump,

Seasonless, herbless, treeless, manless, lifeless—

A lump of death—a chaos of hard clay.

The rivers, lakes and ocean all stood still,

And nothing stirr'd within their silent depths;

Ships sailorless lay rotting on the sea,

And their masts fell down piecemeal: as they dropp'd

They slept on the abyss without a surge—

The waves were dead; the tides were in their grave,

The moon, their mistress, had expir'd before;

The winds were wither'd in the stagnant air,

And the clouds perish'd; Darkness had no need

Of aid from them—She was the Universe.


Lord Byron, Darkness


Words are chained to each other. Concepts circle in my head. I wonder whether they intersect. The infinite game of space, time, and gravity has formed the first circle. The past discussion on freedom, existence, and essence has created another. A post on agency, sentience, and consciousness has added a third. Since Rudolf Claudius invented the word entropy so as to be as similar as possible to the word energy, I imagine a fourth circle that naturally brings together entropy, energy, and information. We see the Universe as “a succession of snapshots that you might take on a walk through the countryside,” while the quantum Universe forces you to consider “somehow all at once,” writes Barbour. In a way, the table below is the first step I take to rearrange snapshots in my head.















Information is a bottomless ocean where it is easy to get lost. On the one hand, we are swept away by currents; on the other, we can’t discriminate between all the many sources. We know too well that it is above all important to learn to think, reflect, and reason. This is what Benjamin Franklin worked on at an early age with the reading of two fundamental works: The essay on human understanding by John Locke and The logic, or, art of thinking by Antoine Arnaud and Pierre Nicole. 


More than 300 years later, it is even harder to find our way through the labyrinth of ideas and concepts. The information philosopher Kun Wu (邬焜) divides information into three different forms: information-in-itself, information-for-itself, and regenerated information. Concepts belong to the third category. Not only do circles intersect with each other, but they collapse into three new interconnected groups that help reconfigure in my head bridges between concepts.


Simplicity is not a winding road,
nor else a bridge across a river's span;
the days do tell of mysteries to decode,
which you and I must tackle, as we can.

The winter snow's no longer pure and white,
and season's, too, are strikers to the core:
sometimes it seems our world is one of spite,
we're afterthoughts in life and little more.

Complexity's an awkward kind of coil,
and narrow minds will often miss the gap;
the fool will fail, himself become the foil,
his flexuous foot that often springs the trap.

Richard Doiron, Simplicity is not a winding road


I have reflected in the past on the Universe’s expanding waist fed by microscopic degrees of freedom. They are spatiotemporal parameters that emerge into existence. If all other arrows could be derived from one arrow of expansion, writes Dieter Zeh, a physical observer would experience the direction of expansion as her future — which cannot be consistently remembered in contrast to part of her past. Degrees of freedom imply an element of free will. Could they be explained by process of give-and-take with the other side of the Janus Point?


Entropy describes the overall degree of energy spreading for the benefit of the Universe's own maintenance and its capacity to grow in an unexpectedly similar and/or differentiated manner. It measures its own agency. Could it be determined to be at “the same magnitude” consistently? While the uniformity of the Universe “at this scale in its current epoch is undoubtedly a significant fact,” writes Barbour, if one looks on smaller scales, the matter distribution in the Universe is “very far from uniform.”


Whether it be matter, consciousness, or information, there is, I feel, existence only in time. Time, writes John Peter Arendzen, is but the measure of phenomena, and by abstracting from phenomena, time ceases to be. Only then space and darkness remain. Because darkness is conceived as the “fluid filling the vessel” of space, it too could be abstracted. Only Void therefore remains. 


The difficulty with information comes from our inability to conceive that it exists on its own. In-itself information stresses that there is matter there is structure and there is information. If the existence of information implies the presence under a veil of form and content of indirect existence, only Void, indeed, remains in the absence of information. In this tightly woven web of concepts, freedom describes the distinctive nature of the existential field. In it, existence precedes the essence of information. 



Information is what Bateson calls “difference which makes a difference” born out of the process of info-autopoiesis. That which moves, including quantum fluctuations, leads conversely to that which exists from the mere existence of information to the rise of the sentient Universe. A cloud in the sky, a planet with a crystalline mantle, feel the push and pull of gravity. Could they, too, be sentient beings? From existence to sentience, it is a matter of information. 


If there is a Janus Point, what binds us to the mirroring Universe on the other side? A negative-mass fluid or dark energy lies in the shadow of the open and public Universe. Barbour points out that the quest for quantum gravity is almost entirely bereft of experimental support. “In its absence, theoreticians can only fall back on whatever principles seem sound and come to hand.” Information entropy describes a degree of randomness. What has yet to know about its own existence reveals itself by expressing itself. A paper last year describes cosmic inflation in terms of a time-dependent quantum density matrix with time playing the role of a stochastic variable.


Conscious beings have found themselves amid fundamental processes that underpin the observed richness of the large-scale cosmic structures. Is humankind the only entity to display such a conscious awareness? I don’t know. But what I know is that we are bound to make tracks and leave footprints in time, taking part in the difference that makes a difference. And so doing, we participate in the complexification process.

When day comes, we ask ourselves, where can we find light in this never-ending shade?

The loss we carry. A sea we must wade.

We braved the belly of the beast.

We’ve learned that quiet isn’t always peace, and the norms and notions of what “just” is isn’t always justice.

And yet the dawn is ours before we knew it.

Somehow we do it.

Somehow we weathered and witnessed a nation that isn’t broken, but simply unfinished.

We, the successors of a country and a time where a skinny Black girl descended from slaves and raised by a single mother can dream of becoming president, only to find herself reciting for one.

And, yes, we are far from polished, far from pristine, but that doesn’t mean we are striving to form a union that is perfect.

We are striving to forge our union with purpose.

To compose a country committed to all cultures, colors, characters and conditions of man.

And so we lift our gaze, not to what stands between us, but what stands before us.

We close the divide because we know to put our future first, we must first put our differences aside.

We lay down our arms so we can reach out our arms to one another.

We seek harm to none and harmony for all.

Let the globe, if nothing else, say this is true.

That even as we grieved, we grew.

That even as we hurt, we hoped.

That even as we tired, we tried.

That we’ll forever be tied together, victorious.

Not because we will never again know defeat, but because we will never again sow division.

Scripture tells us to envision that everyone shall sit under their own vine and fig tree, and no one shall make them afraid.

If we’re to live up to our own time, then victory won’t lie in the blade, but in all the bridges we’ve made.

That is the promise to glade, the hill we climb, if only we dare.

It’s because being American is more than a pride we inherit.

It’s the past we step into and how we repair it.

We’ve seen a force that would shatter our nation, rather than share it.

Would destroy our country if it meant delaying democracy.

And this effort very nearly succeeded.

But while democracy can be periodically delayed, it can never be permanently defeated.

In this truth, in this faith we trust, for while we have our eyes on the future, history has its eyes on us.

This is the era of just redemption.

We feared at its inception.

We did not feel prepared to be the heirs of such a terrifying hour.

But within it we found the power to author a new chapter, to offer hope and laughter to ourselves.

So, while once we asked, how could we possibly prevail over catastrophe, now we assert, how could catastrophe possibly prevail over us?

We will not march back to what was, but move to what shall be: a country that is bruised but whole, benevolent but bold, fierce and free.

We will not be turned around or interrupted by intimidation because we know our inaction and inertia will be the inheritance of the next generation, become the future.

Our blunders become their burdens.

But one thing is certain.

If we merge mercy with might, and might with right, then love becomes our legacy and change our children’s birthright.

So let us leave behind a country better than the one we were left.

Every breath from my bronze-pounded chest, we will raise this wounded world into a wondrous one.

We will rise from the golden hills of the West.

We will rise from the windswept Northeast where our forefathers first realized revolution.

We will rise from the lake-rimmed cities of the Midwestern states.

We will rise from the sun-baked South.

We will rebuild, reconcile, and recover.

And every known nook of our nation and every corner called our country, our people diverse and beautiful, will emerge battered and beautiful.

When day comes, we step out of the shade of flame and unafraid.

The new dawn balloons as we free it.

For there is always light, if only we’re brave enough to see it.

If only we’re brave enough to be it.


Amanda Gorman, The Hill we climb

The Essence of Information

John Peter Arendzen, Summary of ancient cosmogonies

Julian Barbour, The Janus Point 

Gregory Bateson, Steps to an Ecology of Mind

Martin Luther King, Where do we go from here: Chaos or Community?

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The Arrow of Time

Published on by Catherine Toulsaly

What I see is four temporal dimensions: that which is, that which has passed, that which will be, and that which is always in the state of becoming. The first three are subjective. The latter is timelessness.


This past October, I mentioned that I would read Julian Barbour’s latest work. Lee Smolin is quoted to have said that it is simply the most important book he has read on cosmology in several years. What I appreciate in anyone’s writing — and I am only at the beginning of it — is the wealth and the extent of information that creates a sense of harmony. Barbour reminds us that Sir Arthur Stanley Eddington, known for his insightful description of individuals as four-dimensional objects of greatly elongated form with “considerable extension in time and insignificant extension in space,” coined the expression ‘arrow of time.’ At this juncture, I feel the need to write another series of transitional thoughts triggered by the start of Barbour’s essential work. They will help, I hope, with reorganizing concepts and ideas in my head. Needless to say that I will devote the next few posts to it. 


My previous article on Neptune brought me back to the utmost importance of the act of experiencing. Barbour lost his wife and daughter in the midst of writing his latest book on time. I can’t imagine that those tragic events did not mold his personal view of both worlds, the physical and the experiential. It is not that we need to paint the Universe with one brush instead of the other. We need both for the picture to be whole and complete. We feel so powerless as we experience the passage of time on a one-way ticket to a point of no return, whether that be nothingness or whatever we call the other side. The bond between Consciousness and the Physical Universe is, I feel, the most important subject within the mystery of time.


The signs of age are on the moon. It seems pitted, torn, and rent by the past action of long-dead fires, till its surface is like a piece of porous cinder of a planet, which rolls through the void like a ruin of what has been...

S.P. Langley, The Planets and the Moon

How the “arrow of time gets into things so profoundly” is as much a scientific puzzle as it is a philosophical enigma. Scientists struggle to reconcile symmetric laws with irreversible series of events that produce asymmetric results. Janus point  — that is the title of Barbour’s book — refers to the Big Bang “on either side of which the universe’s size increases.” Barbour seems to point to a process that happens simultaneously. Time no longer has one direction, but instead has two “from a common past at the Janus point to two futures in the two directions away from it.”The laws of Nature, writes Vlatko Vedral, are information about information, and outside of it, there is darkness. In a way, Barbour is investigating what ‘darkness’ may be. The reason why it feels like time is unidirectional is the seemingly infinite length of the arrow we stand on, which left us unable to fathom what the other side looks like. 


Barbour introduces an entropy-like quantity called entaxy that reflects the growth of complexity. The expansion of the Universe seems concomitant with the increase of its complexity. The thing with complexity is that it lacks uniformity across the Universe. From our limited observational capabilities, life as we know it is far more likely to get stuck at the bacterial level of complexity, asserts Nick Lane. We could allow our poetic selves to compare complexity-based systems such as a comet, a planet, or a star with Earth-based biological organisms, but that would not be the same. Complexity is darkness.


The planets must find their way through the void like the birds through the air.

Johannes Kepler

Reading gives me a chance to look through an optical prism from a different angle, with each time a new sense of wonder. Astronomers, writes Barbour, “do not see the Universe expanding; they see it changing its shape and from that deduce its expansion.” It reminds me of what Sharon Glotzer said, that there’s “something much more  fundamental to understand about the organization of matter, and by focusing on shape and entropy, we’re getting to the core of that.”Since entropy is, along with agency, one of the most difficult terms to understand, I’d like to review what ‘entropy’ means.  As time emerges from timelessness at the Big Bang and every time a particle/antiparticle pair is created or a new life begins, writes Kerri Welch, gravity emerges from a microscopic description “that doesn’t know about its existence,” adds Erik Verlinde so eloquently. The link between the Universe without gravity and the Universe with gravity is information  “measured in terms of entropy.” The expansion of the Universe reveals three intertwined fundamentals: gravity, information, and entropy in a process that has allowed the synchronic conversion of information into energy. 

I have intentionally formed the word entropy so as to be as similar as possible to the word energy; for the two magnitudes to be denoted by these words are so nearly allied in their physical significance that a certain similarity in designation appears to be desirable.

Rudolf Claudius, quotation from Janus Point, p.40



On the one hand, if entropy is a transformation value, shouldn’t it imply a primary focus on processes rather than on entities? Flows within one flow are processes occurring in the phenomenological realm of the Universe from one given time to the next. In the discussion on content and process, the avant-gardist Carlo Rovelli seems to be instinctively aware that there is neither space nor time, only processes that transform physical quantities. If entropy is indeed so abstract and difficult to visualize, it may be because, in the organized manifestation of the life of feelings, there is not just a difference of form but also content. We can think of the state of a system in the past as a 'preparation' and the future as the outcome, hoping to predict what ‘darkness’ or ’complexity’ is. On the other hand, if entropy is regarded as a probability of particle arrangement, it relates to a state of arrangement and particle movement and, in that sense, reminds me of what agency means, that is the setting of physical associations and the implied ability to make choices from one given time to the next.


With that being said, entaxy refers to the growth of complexity in the Universe that includes “the formation of previously nonexistent subsystems that become effectively self-confined,” writes Barbour. Even those subsystems appear to form in the two directions simultaneously. Barbour not only follows Ludwig Wittgenstein’s footsteps for whom the “sense” of the Universe lies outside the reality of the one coherent and public Universe where “everything is as it is and happens as it does happen.” As he zooms out of the Universe and surveys it from a higher vantage point,  what he has done is following the footprints of time. Events still occur within some form or another of space or/and time. It appears to differ from what Stuart Kauffman defines as res potentia that is before the Big Bang outside of any space but inside of time. 


Could an observer, convinced that the “sense” of the Universe must lie beyond, crawl outside and come back with the tale of the zygote constrained within the walls of a transparent membrane? If space-time is the record of physical reality, it is only one aspect of reality in the infinite game of space, time, and gravity.

The Process of Becoming

Never mind Rovelli and others’ idealism. Reason had become our chief instinct and caused us to act as transcendental correlationists for whom what exists outside the correlation is nothing but indeterminacy, as Alexander Wilson noted. Blurred vision, when faced with the absence of spacetime, explains our failure to distinguish not just what is unknown but what is unimaginable. If time existed on the other side of a cosmological singularity, no matter which fundamentals of reality take part in the circle of concepts and whether some are co-emergent,  it would bring me to the same conclusion of my first transitional thoughts that time comes first. Timelessness hosts the passage of time. From a point in the past — a pre-big-bang phase — remnants of a black hole gave birth to a primordial white hole bursting at once in a bouncing scenario.


Human consciousness, when it stands on the edge staring into oblivion, still can’t quite conceive any notion beyond spacetime. If neither space nor time exists, then can our experiential selves be the only ones to know? I remain cautious, once again, keeping in mind that I ought to go deeper. Barbour’s book provides me with the opportunity to do so. I’ll see what his take is on matters such as white holes crossing over through spacetime or from one universe to the next, wormhole structure between a black hole and a white hole, and the role of dark matter in the Early Universe.  


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