The Intuitive Self

Published on by Catherine Toulsaly

I always thought graveyards
Were the most despicable things.

Per se:
The fallen trees do not claim the ground.
When their years are counted down.
Falling down does not weight their care.

The earth with gravity brings back down.
What once was one with it.
What joy Mother Earth must feel.

The trees only know birth and rebirth.
Not an hommage to the dead.
Too busy to bear the weight of time.
From the old ones the new ones climb.
What joy Mother Earth must feel.

Consider a fate.
Circular and sound.
The richness of one’s life turned back around.
It is my only want, to grow from the ground.

Cassandre Arkema

Sometimes it isn’t about reason. Sometimes it is about sharing each other’s personal experiences and carefully listening and assessing what is being said. William James wrote that no account of the Universe in its totality can be final if it discards other forms of consciousness entirely different from the so-called rational consciousness. “How to regard them is the question, for they are so discontinuous with ordinary consciousness”. One may wonder where consciousness lies. Adding to our pairs of feet, nostrils, ears, and eyes, is our brain too made of half-fields? Does the right hemifield feel closer to heaven when the body turns its head up gazing at clouds?  Words have planted seeds in my head. The individual consciousness appears multidimensional, structured into a self, a being, a living soul, and a person, as might have said Edward Conze. It divides itself into the perceptual mind, the receptual mind, the conceptual mind, and the intuitional mind, the latter being that of the living soul whose ethereal body swings on a string hung from the Moon. 


 

Cloudy morning at Pointe des Châteaux

Cloudy morning at Pointe des Châteaux


Some posts serve as mile markers on a roadmap of the infinite game between the Universe and Consciousness. Others stand like an inn on the side of the road where one rests body and soul. The suggestive dialogue arising from senses are lifelines thrown to the mind lost at sea, wading in the water in the hope that it reaches the other shore. A spark of intuition has come out of the blue. Hints turn loud, then silent inside one’s head. There is, Lois Isenman writes, a subliminal physical sense of the experience of intuition as a rapid closing and opening somewhere in the chest that accompanies the mental experience of seeing a generic signal go down and then up on a graph. “Intuition occurs when a number of different strands of information coalesce below awareness into a novel and significant piece of understanding”. Such a form of consciousness, the elements of which instead of being concepts are intuitions, Maurice Burke writes in 1901, is called cosmic Consciousness. At the root of all altered states of consciousness, of all flow states is an intuition.

My intuition, I must quickly add, deserves the credit to the extent that some of these ideas were initially before their time. Likewise, my confidence in them, in addition to their holding up thus far, rests on my intuition having taken the lead in my investigation, and in an unusual way.

Lois Isenman, Understanding Intuition

I was privileged enough to have Thomas updated me on the continuation of his spiritual experience. What I see in his experiential approach to consciousness is the manifestation of a strengthened and sustained intuition. Intuition shows a direction of a journey whose ultimate destination we do not yet know. It is an exploratory probe going here and there. I recall what Barbour writes about positions and momenta and momentum, I feel, is the intuition. It defines the direction of the object and may trigger “whole classes of phenomena that have not yet come to light” as Lois Isenman writes. Intuition is born at the quantum level. 

 

A higher state of consciousness is achieved when the conscious mind meets the unconscious. Outwardly, yoga and meditation act as soothing agents on muscles and nerves. Inwardly, Thomas bears witness of his own experience and reports a shift — which others have talked about —  from the ego-bound mode of ordinary consciousness toward a right experiential mode prevalent in altered states. He may be the witness of the path taken by his own consciousness to the far-reaching boundaries of unconscious cognition. In the tuck-of-war between consciousness and thought, that he previously reported on, yoga and meditation bring unity to body and mind and allow the leveling and synchronizing of a conscious wave that washes over them. 

The voice of consciousness to which Thomas refers appears to uproot egotistical thoughts and be broadcast louder and louder in his head. According to the Global Neuronal Workspace Theory, there is a central ‘workspace’, primarily residing in frontal regions of the brain. I asked Thomas whether he could use the word ‘resonance’ in the context of the right/left brain as I can’t quite figure out the direction of the arrow: is it an intrusion of the right hemispheric content into waking awareness or is it from the frontal regions of the brain that an exploratory probe is sent — through yoga, meditation or trance — into the right side of the brain? It may also be that the “reporting of when a conscious thought occurred” is being silenced or delayed, making it difficult to pinpoint its whereabouts. In the end, we may be talking about the inability of consciousness to report as it lies unconscious below the radar. 

 

The central question of whether each hemisphere supports an independent conscious agent capable of making its own decisions was raised in a 2020 study. Could the resonance felt in the right hemifield not be identified and spoken of by the left hemifield? The study echoes Thomas’s own questioning about the right half being occupied by consciousness and the left half by thought of which ego has taken possession. Although I sense a difference between trance on the one hand and yoga and meditation on the other, the “trance self” mode appears also to operate within the right-posterior experiential/sensorimotor network domain. A trance may be a higher-order emotional state characterized by an alteration of time and space, an increased relation with what is unconscious and intangible, an access to alternate ways of experiencing internal and external reality, and a dissociative state that the rest of us may otherwise experience only in dreams. How does it feel like to be a bee on a leaf? Will I know if I enter trance? 


 

The Intuitive Self

Conscious awareness represents a fluid equilibrium between anterior/posterior and right/left modes of experience that constantly shift depending on the individual psychobiology, external information input, and cultural paradigms.

Pierre Flor-Henry, Yakov Shapiro, Corine Sombrun, Peter Walla (Reviewing Editor)

While consciousness is the product of the two hemispheres, many unconscious processes run independently, and in parallel across both of them. Even if there is a separation of our subconscious and conscious minds, they appear to both exist simultaneously and interactively in the brain. Thomas describes streams of information split into two halves that yoga and meditation strive to unify. Taken into account the brain laterality and how the two sides of the brain tend to process information differently, the right hemisphere where intuition is largely grounded draws from a collective source. 

 

Thomas observes that consciousness is present in his mind but is “yet detached from the mind and body”. When he designates the ‘I’ as the ego-bound state of consciousness, and the small ‘i’ as the act of conscious selflessness, selflessness and consciousness become one. He describes how consciousness evolves into higher sensitivity of thought. While most spin reality in both directions, he immerses himself in selfless consciousness which allows him to create a sense of continuity. His distinction between the high-order state of consciousness and the ordinary thought has led him to uncover selflessness as an aspect of consciousness and its fundamental bond to the collective consciousness. Meditation during which he reaches the far corners of the unconscious may allow for richer connectivity of the human brain and bring up to the surface what is below awareness. What occurs in an act of deep meditation is a symbiosis of physical and mental feelings and responses.

 

Thomas’ experiential approach towards consciousness is the result of 50 years of yoga practice. He has observed that the right half of the head and face stays composed even when the left half is reactive or agitated because consciousness is detached whereas thought is attached to ego. His experience is reminiscent of the first neurophysiological study of an experimental subject Corine Sombrun whose shamanic state of consciousness has shown to involve a shift from the normally dominant left analytical to the right experiential mode of self-experience as well as from the normally dominant anterior prefrontal to the posterior somatosensory mode. It may be that reality is perceived at different levels depending on the individual being and the extent to which we strive to improve our perception skills. Perhaps these are not discontinuous forms of consciousness but a continuum between more or less conscious brain activities. Unity of consciousness may be the ultimate goal that one is inspired to achieve through any means. Beyond the clouds hampering our inner sight, unity of consciousness exists within the whole Universe.

 

There is a multitude of beings, I feel, coexisting inside our heads. We have the potential to sort them out and be more authentically in sync with our higher self. Lost at sea paddling to reach the other shore, some may succeed better than others at letting go of their earthly feathers.

 

Morning Sun shining through clouds at Pointe des Châteaux

Morning Sun shining through clouds at Pointe des Châteaux

Lois Isenman, Understanding Intuition

William James, The Varieties of Religious Experience

W.R. Klemm, Making a Scientific Case for Conscious Agency and Free Will

Stephen T. Asma, The Evolution of Imagination

 

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Quantum Ontology

Published on by Catherine Toulsaly

Bottlebrush grass

Bottlebrush grass

Two theoretical physicists are on death row and have been in the same cell for ten years. One night, the warden comes and says, ‘You’re going to be executed tomorrow. Any last wishes?’ The first theoretical physicist says, ‘Well, I’ve been in this cell working on a new theory for the last ten years, and I would like to present it to all of the populace of the prison, so my final last good idea doesn’t die with me.’ And the warden says, ‘Sure, we’ll set up a PowerPoint for you, you can make some slides, and present your results.’ He turns to the second theoretical physicist and says, ‘What is your last dying wish?’ The second theoretical physicist says, ‘I would like to be taken out and shot before the other guy’s talk!

Jonathan P. Dowling, Schrödinger’s Web: Race to Build the Quantum Internet

Every now and then, I look back and assess the twists and turns of the path I’ve taken. It feels like all the pieces of the jigsaw puzzle are spread everywhere. On the one hand, studying the subject at hand from every angle is a learning process that allows the emergence of ideas. On the other, the wider the scope of the investigation is, the more difficult it becomes to stretch those ‘mental’ arms reaching for pieces and reassemble them together. Along the way, I hold on to an invisible thread of words and concepts. As a visual learner, I see in pictographs a succession of shapes integrated long ago in human communication and upon which the Universe is based. 

Somehow the unhelpful pronoun ‘something’  has come up again and again. That something from which ‘being’ arises describes a formless existence of an accidental nature, an undetermined and vacuous state of uncertainty. The telling image of a battle over a domain represents time asserting its sovereignty over space and alludes to a hidden process of appropriation of what is merely potential. What does it feel like when time asserts its sovereignty? Although physicists dismiss accidental similarities on the ground that elements of the physical reality cannot be determined by a priori philosophical considerations, but must be found by an appeal to results of experiments and measurements, I somehow relate ‘something’ to the quantum state of the Universe.

…it is only in a highly technical sense that the particle “is there” while there is allegedly “nothing there” where it produces its effect.

Matthias Egg

Cicada on witch-hazel

Cicada on witch-hazel

Quantum Ontology

The purpose of modern physics ultimately isn’t to explain everything. Its objective is more practical: to replicate the physical world and harness the quantum-mechanical properties of physical systems. Quantum fluctuations at the deepest level of movement lead to ‘being’. From bits to qubits, computers open a passage between abstraction and reality, but as we move from light waves to photons, phonons and ions, are we closer to answer those deep philosophical questions? The Universe as the setting of an infinite number of superposed states emerging in a seemingly random manner holds such a depth of meaning to which we may not have access, but we surely can reproduce the processes that we observe, measure, and experiment. 

 

A quantum-based computing system may provide for securely encrypted communication, much faster data transfer, and ‘leaner’ physical storage capabilities. CERN whose computer requirements are rapidly growing is using IBM Quantum’s cloud-enabled quantum computing to analyze 1 petabyte of data per second in the Large Hadron Collider, something that would require 1 million classical CPU cores to do. Quantum entanglement is key to transmit information over long distances, prior to the establishment of a large-scale quantum internet network. To limit interference, turbulence, and background noise, satellite quantum communications benefit from orbiting in the emptiness of space to generate symmetric keys and simultaneously transmit them to establish a direct link between remote users separated by long distances. Bypassing the need for quantum repeaters, two strings of entangled photon pairs were distributed from the satellite Mozi 墨子 — one of the five scientific experimental satellites established by the Chinese Academy of Sciences —  to two ground observatories more than 1,120 kilometers apart. Intercontinental secure key exchanges and the launch of satellites at higher orbit are in preparation. The quantum space race is on with the National Space Quantum Laboratory program, a partnership between NASA and MIT’s Lincoln Laboratory.

 

Early initiatives show pathways and create a sense of urgency for new priorities in the hope to move humanity forward. Not to mention strategic implications in the intelligence, security and defence sectors, those initial successes have fueled a technological race in the field of quantum optics and quantum information. After the Honeywell quantum computer with a quantum volume of 64 was reported just a year ago to be the world’s highest performing quantum computer, a team of Chinese scientists announced in December that they too successfully developed the most powerful quantum computer in the world Jiuzhang 九章, performing in 200 seconds a calculation that on an ordinary supercomputer would take 2.5 billion years to complete.


 

The number 64 comes from 2 raised to the power of 6. A big reason quantum computers can do more is the q-bits can have two values at the same time. Six bits can have, essentially, 64 states at once.

Al Root

Quantum Ontology


The transition period from classical to quantum computing has an indefinite timeline. The goal isn't the replacement of the internet as we know it but a hybrid solution. Researchers at Duke are currently developing what they hope to be the first practical, scalable quantum computer based on ion-trapping technology. But for most of us, the Cloud provides the only feasible way to tap into a quantum computer. Despite the sensitivity of the first generation of quantum computers to interference, noise, and environmental effects, a coordinated approach to tame and manipulate those irregular, complex, and dynamic flows of particles — carriers of quantum information — is underway. Industries, banking institutions, policymakers, academic institutes, and space agencies support their own research, taking advantage of the new technological possibilities to perform, to name a few, financial predictions and chemical simulations, develop quantum sensing technology as part of multi-messenger astronomy, and engineer ways to remove carbon dioxide from the air as green-house gas emissions reach historic levels.

Aspiring towards clarity is also inexorably iterative. Whenever you set out to clarify your thinking, you’re not aiming to articulate an ultimate truth. Rather, you’re aiming at a process, the result of which will always be an act of communication, complete with all the imperfections and contingencies this implies.

Tom Chatfield

Quantum Ontology

The concept of quantum ontology defines in modern times what was merely known 2,000 years ago as ‘something’ deemed to self-organize and localize itself in relation to time and space. I hope future quantum-based computing systems will contribute to lay out a more faithful representation of the Universe. The most profound implication of what is happening today is the convergence of bits, neurons and qubits. A research team reportedly demonstrated that algorithms based on deep neural networks can be applied to better understand the world of quantum physics. Have algorithms become an ordinary mode of communication? David Chalmers and Kelvin McQueen's paper on Consciousness and the collapse of the wave function is out. It may be that a shared resonance from micro-conscious to macro-conscious entities can only happen intermittently during the collapse of particles’ wave functions, which signals the transfer of information and/or consciousness.

Quantum Ontology
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CrossOver

Published on by Catherine Toulsaly

Like a cast listed in the order of appearance, we wonder whether time or space comes first. Or do the two main actors appear in tandem in the first scene? An ancient philosophical debate mirrors the current scientific discussion. If indeed, the Universe is conceptual in nature,  early Taoist philosophy is a good place to start looking for clues. This post stands at the crossroads and invites to a D-tour. The last paragraph of the previous post leads to a digression, an attempt to reconnect with Chinese studies. Barbour’s interesting choice of words, that is “invariant variational’, somehow sticks with me and guides my steps back in time to some primary concepts.

Among all variational problems some are special in being invariant. 'Invariant variational' sounds like an oxymoron, but it isn't: the resolution of the apparent paradox is that the quantity which is being varied has the property of remaining unchanged when expressed in different ways.

Julian Barbour, The Janus Point, p.174

The significance of the more than 2,300-year-old Chinese manuscript Heng Xian 亙先 acquired by the Shanghai Museum in the mid-nineties is the subject of an academic debate, not to mention the circumstances that surrounded its discovery and the sequence of the bamboo slips. How one single character is read and how different the meaning of a lineup of words is depends on the reader’s take. Scholars walk a fine line in an effort to cross-reference various texts. When it comes to the transmission of ideas, their interpretation depends on the faithfulness to the source text and whether we hold the earliest text or one that may have been amended. Changes introduced in later manuscripts still provide insights on which scholars rely. Over time, the choice of words may differ, but ideas remain.

 

What came first is as much the subject of a debate today as it was in the past. Heng Xian says: “Being came out of something, nature came out of Being, sounds came out of nature, words came out of sounds, names came out of words, and things came out of names”. And so from ‘things’ to that which is ‘something’, we ought to retrace our steps and find our way back. But if Heng Xian is such a milestone in the evolution of ideas, why is it that the text as it was reconstructed and made public early 2000s does not explicitly speak of Dao 道? While Dao in chapter 25 of Laozi from the Mawangdui Silk Texts 馬王堆帛書 (also known as Daode Jing 道德經 ) is believed to be the Mother of the Universe, some scholars see it differently and translate the expression 天下母 as the mother of all under heaven. The emphasis on concepts such as 亙 and 或 may be interpreted as a further breakdown of the primordial chain of events. According to Sixin Ding丁四新 from the Department of Philosophy of Tsinghua University in Beijing, who studied the two intricate concepts 亙 and 或, even though the authors of the bamboo manuscript  Heng Xian contemplated cosmology more profoundly, their knowledge about the structure of cosmogony was not yet “fully developed”.  He concludes that Heng Xian uses an indefinite pronoun 或 to refer to a stage in the genesis of the cosmos. 

 

Waxing Crescent (NASA Goddard)

Waxing Crescent (NASA Goddard)

While the first recorded character for the Moon was a waxing crescent, the earliest representational drawing for resembles a crescent between the Earth and the Sky. Such a cosmology-related graph appears to take precedence over the character dao 道 that shows a walking head — the path of humanity. 亙 means to extend over,  to cross over from one area to another, physical or abstract. The inferred meaning may be ‘constancy’ (). Not only the expression hengdao 恆道 appears in the first chapter of Laozi, but the replacement of the character by chang 常 in later texts implies ‘constancy’ in the flow of things. It confirms the existence of a permanent and dynamic principle whose flexibility is rendered by the word ‘flow’. Volition and detachment are attributes of the flow. The two qualities seem to contradict even to neutralize or negate each other. They regulate, however, the flow of the Universe.

 

Waning Crescent ( NASA Goddard)

Waning Crescent ( NASA Goddard)

A wide-ranging research on the complex relationship between the Universe and Consciousness involves accessing the memories of our ancestors, merging thoughts over time and space to prompt further reflection. Such research unfolds in the now as past and future become irrelevant. Chapter 40 of Laozi acknowledges a flow reversal or cyclical aspect in the movement of Dao. It reminds me of Noether’s universal system of transformations and that, for each transformation, there exists an inverse contained in the flow of the Universe. The two corresponding concepts 亙  and 或 were in the back of my mind as I dreamt the other night about a white sphere. The next day in the moonlight at dawn I walked through the garden on the path between native roses, listened to sounds of cicadas, and gazed at flowers of the catalpa tree falling. I wondered why a pictograph of the Moon caught between the Earth and the Sky would convey the idea of eternity. For over 4.5 billion years, the Earth-Moon system has been co-evolving. The Moon remains a constant in human life and her waxing and waning provide evidence of what Barbour calls ‘invariant variational’. 

 

CrossOverCrossOver
CrossOver
CrossOverCrossOverCrossOver

The introducing sentence 亙先無有 of the bamboo manuscript sets the stage for events prior to the formation of the Earth-Moon system and before the Sun came out of a nebula cloud of dust and gas. Some scholars chose to translate it two ways: “In the Constancy, there is first no existence” or constancy “preceded the absence of Being”. Others believe that the two characters 亙先 have to do with the ‘origin of origins’, the ‘absolute primordiality’, the ‘ultimate commencement’ as a reference to the Great Ultimate 大極. Perhaps both interpretations —constancy and an ultimate beginning — do not contradict each other and point to an ultimate state of invariance. Sarah Allan argues that the idea of the Great Ultimate as an abstract point of origin, before there was anything else, seems to be a later theoretical development. I would concur with the idea of an abstract point beyond time and space. Before crossing over into the observable Universe, there was the absence of Being. 

 

Do absence of Being and nothingness differ? While chapter 40 of Laozi states, “All beings come from Being; Being comes from Non-Being,”* the graph 或 adds a new stage in the genesis of the cosmos. It conveys a sense of uncertainty over a state of becoming that is neither being nor nothingness. Zhuangzi states: “Sometimes there is Being, sometimes there is nothingness. Do we ever know if Being and nothing really exist or do not really exist?”** 或 showed originally a circle and a spear or lance on the right (radical halberd) with one or more borders sometimes drawn around the circle. It implicitly refers to a battle over a domain. Neither the outcome nor the protagonists are known. It is a suspended bridge between nothingness and being, the one “without material form”** and may be understood as  ’field’, ’space’ or even ‘sphere’. 

Whether or not we can credit the Heng Xian with the introduction of the abstract concept of space into the early Chinese cosmogonic discourse, its place in the chain of transformations, preceding the appearance of Being, is peculiar enough.

Andrei Gomouline

 I read the other day that the theory of shape dynamics does not assume the existence of a spacetime but a collection of 3-geometries that may fit together to act as a four-dimensional spacetime. 或 conveys Zhuangzi’s concept of a formless existence of an accidental nature, an undetermined and vacuous form that appears as shape space at the start of time. Vacuity is what Tristan Garcia would call “the opposite of something added to the absence of something”. In the primordial chain of events, space or sphere precedes the flow 道 of things and the breath 氣 of nothingness, that is the Universe’s absolute, impersonal consciousness. All primary concepts are connected through it. Erica Brindley, with the spacetime continuum in mind, gives a modern explanation of the text with space emerging before the onset of temporality... While science and philosophy run in circles, poetry offers an escape:

Like the moon advancing to the full,
Like the sun ascending the heavens,
Like the age of the southern hills,
Never waning, never falling,
Like the luxuriance of the fir and the cypress; – May such be thy succeeding line!

The Book of Odes

* Liou Kia-hway, Lao-tseu tao to king, p.115

** Liou Kia-hway, L’oeuvre complète de Tchouang-tseu, p.104, p.40


 

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Taming Infinity

Published on by Catherine Toulsaly

Mayapples

Mayapples

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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Subtleties

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? 

Space

Time

Gravity

Freedom

Existence

Essence

Entropy

Information

Energy

Agency

Sentience

Consciousness

 

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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Thoughtland

Published on by Catherine Toulsaly

Thoughtland

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

Koethe

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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Farfarout

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.”


 

Farfarout
Cinnamon in the Sun

Cinnamon in the Sun

Julian Barbour, The Janus Point

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Boltzmann Brains

Published on by Catherine Toulsaly

Ensō

Ensō

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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