Cosmic Mirror Theory

Cosmic Mirror Theory

Source: Why some physicists really think there’s a ‘mirror universe’ hiding in space-time

Why does the Universe look like a Gemstone? A Jewel? An Opal maybe?

Why does the Universe look like an egg? Brahmanda?

Concept of Mirror is invoked in four ways in Cosmology

  • Shape of the Universe – Multi-connected manifolds – Dodecahedron topology – Reflecting Surfaces – Hall of Mirrors – Cosmic Crystals
  • Mirror Universe – a Parallel universe- Universe having a mirror twin – before the Big Bang – Symmetrical Opposite
  • Black Holes – Black Holes have mirror opposite in White Holes
  • Universe as a Hologram

Key Terms

  • Cosmic Hall of Mirrors
  • Parallel universe
  • Black holes
  • White Holes
  • Big Bang Theory
  • Shape of the Universe
  • Multiverse
  • Indira’s Net
  • Buckminster Fuller
  • Mirror Symmetry
  • Quantum Biology
  • Relational Science
  • Entanglements
  • Action at a distance
  • Holographic Universe
  • Fractal Universe
  • Recursive Universe
  • Universe as a Cow
  • Universe as a Human
  • Universe as Brahmanda
  • CBOE
  • WMAP
  • ACT
  • Curvature of Space
  • Topology of Space
  • Cosmic Topology
  • Cosmic Harmonics
  • Dodecahedral Space
  • Triloka (Three Universes)
  • Trikaal (Three Times)
  • MultiConnected Manifolds
  • Age of Universe – 13.77 Billion Years
  • 14 Lokas in Hinduism – Realms – Levels
  • Anthromorphic Universe
  • Maha Vishnu
  • 5 Sheaths (Kosh) in Humans
  • Tripartite Universe
  • Triguna
  • Interconnected Hypothesis
  • Cosmic Microwave Background CMB
  • Dark Energy
  • Dark Matter
  • Mirrorverse

Shape of the Universe


Cosmic Microwave Background from different probes

Source: Pintrest/478366791654117997/



Source: PLANCK Data 2018

Source: Decoding the cosmic microwave background

Decoding the cosmic microwave background

The Big Bang left behind a unique signature on the sky. Probes such as COBE, WMAP, and Planck taught us how to read it.

By Liz Kruesi | Published: Friday, July 27, 2018

This all-sky map, released in March 2013 and based on 15.5 months of observation, shows tiny fluctuations in the temperature of the CMB. These variations correspond to minute under- and over-densities of matter that ultimately led to the large-scale structure we see in the universe today. The redder areas represent above-average temperatures, and bluer areas show temperatures colder than average.

European Space Agency, Planck Collaboration

A glow undetectable to the human eye permeates the universe. This light is the remnant signature of the cosmic beginning — a dense, hot fireball that burst forth and created all mass, energy, and time. The primordial cosmic microwave background (CMB) radiation has since traveled some 13.8 billion years through the expanding cosmos to our telescopes on Earth and above it.

But the CMB isn’t just light. It holds within it an incredible wealth of knowledge that astronomers have been teasing out for the past few decades. “It’s the earliest view we have of the universe,” says Princeton University cosmologist Joanna Dunkley. “And it gives us so much information because all the things that we now see out in space — the galaxies, the clusters of galaxies — the very earliest seeds of those, we see in this CMB light.”

Extracting these clues from the CMB has taken multiple generations of telescopes on the ground, lofted into the atmosphere, and launched into space. In the mid-1960s, when Arno Penzias and Robert Wilson discovered the CMB’s pervasive microwave static across the sky, it appeared identical everywhere. It would take satellites launched above Earth’s obscuring atmosphere to map that microwave glow to precisions on the order of millionths of a degree. Specifically, three satellites — COBE, WMAP, and Planck — revealed that our current cosmos, which is complex and filled with clusters of galaxies, stars, planets, and black holes, evolved from a surprisingly simple early universe.

The Planck satellite produced the most detailed image of the cosmic microwave background (CMB) to date.

The universe began with the Big Bang 13.8 billion years ago as a fiery sea that expanded rapidly. A few minutes later, the universe’s constituent primordial subatomic particles glommed together into an elemental soup of atomic nuclei containing hydrogen, helium, and trace amounts of lithium. Electrons and light collided and scattered off of those atomic nuclei. Over the next thousands of years, the cosmos continued to expand, giving the particles more room to move and allowing the universe’s temperature to cool bit by bit. Around 380,000 years after the Big Bang, the temperature dropped to about 3,000 kelvins, cool enough for electrons to latch onto hydrogen nuclei. The universe became mostly neutral hydrogen, with some heavier elements swirled in.

With fewer individual particles zooming around, light could finally move about freely. And so it has traveled, mostly unhindered, in the approximately 13.8 billion years since that time of “last scattering.” These photons carry a snapshot of the 380,000-year-old universe.

Since the 1960s, telescopes on Earth have captured that glow in every direction of the sky. While the light 380,000 years into the universe’s history would have been visible to human eyes if we were around, cosmic expansion has since stretched the light into the longer wavelengths of microwaves — at least, that’s the wavelength astronomers had predicted. But would observations match theory?

The three probes

The Cosmic Background Explorer (COBE) launched in 1989. One of its instruments measured the intensity of the microwave glow at wavelengths ranging from 0.1 to 10 millimeters across the entire sky. The COBE science team’s first announcement, in 1990, was the result of that measurement. The radiation’s intensity plotted by wavelength makes it obvious that the CMB has a very specific intensity curve, where the strongest signal is at 2 mm. That wavelength corresponds to a temperature of 2.725 K. (The wavelength of light, and thus how much energy that light carries, is directly related to its temperature; redder light has less energy and a lower temperature than bluer light.)

COBE’s other instrument broke apart the seemingly uniform 2.725 K glow into more detail, looking for spots where the temperature is warmer or colder than average. It turned out there is a difference of only a tiny fraction of a degree, about 0.00001 K, between hotter and colder spots.

Each successive cosmological probe has improved astronomers’ view of the CMB with better resolution, revealing ever-finer details (anisotropies in temperature and density) that hold the key to assembling an accurate picture of our young universe.

This nearly identical cosmic glow with exactly the right temperature was concrete evidence that the entire sky — the entire observable universe — began in a Big Bang. With such tiny temperature differences across vast regions of sky, those spots must have been in contact at early times. COBE leaders John Mather and George Smoot won the 2006 Nobel Prize in Physics for their work.

But there is so much more that scientists can do with the CMB than confirm the Big Bang. “From the anisotropies, the hot and cold spots, we get the initial conditions — how bumpy was the early universe and also what is its composition,” says Mather.

The next CMB satellite was designed to improve upon these anisotropy measurements, mapping them at finer angular resolutions. COBE could map hot and cold spots of about 7° on the sky, while the Wilkinson Microwave Anisotropy Probe (WMAP), launched in 2001 and operated until 2010, could zoom in to a resolution of better than 0.5°. Planck, the CMB satellite that operated from 2009 to 2013, zoomed in even further, to 0.16°.

All of these missions mapped temperatures to the order of 0.00001 to 0.000001 K. To minimize measurement errors related to such small signals, the spacecrafts’ detectors pointed toward two spots on the sky at the same time and measured the temperature difference between them. The satellites swept the entire sky in this fashion, and software generated a map of all those tiny differences. That map holds a treasure-trove of cosmic secrets.

The CMB represents the moment at which the universe became “transparent.” Immediately after its birth, the universe was hot and dense. As it expanded, it cooled, and its density dropped. Within the young universe, photons couldn’t travel very far — a few inches — before colliding with a nearby particle. As the matter in the universe transitioned from plasma (left) to atomic hydrogen (right) 380,000 years after the Big Bang, photons could travel much farther — the width of the universe — without necessarily experiencing a collision. This moment, also called the surface of last scattering, is encoded in the CMB we see today.

Unlocking the early universe
To reveal those secrets, cosmologists study the pattern of hot and cold spots frozen into the CMB and decompose those spots into their constituent sizes. While most of the hot and cold spots are about 1° on the sky, they are overlaid on fluctuations with larger sizes.

“Imagine looking at a smooth pond of water that we might drop pebbles into,” says Dunkley. “If you drop a whole bunch of pebbles in, the ripples will sort of combine together, and you see a whole pattern of ripples across the water. We think of this pattern of slightly different temperatures of this light on the sky a little bit like the pond after it’s covered in ripples.”

The size breakdown of the CMB’s temperature spots, or fluctuations, is like a cosmic Rosetta Stone. The strength of the fluctuations’ signals at different scales is associated with the universe’s age, its ingredients, its expansion rate, and when the first stars lit up the cosmos. By comparing computer models to the signal strengths (which astronomers obtained from analyzing WMAP and Planck data), researchers can piece together what the early universe looked like and how it has evolved.

Thanks to these three cosmic probes, we know the universe began in a Big Bang, and around 380,000 years later, electrons and protons combined, letting light roam free. We know our cosmos is 13.8 billion years old and how fast it is expanding. We know that 31 percent of the universe is matter, but only 5 percent is made of ordinary matter like you and me, while 26 percent is invisible dark matter. Much more of the cosmos is composed of a mysterious, repulsive dark energy — 69 percent.

And perhaps most importantly, astronomers now have a way to find out pieces of information not literally encoded in the CMB itself. That’s because the CMB maps and their statistics have led to the so-called standard model of cosmology.

“We now have a really simple model that describes basically all of our observations,” says Dunkley. “We can track from the very first moments of time all the way through today and make predictions about how large-scale structure evolved. And it has remarkable success. That’s the big thing these satellite missions have given the community.”

Mirror Universe


Our Universe May Be a Giant Hologram

Physicist Brian Greene explains how properties at the black hole’s surface—its event horizon—suggest the unsettling theory that our world is a mere representation of another universe, a shadow of the realm where real events take place.

Brian Greene


Two monster black holes may lie within the double bright area at the center of galaxy NGC 6240. NASA

If, when I was growing up, my room had been adorned with only a single mirror, my childhood daydreams might have been very different. But it had two. And each morning when I opened the closet to get my clothes, the one built into its door aligned with the one on the wall, creating a seemingly endless series of reflections of anything situated between them. It was mesmerizing. All the reflections seemed to move in unison—but that, I knew, was a mere limitation of human perception; at a young age I had learned of light’s finite speed. So in my mind’s eye, I would watch the light’s round-trip journeys. The bob of my head, the sweep of my arm silently echoed between the mirrors, each reflected image nudging the next. Sometimes I would imagine an irreverent me way down the line who refused to fall into place, disrupting the steady progression and creating a new reality that informed the ones that followed. During lulls at school, I would sometimes think about the light I had shed that morning, still endlessly bouncing between the mirrors, and I would join one of my reflected selves, entering an imaginary parallel world constructed of light and driven by fantasy.

To be sure, reflected images don’t have minds of their own. But these youthful flights of fancy, with their imagined parallel realities, resonate with an increasingly prominent theme in modern science—the possibility of worlds lying beyond the one we know.

There was a time when the word universe meant “all there is.” Everything. The whole shebang. The notion of more than one universe, more than one everything, would seemingly be a contradiction in terms. Yet a range of theoretical developments has gradually qualified the interpretation of universe. The word’s meaning now depends on context. Sometimes universe still connotes absolutely everything. Sometimes it refers only to those parts of everything that someone such as you or I could, in principle, have access to. Sometimes it’s applied to separate realms, ones that are partly or fully, temporarily or permanently, inaccessible to us; in this sense, the word relegates our universe 
to membership in a large, perhaps infinitely large, collection.

With its hegemony diminished, universe has given way to other terms that capture the wider canvas on which the totality of reality may be painted. Parallel worlds or parallel universes or multiple universes or alternate universes or the metaverse, megaverse, or multiverse—they’re all synonymous, and they’re all among the words used to embrace not just our universe but a spectrum of others that may be out there.

The strangest version of all parallel universe proposals is one that emerged gradually over 30 years of theoretical studies on the quantum properties of black holes. The work culminated in the last decade, and it suggests, remarkably, that all we experience is nothing but a holographic projection of processes taking place on some distant surface that surrounds us. You can pinch yourself, and what you feel will be real, but it mirrors a parallel process taking place in a different, distant reality.

Plato likened our view of the world to that of an ancient forebear watching shadows meander across a dimly lit cave wall. He imagined our perceptions to be but a faint inkling of a far richer reality that flickers beyond reach. Two millennia later, Plato’s cave may be more than a metaphor. To turn his suggestion on its head, reality—not its mere shadow—may take place on a distant boundary surface, while everything we witness in the three common spatial dimensions is a projection of that faraway unfolding. Reality, that is, may be akin to a hologram. Or, really, a holographic movie.

The journey to this peculiar possibility combines developments deep and far-flung—insights from general relativity; from research on black holes; from thermodynamics, quantum mechanics, and, most recently, string theory. The thread linking these diverse areas is the nature of information in a quantum universe.

Physicists Jacob Bekenstein and Stephen Hawking established that, for a black hole, the information storage capacity is determined not by the volume of its interior but by the area of its surface. But when the math says that a black hole’s store of information is measured by its surface area, does that merely reflect a numerical accounting, or does it mean that the black hole’s surface is where the information is actually stored? It’s a deep issue and has been pursued for decades by some of the most renowned physicists. The answer depends on whether you view the black hole from the outside or from the inside—and from the outside, there’s good reason to believe that information is indeed stored at the event horizon. This doesn’t merely highlight a peculiar feature of black holes. Black holes don’t just tell us about how black holes store information. 
Black holes inform us about information storage 
in any context.

Think of any region of space, such as the room in which you’re reading. Imagine that whatever happens in the region amounts to information processing—information regarding how things are right now is transformed by the laws of physics into information regarding how they will be in a second or a minute or an hour. Since the physical processes we witness, as well as those by which we’re governed, seemingly take place within the region, it’s natural to expect that the information those processes carry is also found within the region. But for black holes, we’ve found that the link between information and surface area goes beyond mere numerical accounting; there’s a concrete sense in which information is stored on their surfaces. Physicists Leonard Susskind and Gerard ’t Hooft stressed that the lesson should be general: Since the information required to describe physical phenomena within any given region of space can be fully encoded by data on a surface that surrounds the region, then there’s reason to think that the surface is where the fundamental physical processes actually happen. Our familiar three-dimensional reality, these bold thinkers suggest, would then be likened to a holographic projection of those distant two-dimensional physical processes.

If this line of reasoning is correct, then there are physical processes taking place on some distant surface that, much as a puppeteer pulls strings, are fully linked to the processes taking place in my fingers, arms, and brain as I type these words at my desk. Our experiences here and that distant reality there would form the most interlocked of parallel worlds. Phenomena in the two—I’ll call them Holographic Parallel Universes—would be so fully joined that their respective evolutions would be as connected as me and my shadow.

 Excerpted from The Hidden Reality by Brian Greene. Copyright © 2011 by Brian Greene. Reprinted with permission by Alfred A. Knopf, a division of Random House, Inc. All rights reserved.

 See the related DISCOVER feature, “The Strange Physicsand SightsInside Black Holes.”

My Related Posts

Shape of the Universe

Mind, Consciousness and Quantum Entanglement

Myth of Invariance: Sound, Music, and Recurrent Events and Structures

On Anticipation: Going Beyond Forecasts and Scenarios

Consciousness of Cosmos: A Fractal, Recursive, Holographic Universe

Geometry of Consciousness

The Great Chain of Being

Maha Vakyas: Great Aphorisms in Vedanta

Indra’s Net: On Interconnectedness

On Synchronicity

Color Science of Gem Stones

Key Sources of Research

CPT-Symmetric Universe

Latham Boyle,1 Kieran Finn,1,2 and Neil Turok1
1Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5
2School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom

PHYSICAL REVIEW LETTERS 121, 251301 (2018)

Why some physicists really think there’s a ‘mirror universe’ hiding in space-time

By Rafi Letzter – Staff Writer June 22, 2020

Cosmology of the Mirror Universe

Paolo Ciarcelluti

April 2003 PhD Thesis

Mirror dark matter:
Cosmology, galaxy structure and direct detection

R. Foot

ARC Centre of Excellence for Particle Physics at the Terascale, School of Physics, University of Melbourne,
Victoria 3010 Australia


Mirror dark matter cosmology and structure formation

Roux, Jean-Samuel

PhD Thesis McGill Univ

White holes: Do black holes have mirror images? 

These black hole opposites would spew energy, be impossible to enter, and might even answer some of the universe’s fundamental questions.By Bill Andrews  |  Published: Friday, June 28, 2019

A cosmic hall of mirrors

Jean-Pierre Luminet
Laboratoire Univers et Théories (LUTH) – CNRS UMR Observatoire de Paris, 92195 Meudon (France)

The fractal universe

SEPTEMBER 12, 2018

Love the Reflections in the Cosmic Mirror

The Shape of the Universe: Ten Possibilities

Is the universe a dodecahedron?


Planck and the cosmic microwave background

The Atacama Cosmology Telescope ACT

Wilkinson Microwave Anisotropy Probe WMAP

Cosmic Topology : Twenty Years After

Jean-Pierre Luminet,

Laboratoire Univers et Th ́eories Observatoire de Paris-CNRS-Universit ́e Paris Diderot (France) email :

October 15, 2013

Cosmic microwave background anisotropies in multi-connected flat spaces

Alain Riazuelo∗
Service de Physique Th ́eorique, CEA/DSM/SPhT, Unit ́e de recherche associ ́ee au CNRS, CEA/Saclay F–91191 Gif-sur-Yvette c ́edex, France

Jeffrey Weeks†
15 Farmer St., Canton NY 13617-1120, USA

Jean-Philippe Uzan‡
Institut d’Astrophysique de Paris, GRεCO, FRE 2435-CNRS, 98bis boulevard Arago, 75014 Paris, France Laboratoire de Physique Th ́eorique, CNRS-UMR 8627,
Universit ́e Paris Sud, Bˆatiment 210, F–91405 Orsay c ́edex, France

Roland Lehoucq§
CE-Saclay, DSM/DAPNIA/Service d’Astrophysique, F–91191 Gif-sur-Yvette c ́edex, France, Laboratoire Univers et Th ́eories, CNRS-UMR 8102,
Observatoire de Paris, F–92195 Meudon c ́edex, France

Jean-Pierre Luminet¶
Laboratoire Univers et Th ́eories, CNRS-UMR 8102, Observatoire de Paris, F–92195 Meudon c ́edex, France (Dated: 13 November 2003)


The Shape of Space after WMAP data

Jean-Pierre Luminet
Laboratoire Univers et Th ́eories, CNRS-UMR 8102, Observatoire de Paris, F–92195 Meudon c ́edex, France.


Click to access a02v361b.pdf

Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background

Geometry and Topology in Relativistic Cosmology

Jean-Pierre Luminet

Laboratoire Univers et Théories, CNRS-UMR 8102, Observatoire de Paris, F-92195 Meudon cedex, France


The Spectral Action and Cosmic Topology

Matilde Marcolli

MAT1314HS Winter 2019, University of Toronto T 12-2 and W 12 BA6180

Click to access IntroNCGToronto10.pdf

Cosmic Topology

M. Lachieze-Rey (1), J.P.Luminet


Cosmic crystallography

R. Lehoucq1, M. Lachi`eze–Rey1,2 and J.P. Luminet3

  1. 1  CE-Saclay, DSM/DAPNIA/Service d’Astrophysique, F-91191 Gif sur Yvette cedex, France
  2. 2  CE-Saclay, DSM/DAPNIA/Service d’Astrophysique, CNRS–URA 2052, F-91191 Gif sur Yvette cedex, France
  3. 3  D ́epartement d’Astrophysique Relativiste et de Cosmologie, CNRS–UPR 176, Observatoire de Paris–Meudon, France

september 1995

The Status of Cosmic Topology after Planck Data 

Jean-Pierre Luminet 1,2

Received: 19 November 2015; Accepted: 7 January 2016; Published: 15 January 2016 Academic Editors: Stephon Alexander, Jean-Michel Alimi, Elias C. Vagenas and Lorenzo Iorio

Cosmic Topology: A Brief Overview

M. J. Rebouc ̧as

Centro Brasileiro de Pesquisas F ́ısicas, Departamento de Relatividade e Part ́ıculas Rua Dr. Xavier Sigaud, 150 , 22290-180 Rio de Janeiro – RJ, Brazil

and G. I. Gomero

The shape of space between WMAP and planck


Jean-Pierre Luminet

The Shape of Space from Einstein to WMAP data

AIP Conference Proceedings 841, 115 (2006);

Jean‐Pierre Luminet

Planck 2013 results. XXVI. Background geometry and topology of the Universe

The Shape and Topology of the Universe

Jean-Pierre Luminet


Signature of topology of the Universe

Vipin Kumar Sharma

University of Lucknow


Planck 2015 results
XVIII. Background geometry and topology of the Universe

How the Universe Got its Spots

Janna Levin1, Evan Scannapieco1, Giancarlo de Gasperis1, Joseph Silk1 and John D. Barrow2 1Center for Particle Astrophysics, UC Berkeley
Berkeley, CA 94720-7304
2Astronomy Centre, University of Sussex
Brighton BN1 9QJ, U.K.


The Conformal Singularity as a Cosmological Mirror: Classical Theory

DOI: 10.1080/21672857.2013.11519718

Michael Ibison

Early Universe cosmology in the light of the mirror dark matter interpretation of the DAMA/Libra signal

Paolo Ciarcellutia Robert Footb

Physics Letters B
Volume 679, Issue 3, 24 August 2009, Pages 278-281

Making Sense of the Big Bang: Wilkinson Microwave Anisotropy Probe


Planck 2018 results. I. Overview and the cosmological legacy of Planck

24. Cosmological Parameters

What Shape Is the Universe? A New Study Suggests We’ve Got It All Wrong

Planck evidence for a closed Universe and a possible crisis for cosmology

Eleonora Di Valentino1, Alessandro Melchiorri  2* and Joseph Silk

Click to access DiValentino2020NatureAst4.196.pdf

A new look at the universe’s oldest light

The Atacama Cosmology Telescope: a measurement of the Cosmic Microwave Background power spectra at 98 and 150 GHz

Steve K. Choi1,2,3, Matthew Hasselfield4,5,6, Shuay-Pwu Patty Ho3, Brian Koopman7, Marius Lungu3,8, Maximilian H. Abitbol9, Graeme E. Addison10, Peter A. R. Ade11, Simone Aiola4,3, David Alonso9

Mapping the Universe

Mark Altaweel | February 18, 2020 | Spatial Analysis

Planck and the cosmic microwave background

Cosmological crisis: We don’t know if the universe is round or flat

What shape is the universe?

As far as cosmologists can tell, space is almost perfectly flat. But what does this mean?

By Cody Cottier  |  Published: Tuesday, February 23, 2021

Is the Universe Curved? Not So Fast

By Paul Sutter December 02, 2019

Planck reveals an almost perfect Universe

2.4. The Cosmic Microwave Background

Decoding the cosmic microwave background

The Big Bang left behind a unique signature on the sky. Probes such as COBE, WMAP, and Planck taught us how to read it.

By Liz Kruesi  |  Published: Friday, July 27, 2018

The Universe Might Be a Giant Loop

By Rafi Letzter – Staff Writer November 04, 2019

Is the universe a dodecahedron?

08 Oct 2003 Isabelle Dumé

Geometry of the Universe :

Cosmological Constraints on Mirror Matter Parameters 

Paolo Ciarcelluti1 and Quentin Wallemacq


What It Means to Live in a Holographic Universe


Our Universe May Be a Giant Hologram

Our universe has antimatter partner on the other side of the Big Bang, say physicists

03 Jan 2019

A cosmic hall of mirrors

26 Sep 2005

Mystery of the Cosmic Mirror

What if the Universe has no end?

Mirror World, E(6) Unification and Cosmology

C.R. Das 1 ∗, L.V. Laperashvili 2 †,
1 Institute of Mathematical Sciences, Chennai, India

2 The Institute of Theoretical and Experimental Physics, Moscow, Russia

Click to access mirror_world_e6_unification_and_cosmology.pdf

We’ve seen signs of a mirror-image universe that is touching our own

Mirror Image Theory Suggests Existence of an Antimatter Universe

Did time flow in two directions from the big bang, making two futures?

Read more:

The Haunting World of the Mirrorverse

Three scientific mysteries which suggest a parallel world

New search for mirror neutron regeneration

L.J. BroussardK.M. BaileyW.B. BaileyJ.L. BarrowK. BerryA. BloseC. CrawfordL. Debeer-SchmittM. FrostA. Galindo-UribarriF.X. GallmeierC.E. GilbertL. HeilbronnE.B. IversonA. JohnstonY. KamyshkovP. LewizI. NovikovS.I. PenttiläS. VavraA.R. Young

17 Dec 2019

New Search for Mirror Neutrons at HFIR

  • October 2017

Leah Broussard
Oak Ridge National Laboratory

Joshua Lawrence Barrow
Fermi National Accelerator Laboratory (Fermilab)

B. Chance

Christopher Crawford
University of Kentucky

Radiation as Self-Action via a Cosmological Mirror

Michael Ibison

09 Nov 2015

Astronomical Review 
Volume 7, 2012 – Issue 3

Consciousness And Parallel Universes: Does A Connection Exist?

Niloy Chattaraj

September 19, 2020

The Holographic Universe Explained

A Thin Sheet of Reality: The Universe as a Hologram

The Multiverse Hypothesis Explained by Max Tegmark

Recursion, Incursion, and Hyper-incursion

Recursion, Incursion, and Hyper-incursion


How do Past and Future inform the present?

What happens in the Present is not only determined by the Past but also by the Future.  Karma and Destiny both play a role as to what is going on in your life Now.

Key Terms

  • Recursion
  • Incursion
  • Hyper Incursion
  • Discrete Processes
  • Cellular Automata
  • Fractal Machine
  • Hypersets
  • Interpenetration
  • Turing Machine
  • Symmetry
  • Non Well Founded Set Theory
  • Sets as Graphs
  • Leela
  • Predetermined Future
  • Bhagya
  • Fate
  • Destiny
  • Karma
  • Anticipation
  • Four Causes of Aristotle
  • Material Cause
  • Formal Cause
  • Efficient Cause
  • Final Cause
  • Left Computer
  • Right Computer
  • Parallel Computing
  • Fifth and the Fourth in Music Theory
  • Bicameral Brain
  • Hemispheric Division of Brain
  • One, Two, Three.  Where is the Fourth?


The recursion consists of the computation of the future value of the variable vector X(t+l) at time t+l from the values of these variables at present and/or past times, t, t-l, t-2 ….by a recursive function :

X (t+ 1) =f(X(t), X(t-1) …p..)

where p is a command parameter vector. So, the past always determines the future, the present being the separation line between the past and the future.

Starting from cellular automata, the concept of Fractal Machines was proposed in which composition rules were propagated along paths in the machine frame. The computation is based on what I called “INclusive reCURSION”, i.e. INCURSION (Dubois, 1992a- b). An incursive relation is defined by:

X(t+l) =f(…, X (t+l), X(t), X(t-1) ..p..).

which consists in the computation of the values of the vector X(t+l) at time t+l from the values X(t-i) at time t-i, i=1, 2 …. , the value X(t) at time t and the value X(t+j) at time t+j, j=l, 2, …. in function of a command vector p. This incursive relation is not trivial because future values of the variable vector at time steps t+l, t+2 …. must be known to compute them at the time step t+ 1.

In a similar way to that in which we define hyper recursion when each recursive step generates multiple solutions, I define HYPERINCURSION. Recursive computational transformations of such incursive relations are given in Dubois and Resconi (1992, 1993a-b).

I have decided to do this for three reasons. First, in relativity theory space and time are considered as a four-vector where time plays a role similar to space. If time t is replaced by space s in the above definition of incursion, we obtain

X(s+ l) =f( …, X(s+ 1), X(s), X (s-l) …p.).

and nobody is astonished: a Laplacean operator looks like this. Second, in control theory, the engineers control engineering systems by defining goals in the future to compute their present state, similarly to our haman anticipative behaviour (Dubois, 1996a-b). Third, I wanted to try to do a generalisation of the recursive and sequential Turing Machine in looking at space-time cellular automata where the order in which the computations are made is taken into account with an inclusive recursion.

We have already proposed some methods to realise the design of any discrete systems with an extension of the recursion by the concept of incursion and hyperincursion based on the Fractal Machine, a new type of Cellular Automata, where time plays a central role. In this framework, the design of the model of any discrete system is based on incursion relations where past, present and future states variables are mixed in such a way that they define an indivisible wholeness invariant. Most incursive relations can be transformed in different sets of recursive algorithms for computation. In the same way, the hyperincursion is an extension of the hyper recursion in which several different solutions can be generated at each time step. By the hyperincursion, the Fractal Machine could compute beyond the theoretical limits of the Turing Machine (Dubois and Resconi, 1993a-b). Holistic properties of the hyperincursion are related to the Golden Ratio with the Fibonacci Series and the Fractal Golden Matrix (Dubois and Resconi, 1992). An incursive method was developed for the inverse problem, the Newton- Raphson method and an application in robotics (Dubois and Resconi, 1995). Control by incursion was applied to feedback systems (Dubois and Resconi, 1994). Chaotic recursions can be synchronised by incursion (1993b). An incursive control of linear, non- linear and chaotic systems was proposed (Dubois, 1995a, Dubois and Resconi, 1994, 1995). The hyperincursive discrete Lotka-Voiterra equations have orbital stability and show the emergence of chaos (Dubois, 1992). By linearisation of this non-linear system, hyperincursive discrete harmonic oscillator equations give stable oscillations and discrete solutions (Dubois, 1995). A general theory of stability by incursion of discrete equations systems was developed with applications to the control of the numerical instabilities of the difference equations of the Lotka-Volterra differential equations as well as the control of the fractal chaos in the Pearl-Verhulst equation (Dubois and Resconi, 1995). The incursion harmonic oscillator shows eigenvalues and wave packet like in quantum mechanics. Backward and forward velocities are defined in this incursion harmonic oscillator. A connection is made between incursion and relativity as well as the electromagnetic field. The foundation of a hyperincursive discrete mechanics was proposed in relation to the quantum mechanics (Dubois and Resconi, 1993b, 1995).

This paper will present new developments and will show that the incursion and hyper-incursion could be a new tool of research and development for describing systems where the present state of such systems is also a function of their future states. The anticipatory property of incursion is an incremental final cause which could be related to the Aristotelian Final Cause.

Aristotle identified four explicit categories of causation: 1. Material cause; 2. Formal cause; 3. Efficient cause; 4. Final cause. Classically, it is considered that modem physics and mechanics only deal with efficient cause and biology with material cause. Robert Rosen (1986) gives another interpretation and asks why a certain Newtonian mechanical system is in the state (phase) Ix(t) (position), v(t) (velocity)]:

1. Aristotle’s “material cause” corresponds to the initial conditions of the system [x(0), v(0)] at time t=0.

2. The current cause at the present time is the set of constraints which convey to the system an “identity”, allowing it to go by recursion from the given initial phase to the latter phase, which corresponds to what Aristotle called formal cause.

3. What we call inputs or boundary conditions are the impressed forces by the environment, called efficient cause by Aristotle.

As pointed out by Robert Rosen, the first three of Aristotle’s causal categories are tacit in the Newtonian formalism: “the introduction of a notion of final cause into the Newtonian picture would amount to allowing a future state or future environment to affect change of state in the present, and this would be incompatible with the whole Newtonian picture. This is one of the main reasons that the concept of Aristotelian finality is considered incompatible with modern science.

In modern physics, Aristotelian ideas of causality are confused with determinism, which is quite different…. That is, determinism is merely a mathematical statement of functional dependence or linkage. As Russell points out, such mathematical relations, in themselves, carry no hint as to which of their variables are dependent and which are independent.”

The final cause could impress the present state of evolving systems, which seems a key phenomenon in biological systems so that the classical mathematical models are unable to explain many of these biological systems. An interesting analysis of the Final Causation was made by Emst von Glasersfeld (1990). The self-referential fractal machine shows that the hyperincursive field dealing with the final cause could be also very important in physical and computational systems. The concepts of incursion and hyper-incursion deal with an extension of the recursive processes for which future states can determine present states of evolving systems. Incursion is defined as invariant functional relations from which several recursive models with interacting variables can be constructed in terms of diverse physical structures (Dubois & Resconi, 1992, 1993b). Anticipation, viewed as an Aristotelian final cause, is of great importance to explain the dynamics of systems and the semantic information (Dubois, 1996a-b). Information is related to the meaning of data. It is important to note that what is usually called Information Theory is only a communication theory dealing with the communication of coded data in channels between a sender and a receptor without any reference to the semantic aspect of the messages. The meaning of the message can only be understood by the receiver if he has the same cultural reference as the sender of the message and even in this case, nobody can be sure that the receiver understands the message exactly as the sender. Because the message is only a sequential explanation of a non-communicable meaning of an idea in the mind of the sender which can be communicated to the receiver so that a certain meaning emerges in his mind. The meaning is relative or subjective in the sense that it depends on the experiential life or imagination of each of us. It is well- known that the semantic information of signs (like the coding of the signals for traffic) are the same for everybody (like having to stop at the red light at a cross roads) due to a collective agreement of their meaning in relation to actions. But the semantic information of an idea, for example, is more difficult to codify. This is perhaps the origin of creativity for which a meaning of something new emerges from a trial to find a meaning for something which has no a priori meaning or a void meaning.

Mind dynamics seems to be a parallel process and the way we express ideas by language is sequential. Is the sequential information the same as the parallel information? Let us explain this by considering the atoms or molecules in a liquid. We can calculate the average velocity of the particles from in two ways. The first way is to consider one particular particle and to measure its velocity during a certain time. One obtains its mean velocity which corresponds to the mean velocity of any particle of the liquid. The sec- ond way is to consider a certain number of particles at a given time and to measure the velocity of each of them. This mean velocity is equal to the first mean velocity. So there are two ways to obtain the same information. One by looking at one particular element along the time dimension and the other by looking at many elements at the same time. For me, explanation corresponds to the sequential measure and understanding to the parallel measure. Notice that ergodicity is only available with simple physical systems, so in general we can say that there are distortions between the sequential and the parallel view of any phenomenon. Perhaps the brain processes are based on ergodicity: the left hemisphere works in a sequential mode while the right hemisphere works in a parallel mode. The left brain explains while the right brain understands. The two brains arecomplementary and necessary.

Today computer science deals with the “left computer”. Fortunately, the informaticians have invented parallel computers which are based on complex multiplication of Turing Machines. It is now the time to reconsider the problem of looking at the “right computer”. Perhaps it will be an extension of the Fractal Machine (Dubois & Resconi, 1993a).

I think that the sequential way deals with the causality principle while the parallel way deals with a finality principle. There is a paradox: causality is related to the successive events in time while finality is related to a collection of events at a simultaneous time, i.e. out of time.Causality is related to recursive computations which give rise to the local generation of patterns in a synchronic way. Finality is related to incursive or hyperincursive symmetry invariance which gives rise to an indivisible wholeness, a holistic property in a diachronic way. Recursion (and Hyper recursion) is defined in the Sets Theory and Incursion (and Hyperincursion) could be defined in the new framework of the Hypersets Theory (Aczel, 1987; Barwise, Moss, 1991).

If the causality principle is rather well acknowledged, a finality principle is still controversial. It would be interesting to re-define these principles. Causality is defined for sequential events. If x(t) represents a variable at time t, a causal rule x(t+l) = f(x(t)) gives the successive states of the variable x at the successive time steps t, t+l, t+2, … from the recursive functionf(x(t)), starting with an initial state x(0) at time t=0. Defined like this, the system has no degrees of freedom: it is completely determined by the function and the initial condition. No new things can happen for such a system: the whole future is completely determined by its past. It is not an evolutionary system but a developmental system. If the system tends to a stable point, x(t+l) = x(t) and it remains in this state for ever. The variable x can represent a vector of states as a generalisation.

In the same way, I think that determinism is confused with predictability, in modern physics. The recent fractal and deterministic chaos theory (Mandeibrot, 1982; Peitgen, Jurgens, Saupe, 1992) is a step beyond classical concepts in physics. If the function is non-linear, chaotic behaviour can appear, what is called (deterministic) chaos. In this case, determinism does not give an accurate prediction of the future of the system from its initial conditions, what is called sensitivity to initial conditions. A chaotic system loses the memory of its past by finite computation. But it is important to point out that an average value, or bounds within which the variable can take its values, can be known;

it is only the precise values at the successive steps which are not predictable. The local information is unpredictable while the global symmetry is predictable. Chaos can presents a fractai geometry which shows a self-similarity of patterns at any scale.

A well-known fractal is the Sierpinski napkin. The self-similarity of pattems at any scale can be viewed as a symmetry invariance at any scale. An interesting property of such fractals is the fact that the final global pattern symmetry can be completely independent of the local pattern symmetry given as the initial condition of the process from which the fractal is built. The symmetry of the fractal structure, a final cause, can be independent of the initial conditions, a material cause. The formal cause is the local symmetry of the generator of the fractal, independently of its material elements and the efficient cause can be related to the recursive process to generate the fractal. In this particular fractal geometry, the final cause is identical to the final cause. The efficient cause is the making of the fractal and the material cause is just a substrate from which the fractal emerges but this substrate doesn’t play a role in the making.

Finally, the concepts of incursion and hyperincursion can be related to the theory of hypersets which are defined as sets containing themselves. This theory of hypersets is an alternative theory to the classical set theory which presents some problems as the in- completeness of G6del: a formal system cannot explain all about itself and some propositions cannot be demonstrated as true or false (undecidability). Fundamental entities of systems which are considered as ontological could be explain in a non-ontological way by self-referential systems.

Please see my related posts

On Anticipation: Going Beyond Forecasts and Scenarios

Autocatalysis, Autopoiesis and Relational Biology

Key sources of Research


Computing Anticipatory Systems with Incursion and Hyperincursion

Daniel M. DUBOIS


Click to access cd554835f0ae367c3d3e3fa40f3e5e5f5f11.pdf




Anticipation in Social Systems:

the Incursion and Communication of Meaning

Loet Leydesdorff 

Daniel M. Dubois

Click to access casys03.pdf





Daniel M. Dubois


Click to access dubois.pdf




Non-wellfounded Set Theory


  • Jon Barwise &
  • Larry Moss

Non-well-founded set theory

Knot Theory and Recursion: Louis H. Kauffman

Knot Theory and Recursion: Louis H. Kauffman


Some knots are tied forever.


Key Terms

  • Louis H Kauffman
  • Heinz Von Foerster
  • George Spencer Brown
  • Francisco Varela
  • Charles Sanders Peirce
  • Recursion
  • Reflexivity
  • Knots
  • Laws of Form
  • Shape of Process
  • Trefoil Knots
  • Triplicity
  • Nonduality
  • Self Reference
  • Eigen Form
  • Form Dynamics
  • Recursive Forms
  • Knot Logic
  • Bio Logic
  • Distinctions
  • Topology
  • Topological Recursion
  • Ganth
  • Granthi – Brahma, Vishnu, Rudra
  • Chakra
  • Braids
  • Bandhu
  • Mitra
  • Vishvamitra
  • Friend
  • Relation
  • Sambandh
  • Love
  • True Love
  • Its a Knotty problem.

In mathematics, a knot is defined as a closed, non-self-intersecting curve that is embedded in three dimensions and cannot be untangled to produce a simple loop (i.e., the unknot). While in common usage, knots can be tied in string and rope such that one or more strands are left open on either side of the knot, the mathematical theory of knots terms an object of this type a “braid” rather than a knot. To a mathematician, an object is a knot only if its free ends are attached in some way so that the resulting structure consists of a single looped strand.

A knot can be generalized to a link, which is simply a knotted collection of one or more closed strands.

The study of knots and their properties is known as knot theory. Knot theorywas given its first impetus when Lord Kelvin proposed a theory that atoms were vortex loops, with different chemical elements consisting of different knotted configurations (Thompson 1867). P. G. Tait then cataloged possible knots by trial and error. Much progress has been made in the intervening years.

Schubert (1949) showed that every knot can be uniquely decomposed (up to the order in which the decomposition is performed) as a knot sum of a class of knots known as prime knots, which cannot themselves be further decomposed (Livingston 1993, p. 5; Adams 1994, pp. 8-9). Knots that can be so decomposed are then known as composite knots. The total number (prime plus composite) of distinct knots (treating mirror images as equivalent) having k=0, 1, … crossings are 1, 0, 0, 1, 1, 2, 5, 8, 25, … (OEIS A086825).

Klein proved that knots cannot exist in an even-dimensional space >=4. It has since been shown that a knot cannot exist in any dimension >=4. Two distinct knots cannot have the same knot complement (Gordon and Luecke 1989), but two links can! (Adams 1994, p. 261).

Knots are most commonly cataloged based on the minimum number of crossings present (the so-called link crossing number). Thistlethwaite has used Dowker notation to enumerate the number of prime knots of up to 13 crossings, and alternating knots up to 14 crossings. In this compilation, mirror images are counted as a single knot type. Hoste et al. (1998) subsequently tabulated all prime knots up to 16 crossings. Hoste and Weeks subsequently began compiling a list of 17-crossing prime knots (Hoste et al. 1998).

Another possible representation for knots uses the braid group. A knot with n+1 crossings is a member of the braid group n.

There is no general algorithm to determine if a tangled curve is a knot or if two given knots are interlocked. Haken (1961) and Hemion (1979) have given algorithms for rigorously determining if two knots are equivalent, but they are too complex to apply even in simple cases (Hoste et al. 1998).


LH Kauffman with Trefoil Knot in the back.

LH Kauffman


From Reflexivity

A Knot

Screen Shot 2020-01-06 at 12.49.45 PM


Trefoil Knot



Screen Shot 2020-01-07 at 6.32.04 AM




From Reflexivity

This slide show has been only an introduction to certain mathematical and conceptual points of view about reflexivity.

In the worlds of scientific, political and economic action these principles come into play in the way structures rise and fall in the play of realities that are created from (almost) nothing by the participants in their desire to profit, have power or even just to have clarity and understanding. Beneath the remarkable and unpredictable structures that arise from such interplay is a lambent simplicity to which we may return, as to the source of the world.


From Laws of Form and the Logic of Non-Duality

This talk will trace how a mathematics of distinction arises directly from the process of discrimination and how that language, understood rightly as an opportunity to join as well as to divide, can aid in the movement between duality and non-duality that is our heritage as human beings on this planet.The purpose of this talk is to express this language and invite your participation in it and to present the possiblity that all our resources physical, scientific, logical, intellectual, empathic are our allies in the journey to transcend separation.

From Laws of Form and the Logic of Non-Duality

True Love.  It is a knotty problem.

Screen Shot 2020-01-07 at 9.51.03 AM


Wikipedia on Knot Theory




Please see my related posts:

Reflexivity, Recursion, and Self Reference

Jay W. Forrester and System Dynamics

Steps to an Ecology of Mind: Recursive Vision of Gregory Bateson

Second Order Cybernetics of Heinz Von Foerster

Cybernetics Group: A Brief History of American Cybernetics

Cybernetics, Autopoiesis, and Social Systems Theory

Cyber-Semiotics: Why Information is not enough

Ratio Club: A Brief History of British Cyberneticians

Autocatalysis, Autopoiesis and Relational Biology

Feedback Thought in Economics and Finance

Increasing Returns and Path Dependence in Economics

Boundaries and Distinctions

Boundaries and Relational Sociology

Boundaries and Networks

Socio-Cybernetics and Constructivist Approaches

Society as Communication: Social Systems Theory of Niklas Luhmann

Semiotics, Bio-Semiotics and Cyber Semiotics

Meta Integral Theories: Integral Theory, Critical Realism, and Complex Thought

Networks and Hierarchies


Key Sources of Research:


Home Page of Louis H. Kauffman

Recursive Distinctioning

By Joel Isaacson and Louis H. Kauffman


Click to access JSP-Spr-2016-8_Kauffman-Isaacson-Final-v2.pdf



Knot Logic – Logical Connection and Topological Connection

by Louis H. Kauffman

Click to access 1508.06028.pdf




by Louis H. Kauffman


Click to access KNOTS.pdf





Louis H. Kaufman, UIC

Click to access BioL.pdf

New Invariants in the Theory of Knots

Louis H. Kaufman, UIC




Eigenform – An Introduction

by Louis H. Kauffman

Click to access 2007_813_Kauffman.pdf



Knot Logic and Topological Quantum Computing with Majorana Fermions

Louis H. Kauffman


Click to access arXiv%3A1301.6214.pdf




by Louis H. Kauffman

Click to access videoLKss-slides.pdf




Eigenforms, Discrete Processes and Quantum Processes

Louis H Kauffman 2012 J. Phys.: Conf. Ser. 361 012034




Eigenforms — Objects as Tokens for Eigenbehaviors

by Louis H. Kauffman

Click to access 1817.pdf




Reflexivity and Eigenform The Shape of Process

Louis H. Kauffman A University of


Click to access ReflexPublished.pdf






Louis H. Kauffman


Click to access Eigen.pdf





Louis H. Kauffman UIC, Chicago


Click to access Eigenform.pdf



Form Dynamics

Click to access FormDynamics.pdf



Arithmetics in the Form

Click to access ArithForm.pdf




Self Reference and Recursive Forms

Click to access SelfRefRecurForm.pdf

Click to access Relativity.pdf




Laws of Form and the Logic of Non-Duality

Louis H. Kauffman, UIC


Click to access KauffSAND.pdf




Laws of Form – An Exploration in Mathematics and Foundations

by Louis H. Kauffman UIC


Click to access Laws.pdf




The Mathematics of Charles Sanders Peirce

Louis H. Kauffman1


Click to access Peirce.pdf




A Recursive Approach to the Kauffman Bracket

Abdul Rauf Nizami, Mobeen Munir, Umer Saleem, Ansa Ramzan

Division of Science and Technology, University of Education, Lahore, Pakistan


On Synchronicity

On Synchronicity

There are invisible ties between us.


Click to access Synchronicity2010.pdf

Causality has to do with events that happen in sequence, a cause producing an effect, whereas synchronicity has to do with events that happen together.

Synchronicism is the prejudice of the East, causality is the modern prejudice of the West.  – Carl Jung, 1929



Key Terms

  • Synchronicity
  • Serendipity
  • Interconnected Universe
  • Quantum Entanglements
  • Fractal Universe
  • Recursive Universe
  • Platonic Solids
  • Carl G Jung
  • Events in Sequence
  • Events in Parallel
  • Space Structure
  • Ether
  • Geometry of space
  • Complex Numbers
  • Shri Yantra Geometry
  • Mind and Matter
  • Brain and Mind
  • Parapsychology
  • Occult
  • Esoteric 


The history of coincidence studies can be told through the stories of thefour people who coined words for the types of coincidences they noticed in their lives. The most famous is Carl Jung and synchronicity, but he was not the first.

Serendipity: Horace Walpole (1717-1797)


Horace Walpole, a member of the British House of Commons in the 18th century, recognized in himself a talent for finding what he needed just when he needed it.A gift in the form of a portrait of a Grand Duchess whom Walpole had long admired arrived from his distant cousin in Florence, Italy. Walpole needed a coat of arms to decorate the new picture frame and just happened to find it an old book. On January 28, 1754, Walpole, thrilled with this coincidence, wrote to his cousin Horace, giving a name to his ability to find things unexpectedly—serendipity.

He got the name from a fairy tale called “The Travels and Adventures of Three Princes of Sarendip.” Sarendip (or Serendib) is an ancient name for the island nation Sri Lanka off India’s southern coast. The king of the fable recognized that education requires more than learning from books, so he sent his sons out of the country to broaden their experience. Throughout the story, the clever princes carefully observed their surroundings, and then used their observations in ways that saved them from danger and death.

For Walpole, serendipity meant finding something by informed observation (sagacity as he called it) and by accident. The main ingredients of serendipity include luck, chance, active searching, and informed observation.

Seriality: Paul Kammerer (1880-1926)


Biologist Paul Kammerer spent hours sitting on benches in various public parks in Vienna noting repetitions among the people who passed by. He classified them by sex, age, dress, whether they carried umbrellas or parcels, and by many other details. He did the same during the long train rides from his home to his office in Vienna. Kammerer was not particularly interested in meaning—only repeated sequences of numbers, names, words, and letters. Two examples can illustrate his thinking: His wife was in a waiting room reading about a painter named Schwalbach when a patient named Mrs. Schwalbach was called into the consultation room.A second example involved his friend Prince Rohan. On the train his wife was reading a novel with a character “Mrs. Rohan.” She then saw a man get on the train who looked like Prince Rohan. Later that night the Prince himself unexpectedly dropped by their house for a visit.

He defined “seriality” as “a recurrence of the same or similar things or events in time and space” which, “are not connected by the same acting cause.”  To him these repetitions were simply natural phenomena.

Kammerer thought these similarities were part of the structure of natural law, and in his 1919 book Das Gesetz Der Serie outlined what he thought these laws to be along with a broad set of classifications of their types and qualities.

Synchronicity: Carl Jung (1875-1961)

Psychologist Carl G. Jung

Carl Jung grew up in Swiss family that, on his mother’s side, embraced the paranormal. His personal experiences included apparitions (the disembodied figure of another person) and poltergeists (troublesome ghosts), spiritualistic communications (communication with people after their deaths), and materializations (creation of matter from unknown sources). His experiences also included telepathic, clairvoyant, and precognitive dreams, prophetic visions, psychokinetic events, and out-of-body and near-death experiences.

He invented the word synchronicity from the Greek syn—with, together—andchronos—time. Synchronicity means moving-together-in-time. Its fundamental characteristic is the surprise that occurs when a thought in the mind is mirrored by an external event to which it has no apparent causal connection. He also used the word synchronicity to refer to “an acausal connecting principle” that he placed on equal status with causation.

He included many strange events under the synchronicity umbrella including telepathy, precognition, and clairvoyance, along with poltergeists, apparitions, divination (e.g. the I Ching), and astrology. The definition of synchronicity has been stretched in many different directions.

Simulpathity: Bernard Beitman (1942–) Founder of Coincidence Studies


The term “simulpathity” defines a specific subclass of meaningful coincidences: the simultaneous experience at a distance by one person of another person’s distress. The experience occurs without the two people being together in the same place and sometimes without conscious awareness of its source. One person is in pain and another person feels distress for no apparent reason. Sometimes the distress is very similar to the other person’s pain. Often, the two people share a strong emotional bond. The largest number of simulpathity reports comes from twins, although reports involving mothers and their children are also prominent.

Simulpathity suggests that the individuals are more closely bonded than current scientific thought holds possible.

Simulpathity — from the Latin simul (simultaneous) and the Greek pathos (suffering) — differs from “sympathy.” The sympathetic person is aware of the suffering of the other but does not usually feel it. In the experience of simulpathity, one person suffers along with the other person and can experiences some form of that suffering. Only later is the simultaneity of the distress recognized, although some twins know just why they are feeling pain—the other twin is now feeling it.

Please see my related posts:

Interconnected Pythagorean Triples using Central Squares Theory

Indra’s Net: On Interconnectedness

The Great Chain of Being

On Holons and Holarchy

Mind, Consciousness and Quantum Entanglement

Geometry of Consciousness

Systems View of Life: A Synthesis by Fritjof Capra

Consciousness of Cosmos: A Fractal, Recursive, Holographic Universe

Myth of Invariance: Sound, Music, and Recurrent Events and Structures

Shape of the Universe

Reflexivity, Recursion, and Self Reference

Key Sources of Research


Synchronicity: Nature and Psyche in an Interconnected Universe

Joseph Cambray



Synchronicity and Healing



Click to access 18-Beitman-Chap18.pdf




An Acausal Connecting Principle

CG Jung





Christopher Jargodzki


Click to access Synchronicity2010.pdf

Synchronicity, Mind, and Matter

Wlodzislaw Duch




Synchronicity: did Jung have it right?

Kurt Forrer


Click to access bb26804cdc465b355e2f2e09c574d50dc4bb.pdf




C.G. Jung’s Synchronicity and Quantum Entanglement:  Schrodinger’s Cat ‘Wanders’ Between Chromosomes


Click to access Limar.Synchronicity.pdf

Synchronicity: The Bridge Between Matter and Mind

F. David Peat
Bantam Books (1987)

Emotions Over Time: Synchronicity and Development of Subjective, Physiological, and Facial Affective Reactions to Music

C. G. Jung’s Psychology of Religion and Synchronicity

By Robert Aziz

Jung on Synchronicity and the Paranormal

By Carl Gustav Jung



Synchronicity and Emergence


Click to access Cambray.pdf

Jung, synchronicity, & human destiny: Noncausal dimensions of human experience.

Synchronicity: Science, Myth, and the Trickster

Allan Combs
Marlowe & Co. (1996)

Synchronicity, Science and Soul-Making: Understanding Jungian Synchronicity …

By Victor Mansfield

Synchronicity: Nature and Psyche in an Interconnected Universe

By Joseph Cambray

The Hidden Geometry of Trade Networks

The Hidden Geometry of Trade Networks


From The hidden hyperbolic geometry of international trade: World Trade Atlas 1870–2013



Key Terms:

  • Trade Networks
  • Complex Networks
  • Preferential Attachment
  • Positive Feedback
  • Fractals
  • Power Laws
  • Hyperbolic Geometry
  • Economic Geography
  • Regional Trading Blocks
  • Bilateral Trade
  • Multilateral Trade
  • Free Trade Agreements
  • Metabolism of a City
  • Metabolism of a Nation
  • Metabolism of the World
  • Industrial Ecology
  • Social Ecology
  • Growth and Form



From The hidden hyperbolic geometry of international trade: World Trade Atlas 1870–2013

Here, we present the World Trade Atlas 1870–2013, a collection of annual world trade maps in which distance combines economic size and the different dimensions that affect international trade beyond mere geography. Trade distances, based on a gravity model predicting the existence of significant trade channels, are such that the closer countries are in trade space, the greater their chance of becoming connected. The atlas provides us with information regarding the long-term evolution of the international trade system and demonstrates that, in terms of trade, the world is not flat but hyperbolic, as a reflection of its complex architecture. The departure from flatness has been increasing since World War I, meaning that differences in trade distances are growing and trade networks are becoming more hierarchical. Smaller-scale economies are moving away from other countries except for the largest economies; meanwhile those large economies are increasing their chances of becoming connected worldwide. At the same time, Preferential Trade Agreements do not fit in perfectly with natural communities within the trade space and have not necessarily reduced internal trade barriers. We discuss an interpretation in terms of globalization, hierarchization, and localization; three simultaneous forces that shape the international trade system.

From The hidden hyperbolic geometry of international trade: World Trade Atlas 1870–2013

When it comes to international trade, the evidence suggests that we are far from a distance-free world. Distance still matters1 and in many dimensions: cultural, administrative or political, economic, and geographic. This is widely supported by empirical evidence concerning the magnitude of bilateral trade flows. The gravity model of trade2–4, in analogy to Newton’s law of gravitation, accurately predicts that the volume of trade exchanged between two countries increases with their economic sizes and decreases with their geographical separation. The precision of that model improves when it is supplemented with other factors, such as colony–colonizer relationships, a shared common language, or the effects of political borders and a common currency5–7. Despite the success of the gravity model at replicating trade volumes, it performs very poorly at predicting the existence of a trade connection between a given pair of countries8; an obvious limitation that prevents it from explaining the striking regularities observed in the complex architecture of the world trade web9–13. One of the reasons for this flaw is that the gravity model focuses on detached bilateral relationships and so overlooks multilateral trade resistance and other network effects14.

Another drawback of the classical gravity model is that geography is not the only factor that defines distance in international trade. Here, we use a systems approach based on network science methodologies15,16 to propose a gravity model for the existence of significant trade channels between pairs of countries in the world. The gravity model is based on economic sizes and on an effective distance which incorporates different dimensions that affect international trade, not only geography, implicitly encoded on the complex patterns of trade interactions. Our gravity model is based on the connectivity law proposed for complex networks with underlying metric spaces17,18 and it can be represented in a pure geometric approach using a hyperbolic space, which has been conjectured as the natural geometry underlying complex networks19–22. In the hyperbolic trade space, distance combines economic size and effective distance into a sole distance metric, such that the closer countries are in hyperbolic trade space, the greater their chance of becoming connected. We estimate this trade distance from empirical data using adapted statistical inference techniques23,24, which allow us to represent international trade through World Trade Maps (WTMs). These define a coordinate system in which countries are located in relative positions according to the aggregate trade barriers between them. The maps are annual and cover a time span of fourteen decades. The collection as a whole, referred to as the World Trade Atlas 1870–2013, is presented via spatial projections25, Table S5, and trade distance matrices, Table S6. Beyond the obvious advantages of visualization, the World Trade Atlas 1870–2013 significantly increases our understanding of the long-term evolution of the international trade system and helps us to address a number of important and challenging questions. In particular: How far, in terms of trade, have countries traveled in recent history? What role does each country play in the maps and how have those roles evolved over time? Are Preferential Trade Agreements (PTAs) consistent with natural communities as measured by trade distances? Has the formation of PTAs led to lesser or greater barriers to trade within blocs? Is trade distance becoming increasingly irrelevant?

The answers to these questions can be summarized by asserting that, in terms of trade, the world is not flat; it is hyperbolic. Differences in trade distances are growing and becoming more heterogeneous and hierarchical; at the same time as they define natural trade communities—not fully consistent with PTAs. Countries are becoming more interconnected and clustered into hierarchical trade blocs than ever before.

Please see my related posts:

Networks and Hierarchies

Increasing Returns, Path Dependence, Circular and Cumulative Causation in Economics

Relational Turn in Economic Geography

Boundaries and Networks

Multilevel Approach to Research in Organizations

Regional Trading Blocs and Economic Integration

Increasing Returns and Path Dependence in Economics

Growth and Form in Nature: Power Laws and Fractals

Key Sources of Research:


The hidden hyperbolic geometry of international trade: World Trade Atlas 1870–2013

Guillermo García-Pérez  Marián Boguñá, Antoine Allard & M. Ángeles Serrano


Click to access srep33441.pdf



Uncovering the hidden geometry behind metabolic networks


Molecular BioSystems · March 2012


Click to access 1109.1934.pdf



The hidden geometry of complex networks



Click to access s1_to_pdf.pdf

Click to access Curs_Intro_networks.pdf




Deciphering the global organization of clustering in real complex networks

Pol Colomer-de-Simo ́n1, M. A ́ ngeles Serrano1, Mariano G. Beiro ́2, J. Ignacio Alvarez-Hamelin2 & Maria ́n Bogun ̃a ́1


Click to access srep02517.pdf






Hidden geometric correlations in real multiplex networks


Kaj-KoljaKleineberg,1,∗ Mari ́anBogun ̃ ́a,1 M.A ́ngelesSerrano,2,1 andFragkiskosPapadopoulos

Click to access 1601.04071.pdf






Emergent Hyperbolic Network Geometry

Ginestra Bianconi1 & Christoph Rahmede


Click to access srep41974.pdf





The geometric nature of weights in real complex networks


Antoine Allard1,2, M. A ́ngeles Serrano1,2,3, Guillermo Garc ́ıa-Pe ́rez1,2 & Maria ́n Bogun ̃a ́

Click to access ncomms14103.pdf




Network Geometry and Complexity

Daan Mulder · Ginestra Bianconi


Click to access 1711.06290.pdf




Multiscale unfolding of real networks by geometric renormalization


Guillermo Garc ́ıa-P ́erez,1,2 Mari ́an Bogun ̃ ́a,1,2 and M. A ́ngeles Serrano


Click to access 1706.00394.pdf




Topology of the World Trade Web

Ma A ́ngeles Serrano and Mari ́an Bogun ̃a ́


Click to access 0301015.pdf



Patterns of dominant flows in the world trade web


M. A ́ngeles Serrano,1 Mari ́an Bogun ̃ ́a,2 and Alessandro Vespignani3,4


Click to access 0704.1225.pdf





Clustering and the hyperbolic geometry of complex networks

Elisabetta Candellero and Nikolaos Fountoulakis


Click to access paper8waw14.pdf





Hyperbolic Geometry of Complex Networks


Dmitri Krioukov, Fragkiskos Papadopoulos, Maksim Kitsak, Amin Vahdat, and Mari ́an Boguna

Click to access hyperbolic_geometry_complex.pdf






On Hyperbolic Geometry Structure of Complex Networks

Wenjie Fang


Click to access 531c6644768ad78e86843e297fed442769cb.pdf


Indra’s Net: On Interconnectedness

Indra’s Net: On Interconnectedness



Key Terms

  • Indra’s Net
  • Indrajal
  • Felix Klein
  • Henri Poincare
  • Hyperbolic Geometry
  • Atharva Veda
  • Avatamsaka Sutra of Hua Yen Buddhism
  • Brahmajala Sutra of Mahayana Buddhism
  • Non-Euclidian Geometry
  • Hyperbolic Manifolds
  • Group Theory
  • Fractals
  • Benoit Mandelbrot
  • Mobius Maps
  • David Mumford
  • David Wright
  • Caroline Series
  • Indrajal Comics (a Publishing house in India now defunct)
  • Nicolai Lobachevsky
  • Johann Bolyai
  • Carl F Gauss


From The Avatamsaka Sutra Francis H. Cook
Hua-Yen Buddhism: The Jewel Net of Indra 1977

Indra’s Net

Far away in the heavenly abode of the Great God Indra, the protector and nurturer of life, there is a wonderful net which stretches out indefinitely in all directions, in accordance with the extravagant tastes of deities.

At the net’s every node, is hung a single glittering jewel and since the net itself is infinite in dimension, the jewels are infinite in number. There hang the jewels, glittering like stars of the first magnitude, a wonderful sight to behold.

If we now arbitrarily select one of these jewels for inspection and look closely at it, we will discover that in its polished surface there are reflected all the other jewels in the net, which sparkle in the magnificence of its totality.

Not only that, but each of the jewels reflected in this one jewel is also reflecting all the other jewels, so that the process of reflection is infinite. As each gem reflects every other one and everything else in the universe, so are you affected by every other system in the universe.



The metaphor of Indra’s Jeweled Net is attributed to an ancient Buddhist named Tu- Shun (557-640 B.C.E.) who asks us to envision a vast net that:

  • At each juncture there lies a jewel
  • Each jewel reflects all the other jewels in this cosmic matrix
  • Every jewel represents an individual life form, atom, cell or unit of consciousness
  • Each jewel, in turn, is intrinsically and intimately connected to all the others
  • A change in one gem is reflected in all the others

The moral of Indra’s net is that the compassionate and the constructive interventions a person makes or does can produce a ripple effect of beneficial action that will reverberate throughout the universe or until it plays out.

By the same token you cannot damage one strand of the web without damaging the others or setting off a cascade effect of destruction.



From The Indra’s Net

“Far away in the heavenly abode of the great god Indra, there is a wonderful net which has been hung by some cunning artificer in such a manner that it stretches out indefinitely in all directions. In accordance with the extravagant tastes of deities, the artificer has hung a single glittering jewel at the net’s every node, and since the net itself is infinite in dimension, the jewels are infinite in number. There hang the jewels, glittering like stars of the first magnitude, a wonderful sight to behold. If we now arbitrarily select one of these jewels for inspection and look closely at it, we will discover that in its polished surface there are reflected all the other jewels in the net, infinite in number. Not only that, but each of the jewels reflected in this one jewel is also reflecting all the other jewels, so that the process of reflection is infinite. The Hua’yen school [of Buddhism] has been fond of this image, mentioned many times in its literature, because it symbolizes a cosmos in which there is an infinitely repeated interrelationship among all the members of the cosmos. This relationship is said to be one of simultaneous mutual identity and mututal intercausality.”

~ Francis H. Cook, Hua-yen Buddhism: The Jewel Net of Indra

There are several aspects of Indra’s Net, as described in the above quote, that signify it as a crystal clear allegory of reality:

1. The Holographic Nature of the Universe

Long before the existence of the hologram, the jeweled net is an excellent description of the special characteristic of holograms: that every point of the hologram contains information regarding all other points. This reflective nature of the jewels is an obvious reference to this.

This kind of analogy has been suggested by science as a theory for an essential characteristic of the cosmos, as well as as the functioning of the human brain, as beautifully described inThe Holograpic Universe by Michael Talbot.

2. The Interconnectedness of All Thingss

When any jewel in the net is touched, all other jewels in the node are affected. This speaks to the hidden interconnectedness and interdependency of everything and everyone in the universe, and has an indirect reference to the concept of “Dependent Origination” in Buddhism. Additionally, Indra’s Net is a definitive ancient correlate of Bell’s Theorum, or the theory of non-local causes.

3. Lack of a substantive self

Each node, representing an individual, simply reflects the qualities of all other nodes, inferring the notion of ‘not-self’ or a lack of a solid and real inherent self, as seen in the Advaita Vedanta school of Hinduism and Buddhism in general.

4. Non-locality

Indra’s Net shoots holes in the assumption or imputation of a solid and fixed universe ‘out there’. The capacity of one jewel to reflect the light of another jewel from the other edge of infinity is something that is difficult for the linear mind, rational mind to comprehend. The fact that all nodes are simply reflections indicates that there is no particular single source point from where it all arises.

5. Innate Wisdom

The ability to reflect the entirety of all light in the universe attests to the inherent transcendant wisdom that is at the core of all nodes, representing all sentient beings, and to the inherent Buddha Nature.

6. Illusion or Maya

The fact that all nodes are simply a reflection of all others implies the illusory nature of all appearances. Appearances are thus not reality but a reflection of reality.

7. Universal Creativity

A familiar concept in various high dharmas is one of an impersonal creative intelligence that springs forth into reality through the instruments of all living beings.

8. The Mirror-like Nature of Mind

The capacity to reflect all things attests to the mind being a mirror of reality, not its basis. This is a common thesis among various schools and religions.

This article is from:


The Vedic metaphor of Indra’s Net

The metaphor of Indra’s net, with its poetic description of the indivisibility of the universe, captures the essence of Hinduism’s vibrant and open spirit.

The Vedic metaphor of Indra’s Net


Indra’s Net is a metaphor for the profound cosmology and outlook that permeates Hinduism. Indra’s Net symbolizes the universe as a web of connections and inter-dependencies among all its members, wherein every member is both a manifestation of the whole and inseparable from the whole. This concept is the foundation for Vedic cosmology and it later went on to become the central principle of Buddhism, and from there spread into mainstream Western discourse across several disciplines.

The metaphor of Indra’s Net originates from the Atharva Veda (one of the four Vedas), which likens the world to a net woven by the great deity Shakra or Indra. The net is said to be infinite, and to spread in all directions with no beginning or end. At each node of the net is a jewel, so arranged that every jewel reflects all the other jewels. No jewel exists by itself independently of the rest. Everything is related to everything else; nothing is isolated. [i]

Indeed, the fundamental idea of unity-in-diversity underpins all dharmic traditions; even though there are many perspectives from which Indra’s Net may be viewed and appreciated, it is ultimately recognized as one indivisible and infinite unity. From the Hindu viewpoint, the One that manifests as many is named Brahman; even seemingly disparate elements are in fact nothing other than reflections of Brahman, and hence of one another. This notion of an organic unity is a signature of Hinduism, and distinguishes it from all major Western religions, philosophies and cultures.

Each jewel of Indra’s Net includes the reflections of all the other jewels; the significance of this symbolism is that each entity in the universe contains within itself the entire universe. This idea, rather than positing interdependence among separately existing entities, asserts that the whole does not owe its existence to the coming together of individual parts that have independent existence. Indeed, the existence of each individual part is contingent upon, and relative to, the existence of the whole and of all the other parts. Yet, paradoxically, each individual part also ‘contains’ the whole within itself. Put simply, the whole and the parts are inseparable.

Every jewel in Indra’s Net is a microcosm of the whole net; every component is the cause of the whole and also the effect of the whole. Nothing exists outside the net. [ii] In the Hindu worldview, the only essence that ultimately exists is Brahman; Brahman is the foundation for Indra’s Net, and no jewel exists apart from Brahman.

The jewels of Indra’s Net are not meant to symbolize static substances. Each jewel is merely a reflection of other jewels, and individual jewels always remain in flux. Each jewel exists only momentarily, to be continuously replaced by its successor, in mutual causation with other jewels. Just as the interdependent cells of the human body are perpetually changing, so also everything in Indra’s Net is perpetually in flux. Reality is always in the flux of becoming. This concept is different from the notion of real, independently existing entities undergoing modification, or static entities that happen to be woven together.

Swami Vivekananda applied the great Upanishadic saying, ‘tat tvam asi’ (‘that thou art’) as the basis for Hindu ethics. He said, in essence, that we are all jewels in Indra’s Net (even though he did not use this metaphor to say it). Thus, Vivekananda defined a Hindu platform for determining ethical conduct, not only towards all humans but towards animals and all entities in general—because everyone and everything is a jewel in Indra’s Net.

The Sanskrit word bandhu is frequently used to describe the interrelationship between the jewels of Indra’s Net. ‘Bandhu’ defines a corresponding entity; for example, a relationship between x and y can be stated as ‘x is a bandhu of y’. In traditional Indian discourse, this term is often used to explain the unity between the whole and its seemingly diverse parts. For example, ancient thinkers have described specific bandhus which express the paradoxical relationship of the microcosm to the macrocosm. While the microcosm is generally perceived as a map of the macrocosm, it is also the case that both microcosm and macrocosm continuously mirror one another.

Bandhu can also refer to the connections among various facets of our overall unified reality, linking sounds, numbers, colors and ideas together. No object—whether physical, mental, emotional, or conceptual—has any existence by itself and is merely another facet of this unified whole. In addition, bandhu describes how the transcendental worlds correspond with the perceptible world, implying that whatever we perceive through our senses is but a pointer to something beyond.

Kapila Vatsyayan, a scholar of classical Indian art, has cited many examples of bandhu in the form of common metaphors. Significant symbols may be found in the Rig Veda, the Natya-shastra (a seminal text on aesthetics and performing arts) and the Tantrasamuccaya (a text on temple architecture). The seed (bija) is often used to symbolize the beginnings. The tree (vriksha) rises from the bija and represents the vertical pole uniting the realms. The nabhi (navel) or the garbha (womb) brings together the concepts of the un-manifest (avyakta) and the manifest (vyakta). The bindu (point or dot) is the reference point or metaphorical centre around which are drawn geometrical shapes, which in turn facilitate the comprehension of notions of time and space. The sunya (void) is a symbol of fullness and emptiness. From its arupa nature (formless) arises the rupa nature (form) and the parirupa (beyond form). There is equivalence in the relationship between sunya (emptiness) and purna (completeness or wholeness), the paradox being that the void has within it the whole. [iii]

In Hinduism, the concept of unity-in-diversity can also be understood as a manifestation of Brahman, an agency that penetrates, pervades and harmonizes the entire universe. Brahman enters and shapes the mould of every entity giving it form, substance and individuality. It is only human pre-conditioning that causes us to visualize the multiplicity of forms as separate entities, and hence the world appears to be full of contradictions. The Brhadaranyaka Upanishad says:

Brahman is responsible for the interconnectedness of things and has become the living and the non-living; the visible and the invisible; the creatures which are two-footed and those that are four-footed. He became the subtle body and then the gross body by means of a subtle instrument known as the subtle body. This very Being became the vital consciousness of all. This is known as the Madhu¬Vidya, the sense of the ‘honey’ of all beings, the knowledge of the inter-dependence of things and the vital connection of everything, under every condition, at every time, everywhere.  [iv]

Hinduism devotes much thought to exploring the relationships between the jewels of Indra’s Net, and how they are manifestations and reflections of each other. Hindu thought is distinct from Abrahamic religions, which are premised on the existence of one separate God, one absolute event in history, and one inviolable set of injunctions. Hindus, for better or for worse, tend to be natural de-centralists. This is why it is hard to understand Hinduism, and difficult to organize and mobilize Hindus under an overarching corporate institution. It is also why Hinduism has proved, thus far, difficult to destroy. This idea can be referred as ‘integral unity’. The integral unity of the whole manifests itself in the parts, and they, in turn, aspire to unite with the whole; this principle is reflected in every domain of dharmic knowledge, including philosophy, science, religion, ethics, spirituality, art, music, dance, education, literature, oral narratives, politics, marriage rituals, economics, and social structures. Each domain of dharmic knowledge is itself a jewel in Indra’s Net, and reflects all the others. In other words, the same underlying principles are represented in these specialties in different ways.

For example, Hindu dance is not merely an isolated form of cultural expression but a complete and rigorous discipline through which one may learn and experience philosophy. This quality of correspondences across many domains of knowledge is striking. Music and sacred dance have a formal grammar based on Hindu cosmology. The Sanskrit Natya-shastra, a seminal text on performing arts and aesthetics, treats natya as a total art form; its scope includes: representation, poetry, dance, music, make-up, indeed every aspect of life. The Natya-shastra presents an integral view encompassing the Vedic rituals, Shaivite dance and music, and the epics. The eight traditional rasas it describes (love, humour, heroism, wonder, anger, sorrow, disgust, and fear) mirror a complete experience of the real world like the jewels of Indra’s Net, and together facilitate a practitioner’s pursuit of the purusharthas(human goals).

Some other examples across various domains are as follows:

  • The Vedic ritual altar is a representation of the entire cosmos.
  • The architecture of Hindu temples is based on physical dimensions which correspond to various astronomical metrics.
  • The yantra, an important device of sacred geometry, represents the whole universe.
  • Any deity can be conceived of in multiple ways: as a personal manifestation of the divine, as a metaphor for certain cosmic qualities and powers, and as an amalgamation of qualities and energies to be invoked and established in a person through ritual, meditation and yoga. Based on individual preferences, a deity can be approached as another entity in the mode of devotion, or as an object of meditation, or as a means for self-realization within oneself.
  • In Ayurvedic diagnosis, a correspondence is posited between specific points on the tongue and all parts of the entire body; thus, an expert in this field examines the tongue as a means of analysing the patient’s overall condition. The tongue is thus a jewel in which the entire physical and psychic body is reflected. The core principle of integral unity is encoded in the symbolism of Indian art, architecture, literature, ritual, mythology, festivals, and customs, all of which are intended to facilitate access to higher knowledge that goes beyond the conventional scope of any specific domain. Integration between disciplines is built-in and no effort is needed to create unity by bringing separate parts together. Even when certain disciplines and practices were destroyed, other disciplines encoding the same principles survived and helped preserve and re-ignite the overall tradition.

Dharmic cosmology is governed by bandhu interconnections among the astronomical, terrestrial, physiological, and spiritual realms; and each of these realms is itself connected, in the broadest sense, with the arts, healing systems, and culture. As discussed previously, bandhu describes a correspondence between the whole universe and the individual consciousness, which can be explored and developed from many alternative starting points. Thus, dharmic traditions have a common current that impels the individual along a natural quest to discover the reality beneath the appearances and to appreciate relationships among seemingly unrelated phenomena.

Dharmic traditions consider the common experience of reality as merely the transient reflection of a system in flux, interconnected with other realities across the past, present and future. In this flux, which affects all phenomena, repeating patterns may appear as static and independent ‘objects’, but this perception is just an illusory artifact of the limited mind. The individual person, of course, is himself a part of this flux. With the aid of meditation, he is able to witness reality as a detached observer—to see the personal ego, and indeed all fixed objects, as mere reflections of a moment in the flux.

Indra’s Net and Buddhism

Important Buddhist texts use Indra’s Net to describe an infinite universe with no beginning or end, in which every element is mutually related to every other element. Indra’s Net is a quintessential metaphor for Buddhist philosophy, describing how everything exists only in mutual causation with everything else, and nothing can be isolated.

The Avatamsaka Sutra (which means ‘Flower Garland’) of Mahayana Buddhism uses the metaphor of Indra’s Net to explain cosmic interpenetration. This sutra explains everything as both a mirror reflecting all and an image reflected by all. Everything is simultaneously cause and effect, support and supported. This important sutra was translated from Sanskrit, and its logic further developed in China under the name of Hua-yen Buddhism.

The Hua-yen tradition was developed by a series of thinkers, most notably Fa-tsang (cE 643-712). Through him, it passed on to Korea and other East Asian countries, becoming known as ‘Kegon’ in Japan. Hua-yen is praised as the highest development of Chinese Buddhist thought. D.T. Suzuki called Hua-yen the philosophy of Zen, and Zen the meditation practice of Hua-yen. Francis Cook explains the core philosophy of Hua-yen as follows:

Far away in the heavenly abode of the great god Indra, there is a wonderful net that has been hung by some cunning artificer in such a manner that it stretches out infinitely in all directions. In accordance with the extravagant tastes of deities, the artificer has hung a single glittering jewel in each ‘eye’ of the net, and since the net itself is infinite in all dimensions, the jewels are infinite in number. There hang the jewels, glittering like stars of the first magnitude, a wonderful sight to behold. If we now arbitrarily select one of these jewels for inspection and look closely at it, we will discover that in its polished surface there are reflected all the other jewels in the net, infinite in number. Not only that, but each of the jewels reflected in this one jewel is also reflecting all the other jewels, so that there is an infinite reflecting process occurring. [v]

Cook goes on to explain that Indra’s Net ‘symbolizes a cosmos in which there is an infinitely repeated interrelationship among all the members of the cosmos’. He adds that ‘the cosmos is, in short, a self-creating, self-maintaining, and self-defining organism’. Furthermore, there is no theory of a beginning time, and such a universe has no hierarchy. ‘There is no center, or, perhaps if there is one, it is everywhere.’

Hua-yen is built on the primary concern of Indian thought which is about the nature of causation. This is evident in the Sanskrit name for Hua-yen, ‘dharmadhatu pratityasamutpada’ (the interdependent co-arising which is the universe). Key principles of Madhyamika Buddhism, regarding non-substantiality and non-origination, have exact equivalents in Hua-yen. The Avatamsaka philosophy emphasizes the illusory nature of things when they are seen separately. [vi]

David Loy, a Buddhist practitioner and scholar who has spent most of his life in Kyoto, uses the analog of lila (play) to refer to the Buddhist ideal of life. While the ordinary ego is a player struggling, out of anxiety, to ground itself in the net, the liberated player has realized that he is the net. There is no separate ‘me’ to possess anything, nor any separate thing to be possessed. He explains:

Life becomes play; … the issue is whether we suffer our games because they are the means whereby we hope to ground ourselves somewhere in Indra’s Net, or whether we dance freely within the Net because we are it. The dangers of relativism in ethics are vitiated to the extent I realize my interdependence with other beings: I shall indeed love my neighbour as myself when I experience that I am my neighbor.  [vii]

It is interesting to note that over a period of many centuries Buddhist thinkers across East Asia have meticulously preserved the Sanskrit terms originally used to define Buddhist ideas, and fully credited Indian sources. Recently, however, as Buddhist ideas have travelled to the West and spread across many disciplines, the tendency has been to disconnect Hinduism from these ideas. Thankfully, the term ‘Indra’s Net’ has been preserved, and this allows scholars like myself to retrace the Vedic origins of these widely popular ideas.

Influences on modern society

Indra’s Net has inspired thinkers and movements in the West ranging from philosophy to ecology. David Loy has described how the major milestones of Western post-modernist thought resemble the ideas inherent in Indra’s Net. He cites Sigmund Freud’s approach in psychology, Ferdinand Saussure’s work in linguistics, Roland Barthes’s ideas in literary theory, and Jacques Derrida’s approaches to deconstruction as examples of twentieth-century pioneers who have utilized the ideas of Indra’s Net (mostly without explicit acknowledgement). The result of this has been nothing short of a revolution in Western philosophy, shaking the age-old Western premise that entities have separate, absolute, independent existences. Deconstructing the self-existence of things is the very signature principle of post-modern thought, and is a subset of the philosophical ideas contained in Indra’s Net. [viii]

Gregory Fahy has examined John Dewey’s idea of local, contextual and relational metaphysics as a subset of the Hua-yen thinking of Indra’s Net. [ix] Mathematicians studying chaos theory and fractals have described the beauty of structures as ‘Indra’s net’, ‘Indra’s necklace’ and ‘Indra’s pearls’. [x] In physics, the notion of quantum entanglement is a special case of the kind of interconnectivity we are describing. It is not at all surprising that Indra’s Net has been used as a metaphor to explain holograms, wherein, by definition, each part also includes the whole within itself. Indra’s Net has also been cited as the metaphor for the internet.

In the field of environmentalism, Leslie Paul Thiele has explained that Indra’s Net represents the Sanskrit concept of prajna (the wisdom of the interdependency of things), with the key implication that causes and effects are inseparable. He mentions that the word ‘ecology’ was coined in 1873 to mean the interactive relations between plants and animals, and that its meaning has recently expanded to include all of nature’s interrelationships in a wider sense. Sustainability is inherently a matter of interdependence, so the applicability of these ideas to the modern ecology movement is obvious. [xi] Indra’s Net, of course, embodies a far wider scope than just the material aspects of nature.

The basic principle is that each individual is both the cause for the whole and is caused by the whole. Ecological interdependence implies that if any one part of a system is disturbed, the whole system is affected. In this regard, Francis Cook has described Indra’s Net as a kind of ‘cosmic ecology’. [xii] Unlike in Western (disembodied) philosophy, nature is not seen as a backdrop for human existence; rather, humans are seen as inseparable from nature. A special issue of the journal Philosophy East and West was devoted to the applications of Indra’s Net to the field of environmental ethics. [xiii]

Another example of contemporary applications is an NGO called Indra’s Net Community, a South Korean movement that addresses concerns in the daily lives of lay people. Inspired by the interdependency principle of Indra’s Net, it was started by a group of visionary monks. They established grassroots communities to promote an alternative lifestyle in response to contemporary society’s emphasis on mass consumption, commercialism, competition, and the exploitation of natural resources. [xiv]


[i] The mantra is: ‘brihaddhi jaalam brihatah shakrasya vaajinivatah’ (8.8.6). ‘Ayam loko jaalamaasit shakrasya mahato mahaan’ (8.8.8).

[ii] However, from the viewpoint within the provisional reality, all jewels are not the same. We must note the Buddhist (and Vedantin) notion of two truths, phenomenal and absolute. There is spiritual progress only from a phenomenal point of view.

[iii] Vatsyayan, 1997.

[iv] Brhadaranyaka Upanishad (2:5.17-18) http://www.swami-krishnananda. org/brdup/brhad_II-05.html

[v] Cook, 1977, p. 2.

[vi] In early Pali texts, there is the notion of ‘paticca samuppada’ (dependent, co-arising or interconnected origination). Nagarjuna established one of the central principles that there are no isolated entities bearing essential natures or existing as themselves. This is referred to as things being empty of their own separate distinct existence, i.e., not having any ultimate sva-bhava or self-nature. This developed into the Avatamsaka tradition’s idea of sunyata along with interdependence comprised all reality. One of the famous chapters of the Avatamsaka Sutra includes the following explanation of interpenetration: ‘All the lion’s organs, the tip of every hair, being of gold, include the whole lion. Each of them permeates the whole lion; the eyes are the ears, the ears are the nose, the nose is the tongue and the tongue is the body. They come into being freely, without difficulty, without impediment.’ Here the gold symbolizes the substance and the lion symbolizes the form.

[vii] Loy, 1993, p. 484.

[viii] Loy, 1993.

[ix] Fahy, 2012.

[x] See, for example, Mumford, 2002 and Debnath, 2006. The metaphor has also been applied to new ideas proposed in library science (Bair-Mundy, 1998).

[xi] Thiele, 2011.

[xii] Cook, 1977.

[xiii] Philosophy East and West, vol. 37, no. 2, April 1987.

[xiv] Park, 2010. Indra’s Net has also been cited by activists who argue against climate change and other environmental concerns (Tam, 2008). There are also co-dependency arguments for helping salmon survive (Allendorf, 1998).



Please see my related posts:

The Great Chain of Being

On Holons and Holarchy

Consciousness of Cosmos: A Fractal, Recursive, Holographic Universe

Reflexivity, Recursion, and Self Reference

Geometry of Consciousness

Mind, Consciousness and Quantum Entanglement

Systems View of Life: A Synthesis by Fritjof Capra

Shape of the Universe



Key Sources of Research:

The Indra’s Net



Indra’s Net




Noneuclidean Symmetry and Indra’s Pearls

Caroline Series

David Wright


Click to access bridges2006-25.pdf


The Vedic metaphor of Indra’s Net





David Mumford, Caroline Series and David Wright


Click to access 9780521352536_frontmatter.pdf



Caroline Mary Series: Pearl of Hyperbolic Manifolds


Click to access NUS2013.pdf




Benoit B. Mandelbrot



Click to access mandelbrot-benoit.pdf




Hyperbolic Geometry & Kleinian Groups


Click to access greg-jackson-thirdyear-project.pdf



Nature and Psyche in an Interconnected Universe

Joseph Cambray

TexasA&M University Press 2009


Click to access Cambray-synchronicity-ed..pdf



Poincare and his disk

Etienne Ghys


Click to access Poincarediskenglish.pdf



Iteration and its Consequences
Indra’s Pearls: The Vision of Felix Klein.

By David Mumford, Caroline Series, and David Wright,

Cambridge University Press,

New York, 2002,


Click to access 468.pdf



Indra’s Pearls:  Geometry and Symmetry

Caroline Series

University of Cambridge

This is the 2010 joint London Mathematical Society / Gresham College lecture.


Shape of the Universe

Shape of the Universe



From The Status of Cosmic Topology after Planck Data

In the last decade, the study of the overall shape of the universe, called Cosmic Topology, has become testable by astronomical observations, especially the data from the Cosmic Microwave Background (hereafter CMB) obtained by WMAP and Planck telescopes. Cosmic Topology involves both global topological features and more local geometrical properties such as curvature. It deals with questions such as whether space is finite or infinite, simply connected or multi connected, and smaller or greater than its observable counterpart. A striking feature of some relativistic, multi ­connected small universe models is to create multiples images of faraway cosmic sources. While the last CMB (Planck) data fit well the simplest model of a zero curvature, infinite space model, they remain consistent with more complex shapes such as the spherical Poincaré Dodecahedral Space, the flat hypertorus or the hyperbolic Picard horn.

From The Status of Cosmic Topology after Planck Data

The overall topology of the universe has become an important concern in astronomy and cosmology. Even if particularly simple and elegant models such as the PDS and the hypertorus are now claimed to be ruled out at a subhorizon scale, many more complex models of multi-­connected space cannot be eliminated as such. In addition, even if the size of a multi-­connected space is larger (but not too much) than that of the observable universe, we could still discover an imprint in the CMB, even while no pair of circles, much less ghost galaxy images, would remain. The topology of the universe could therefore provide information on what happens outside of the cosmological horizon [35].

Whatever the observational constraints, a lot of unsolved theoretical questions remain. The most fundamental one is the expected link between the present-day topology of space and its quantum origin, since classical general relativity does not allow for topological changes during the course of cosmic evolution. Theories of quantum gravity should allow us to address the problem of a quantum origin of space topology. For instance, in quantum cosmology, the question of the topology of the universe is completely natural. Quantum cosmologists seek to understand the quantum mechanism whereby our universe (as well as other ones in the framework of multiverse theories) came into being, endowed with a given geometrical and topological structure. We do not yet have a correct quantum theory of gravity, but there is no sign that such a theory would a priori demand that the universe have a trivial topology. Wheeler first suggested that the topology of space-­time might fluctuate at a quantum level, leading to the notion of a space-­time foam [36]. Additionally, some simplified solutions of the Wheeler-­‐‑de Witt equations for quantum cosmology show that the sum over all topologies involved in the calculation of the wavefunction of the universe is dominated by spaces with small volumes and multi-­connected topologies [37]. In the approach of brane worlds in string/M-­theories, the extra-­dimensions are often assumed to form a compact Calabi-­Yau manifold; in such a case, it would be strange that only the ordinary, large dimensions of our 3-­brane would not be compact like the extra ones. However, still at an early stage of development, string quantum cosmology can only provide heuristic indications on the way multi-­connected spaces would be favored.



Key People:

  • Jeffrey Weeks
  • Jean-Pierre Luminet
  • Neil Cornish


Key Sources of Research:


The Poincaré Dodecahedral Space and the Mystery of the Missing Fluctuations

Jeffrey Weeks


Click to access fea-weeks.pdf


Dodecahedral space topology as anexplanation for weak wide-angletemperature correlations in thecosmic microwave background

Jean-Pierre Luminet, Jeffrey R. Weeks, Alain Riazuelo ,Roland Lehoucq & Jean-Philippe Uzan

Click to access luminet-nat.pdf


A cosmic hall of mirrors


Jean-Pierre Luminet

Click to access 0509171.pdf



The Shape and Topology of the Universe

Jean-Pierre Luminet



Click to access 0802.2236.pdf


Luminet, Jean-Pierre.

The wraparound universe.

CRC Press, 2008.


Cosmic Topology : Twenty Years After

Jean-Pierre Luminet



Click to access 1310.1245.pdf


The Shape of Space after WMAP data

Jean-Pierre Luminet


Click to access v36_107.pdf



The Status of Cosmic Topology after Planck Data

Jean-Pierre Luminet

Click to access 1601.03884v2.pdf



Geometry and Topology in Relativistic Cosmology

Jean-Pierre Luminet


Click to access 0704.3374.pdf



Constraints on the Topology of the Universe: Extension to General Geometries

Pascal M. Vaudrevange,  Glenn D. Starkman, Neil J. Cornish, and David N. Spergel


Click to access 1206.2939.pdf



Topology of compact space forms from Platonic solids. I.

A. Cavicchioli∗, F. Spaggiari, A.I. Telloni


Topology of compact space forms from Platonic solids. II

A. Cavicchioli∗, F. Spaggiari, A.I. Telloni


Ancient Map of Universe and Modern Science

Jeoraj Jain


Discovering the Total Contents of the Universe

Jeoraj Jain


Poundstone, William.

The recursive universe: cosmic complexity and the limits of scientific knowledge.

Courier Corporation, 2013.