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
  • PLANCK
  • 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

Source: A COSMIC HALL OF MIRRORS

Cosmic Microwave Background from different probes

Source: Pintrest/478366791654117997/

Source: MAKING SENSE OF THE BIG BANG: WILKINSON MICROWAVE ANISOTROPY PROBE

Source: MAKING SENSE OF THE BIG BANG: WILKINSON MICROWAVE ANISOTROPY PROBE

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

Source: WHAT IF THE UNIVERSE HAS NO END?

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

ngc6240

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.”

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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)

https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.121.251301

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.251301

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

By Rafi Letzter – Staff Writer June 22, 2020

https://www.livescience.com/truth-behind-nasa-mirror-parallel-universe.html

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

2014

Mirror dark matter cosmology and structure formation

Roux, Jean-Samuel

PhD Thesis McGill Univ

https://escholarship.mcgill.ca/concern/theses/8623j3647

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

https://astronomy.com/news/2019/06/white-holes-do-black-holes-have-mirror-images

A cosmic hall of mirrors

Jean-Pierre Luminet
Laboratoire Univers et Théories (LUTH) – CNRS UMR Observatoire de Paris, 92195 Meudon (France) Jean-pierre.luminet@obspm.fr

The fractal universe

SEPTEMBER 12, 2018

Love the Reflections in the Cosmic Mirror

https://www.3ho.org/love-reflections-cosmic-mirror

The Shape of the Universe: Ten Possibilities

Is the universe a dodecahedron?

PLANCK IMAGE GALLERY

https://www.cosmos.esa.int/web/planck/picture-gallery

http://pla.esac.esa.int/pla/#home

Planck and the cosmic microwave background

https://www.esa.int/Science_Exploration/Space_Science/Planck/Planck_and_the_cosmic_microwave_background

The Atacama Cosmology Telescope ACT

https://act.princeton.edu/publications

Wilkinson Microwave Anisotropy Probe WMAP

https://map.gsfc.nasa.gov

Cosmic Topology : Twenty Years After

Jean-Pierre Luminet,

Laboratoire Univers et Th ́eories Observatoire de Paris-CNRS-Universit ́e Paris Diderot (France) email : jean-pierre.luminet@obspm.fr

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)

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.69.103518

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.

2005

Click to access a02v361b.pdf

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

https://pubmed.ncbi.nlm.nih.gov/14534579/

https://www.nature.com/articles/nature01944

Geometry and Topology in Relativistic Cosmology

Jean-Pierre Luminet

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

2007

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

1996

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

https://www.mdpi.com/2218-1997/2/1/1

https://hal.archives-ouvertes.fr/hal-01291848/document

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

2006

Jean-Pierre Luminet

The Shape of Space from Einstein to WMAP data

AIP Conference Proceedings 841, 115 (2006); https://doi.org/10.1063/1.2218171

Jean‐Pierre Luminet

https://aip.scitation.org/doi/abs/10.1063/1.2218171

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

The Shape and Topology of the Universe

Jean-Pierre Luminet

2008

Signature of topology of the Universe

Vipin Kumar Sharma

University of Lucknow

2018

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.

1998

The Conformal Singularity as a Cosmological Mirror: Classical Theory

DOI: 10.1080/21672857.2013.11519718

Michael Ibison

https://www.researchgate.net/publication/284231928_The_Conformal_Singularity_as_a_Cosmological_Mirror_Classical_Theory

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

https://www.sciencedirect.com/science/article/pii/S0370269309008892

Making Sense of the Big Bang: Wilkinson Microwave Anisotropy Probe

2016

https://www.nasa.gov/feature/making-sense-of-the-big-bang-wilkinson-microwave-anisotropy-probe

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

https://arxiv.org/abs/1807.06205

24. Cosmological Parameters

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

https://www.quantamagazine.org/what-shape-is-the-universe-closed-or-flat-20191104/

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

https://iopscience.iop.org/article/10.1088/1475-7516/2020/12/045/pdf

Mapping the Universe

Mark Altaweel | February 18, 2020 | Spatial Analysis

https://www.gislounge.com/mapping-the-universe/

Planck and the cosmic microwave background

https://www.esa.int/Science_Exploration/Space_Science/Planck/Planck_and_the_cosmic_microwave_background

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

https://www.newscientist.com/article/2222159-cosmological-crisis-we-dont-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

https://astronomy.com/news/2021/02/what-shape-is-the-universe

Is the Universe Curved? Not So Fast

By Paul Sutter December 02, 2019

https://www.space.com/universe-shape-flat-closed-debate.html

Planck reveals an almost perfect Universe

https://www.esa.int/Science_Exploration/Space_Science/Planck/Planck_reveals_an_almost_perfect_Universe

2.4. The Cosmic Microwave Background

https://ned.ipac.caltech.edu/level5/March03/Freedman/Freedman2_4.html

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

https://astronomy.com/magazine/2018/07/decoding-the-cosmic-microwave-background

The Universe Might Be a Giant Loop

By Rafi Letzter – Staff Writer November 04, 2019

https://www.livescience.com/universe-may-be-curved.html

Is the universe a dodecahedron?

08 Oct 2003 Isabelle Dumé

Geometry of the Universe :

http://abyss.uoregon.edu/~js/cosmo/lectures/lec15.html

Cosmological Constraints on Mirror Matter Parameters 

Paolo Ciarcelluti1 and Quentin Wallemacq

2014

https://www.hindawi.com/journals/ahep/2014/148319/

What It Means to Live in a Holographic Universe

POSTED BY BRIAN KOBERLEIN ON MAY 07, 2014

https://nautil.us/blog/what-it-means-to-live-in-a-holographic-universe

Our Universe May Be a Giant Hologram

https://www.discovermagazine.com/technology/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

https://link.springer.com/chapter/10.1007/978-1-4899-3332-4_8

What if the Universe has no end?

https://www.bbc.com/future/article/20200117-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

https://www.newscientist.com/article/mg24232330-200-weve-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: https://www.newscientist.com/article/mg24933240-900-did-time-flow-in-two-directions-from-the-big-bang-making-two-futures/#ixzz6oN4RV5dL

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

https://arxiv.org/abs/1912.08264

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

https://www.researchgate.net/publication/320180295_New_Search_for_Mirror_Neutrons_at_HFIR

Radiation as Self-Action via a Cosmological Mirror

Michael Ibison

09 Nov 2015


Astronomical Review 
Volume 7, 2012 – Issue 3

https://www.tandfonline.com/doi/abs/10.1080/21672857.2012.11519706

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

Nature’s Fantastical Palette: Color From Structure

Nature’s Fantastical Palette: Color From Structure

Peacock Feathers

Source: STRUCTURAL COLORATION IN NATURE

Key Terms

  • Iridescence
  • Nanostructures
  • Color from Pigments
  • Color from Structures
  • Smart Pigments
  • Material Science
  • Color from Bioluminescence
  • Color Change
  • Photonics
  • Biomimicry
  • Non Iridescent Colors
  • Iridescent Colors
  • Photonic Crystals (PhC)
  • Diffraction Grating
  • Specular Reflection
  • Braggs Diffraction
  • 1D Grating
  • 2D and 3D Photonic Crystals
  • Optical Nanotechnology
  • Multilayer Filters
  • Biomimetics
  • Peacock
  • Morpho Butterflies
  • Interference
  • Colloidal Crystals
  • Colloidal Amorphous Array
  • Microfluidics
  • Photonic Pigments
  • Reflective Displays (E-Ink)
  • Colloidal Assembly
  • Photonic Glass (PG)
  • Plasmonic Films
  • Inverse-Opals
  • Braggs Stacks
  • Dielectric Structural Colors
  • Plasmonic Structural Colors
  • Amorphous Photonic Structures
  • Melanin
  • Dopamine
  • Poly Dopamine
  • Plasmonic Metasurfaces

Source: GOLD BUGS AND BEYOND: A REVIEW OF IRIDESCENCE AND STRUCTURAL COLOUR MECHANISMS IN BEETLES (COLEOPTERA)

Source: GOLD BUGS AND BEYOND: A REVIEW OF IRIDESCENCE AND STRUCTURAL COLOUR MECHANISMS IN BEETLES (COLEOPTERA)

Source: Structural color and its interaction with other color-producing elements: perspectives from spiders

Color Vision

Source: Structural Color and Odors: Towards a Photonic Crystal Nose Platform

Color Sources

  • From Pigments
  • From Bioluminescenece
  • From Structure

Source: Chromic Phenomena: Technological Applications of Colour Chemistry

Source: Chromic Phenomena: Technological Applications of Colour Chemistry

Structural Color in Nature

  • Peacock
  • Butterflies
  • Beetles
  • Parrots
  • Birds
  • Moth

Peacock Colors

Feathers of Peacock

Source: Structural colors: from natural to artificial systems

Colors of Marpho Butterfly

Closeup of Marpho Butterfly

Structure and Color

  • Iridescent – (Colloidal Crystals)- Angle Dependent – Regular Structure
  • Non Iridescent – (Colloidal Amorphous Arrays) – Angle Independent – Irregular Structure

Optics of Structural Colors

  • Interference
  • Diffraction Gratings
  • Scattering
  • Reflection

Nano Structures Responsible for Colors

Source: Structural color and its interaction with other color-producing elements: perspectives from spiders

  • Christmas Tree
  • Multilayer – 1 D Periodicity
  • Photonic Crystals – 2 D and 3 D
  • Diffraction Grating
  • Quasi Ordered Photonic Crystal
  • Disorder Structure

Source: BIO-INSPIRED VARIABLE STRUCTURAL COLOR MATERIALS

  • 1 D Gratings
  • 1 D Periodicity Multilayers
  • 1 D Discrete Periodicity
  • 2 D Gratings
  • 2 D Periodicity
  • Closed Packed Spheres of Solid Materials
  • Inverse Opal Analogoues

Source: STRUCTURAL COLORATION IN NATURE

  • Thin Film Interference
  • Multi Film Interference
  • Diffraction Gratings
  • Coherent Scattering
  • Incoherent Scattering
  • 1 D Photonic Crystals
  • 2 D Photonic Crystals
  • 3 D Photonic Crystals

Source: Structural Color and Odors: Towards a Photonic Crystal Nose Platform

Source: PHYSICS OF STRUCTURAL COLORS

Source: PHOTOPHYSICS OF STRUCTURAL COLOR IN THE MORPHO BUTTERFLIES

Source: Gold bugs and beyond: a review of iridescence and structural colour mechanisms in beetles (Coleoptera)

  • Cuticular Multilayer Reflector
  • Epicuticular Reflector
  • Exocuticular Reflector
  • Endocuticular Reflector

Source: Gold bugs and beyond: a review of iridescence and structural colour mechanisms in beetles (Coleoptera)

  • Multilayer Reflectors
  • Diffraction Gratings
  • 3 D Photonic Crystals

Multilayer reflectors in beetles have also been described as ‘thin-layer stacks’, ‘one-dimensional photonic crystals’ and ‘thin-film reflectors’ (e.g. Parker 1998, 2002; Vigneron et al. 2006). The vocabulary used to describe these structures is somewhat dispersive, as the variously intersecting disciplines of entomology, physics and applied optics (e.g. laser technology, fibre-optic data transmission, telescopes and microscopy) have all developed slightly different suites of terminology. Other synonyms for ‘multilayer reflector’ include multilayer stack, quarter wave stack, interference reflector and dielectric mirror.

We propose that the term multilayer reflector be applied to such structures in Coleoptera; this describes the multilayered nature of cuticular chitin lamellae (which are not true films) and the reflective mechanism by which colour is produced.

The terms ‘metallic colours’ or ‘metallic iridescence’ can be used to distinguish multilayer effects from those produced by other optical structures. Multilayer reflectance can typically be diagnosed as such by its limited palette (usually one or two apparent hues per reflector), blue shift with decreased observation angle and fixed position on the cuticle surface.

Source: Gold bugs and beyond: a review of iridescence and structural colour mechanisms in beetles (Coleoptera)

Three-dimensional crystalline structures producing scintillating, gem-like reflectance were described by Parker et al. (2003) in the entimine weevil Metapocyrtus sp. (initially misidentified as Pachyrrhynchus argus); by Welch et al. (2007) in Pachyrrhynchus congestus, and recently in another entimine weevil, Lamprocyphus augustus, by Galusha et al. (2008). The photonic crystals found in the scales of pachyrrhynchine weevils (Pachyrrhynchus and Metapocyrtus) have a close-packed hexagonal arrangement analogous to (mineral) opal, while the photonic crystal of Lamprocyphus has a diamond-based lattice (i.e. a face-centred cubic system rather than a hexagonal one).

Although the term ‘photonic crystal’ applies to any ordered subwavelength structure that affects the propagation of specific wavelengths of light (Parker & Townley 2007), it is the three-dimensionally ordered structures to which the term is most commonly applied. We recommend use of the term ‘three-dimensional photonic crystal’, which distinguishes these structures from the one-dimensional periodicity of multilayer reflectors or Bragg gratings. The terms ‘opal’ and ‘diamond based’ have been used to describe iridescence in weevil scales, but refer to phenomena that are relatively similar from an organismal perspective; it is important to note that these terms refer to crystalline lattice morphology and not the appearance of the scales themselves. Maldovan & Thomas (2004) provided an excellent overview of diamond-based lattice morphology (as observed in Lamprocyphus) in photonic crystals; Yablonovitch (1993) provided a thorough introduction to the photonic band-gap mechanism by which colours are produced in three-dimensional photonic crystals.

Source: Gold bugs and beyond: a review of iridescence and structural colour mechanisms in beetles (Coleoptera)

A diffraction grating is any nanoscale array of parallel ridges or slits that disperses white light into its constituent wavelengths (figure 8a shows a grating in cross section). Because white light consists of many different wavelengths, it diffracts into full spectra, creating the rainbow-like reflectance shown in figures 1a,b, 8c and 9b,d. While man-made diffraction gratings can disperse light via reflection or transmission, all beetle gratings are strictly reflection mechanisms.

Source: Gold bugs and beyond: a review of iridescence and structural colour mechanisms in beetles (Coleoptera)

http://photobiology.info/Ball.html

Nature’s Fantastical Palette: Color from Structure

Philip Ball
18 Hillcourt Road
East Dulwich
London SE22 0PE, UK
p.ball@btinternet.com

The changing hues of a peacock’s splendid tail feathers have always captivated the curious mind (Figure 1). The seventeenth-century English scientist Robert Hooke called them ‘fantastical’ because the colors could be made to disappear by wetting the feathers (Hooke, 1665). Using the newly invented microscope, Hooke looked at peacock feathers and saw that they were covered with tiny ridges, which he figured might be the origin of the colors. 

Figure 1

Figure 1. The shifting colors of the peacock’s tail have had metaphorical interpretations for centuries.

Hooke was on the right track. The bright, often iridescent colors of bird plumage, insect cuticle and butterfly wings are ‘structural’; produced not by light absorption by pigments, but light scattering from a regular array of objects just a few hundreds of nanometers (millionths of a millimeter) in size (Vukusic & Sambles, 2003; Vukusic, 2004; Wolpert, 2009). This scattering favors particular wavelengths depending on the size and spacing of the scatterers, and so it picks out specific colors from the full spectrum of sunlight. Because the precise hue may depend also on the viewing angle, structural colors are often iridescent, changing from blue to green or orange to yellow. And because they involve reflection rather than absorption, these colors can be startlingly brilliant. The Blue Morpho butterflies of South and Central America are visible from a quarter of a mile away, seeming almost to shine when sunlight penetrates the tropical forest canopy and bounces off their wings. 

Structural colors are just one example of how living organisms manipulate and channel light using delicately arranged micro- and nanostructures. These biological designs offer inspiration to engineers seeking to control light in optical technologies, and could lead to more brilliant visual displays, new chemical sensors, and better storage, transmission and processing of information. To make effective use of such tricks, we need to understand how nature creates and deploys these tiny optical structures; indeed, we must learn a new language of color production and mixing. 

Rather little is known about how many of these biological structures are put together, how they evolved, and how evolution has made creative use of the color and light effects they offer. But one thing is clear; nature doesn’t have the sophisticated patterning technologies, such as drilling with electron beams, that microengineers can use to laboriously carve such structures from solid blocks. Ingenuity is used instead of finesse; these biological structures must make themselves from the component parts. 

If we can master that art, we might develop new, cheap technologies to make such things as materials that change color or appearance, like the camouflage skins of some fish and squid, or fibres that guide and channel light with virtually no leakage, or chemically controlled light shutters. Here I look at some of nature’s tricks for turning structure into color; and the ways they are being exploited in artificial materials and devices (Ball, 2012). 

Layers

Although the ridges seen by Hooke on butterfly wing scales do scatter light, the bright colors of the reflected light generally come from invisible structures beneath the surface. In the natural world, they offer a robust way of generating color that is not hostage to the fate of delicate, light-sensitive organic pigments. 

The colored scales and feathers of birds, fish and butterflies typically contain organized microscopic layers or rods of a dense light-scattering material embedded in a matrix of a different substance. Because the distance between the scatterers is roughly the same as the wavelengths of visible light, the stacks cause the wave phenomenon of diffraction, in which reflected waves interfere with one another. Depending on the angle of reflection, light rays of a certain wavelength interfere constructively when they bounce off successive layers in the stack, boosting the corresponding color in the reflected light (Vukusic and Sambles, 2003; Vukusic, 2004; Wolpert, 2009). It is much the same process that elicits the chromatic spectrum in light glancing off a tilted CD. 

In butterfly wing scales the reflecting stacks are made of cuticle; a hard material containing the natural polymer chitin, separated by air-filled voids. In bird feathers, the stacks are platelets or rods of the dark pigment melanin; sometimes hollow, as in the Black Inca hummingbird, Coeligena prunellei, embedded in keratin, the protein from which our hair and fingernails are made (Figure 2). Analogous diffraction gratings made from alternating ultrathin layers of two materials are widely used in optical technologies to select and reflect light of a single color. For example, mirrors made from multiple layers of semiconductors are used as reflectors and color filters in devices ranging from astronomical telescopes to solid-state lasers and spectrometers. 

Figure 2

Figure 2. The iridescent blues and greens in the feathers of hummingbirds such as this Black Inca (left; part of blue iridescence highlighted with white box) are created by platelets of melanin pigment punctuated with air holes (right), which act as a photonic crystal to reflect light of a particular wavelength. K=keratin, A=air, M=melanin. (From Shawkey et al., 2009)

The male bird of paradise Lawes’ parotia (Parotia lawesii) has a particularly neat twist on this trick (Figure 3). The barbules (hair-like structures on the feather barbs) of its breast feathers contain layers of melanin spaced at a distance that creates bright orange-yellow reflection. But, as Stavenga and colleagues have recently discovered, each barbule has a V-shaped or boomerang cross-section, with sloping surfaces that also act as reflectors of blue light (Stavenga et al., 2011). Slight movements of the feathers during the bird’s courtship ritual can switch the color abruptly between yellow-orange and blue-green; guaranteed to catch a female’s eye. Stavenga suspects that technologists will want to use this trick for producing dramatic chromatic shifts. “I suspect the fashion or automobile industries will in due time make bent structures or flakes that will exploit these angular color changes”, he says. 

Figure 3a
Figure 3b

Figure 3. A striking color change in the feathers of the male Lawes’ parotia, from yellow-orange (a) to blue-green (b), is caused by the presence of two mirror-like reflectors in the feather barbules (c): layers of melanin rods reflect yellow light, while the sloping faces of the boomerang-shaped barbule cross-section reflect blue at oblique angles. Scale bar in b: 1 cm. (From Stavenga et al., 2011)

Christmas Trees

The butterflies Morpho didius and Morpho rhetenor obtain their dazzling blue color not from simple multilayer’s but from more complex nanostructures in the wing scales: arrays of ornate chitin ‘Christmas Trees’ that sprout at the surface (Vukusic & Sambles, 2003) (Figure 4). Each ‘tree’ presents a stack of disk-like layers to the incoming light, which acts as another kind of diffraction grating. These arrays may reflect up to 80 percent of the incident blue light. And because they are not flat, they can reflect a single color over a range of viewing angles, somewhat reducing the iridescence; organisms don’t always want to change color or get dimmer when seen from different directions. 

Figure 4

Figure 4. The butterfly Morpho didius (left) obtains its dazzling blue color from delicate ‘Christmas Tree’ light-scattering structures (right), made from chitin, that sprout within the wing scales. (Left, courtesy of Peter Vukusic. Right (micrograph) from Vukusic and Sambles, 2003.)

The precise color reflected depends on the refractive index contrast between the nanostructures and the surrounding medium. This is usually air, but as Robert Hooke observed, wetting such surfaces alters the refractive index contrast, and changes the color in a way that is closely linked to the wetting liquid’s refractive index. For that reason, artificial Morpho-like structures carved into solids using microlithographic techniques are being developed by researchers at GE Global Research in New York, in collaboration with others at the State University of New York at Albany and butterfly-wing expert Pete Vukusic at the University of Exeter in England, as color-change chemical sensors that can identify a range of different liquids (Potyrailo, 2011). These might find applications for sensing emissions at power plants, monitoring of food safety, and testing of water purity. 

Reflecting Bowls

The bright green color of the Emerald Swallowtail butterfly (Papilio palinurus), found widely in southeast Asia, is not produced by green light at all. The wing scales are covered with a honeycomb array of tiny bowl-shaped depressions just a few micrometers across, lined with alternating layers of chitin cuticle and air which act as reflective mirrors. Light bouncing off the bottoms of the bowls is preferentially reflected in the yellow part of the spectrum. But from the sides it is reflected twice before bouncing back, and this selects blue. Our eyes can’t resolve these yellow spots and blue rings, which merge to create the perception of green (Vukusic & Sambles, 2003). 

Figure 5

Figure 5. The green of the Emerald Swallowtail butterfly (left) comes from the optical mixing of blue and yellow reflections from tiny bowl-like depressions in the wing scales (right). (Right figure, courtesy of Christopher Summers, Georgia Institute of Technology) 

This way of making color has been copied by Summers and coworkers (Crne et al., 2011). To create the tiny bowls, they let water vapour condense as microscopic droplets, called breath figures, on the surface of a polymer dissolved in a volatile solvent. The solvent gradually evaporates to form a solid polymer film, while the water droplets pack together on the surface of the drying solution much like greengrocers’ oranges and apples in crates, sinking into the setting film to imprint an array of holes. By pulling off the top part of the film, Summers and colleagues were left with a surface with hemispherical bowl-like dimples. They then used this structure as a template on which they deposited alternating thin layers of titania and alumina to make a multilayer reflector, like that lining the bowls of the butterfly wing scales (Figure 6). 

Figure 6

Figure 6. An artificial micro-structured surface that mimics the green color of the Emerald Swallowtail. Scale bar: 5 µm. (Courtesy of Christopher Summers, Georgia Institute of Technology)

Because each reflection changes the polarization of the light, under crossed polarizing filters the yellow light bouncing back from a single reflection at the bowl centers disappears, while the twice-reflected blue-green light from the rims remains. This could offer a distinctive authentification mark on bank and credit cards. Apparently just a simple green reflective coating, such a material would in fact carry a hidden polarized signature in the reflected blue and yellow light that would be hard to counterfeit. But Summers’ collaborator Mohan Srinivasarao admits that the main reason for seeking to replicate the butterfly’s green color was that “it’s beautiful in its own right”. 

Ordered Nanosponges

Scattering by regular arrays of microscopic objects can, for some arrangements, totally exclude light within a particular band of wavelengths, called the photonic band gap (Vukusic, 2004). These so-called photonic crystals occur naturally, for example, in opal, a biogenic form of silica in which the scatterers are tiny mineral spheres. Artificial photonic crystals can be used to confine light within narrow channels, creating waveguides that might be deployed to guide light around on silicon chips for optical information technology. 

Nature has already got there first. Under the electron microscope, the wing scales the Emerald Patched Cattleheart Butterfly (Parides sesostris) display zigzagging, herring-bone arrays: patches of an orderly sponge made from chitin with holes a hundred nanometers or so across. Each patch is a photonic crystal seen from a different alignment. Stavenga and Michielsen have found that these labyrinths in the wing-scales of P. sesostris and some species of papilionid and lycaenid butterflies have a structure known to mathematicians as a gyroid (Michielsen & Stavenga, 2008). In P. sesostris the structure has a photonic band gap that enables it to reflect light within the green part of the spectrum over a wide range of incident angles (Figure 7). Some weevils and other beetles also derive their iridescent color from three-dimensional photonic crystals made of chitin. 

Figure 7

Figure 7. The wing scales of P. sesostris (top left, and close-up, top right) contain photonic crystals of chitin (bottom, middle and right) Scale bars: left, 100 µm; middle, 2 µm; right, 2 µm. (Bottom figure, from Saranathan et al., 2010)

Richard Prum and coworkers have figured out how these photonic crystals grow (Saranathan et al., 2010). The molecules in the soft membranes that template the deposition of chitin during wing-scale growth become spontaneously organized into the ‘crystalline sponge’. Biological membranes are made up of long, tadpole-like molecules called lipids, which have a water-soluble head and an oily tail. To shield the tails from water, they cluster side by side into sheets with the heads pointing outwards; the sheets then sit back to back in bilayer membranes. Pores in these membrane induce curvature, partly exposing the lipid tails and therefore incurring a cost in energy. For this reason, the pores in effect repel one another, and this can force them to become arranged in a regular way, an equal distance apart. Periodic membrane structures have been found in the cells of many different organisms, from bacteria to rats (Hyde et al., 1997). 

In P. sesostris wing-scale progenitor cells, the outer ‘plasma membrane’ and the folded membrane of the inner compartments called the endoplasmic reticulum, where lipids and other molecules are made, come together to form a so-called double-gyroid structure (Figure 8, left), in which two interweaving sets of channels divide up space into three networks that interpenetrate, but are isolated from one another. One of these is then filled with chitin, which hardens into a robust form while the cell dies and the rest of the material is degraded, leaving behind the single gyroid phase (Saranathan et al., 2010). 

It has been suggested that these natural nanostructures might be used as the templates for making artificial ones, for example, by filling the empty space around the chitin with a polymer or an inorganic solid, and then dissolving away the chitin (Saranathan et al., 2010). But it is also possible to mimic the structures from scratch. For instance, artificial bilayer membranes made from lipid-like molecules called surfactants will also form orderly sponges, and so will so-called block copolymers, in which the chain-like molecules consist of two stretches with different chemical composition (Hyde et al., 1997). Ulrich Wiesner and coworkers (Stefik et al., 2012) have mixed liquid block copolymers with nanoparticles of niobium and titanium oxide, and let the polymers form into gyroid and other ordered ‘nanosponge’ structures that usher the nanoparticles into the same arrays. When this composite is heated, the polymer is burnt away while the mineral nanoparticles coalesce into continuous networks (Figure 8, center). 

These porous solids could find a wide range of uses. Thin porous films of titanium dioxide nanoparticles coated in light-absorbing dyes are already used in low-cost solar cells. These orderly gyroid networks can offer improvements, partly because the solid material through which light-excited electrons are harvested is continuously connected rather than relying on random electrical contacts between nanoparticles. And the researchers have calculated that double-gyroid nanosponges made from metals such as silver or aluminum, which might similarly be assembled from nanoparticles guided by block copolymers, could have the weird property of a negative refractive index, meaning that they would bend light ‘the wrong way’ (Hur et al., 2011). Such materials could be used to make so-called superlenses for optical microscopes that can image objects smaller than the wavelength of light; something that isn’t possible with conventional lenses. 

Inspired by the butterfly structures, Mark Turner and colleagues (Turner et al., 2011) have used laser beams to ‘write’ these intricate three-dimensional photonic crystals directly into a commercial light-polymerizable ‘photoresist’ material (Figure 8, right). Being somewhat ‘scaled-up’ versions of the natural nanostructures, these had photonic band gaps in the infrared part of the spectrum. Current telecommunications operates mostly at infrared wavelengths, and these structures could find uses there; some, for example, have a corkscrew lattice that make them respond differently to circularly polarized light with a left- or right-handed twist. 

Figure 8

Figure 8. The gyroid phase (left), and structures mimicking the ‘butterfly gyroid’: (middle) a network of titania organized by self-assembly of a block copolymer, and (right) a larger-scale lattice made by setting a light-sensitive polymer with laser beams (scale bar: 10 µm). (Left figure, courtesy of Matthias Weber, Indiana University. Middle figure, from Stefik et al., 2012. Right figure, from Turner et al., 2011)

Photonic Crystal Fibers

The spines of some marine polychaete worms, such as Aphrodita (the sea mouse) and Pherusa, are tubular structures containing hexagonally packed hollow cylindrical channels a few hundred nanometers across and made from chitin. These arrays act as two-dimensional photonic crystals that reflect light strongly in the long-wavelength part of the spectrum, which gives the Aphrodite spine a deep, iridescent red color (Figure 9) (Parker et al., 2001; Trzeciak & Vukusic, 2009). 

Figure 9a
Figure 9b
Figure 9c

Figure 9. The tiny spines of polychaete worms such as the sea mouse (Polychaeta: Aphroditidae; top left) are natural photonic crystals. Seen close up in cross section, they consist of regularly packed hollow channels with walls of chitin. Middle left: cross-section from Pherusa (scale bar: 2 µm); center: side view of channels from Aphrodita; right: the red color of light passing through a spine of Aphrodita. Artificial photonic fibres like this can easily be made by heating and drawing out bundles of glass capillaries (bottom). They can confine light within the ‘solid’ channels even around tight bends. (Note the solid ‘defect’ in the central channel.) (Top, middle center and middle right, courtesy of Andrew Parker, University of Oxford. Middle left, from Trzeciak & Vukusic, 2009. Bottom, from Russell, 2003)

It is not clear if the optical properties of the polychaete spines have any biological function. But there are certainly uses for such light-manipulating fibres in optical technology. For example, Philip Russell and collaborators (Russell, 2003) have made them by stacking glass capillaries into hexagonally packed bundles and drawing them out under heat into narrow fibers laced through with holes. If ‘defects’ are introduced into the array of tubular channels, either by including a wider capillary or a solid rod in the bundle, light can pass along the defect while being excluded from the photonic crystal, creating an optical fiber with a cladding that is essentially impermeable to light of wavelengths within the band gap. Photonic crystal fibers like this can guide light around tighter bends than is usually possible with conventional fibers, where the light is confined less reliably by internal reflection at the fibre surface. As a result, these fibers would work better for guiding light in tightly confined spaces, such as on optical microchips. And because photonic crystal fibers are in general less ‘leaky’ than conventional ones, they could be replace them in optical telecommunications networks, requiring less power, and obviating the need for amplifiers to boost signals sent over long distances.  

Disordered Nanosponges

The splendid blue and green plumage of many birds, while also being physical rather than pigmented colors, lacks the iridescence of the hummingbird or the peacock. Instead, they have the same color viewed from any angle. They scatter light from sponge-like keratin nanostructures; but because these structures are disordered, the scattering is diffuse, like the blue of the sky, rather than mirror-like and iridescent (Dufresne et al., 2009). 

In the blue-and-yellow macaw, Ara ararauna, (Figure 10), and the black-capped kingfisher Halcyon pileata, the empty spaces in the keratin matrix of the feather barbs form tortuous channels about 100 nm wide. A similar random network of filaments in the cuticle of the Cyphochilus beetle gives it a dazzlingly bright white shell. In some other birds, such as the blue-crowned manakin, Lepidothrix coronata, the air holes are instead little spherical bubbles connected by tiny cavities. 

Figure 10a
Figure 10b

Figure 10. The blue feathers of the blue-and-yellow macaw contain sponge-like labyrinths of air and keratin (bottom left), which scatter blue light strongly in all directions. Some other feathers derive similar colors from spherical ‘bubble-like’ air holes in the keratin matrix (bottom right). Scale bars: 500 nm. (Bottom figure, from Dufresne et al., 2009)

It is believed that both of these structures are formed as keratin separates out spontaneously from the fluid cytoplasm of feather-forming cells, like oil from water (Dufresne et al., 2009). In liquid mixtures, such as solidifying molten metal alloys or polymers, such phase separation creates different structures in different conditions. If the mixture is intrinsically unstable, the components separate into disorderly, interwoven channels in a process called spinodal decomposition. But if the mixture is metastable (provisionally stable), like water supersaturated with dissolved gas, then the separating phase will form discrete blobs or bubbles that grow from very tiny ‘seeds’ or nuclei. Prum thinks that either of these processes may happen as bird feathers develop, and that birds have evolved a way of controlling the rate of keratin phase separation so that they can arrest the nanostructure at a certain size. Once the cells have died and dried, this size determines the wavelength of scattered light, and thus the feather’s color. 

This kind of diffuse light-scattering has been used for centuries as a way of making colors in technology. In milk, microscopic droplets of fat with a wide range of sizes cause scattering of all visible wavelengths, and give the liquid its opaque whiteness. Michael Faraday discovered in the nineteenth century that light scattering from nanoscale particles of gold suspended in water can create a deep reddish-purple color with a precise hue that depends on the size of the particles. Glassmakers had been using alchemical recipes to precipitate nanoscale gold particles in molten silica to make ruby glass ever since ancient times. 

Today, engineers are looking at how these random networks and particle arrays can give rise to strongly colored and high-opacity materials. Pete Vukusic and colleagues (Hallam et al., 2009) have mimicked the cuticle of Cyphochilus beetles in random porous networks made from interconnected filaments of the minerals calcium carbonate and titanium dioxide mixed with a polymer and oil liquid binders and left to dry. Guided by the size and density of filaments in the beetle shell, they were able to make thin coatings with brilliant whiteness. Meanwhile Prum, his colleague Eric Dufresne and their coworkers at Yale University (Forster et al., 2010) have mimicked the disordered sponges of bird feathers by creating films of randomly packed microscopic polymer beads, which have blue-green colors (Figure 11). 

Figure 11

Figure 11. This thin film of randomly arrayed polymer microspheres mimics the keratin matrix in the blue feathers of the blue-crowned manakin. (From Forster et al., 2010)

Color Change

One of the most enviable optical tricks in nature is to produce reversible color changes. The reflective, protean colors in the skins of squid such as the Loligidinae family are produced by a protein called reflectin, arranged into plate-like stacks in cells called iridophores, which again act as color-selective reflectors (Figure 12). The color changes are thought to be involved in both camouflage and communication between squid for mating and displays of aggression. 

Figure 12

Figure 12. Stacked plates of the reflectin protein (left) in iridophore cells (center) create tunable reflective colors in squid (right). (Center figure, courtesy of Daniel Morse, University of California at Santa Barbara)

Daniel Morse and colleagues have recently figured out how the color changes of iridophores are achieved (Tao et al., 2010). The reflectin proteins crumple up into nanoparticles, which pack together into dense arrays that make up the flat layers. These layers are sandwiched between deep folds of the cell membrane. The color change can be triggered by neurotransmitter lipid molecules called acetylcholine, which activate a biochemical process that fixes electrically charged phosphate chemical groups onto the reflectin protein. These groups largely neutralize the proteins’ intrinsic charge and allow them to pack more closely together, increasing the reflectivity of the layers. At the same time, this compaction squeezes water from between the protein particles and out of the cell, and enables the reflectin layers to sit closer together. 

Morse and colleagues (Holt et al., 2010) think that it should be possible to copy some of these tricks in optical devices, perhaps even using reflectins themselves. They have inserted the gene encoding a reflectin protein from the long-finned squid Loligo pealeii into Escherichia colibacteria. When expressed, the protein spontaneously collapses into nanoparticles (Tao et al., 2010). The size of these particles can be tuned by controlling the interactions between charged groups on the proteins using salt. Held between stacks of permeable membranes, these materials might therefore swell and contract, altering the reflected wavelengths, in response to chemical triggers. Morse and colleagues have also taken inspiration from reflectins to develop a light switch based on a wholly synthetic light-sensitive polymer. They use an electric field both to change the refractive index of the polymer and to pull salt into the polymer film to swell it. As with iridophores, this combination of effects alters the material’s response to light dramatically, switching it from transparent to opaque; all without moving parts or high-tech manufacturing methods. The team are currently working with Raytheon Vision Systems, an optics company in Goleta, California, to use this system in fast shutters for infrared cameras. 

The Art and Science of Natural Color Mixing

Many of the optical effects found in nature are not purely due to structural colors, but arise from their combination with absorbing pigments (Shawkey et al., 2009). In squid, a thin pigment layer above the reflective layer acts as a filter that can modify the appearance, for example, making it mottled; reflective and absorbing to different degrees in different places. In bird feathers, the physical colors resulting from melanin nanostructures embedded in a keratin protein matrix can be tuned by light-absorbing filters of pigments, such as carotenoids, which absorb red and yellow light. The characteristic green plumage of parrots seems to be produced by laying a yellow pigment over a blue reflective layer of melanin and keratin (Figure 13). And the purple wing tips of Purple Tip butterflies come from red pigments beneath a blue iridescent surface. 

Figure 13

Figure 13. Green is a characteristic color of parrots, but their plumage contains no green pigment, nor is it purely a structural color. Rather, it results from ‘structural blue’ overlaid with a filter of yellow pigment.

Chameleons display perhaps the most advanced mastery of these mixing tricks. Their spectacular color changes are produced by three separate systems for modifying the reflected light, stacked one atop the other. The first layer consists of cells containing red and yellow light-absorbing pigment particles, the location of which within the cell determines the color intensity. Below these are iridophores like those of squid, from which blue and white light may be selectively reflected by crystalline layers of the molecule guanine (also a component of DNA). Finally there is a layer of cells containing the dark pigment melanin, which act like the colored ‘ground’ layers of Old Master paintings to modify the reflection of light that penetrates through the first two layers. This combination of reflection and absorption enables the chameleon to adapt its skin color across a wide, albeit species-specific, range to signal warning, for mating displays, and for camouflage (Forbes, 2009). 

How pigments alter and adjust the reflected light in such cases is still imperfectly understood. One problem is that the combinations are so diverse; more than 20 different arrangements of melanin, keratin and air have been identified in the plumage of birds. Moreover, melanin is itself a light absorber, creating colors ranging from yellow to black. The bright white markings on the blue wings of the Morpho cypris butterfly are produced by simply removing the melanin from reflective multilayer structures; the mirrors remain, but the pigments do not. 

In such ways, evolution has made creative use of the limited range of materials at its disposal to generate a riot of profuse coloration and markings. A better understanding of how this is achieved could give painters and visual artists access to entirely new ways of making colors based on iridescent and pearlescent pigments, whose use has so far been largely restricted to less sophisticated applications in the automobile and cosmetic industries (Schenk & Parker, 2011). 

Painter Franziska Schenk has been exploring the mixing of structural and pigmented color during her stay as artist-in-residence in the Department of Biosciences at the University of Birmingham in the UK (Schenk, 2009). With iridescent particles, says Schenk, “the established methods of easel painting no longer apply. Their conversion to painting requires something truly innovative.” 

Schenk used iridescent particles to reproduce the starting blue of the Morpho wing in a series of paintings that change color when lit or viewed from different angles (Figure 14). The background color on which the particles are placed is central to the effect. On white, the light not reflected from the blue particles passes through and bounces off the base. This means that when not seen face-on, the blue quickly fades and is replaced by a muted yellow. But on a black background, all non-blue light is absorbed, and the blue is more pure and intense. 

Figure 14

Figure 14. Painting of a Morpho butterfly wing by Franziska Schenk, using blue pearlescent pigments. The color changes depending on the angle of illumination, as well as on the nature of the background color. (Courtesy of Franziska Schenk)

Although the brilliance of these colors doesn’t approach that of butterfly wings, it takes advantage of recent improvements in synthetic pearlescent particles. The first of these were made by coating mica flakes with multilayers of metal oxides to generate the diffraction grating. But because the mica surfaces were not perfectly smooth and the grain sizes varied, there was always a range in the precise colors and intensities of the particles. Schenk has used pigments in which the mica substrate is replaced by a transparent borosilicate glass, which is smoother and gives a purer hue. She believes that “iridescent technology is destined to introduce a previously unimaginable level of intensity and depth, thus adding beauty, luster and a dynamic dimension to art”. Schenk’s Studies of Cuttlefish (Figure 15) is a painting that uses iridescent flakes mixed with beads and wax. 

Figure 15

Figure 15. “Studies of Cuttlefish” by Franziska Schenk, using iridescent flakes mixed with beads and wax. (Courtesy of Franziska Schenk)

Another series of cuttlefish, “Mantle of Many Colours” (Figure 16), was made with iridescent paint that differs in appearance depending on the conditions and angle of lighting, which results in a compelling chameleon effect that traditional paints simply cannot create. The colors change from greens to purples as the viewing angle shifts. “Still images, together with any attempt to verbally describe the effect, are pretty limiting”, Schenk admits; you have to see these things in the flesh to appreciate their full impact. 

Figure 16

Figure 16. “Mantle of Many Colours” by Franziska Schenk, which uses iridescent paint, as seen from different angles. (Courtesy of Franziska Schenk)

Conclusion

“Every day you play with the light of the universe”, wrote the Chilean poet Pablo Neruda, but he had no idea how literally true this would become. Our technologies for transmitting, manipulating and displaying information, whether for work or play, depend increasingly on our ability to control light; to harness and transform color. Some of nature’s most stunning sights depend on such a facility too, and often they show us that beauty can be inextricably linked to utility. We are impressed by plumage, by markings and animal displays, that are specifically designed by evolution to make such an impression. And nature has found ways to make this chromatic exuberance robust, changeable, responsive, and cheap and reliable to manufacture. In shaping color without the chemical contingency of pigments, there seems to be little we can dream up that nature has not already anticipated, exploiting its capacity to fashion intricate fabrics and structures on the tiniest scales. We can only learn, and admire. 

References

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05/30/12 

Technology of Nanostructures

Colloidal Self Assembly for fabrication of Photonic nanostructures including

  • Colloidal crystals
  • Composite and Inverse Opals
  • Photonic Glasses

Applications

  • Displays
  • Optical Devices
  • Photochemistry
  • Biological Sensors

Source: Self-assembled colloidal structures for photonics

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(73) Assignee:SNUR&DBFoundation,Seoul(KR)

US8,889,234B2 /2014

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NATURE | VOL 396 | 5 NOVEMBER 1998

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Structural color

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https://manoharan.seas.harvard.edu/structural-color

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Structural color printing: full color printing with single ink

Hyoki KimJianping GeJunhoi KimSung-Eun ChoiHosuk LeeHowon LeeWook ParkYadong YinSunghoon Kwon

Proceedings Volume 7609, Photonic and Phononic Crystal Materials and Devices X; 760916 (2010)

https://www.spiedigitallibrary.org/conference-proceedings-of-spie/7609/760916/Structural-color-printing-full-color-printing-with-single-ink/10.1117/12.841420.short?SSO=1

Structural colors in nature: the role of regularity and irregularity in the structure

Shuichi Kinoshita 1Shinya Yoshioka

Chemphyschem 2005 Aug 12;6(8):1442-59

https://pubmed.ncbi.nlm.nih.gov/16015669/

Mechanisms of structural colour in the Morpho butterfly: cooperation of regularity and irregularity in an iridescent scale.

Shuichi KinoshitaShinya Yoshioka, and  Kenji Kawagoe

Proc Biol Sci. 2002 Jul 22;269(1499):1417-21.

https://pubmed.ncbi.nlm.nih.gov/12137569/

Structural Colours in Feathers

Nature volume 112, page243(1923)

https://www.nature.com/articles/112243a0


Angle-independent Structural Coloured Materials inspired by Blue Feather Barbs

Yukikazu TAKEOKA
NIPPON GOMU KYOKAISHI (2014)

Stimuli-responsive opals: colloidal crystals and colloidal amorphous arrays for use in functional structurally colored materials

Yukikazu Takeoka
Journal of Materials Chemistry C (2013)

Angle-independent structural coloured amorphous arrays

Yukikazu Takeoka
Journal of Materials Chemistry (2012)

Full-Spectrum Photonic Pigments with Non-iridescent Structural Colors through Colloidal Assembly

Jin-Gyu Park, Shin-Hyun Kim, Sofia Magkiriadou, Tae Min Choi, Young-Seok Kim, Vinothan N. Manoharan*

Angewandte Chemie International Edition 53(11): 2899 (2014)

https://dash.harvard.edu/bitstream/handle/1/24873725/submitted_version-postprint.pdf?sequence=1

Amorphous Photonic Structures with Brilliant and Noniridescent Colors via Polymer-Assisted Colloidal Assembly

Yang Hu, Dongpeng Yang,* and Shaoming Huang*

ACS Omega 2019, 4, 18771−18779

https://pubs.acs.org/doi/pdf/10.1021/acsomega.9b02734

Viburnum tinus Fruits Use Lipids to Produce Metallic Blue Structural Color

Rox Middleton,1,8,10 Miranda Sinnott-Armstrong,2,9,10 Yu Ogawa,3 Gianni Jacucci,1 Edwige Moyroud,4,5 Paula J. Rudall,6 Chrissie Prychid,6 Maria Conejero,6 Beverley J. Glover,7 Michael J. Donoghue,2 and Silvia Vignolini

In-Plane Direct-Write Assembly of Iridescent Colloidal Crystals

Alvin T. L. Tan, Sara Nagelberg, Elizabeth Chang-Davidson, Joel Tan, Joel K. W. Yang, Mathias Kolle, and A. John Hart

Fabrication of non-iridescent structural color on silk surface by rapid T polymerization of dopamine

Xiaowei Zhu, Biaobiao Yan, Xiaojie Yan, Tianchen Wei, Hongli Yao, Md Shipan Mia, Tieling Xing*, Guoqiang Chen

Bioinspired Stimuli-Responsive Color-Changing Systems

Golnaz Isapour and Marco Lattuada

Advanced Materials 30(19): 1707069

Plasmonic films based on colloidal lithography

Bin Ai a, Ye Yu a, Helmuth Möhwald b, Gang Zhang a,⁎, Bai Yang

Advances in Colloid and Interface Science

Printing a Wide Gamut of Saturated Structural Colors Using Binary Mixtures, With Applications in Anti-Counterfeiting

March 2020

ACS Applied Materials & Interfaces 

https://www.researchgate.net/publication/340326621_Printing_a_Wide_Gamut_of_Saturated_Structural_Colors_Using_Binary_Mixtures_With_Applications_in_Anti-Counterfeiting

Template Synthesis for Stimuli-Responsive Angle Independent Structural Colored Smart Materials

Mohammad Harun-Ur-Rashid1, Abu Bin Imran1, Takahiro Seki1, Yukikazu Takeoka1*, Masahiko Ishii2 and Hiroshi Nakamura2

https://www.jstage.jst.go.jp/article/tmrsj/34/2/34_333/_pdf

Optical Characterization of the Photonic Ball as a Structurally Colored Pigment

Ryosuke Ohnuki,* Miki Sakai, Yukikazu Takeoka, and Shinya Yoshioka

2020

HIGHLY DIFFRACTING, COLORSHIFTING, POLYMERIZED CRYSTALLINE COLLODAL ARRAYS OF HIGHILY CHARGED POLYMER SPHERES, PAINTS AND COATINGS AND PROCESSES FOR MAKING THE SAME

Matti Ben-Moshe, Reut(IL);

Sanford A. Asher, Pitsburgh, PA(US);

Justin J.Bohn, Pitsburgh, PA(US)

US7,902,272B2 /2011

Structural colors: from natural to artificial systems

Yulan Fu,1 Cary A. Tippets,2 Eugenii U. Donev3 and Rene Lopez

WIREs Nanomed Nanobiotechnol 2016

Structural color and its interaction with other color-producing elements: perspectives from spiders

Bor-Kai Hsiung*, Todd A Blackledge, and Matthew D Shawkey
Department of Biology and Integrated Bioscience Program, The University of Akron, Akron, Ohio

Self-assembled colloidal structures for photonics

Shin-Hyun Kim1, Su Yeon Lee2, Seung-Man Yang2* and Gi-Ra Yi3*

Harvard University, USA, KAIST and Chungbuk National University, Korea

Chameleon-Inspired Strain-Accommodating Smart Skin

Yixiao Dong,† Alisina Bazrafshan,† Anastassia Pokutta,‡ Fatiesa Sulejmani,‡ Wei Sun,‡ J. Dale Combs,† Kimberly C. Clarke,† and Khalid Salaita

ACS Nano XXXX, XXX, XXX−XXX

A composite hydrogels-based photonic crystal multi-sensor

Cheng Chen1, Zhigang Zhu1, Xiangrong Zhu1, Wei Yu1, Mingju Liu1, Qiaoqiao Ge1 and Wei-Heng Shih2

Published 16 April 2015 • 
Materials Research ExpressVolume 2Number 4

https://iopscience.iop.org/article/10.1088/2053-1591/2/4/046201/pdf

Template Synthesis for Stimuli-Responsive Angle Independent Structural Colored Smart Materials

Article in Transactions of the Materials Research Society of Japan

February 2009

PATTERNED SILK INVERSE OPAL PHOTONIC CRYSTALS WITH TUNABLE, GEOMETRICALLY DEFINED STRUCTURAL COLOR

US Patent US2019/018731A1

Fiorenzo G.Omenetto, Lexington,MA (US);

YuWang, Medford, MA (US)

Bioinspired colloidal materials with special optical, mechanical, and cell-mimetic functions

Taiji Zhang, Yurong Ma and Limin Qi*

J. Mater. Chem. B, 2013, 1, 251

DYNAMICALLY TUNABLE PLASMONIC STRUCTURAL COLOR

DANIEL FRANKLIN

PhD Thesis 2018

Wetting in Color: Colorimetric Differentiation of Organic Liquids with High Selectivity

Ian B. Burgess,†,* Natalie Koay,‡,§, Kevin P. Raymond,‡,§, Mathias Kolle,† Marko Loncar,† and Joanna Aizenberg†,‡,^,*

Biologically inspired LED lens from cuticular nanostructures of firefly lantern

Jae-Jun Kima, Youngseop Leea, Ha Gon Kimb, Ki-Ju Choic, Hee-Seok Kweonc, Seongchong Parkd, and Ki-Hun Jeong

PNAS | November 13, 2012 | vol. 109 | no. 46

Functional Micro–Nano Structure with Variable Colour: Applications for Anti-Counterfeiting

Hailu Liu , Dong Xie, Huayan Shen, Fayong Li, and Junjia Chen

Hindawi
Advances in Polymer Technology
Volume 2019, Article ID 6519018, 26 pages

REVIEW ARTICLE
515 million years of structural colour

Andrew Richard Parker

J. Opt. A: Pure Appl. Opt. (2000) R15–R28

Colloidal Crystals from Microfluidics

Feika Bian, Lingyu Sun, Lijun Cai, Yu Wang, Yuetong Wang, and Yuanjin Zhao

Small 2019, 1903931

Nanochemistry Chapter 1

Mimicking the colourful wing scale structure of the Papilio blumei butterfly

Mathias Kolle1,2, Pedro M. Salgard-Cunha1, Maik R. J. Scherer1, Fumin Huang1, Pete Vukusic3, Sumeet Mahajan1, Jeremy J. Baumberg1 & Ullrich Steiner

Cambridge Univ

Nature Nanotechnology, 2010, (5) 511-515

Bioinspired bright noniridescent photonic melanin supraballs

Ming Xiao,1* Ziying Hu,2,3* Zhao Wang,4 Yiwen Li,5 Alejandro Diaz Tormo,6 Nicolas Le Thomas,6 Boxiang Wang,7 Nathan C. Gianneschi,2,3,4† Matthew D. Shawkey,8,9† Ali Dhinojwala

Sci. Adv. 2017;3:e1701151 15 September 2017

Structural Color and Odors: Towards a Photonic Crystal Nose Platform

Leonardo da Silva Bonifacio

PhD Thesis 2010

The Self-Assembly of Cellulose Nanocrystals: Hierarchical Design of Visual Appearance

Richard M. Parker, Giulia Guidetti, Cyan A. Williams, Tianheng Zhao, Aurimas Narkevicius, Silvia Vignolini,* and Bruno Frka-Petesic

Adv. Mater. 201830, 1704477

https://onlinelibrary.wiley.com/doi/pdf/10.1002/adma.201704477

Bio-inspired design of multiscale structures for function integration

Kesong Liua, Lei Jiang

A ROBUST SMART FILM :REVERSIBLY SWITCHING FROM HIGH TRANSPARENCY TO ANGLE-INDEPENDENT STRUCTURAL COLOR DISPLAY

US Patent 2018

US2018/024876A1

Inventors:Shu YANG, BlueBel, PA(US);

Deng teng GE, Shanzhai(CN);

Elaine LEE,Brooklyn,NY (US)

Click to access US20180244876A1.pdf

Optimization of sharp and viewing-angle-independent structural color

Chia Wei Hsu,1,2,∗ Owen D. Miller,3 Steven G. Johnson,3 and Marin Soljacˇic ́1

Bioinspired living structural color hydrogels

Fanfan Fu, Luoran Shang, Zhuoyue Chen, Yunru Yu, Yuanjin Zhao

SCIENCE ROBOTICS

Measuring and specifying goniochromatic colors

Alejandro Ferrero1, Joaquín Campos1, Esther Perales2, Ana M. Rabal1, Francisco Martínez-Verdú2, Alicia Pons1, Elisabet Chorro2 and M. Luisa Hernanz

Bio-Inspired Photonic Structures: Prototypes, Fabrications and Devices

By Feng Liu, Biqin Dong and Xiaohan Liu

Submitted: November 5th 2011Reviewed: May 28th 2012Published: September 19th 2012

https://www.intechopen.com/books/optical-devices-in-communication-and-computation/bio-inspired-photonic-structures-prototypes-fabrications-and-devices

Photobiology

The Science of Light and Life
  • Lars Olof Björn

https://link.springer.com/book/10.1007/978-1-4939-1468-5

“Guanigma”: The Revised Structure of Biogenic Anhydrous Guanine 

Anna Hirsch,† Dvir Gur,‡ Iryna Polishchuk,§ Davide Levy,§ Boaz Pokroy,§ Aurora J. Cruz-Cabeza,∥ Lia Addadi,*,‡ Leeor Kronik,*,† and Leslie Leiserowitz*,†

Natural photonics 

Pate Vukusic

Stimuli-Responsive Structurally Colored Films from Bioinspired Synthetic Melanin Nanoparticles

Ming Xiao,†,# Yiwen Li,‡,#,○ Jiuzhou Zhao,† Zhao Wang,‡ Min Gao,§ Nathan C. Gianneschi,*,‡ Ali Dhinojwala,*,† and Matthew D. Shawkey

Chem. Mater. 2016, 28, 5516−5521

A Microfluidic Chip with Integrated Colloidal Crystal for Online Optical Analysis

Siew-Kit Hoi, Xiao Chen, Vanga Sudheer Kumar, Sureerat Homhuan, Chorng-Haur Sow, and Andrew A. Bettiol*

Highly monodisperse zwitterion functionalized non-spherical polymer particles with tunable iridescence

Vivek Arjunan Vasantha*aWendy RusliaChen JunhuiaZhao WenguangaKandammathe Valiyaveedu SreekanthbcRanjan Singhbc and Anbanandam Parthiban*a 

 RSC Adv., 2019, 9, 27199-27207

https://pubs.rsc.org/en/content/articlehtml/2019/ra/c9ra05162g

Stimuli-responsive opals: colloidal crystals and colloidal amorphous arrays for use in functional structurally colored materials

Yukikazu Takeoka

J. Mater. Chem. C, 2013, 1, 6059

Biomimetic and Bioinspired Photonic Structures

Wu Yi, Ding-Bang Xiong * and Di Zhang

Nano Adv., 2016, 1, 62–70.

Bio-inspired photonic crystal patterns

Pingping Wu,abJingxia Wang *abc  and  Lei Jiang

https://pubs.rsc.org/no/content/articlelanding/2020/mh/c9mh01389j/unauth#!divAbstract

Stretchable and reflective displays: materials, technologies and strategies

Nano Convergence volume 6, Article number: 21 (2019)

https://nanoconvergencejournal.springeropen.com/articles/10.1186/s40580-019-0190-5

Colloidal Lithography

By Ye Yu and Gang Zhang

2013

https://www.intechopen.com/books/updates-in-advanced-lithography/colloidal-lithography

Structure and mechanical properties of beetle wings: a review 

Jiyu Sun and Bharat Bhushan

RSC Advances, 2012, 2, 12606–12623

A highly conspicuous mineralized composite photonic architecture in the translucent shell of the blue-rayed limpet

Ling LiStefan KolleJames C. WeaverChristine OrtizJoanna Aizenberg & Mathias Kolle 

Nature Communications volume 6, Article number: 6322 (2015) 

https://www.nature.com/articles/ncomms7322/

Fabrication of 3D polymeric photonic arrays and related applications 

A. Yadav a, *, A. Kaushik b, Y. Mishra c, V. Agrawal d, A. Ahmadivan e, K. Maliutina f, Y. Liu g, Z. Ouyang h, W. Dong a, **, G.J. Cheng

Materials Today Chemistry, https://doi.org/10.1016/j.mtchem.2019.100208

Reversible Design of Dynamic Assemblies at Small Scales

Fernando Soto, Jie Wang, Shreya Deshmukh, and Utkan Demirci

Adv. Intell. Syst. 2020, 2000193

https://onlinelibrary.wiley.com/doi/pdf/10.1002/aisy.202000193

Biological composites— complex structures for functional diversity.

Eder, M., Shahrouz, A., & Fratzl, P. (2018).

Science, 362(6414), 543-547.

Stimuli-Responsive Optical Nanomaterials

Zhiwei Li, and Yadong Yin

https://onlinelibrary.wiley.com/doi/am-pdf/10.1002/adma.201807061

Bio-Inspired Structural Colors Produced via Self-Assembly of Synthetic Melanin Nanoparticles

Ming Xiao,†,^ Yiwen Li,‡,^ Michael C. Allen,§ Dimitri D. Deheyn,§ Xiujun Yue,‡ Jiuzhou Zhao,† Nathan C. Gianneschi,*,‡ Matthew D. Shawkey,*, and Ali Dhinojwala

ACS Nano 2015

https://pubs.acs.org/doi/pdf/10.1021/acsnano.5b01298

Pigments Based on Colloidal Photonic Crystals

Carlos Israel Aguirre Vélez

PhD Thesis 2010

Structural Colors in Nature: The Role of Regularity and Irregularity in the Structure

Shuichi Kinoshita* and Shinya Yoshioka

ChemPhysChem 2005, 6, 1442 – 1459

Flexible mechanochromic photonic crystals: routes to visual sensors and their mechanical properties

Rui Zhang, Qing Wang  and Xu Zheng

J. Mater. Chem. C, 2018, 6, 3182

Designing visual appearance using a structured surface

VILLADS EGEDE JOHANSEN,1,* LASSE HØJLUND THAMDRUP,2 KRISTIAN SMISTRUP,2 THEODOR NIELSEN,2 OLE SIGMUND,1 AND PETER VUKUSIC

Vol. 2, No. 3 / March 2015 / Optica

Subwavelength nanocavity for flexible structural transmissive color generation with a wide viewing angle

KYU-TAE LEE,1 JI-YUN JANG,2 SANG JIN PARK,2 UJWAL KUMAR THAKUR,2 CHENGANG JI,1 L. JAY GUO,1 AND HUI JOON PARK

Vol. 3, No. 12 / December 2016 / Optica

Color and Texture Morphing with Colloids on Multilayered Surfaces

Ziguang Chen,†,‡,⊥ Shumin Li,†,‡,⊥ Andrew Arkebauer,§ George Gogos,† and Li Tan

ACS Appl. Mater. Interfaces 2015, 7, 10125−10131

https://pubs.acs.org/doi/pdf/10.1021/am5087215

Electrodeposition of Large Area, Angle-Insensitive Multilayered Structural Colors

Chengang Ji,1,† Saurabh Acharya,1,† Kaito Yamada,2 Stephen Maldonado,2,3,* and L. Jay Guo

https://par.nsf.gov/servlets/purl/10111165

Bright and Vivid Diffractive-Plasmonic Structural Colors

Emerson G. Melo,†,‡,§ Ana L. A. Ribeiro,†,‡ Rodrigo S. Benevides,†,‡ Antonio A. G. V. Zuben,†,‡ Marcos V. P. Santos,† Alexandre A. Silva,¶ Gustavo S. Wiederhecker,†,‡ and Thiago P. M. Alegre

2019

Biomimetic photonic structures for optical sensing

Raúl J. Martín-Palmaa, Mathias Kolle

Optics and Laser Technology 109

2019

􏰀􏰁􏰂􏰃􏰄􏰅 􏰇􏰈􏰉 􏰊􏰇􏰅􏰋􏰌 􏰍􏰋􏰄􏰎􏰈􏰏􏰐􏰏􏰑􏰒 􏰓􏰔􏰕 􏰖􏰗􏰔􏰓􏰕􏰘 􏰗􏰙􏰔􏰚􏰀􏰁􏰂􏰃􏰄􏰅 􏰇􏰈􏰉 􏰊􏰇􏰅􏰋􏰌 􏰍􏰋􏰄􏰎􏰈􏰏􏰐􏰏􏰑􏰒 􏰓􏰔􏰕 􏰖􏰗􏰔􏰓􏰕􏰘 􏰗􏰙􏰔􏰚􏰗􏰙􏰙

Colloidal Self-Assembly Concepts for Plasmonic Metasurfaces

Martin Mayer, Max J. Schnepf, Tobias A. F. König,* and Andreas Fery

Adv. Optical Mater. 20197, 1800564

https://onlinelibrary.wiley.com/doi/pdf/10.1002/adom.201800564

Flourishing Smart Flexible Membranes Beyond Paper

Anal. Chem. 2019, 91, 7, 4224–4234

Publication Date:March 18, 2019

https://doi.org/10.1021/acs.analchem.9b00743

https://pubs.acs.org/doi/full/10.1021/acs.analchem.9b00743

Biological vs. Electronic Adaptive Coloration: How Can One Inform the Other?

Eric Kreit1, Lydia M. Mäthger2, Roger T. Hanlon2, Patrick B. Dennis3, Rajesh R. Naik3, Eric Forsythe4 and Jason Heikenfeld1*

Dynamic plasmonic color generation enabled by functional materials

  1. Frank Neubrech
  2. Xiaoyang Duan
  3. Na Liu

Science Advances  04 Sep 2020:
Vol. 6, no. 36, eabc2709
DOI: 10.1126/sciadv.abc2709

https://advances.sciencemag.org/content/6/36/eabc2709

The New Generation of Physical Effect Colorants

Faiz Rahman and Nigel P. Johnson

Optics and Photonics News

2008

https://www.osa-opn.org/home/articles/volume_19/issue_2/features/the_new_generation_of_physical_effect_colorants/

The Japanese jewel beetle: a painter’s challenge

Franziska Schenk1, Bodo D Wiltsand Doekele G Stavenga2

Bioinspir. Biomim. (2013) 045002 (10pp)

Gold bugs and beyond: a review of iridescence and structural colour mechanisms in beetles (Coleoptera)

Ainsley E. Seago1,*, Parrish Brady2, Jean-Pol Vigneron3 and Tom D. Schultz4

Iridescence as Camouflage

Karin Kjernsmo,1,4,* Heather M. Whitney,1 Nicholas E. Scott-Samuel,2 Joanna R. Hall,2 Henry Knowles,1 Laszlo Talas,2,3 and Innes C. Cuthill1

Current Biology

VOLUME 30, ISSUE 3, P551-555.E3, FEBRUARY 03, 2020

https://www.cell.com/current-biology/pdfExtended/S0960-9822(19)31608-2

https://www.cell.com/current-biology/fulltext/S0960-9822(19)31608-2?_returnURL=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS0960982219316082%3Fshowall%3Dtrue

Chromic Phenomena: Technological Applications of Colour Chemistry

Peter Bamfield

Book, Royal Society of Chemistry 2018 edition

Amorphous diamond-structured photonic crystal in the feather barbs of the scarlet macaw

Haiwei Yina,1, Biqin Donga,1, Xiaohan Liua, Tianrong Zhana, Lei Shia, Jian Zia,2, and Eli Yablonovitchb,2

PNAS | July 24, 2012 | vol. 109 | no. 30

Amorphous Photonic Crystals with Only Short-Range Order

Lei Shi, Yafeng Zhang, Biqin Dong, Tianrong Zhan, Xiaohan Liu,* and Jian Zi

Adv. Mater. 201325, 5314–5320

Diamond-structured photonic crystals

Nature Materials  volume 3, pages593–600(2004)

https://www.nature.com/articles/nmat1201

Nano-Optics in the Biological World: Beetles, Butterflies, Birds, and Moths

Mohan Srinivasarao*

Fiber and Polymer Science Program, North Carolina State University, Raleigh, North Carolina 27695-8301

Chem. Rev. 1999, 99, 1935−1961

515 million years of structural colour

Andrew Richard Parker

Department of Zoology, University of Oxford, South Parks Road, Oxford OX1 3PS, UK

E-mail: andrew.parker@zoo.ox.ac.uk

J. Opt. A: Pure Appl. Opt. (2000) R15–R28

Photophysics of Structural Color in the Morpho Butterflies

Shuichi KINOSHITA1,2*, Shinya YOSHIOKA1,2, Yasuhiro FUJII2 and Naoko OKAMOTO

Forma17, 103–121, 2002

Photonic structures in biology

  • October 2004

Peter Vukusic

https://www.researchgate.net/publication/235888153_Photonic_structures_in_biology

Physics of structural colors

S Kinoshita, S Yoshioka and J Miyazaki

Graduate School of Frontier Biosciences, Osaka University, Suita, Osaka 565-0871, Japan

E-mail: skino@fbs.osaka-u.ac.jp

Rep. Prog. Phys. 71 (2008) 076401 (30pp)

https://www.researchgate.net/publication/231075466_Physics_of_structural_colors

Coloration strategies in peacock feathers

Jian Zi*, Xindi Yu, Yizhou Li, Xinhua Hu, Chun Xu, Xingjun Wang, Xiaohan Liu*, and Rongtang Fu

A Review of Electronic Paper Display Technologies from the Standpoint of SID Symposium Digests

Tatsumi Takahashi

Review of Paper-Like Display Technologies

Peng Fei Bai1, Robert A. Hayes1, Ming Liang Jin1, Ling Ling Shui1, Zi Chuan Yi1, L. Wang1, Xiao Zhang1, and Guo Fu Zhou1, 2

Progress In Electromagnetics Research, Vol. 147, 95–116, 2014

Stretchable and reflective displays: materials, technologies and strategies

Nano Convergence volume 6, Article number: 21 (2019)

https://nanoconvergencejournal.springeropen.com/articles/10.1186/s40580-019-0190-5

Review Paper: A critical review of the present and future prospects for electronic paper

Jason Heikenfeld (SID Senior Member) Paul Drzaic (SID Fellow)
Jong-Souk Yeo (SID Member)
Tim Koch (SID Member)

Journal of the SID 19/2, 2011

Biological versus electronic adaptive coloration: how can one inform the other?

Eric Kreit1, Lydia M. Ma ̈thger2, Roger T. Hanlon2, Patrick B. Dennis3, Rajesh R. Naik3, Eric Forsythe4 and Jason Heikenfeld1

J R Soc Interface 10: 20120601.

https://royalsocietypublishing.org/doi/pdf/10.1098/rsif.2012.0601

Transmissive/Reflective Structural Color Filters: Theory and Applications


Yan Yu,1,2 Long Wen,2 Shichao Song,2 and Qin Chen

Volume 2014 |Article ID 212637 | https://doi.org/10.1155/2014/212637

https://www.hindawi.com/journals/jnm/2014/212637/

Interferometric modulator display

https://en.wikipedia.org/wiki/Interferometric_modulator_display

Qualcomm resurrects Mirasol reflective displays with new 576 ppi smartphone panel

https://www.theverge.com/2013/5/22/4354642/high-res-mirasol-display-for-smartphones-demonstrated

Iridescence-controlled and flexibly tunable retroreflective structural color film for smart displays

  • Wen Fan
  • Jing Zeng
  • Qiaoqiang Gan
  • Dengxin Ji
  • Haomin Song
  • Wenzhe Liu
  • Lei Shi
  • Limin Wu

Science Advances  09 Aug 2019:
Vol. 5, no. 8, eaaw8755
DOI: 10.1126/sciadv.aaw8755

Click to access eaaw8755.full.pdf

Artificial Structural Color Pixels: A Review 

by Yuqian Zhao 1Yong Zhao 1,*Sheng Hu 1Jiangtao Lv 1Yu Ying 2Gediminas Gervinskas 3 and Guangyuan Si 

Materials 201710(8), 944; https://doi.org/10.3390/ma10080944

https://www.mdpi.com/1996-1944/10/8/944/htm

Dynamically Tunable Plasmonic Structural Color

Daniel Franklin
University of Central Florida 2018

PHD Thesis

Colors with plasmonic nanostructures: A full-spectrum review 

Applied Physics Reviews 6, 041308 (2019); https://doi.org/10.1063/1.5110051

https://aip.scitation.org/doi/abs/10.1063/1.5110051?journalCode=are

Dynamic plasmonic color generation enabled by functional materials

Frank Neubrech1,2, Xiaoyang Duan1,2, Na Liu3,4*

Bright and Vivid Diffractive–Plasmonic Reflective Filters for Color Generation

  • Emerson G. Melo, 
  • Ana L. A. Ribeiro, 
  • Rodrigo S. Benevides, 
  • Antonio A. G. V. Zuben, 
  • Marcos V. Puydinger dos Santos, 
  • Alexandre A. Silva, 
  • Gustavo S. Wiederhecker, and 
  • Thiago P. M. Alegre*

ACS Appl. Nano Mater. 2020, 3, 2, 1111–1117Publication Date:December 31, 2019 https://doi.org/10.1021/acsanm.9b02508

https://pubs.acs.org/doi/full/10.1021/acsanm.9b02508

Active control of plasmonic colors: emerging display technologies

Kunli Xiong, Daniel Tordera, Magnus Jonsson and Andreas B. Dahlin

Rep Prog Phys. 2019 Feb;82(2):024501.

doi: 10.1088/1361-6633/aaf844.

https://pubmed.ncbi.nlm.nih.gov/30640724/

Self-assembled plasmonics for angle-independent structural color displays with actively addressed black states

Daniel Franklina,b, Ziqian Hec, Pamela Mastranzo Ortegab, Alireza Safaeia,b, Pablo Cencillo-Abadb, Shin-Tson Wuc, and Debashis Chandaa,b,c,1

https://www.pnas.org/content/117/24/13350

Bio-inspired intelligent structural color materials

Luoran Shang, Weixia Zhang, Ke Xuc and Yuanjin Zhao

Mater. Horiz., 2019,6, 945-958 

https://pubs.rsc.org/en/content/articlelanding/2019/mh/c9mh00101h#!divAbstract

Advanced Plasmonic Materials for Dynamic Color Display

DOI: 10.1002/adma.201704338

https://www.researchgate.net/publication/320997060_Advanced_Plasmonic_Materials_for_Dynamic_Color_Display

Polarization-independent actively tunable colour generation on imprinted plasmonic surfaces

Nature Communications volume 6, Article number: 7337 (2015)

https://www.nature.com/articles/ncomms8337

Tunable plasmonic color filter 

Rosanna Mastria, Karl Jonas Riisnaes, Monica Craciun, and Saverio Russo

Frontiers in Optics / Laser Science OSA Technical Digest (Optical Society of America, 2020),paper JTh4B.7•

https://doi.org/10.1364/FIO.2020.JTh4B.7

https://www.osapublishing.org/abstract.cfm?uri=FiO-2020-JTh4B.7

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?

From GENERATION OF FRACTALS FROM INCURSIVE AUTOMATA, DIGITAL DIFFUSION AND WAVE EQUATION SYSTEMS

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

 

 

 

GENERATION OF FRACTALS FROM INCURSIVE AUTOMATA, DIGITAL DIFFUSION AND WAVE EQUATION SYSTEMS

Daniel M. Dubois

 

Click to access dubois.pdf

 

 

 

Non-wellfounded Set Theory

https://plato.stanford.edu/entries/nonwellfounded-set-theory/

Hypersets

  • Jon Barwise &
  • Larry Moss

https://link.springer.com/article/10.1007/BF03028340

Non-well-founded set theory

https://en.wikipedia.org/wiki/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.

 

http://mathworld.wolfram.com/Knot.html

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

Tricoloring

 

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

Tabela_de_nós_matemáticos_01,_crop

 

 

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

http://homepages.math.uic.edu/~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

 

 

KNOTS

by Louis H. Kauffman

 

Click to access KNOTS.pdf

 

 

 

BioLogic

Louis H. Kaufman, UIC

Click to access BioL.pdf

New Invariants in the Theory of Knots

Louis H. Kaufman, UIC

https://www.researchgate.net/publication/238648076_New_Invariants_in_the_Theory_of_Knots

 

 

 

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

 

 

Reflexivity

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

https://iopscience.iop.org/article/10.1088/1742-6596/361/1/012034/pdf

 

 

 

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

 

 

 

FORMAL SYSTEMS

EigenForm

Louis H. Kauffman

 

Click to access Eigen.pdf

 

 

 

EigenForm

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

https://www.scirp.org/html/11-7402327_50601.htm

 

Interconnected Pythagorean Triples using Central Squares Theory

Interconnected Pythagorean Triples using Central Squares Theory

 

 

Triples are connected through Squares.

 

 

Key Terms

  • Pythagorean Theorem
  • Pythagorean Triples
  • Pythagorean Family of Triples
  • Plato family of Triples
  • 3D Pythagorean Theorem
  • Octahedron in 3D
  • Square in 2D
  • Square and Triangles
  • Pythagorean Tree
  • Geometrical Gear
  • 3D Geometrical Gear
  • Interconnected Triples
  • Tripartite Universe
  • Tri-loka
  • Great Pyramids
  • Set, Osiris, Isis
  • IS RA EL
  • Herma-polis and Helio-polis
  • Set/Thoth and RA/Atum
  • Shadows and Pillers
  • Saturn and Jupiter
  • Moon and Sun
  • Silver and Gold
  • Tamas and Rajas
  • Serpent and Eagle
  • Set and Horus
  • Fourth and Fifth
  • Descent and Ascent
  • Ganesh and Hanuman
  • Mars Planet
  • Sun, Earth, Moon
  • Three Parts of the Soul
  • Fundamental Triplicity
  • Inverted Pipal Tree in Hindu Cosmology
  • Vastu Purush Mandala
  • Brahma in Vedic Physics
  • Brahma, Vishnu, Mahesh/Shiv
  • Ram, Lakshman, Sita
  • Krishna, Baldev/Balram, Subhadra
  • Surya Vanshi  and Chandra Vanshi – Solar and Lunar Dynasties
  • Tripitaka in Buddhism
  • Eightfold path in Buddhism
  • Lotus and Diamond Sutra in Buddhism
  • Vajra and Lotus
  • Indra, Brahma, Buddha
  • Three Gunas – Satva, Rajas, Tamas
  • Three Sheaths – Gross, Subtle, Causal
  • Three Nadis: Pingala(Sun), Ida(Moon), Sushumna(Fire)
  • Three Doshas: Vata, Kapha, Pitta
  • Three Gods: Brahma, Rudra, Vishnu
  • Path: Ascending, Descending, Bidirectional
  • Three inner layers of Sushumna Nadi: Chitrini, Vajra, Brahma
  • Plimpton 322

 

Pythagorean Family of Triples

  • 3 4 5
  • 5 12 13
  • 7 24 25
  • 9 40 41

 

Plato Family of Triples

  • 3 4 5
  • 8 15 17
  • 12 35 37
  • 16 63 65

 

Pythagoras triples explained via central squares

Screen Shot 2019-09-28 at 2.11.35 PMScreen Shot 2019-09-28 at 2.03.32 PMScreen Shot 2019-09-28 at 2.06.47 PM

Anatomy of the Pythagoras’ tree

Screen Shot 2019-09-28 at 5.41.36 PM

 

Key sources of Research

Pythagoras triples explained via central squares

Luis Teia Gomes

 

Click to access EJ1093370.pdf

 

 

Anatomy of the Pythagoras’ tree

Luis Teia

The University of Lund, Sweden

luistheya@gmail.com

 

Click to access EJ1121416.pdf

Click to access Anatomy-of-the-Pythagoras-Tree.pdf

 

 

 

Fermat’s Theorem – a Geometrical View

 

Article · March 2017

 

Click to access Fermats-Theorem-a-Geometrical-View.pdf

 

The Pythagorean geometric gear

 

Luis Teia

University of Lund, Sweden

luistheya@gmail.com

 

Click to access The-Pythagorean-Geometric-Gear.pdf

 

 

Geometry of the 3 D Pythagoras ’ Theorem

  • Luis Teia
  • Published 2016

https://www.semanticscholar.org/paper/Geometry-of-the-3-D-Pythagoras-’-Theorem-Teia/87f4e288ef79ed7df384956ab5b6238d99301865

http://www.ccsenet.org/journal/index.php/jmr/article/download/64646/34833

 

 

 

Special Case of the Three-Dimensional Pythagorean Gear

(Australian Senior Mathematics Journal)

Article in Journal of the Australian Mathematical Society ·

December 2018

 

Click to access Special-Case-of-the-Three-Dimensional-Pythagorean-Gear-Australian-Senior-Mathematics-Journal.pdf

 

Geometry of 3D Pythagorean Theorem

 

 

 

 

 

The Pythagorean Tree: A New Species

H. Lee Price

September, 2008

 

Click to access 0809.4324.pdf

 

 

 

Pythagoras’ garden, revisited

  • Frank R. Bernhart, H. Lee Price
  • Published 2012

https://www.semanticscholar.org/paper/Pythagoras%27-garden%2C-revisited-Bernhart-Price/96e1d0c6c41d17dc103d1eea7a078c8e640cb903

 

Neuro-Accounting: Accounting, Brain, and Evolution

Neuro-Accounting:  Accounting, Brain, and Evolution

 

 

Key Terms

  • Neuro Accounting
  • Neuro Economics
  • Sudipta Basu
  • John Dickhaut
  • Kevin McCabe
  • Michael Hudson
  • Brain
  • Evolution
  • Culturally evolved Accounting
  • Biologically evolved Brain

 

 

From Neuroaccounting: Consilience between the Biologically Evolved Brain and Culturally Evolved Accounting Principles

We develop the hypothesis that culturally evolved accounting principles will be ultimately explained by their consilience with how the human brain has evolved biologically to evaluate social and economic exchange. We provide background on the structure and evolution of the brain, the measurement of brain behavior during economic decision making, and the brain’s central role in building economic institutions. We describe the emergence of modern accounting principles and argue that the primary function of accounting in evaluating exchange is to provide quantified information on the net benefits of past exchanges. We review evidence documented by neuroscientists that is consistent with the hypothesis that longstanding accounting principles 􏰁e.g., Revenue Realization and Conservatism􏰀 have distinct parallels in brain behaviors. Our analysis of Neuroaccounting extends Basu and Waymire 􏰁2006􏰀 to provide a new way to scientifically view accounting, which has implications for how we think about the origins and persistence of longstanding accounting principles.

 

 

 

Key Sources of Research:

 

Neuroaccounting: Consilience between the Biologically Evolved Brain and Culturally Evolved Accounting Principles

John Dickhaut, Sudipta Basu, Kevin McCabe, and Greg Waymire

Click to access 0c960538572c84f0dc000000.pdf

 

 

 

 

Recordkeeping and Human Evolution

Sudipta Basu and Gregory B. Waymire

2005

Click to access 00b49521c9d8edb99c000000.pdf

 

 

 

NeuroAccounting, Part I

The Primate Brain and Reciprocal Exchange

by

John Dickhaut Sudipta Basu Kevin McCabe Gregory Waymire

 

Click to access 0fcfd50577041d8f23000000.pdf

 

 

 

NeuroAccounting, Part II

Consilience Between Accounting Principles and the Primate Brain

by

John Dickhaut Sudipta Basu Kevin McCabe Gregory Waymire

Click to access 0fcfd5057704201078000000.pdf

 

 

 

 

Memory, transaction records, and The Wealth of Nations

Sudipta Basu , Marcus Kirk , Greg Waymire

 

Click to access BasuKirkWaymireAOS05Memory.pdf

 

 

 

 

Recordkeeping alters economic history by promoting reciprocity

Sudipta Basua, John Dickhautb, Gary Hechtc, Kristy Towryc, and Gregory Waymirec,1

Click to access 1009.full.pdf

 

 

 

 

The Role of Accounting in Civilization’s Economic Takeoff

Michael Hudson

 

Click to access hudson.pdf

On Holons and Holarchy

On Holons and Holarchy

 

Key Terms

  • Holons
  • Holarchy
  • Hierarchy
  • Fractals
  • Holonomic
  • Holographic
  • Heterarchy
  • Parts and Whole
  • Networks
  • Matryoshka Dolls
  • Recursion
  • Nested Levels
  • Reflective Spheres
  • Hyper Sets
  • Boundaries

 

.

From The Holonic Revolution Holons, Holarchies and Holonic Networks. The Ghost in the Production Machine

 

A minor conceptual revolution has been under way for less than forty years now, beginning in 1967 with the publication of Arthur Koestler’s The Ghost in the Machine – a phantasmagorical book in terms of the breath and variety of its content – which formally introduced the concepts of holon and holarchy (the hierarchical ordering of holons).

Koestler’s idea is clear and simple: in observing the Universe surrounding us (at the physical and biological level and in the real or formal sense) we must take into account the whole/part relationship between observed “entities”. In other words, we must not only consider atoms, molecules, cells, individuals, systems, words or concepts as autonomous and independent units, but we must always be aware that each of these units is at the same time a whole – composed of smaller parts – and part of a larger whole.

In fact, they are holons.

By systematically applying the whole/part observational relationship, or the equivalent one of containing/contained, the Universe appears to us as a hierarchy of holons: that is, as a holarchy where, at each hierarchical level, the holons undergo the effects of the structural or operational variations of the subordinate holons and in turn produce variations in the behaviour of the superordinate ones.

The entire machine of life and of the Universe itself evolves toward ever more complex states, as if a ghost were operating the machine.

The concepts of holon and holarchy have since been used, especially in recent times, by a number of writers in a variety of disciplines and contexts, and these concepts are rapidly spreading to all sectors of research. Physics (Capra 1982), engineering (Babiceanu et al. 2005; Dani et al. 2004)), robotics, biology (Shafaei – Aghaee, 2008), organizational studies, management science (Zhang et al. 2003; Ng et al. 1996), business administration and entrepreneurship (Chirn – McFarlane 2001), production and supply chain systems (McFarlane – Bussmann 2000; Akturk – Turkcan 2000; Amiri 2006). Connected to these ideas are those of holonic networks, holonic and virtual enterprises, virtual organizations, agile manufacturing networks, holonic manufacturing systems, fractal enterprise and bionic manufacturing (Chapter 5)

 

This short essay, written from an economic-business point of view, has four objectives.

The first (covering the first two chapters) provides the reader with a brief but precise theoretical framework for understanding the meaning of the new terms that increasingly come up in business literature (outside Italy as well) and which refer directly or indirectly to the ideas of holon and holarchy. Connected to these terms are those of holonic network, holonic firm and enterprise, holonic manufacturing systems, holonic production, bionic production, fractal enterprise, and virtual enterprise, to name but a few.

Since I have observed that often the term “holon” has been improperly used, without any reference to the original sources, leading to models and conclusions that are absolutely inappropriate, I feel it is useful to provide the theoretical framework within which these terms can be properly used, considering not only Koestler’s definition but also the ideas of Ken Wilber, which are based on this notion.

I also feel it is useful to examine several fundamental classes of holarchies in order to show that the idea of a hierarchical order among classes of holons can be applied to a variety of contexts. In particular I have presented Koestler’s Self-organizing Open Hierarchical Order, Wilber’s Kosmos and Shimizu’s Autonomic Cognitive Computer as applications that illustrate the concept of a holon.

The second objective (presented in Chapter 3) is to extend the notion of holon while respecting its original meaning, in order to apply it to organizations.

Starting from the definition of organizations as systems whose organs are composed of individuals or groups of individuals, I have attempted to demonstrate two interconnected aspects: on the one hand, that organizations are holons that derive from a holarchy of organs (from their functionalities), and on the other that organizations can be formed by other holon-organizations – which I have labelled orgons – that are connected in a holarchy that I have called an orgonization.

When we observe the functionality and the function of its organs we see that an organization can be thought of as a macro system whose purpose is the attainment of a macro objective. It immediately follows that it can be compared to an Holonic Manufacturing System, or to an Autonomic Cognitive Computer; that is, to a holarchy of operators at different levels – each included in the other, so as to form parts of ever smaller size – each capable of pursuing part of the macro objective.

When there is a larger objective to achieve, rather than add levels to the organization we can form an organization of organizations, that is an orgonization with unique characteristics.

The third objective is to show (Chapter 4) how holons can be connected not only in the typical hierarchical structure – the holarchy – but, by stretching somewhat the original meaning, also in a reticular structure in order to form holonic networks in which the vertical ordering (above and below) is replaced by a horizontal one (before and after).

Within the holonic networks the holons maintain their autonomy and their whole/part relationship, which together characterize holarchies. However, for this reason the dominant feature is their horizontal systemic interconnections; each holon becomes a node of input-output interconnections between holons that come before and those that come after in the structure.

I have thus discovered that even holonic networks can be made up of orgons that form orgonic networks.

Since holarchies, orgonizations, holonic networks and orgonic networks are present everywhere – in firms and between firms, as well as in the economic system of which they are a vital part – it is useful to present a general survey.

Among the many types of holonic networks, I have chosen to examine the main sources of inspiration for those production systems referred to as the Holonic Manufacturing Systems, comparing these to those defined as Bionic and Fractal Manufacturing Systems. I have also considered the numerous forms of Inter- organizational Networks as well as the Holonic and Virtual Organizations.

The fourth objective (Chapter 5) is perhaps the most ambitious one, since I have tried to extend the holonic vision to the global production-economic system, or Production Kosmos.

Globally we are witnessing the continual and accelerated economic progress of mankind. There is an increase in the quantity and quality of needs that are satisfied and those still to be satisfied, and in the aspirations achieved and yet to be achieved. The increase in productivity and quality is unstoppable, and appears to guide the other variables in the system.

It is natural to ask who activates and governs such phenomena. The answer is that they are self-generated and self-organized in the context of reticular holarchies and orgonic networks formed by production enterprises – or production organizations – that comprise the integrated process of global production.

On a continental scale, it makes sense to consider production in terms of networks of orgons in which, by choice or not, every firm that produces final consumption goods is linked at several levels to a number of other suppliers of materials, components, machines and other structural factors. We can easily observe that the large continental production networks – in North America, China, Japan, India and Europe – are not yet integrated but are becoming larger and increasingly connected, while other local networks are developing in other countries.

In order to understand how things are evolving in a context where there is a connection between firm and production organization we need a conceptual framework that does not limit our observations to the single production units, searching therein for the laws of survival, but one which, at least in principle, is able to explain how the large orgonic networks internally produce self-organization and self-development.

The theory of systems provides two particularly interesting approaches: one that considers firms as adaptive systems that operate according to local rules and that spontaneously and inevitably generate production networks understood as complex adaptive systems, and that which considers production organizations as holons that, given their arrangement in a multi-level holarchy, generate the production networks in which progress appears as the inevitable consequence of the holarchic ordering of the Economic-Production Kosmos.

This essay considers the second approach, presenting the holarchic model of the analysis of production networks. It assumes that in an economy based on knowledge, where the limits of time and space are tenuous, production must increasingly refer not to a single firm but to a system of firms (a super-organizational network) or to operational units (inter-organizational network) conceived of as an operative, information or cognitive network.

It truly appears there is a Ghost in the Machine, whose invisible hand produces growing levels of productivity and quality, increases the quality and quantity of satisfied needs and aspirations, and reduces the burden of work, thereby continually increasing the level of progress in the entire Kosmos.

It is useful to conclude with a bibliographical note.

The conceptual revolution begun in 1967 has not yet led to a relevant number of monographs. On the other hand, there is a substantial bibliography containing journal articles, papers presented at congresses, and opinions and documents from discussion forums. The Internet has been crucial for gaining access to recent material.

 

 

Note:

You may know of Russian Dolls – Nested Dolls.  They are known as Matryoshka Dolls.  I came across this russian paper investigating roots of dolls.

Eastern Roots of Russia’s most famous Toy

May I suggest that name/concept of these dolls could have originated from SAPTA MATRIKA (7 Divine Mothers) of Indian Hindu Tantra Philosophy.

 

 

A Brief History of Holons

Mark Edwards

This concept has a long and respectable ancestry. So much so that defenders of orthodoxy are inclined to dismiss it as “old hat” – and often in the same breath to deny its validity. Yet I hope to show as we go along that this old hat, handled with some affection, can produce lively rabbits.
(Arthur Koestler, 1967, p.45)

Introduction

The idea of hierarchy and of their constituent part-wholes, or holons, has, as Arthur Koestler points out in the opening quote, a long and distinguished history. There are many philosophers who have proposed abstract systems for explaining natural and social phenomena. In pre-Socratic Greece Leuciddus and Deocritus developed the abstract concept of the atom and used it to develop a philosophy that could explain all observed events. Aristotle used hierarchy as the methodology for accumulating and connecting biological knowledge. Hierachy was perhaps the dominant way of viewing the connection between the natural, the human and the supernatural orders of being through the middles ages. In the 17th century Leibnitz proposed his “monad” as an irreducible unit for explaining not only the material world but the inner world of the soul.

In the early twentieth century there was a flurry of interest in holism and hierarchy that owed its genesis to the impact of Darwin’s evolutionary theory. I think the contribution of Jan Smuts in his publication of “Evolution and Holism” in 1926 is particularly important. Smuts was a soldier, a revolutionist republican, a lawyer, the Premier of the Republic of South Africa for several years (before the instigation of political apartheid), a globalist, and one of the founders of the United nations. writers of the UN founding charter. He also was a philosopher who saw the deep connections between the natural and social worlds and his concept of holism clearly influenced Wilber’s ideas in this area. Wilber quotes Smuts at the very beginning of his first major work that fully utilised the concept of hierarchy – “The Atman Project” – “Everywhere we look in nature we see nothing but wholes” (cited in Wilber, 1980). While all these various threads of ideas included the consideration of hierarchical networks and levels and orders of development it was not until the work of writer-philosopher Arthur Koestler that a fully theory of holarchy and holons was proposed.

Arthur Koestler – The father of Holon theory

 

The Ghost in the Machine

 

Some 35 years ago, in 1967, Arthur Koestler proposed the term “holon” in his book “The Ghost in the Machine”. Arthur Koestler was born in 1905 and died in 1983. During the 1930’s and 1040’s Koestler was a journalist who covered the Spanish civil war and World War II from the perspective of the ordinary people who were swept up in the great social tumult of those times. After the war he turned to turned to writing books in both fiction and non-fiction genres. He was one of the most widely read political novelists of all time. Koestler said that he wrote his novels, “out of my quarrels with the human condition”. His other non-fiction books, including, “The Ghost in the machine” were “attempts to analyse that same condition in scientific terms”.

Like Jan Smuts, Arthur Koestler led an extremely eventful life and he participated fully in some of the most important political and social events of his times. Again, similarly with Smuts, Koestler’s engagement with the events of the day included not only social action and participatory involvement at a personal level but he also lived a life of deep connection with the world of culture and inner experience. In the following quote from his book, “The Act of Creation”, Koestler is referring to the relationship between subjective and objective knowledge quests and it shows the awareness he had of both interior and exterior aspects of life.

Einstein’s space is no closer to reality than Van Gogh’s sky. The glory of science is not in a truth more absolute than the truth of Bach or Tolstoy, but in the act of creation itself. The scientist’s discoveries impose his own order on chaos, as the composer or painter imposes his; an order that always refers to limited aspects of reality, and is based on the observer’s frame of reference, which differs from period to period as a Rembrant nude differs from a nude by Manet.
Arthur Koestler, 1970, p. 253It is interesting to look at Koestler’s life in terms of Wilber’s Quadrants framework. He was a philosopher and held a rich interest in art and cultural concerns. He was active socially and for many years was involved in various social movements and was nominated for the Nobel prize for literature three times. His personal life was one of great behavioural involvement with the great dramas of revolution, war and social dislocation that characterised the early and middle twentieth century. He also explored the inner worlds of subjective experience and imagination and wrote some of the most memorable political novels of his times. Looking at his life it is clear that his great span and depth of involvements and experiences should be reflected in his philosophy and in the specific detail of the holon theory that he largely created.

Koestler’s Holon

The idea of the holon occupies a central position in Koestler’s thinking about the human condition. He developed the construct to deal with three central problems that he saw facing the social sciences of the post-war generation. First he saw the need for some model that could unite and integrate the reductionist and mechanistic worldview of the “scientific” and behavioural psychologies with the holistic and humanistic worldview of the Freudian, Rogerian and Gestalt psychologies. Second, he recognised the importance and relevance of evolutionary processes in the social sciences and wanted to provide some theoretical system that could apply evolutionary conceptualisations to both realms. Third, he wanted to develop a model of human social systems that was equally at home in analysing the micro-level of individuality and the macro-level of collectivity. He wanted to propose some basic model of explanation that was relevant across the great span of human activity and involvement.

Koestler acknowledged that his “holon” construct had, in fact, a very venerable and ancient ancestry in western philosophy. Several important philosophers including Leibniz and Hegel had drawn attention to the importance of such things as hierarchy and developmental levels. Koestler saw himself in a line of such thinkers who wanted to bring together different knowledge quests and schools of scientific endeavour instead of pursuing the ongoing specialisation in scientific knowledge that has characterised modern scientific schools. Holon theory was Koestler’s attempt at an integrative philosophy of science and he expected that the holon theory or something similar would form the basis for any truly holistic future scientific worldview. He approvingly quotes one Needham who said that, “The hierarchy of relations … will perhaps be the leading idea of the future”. So, the holon construct was no small thing for Koestler and it is clear that he regarded his holonic principles as a solid attempt at an integrative philosophy of human existence.

So what is a holon. The word is a combination of the Greek “holos” meaning whole, with the suffix “on” which, as in proton or neutron, suggests a particle or part. The holon, then, is a part-whole. It is a nodal point in a hierarchy that describes the relationship between entities that are self-complete wholes and entities that are seen to be other dependent parts. As one’s point of focus moves up, down, and/or across the nodes of a hierarchical structure so one’s perception of what is a whole and what is a part will also change.

The evolutionary holon

In introducing the idea of the holon Koestler quotes the story told to him by Herbert Simon, a Nobel prize winner, and called the ‘parable of the two watchmakers’. The parable goes like this:

There once were two watchmakers, named Bios and Mekhos, who made very fine watches. The phones in their workshops rang frequently; new customers were constantly calling them. However, Bios prospered while Mekhos became poorer and poorer. In the end, Mekhos lost his shop and worked as a mechanic for Bios. What was the reason behind this?

The watches consisted of about 1000 parts each. The watches that Mekhos made were designed such that, when he had to put down a partly assembled watch (for instance, to answer the phone), it immediately fell into pieces and had to be completely reassembled from the basic elements. On the other hand Bios designed his watches so that he could put together subassemblies of about ten components each. Ten of these subassemblies could be put together to make a larger sub-assembly. Finally, ten of the larger subassemblies constituted the whole watch. When Bios had to put his watches down to attend to some interruption they did not break up into their elemental parts but only into their sub-assemblies.

Now, the watchmakers were each disturbed at the same rate of once per hundred assembly operations. However, due to their different assembly methods, it took Mekhos four thousand times longer than Bios to complete a single watch.Koestler relates this story to show that the hierarchical organisation of systems is an inbuilt feature of life – biological life but also any complex evolving system. not only is the time needed for the development greatly shortened when hierarchical methods are used but there are also inherent benefits in terms of maintenance, regulation and restoration. Koestler sees the hierarchical ordering of life as such a fundamental aspect of development that he says (1967, p. 47),

We do not know what forms of life have evolved on other planets in the universe, but we can safely assume that wherever there is life, it must be hierarchically organised (emphasis in the original)Koestler wants to show two things with this parable. First, that complex systems will evolve from simple systems much more rapidly if there are stable intermediate forms than if there are not, i.e. if they are hierarchically organised. Second, and more importantly, he wants to show that the resulting complex systems will always be hierarchic and that hierarchy is the natural and ubiquitous outcome of the development of structural form. After establishing the universal importance of hierarchy to the development of complex systems Koestler went on to propose that these hierarchies could be analysed in terms of the stable intermediate nodes or forms through which their structure is defined. It was to these intermediate forms that Koestler conferred the new label of “holon”.

Koester was a keen student of psychology and was well aware of the problems besetting the reductionist behavioural approaches to psychological theory. He was also conversant with the European schools such as the more holistic Gestalt psychology and he saw his holon theory as a way to move beyond the inadequacies of these contending models. He saw the great dehumanising effect of atomistic psychologies but also recognised the limitations of the holistic schools. As he puts it (1967, p.49)

in spite of its lasting merits, ‘holism’ as a general attitude to psychology turned out to be as one-sided as atomism was, because both treated ‘whole’ and part’ as absolutes, both failed to take into account the hierarchic scaffolding of intermediate structures of sub-wholes … the Behaviourist never gets higher that the bottom layer of stones, and the holist never gets down from the apex.Koester saw holon theory as a broad philosophy of science that showed a way out of the interminable and centuries-long debate over the relative merits of reductionism and holism.

Holons and holarchies

Koestler noted that in every order of existence, from physical to chemical to biological and social systems, entirely self supporting, non-interacting entities did not exist. And more importantly, that entities can be seen to lie in holarchical relationship with each other. He called systems of such entities Open Hierarchical Systems (OHS) and these have subsequently been called holarchies. Every identifiable unit of organization, such as a single cell in an animal or a family unit in a society, comprises more basic units (mitochondria and nucleus, parents and siblings) while at the same time forming a part of a larger unit of organization (a muscle tissue and organ, community and society). A holon, as Koestler devised the term, is an identifiable part of a system that has a unique identity, yet is made up of sub-ordinate parts and in turn is part of a larger whole.

Koestler’s holons were not thought of as entities or objects but as systematic ways of relating theoretical structures. In other words, holons were arbitrary points of reference for interpreting reality. To quote Koestler (1967, pg. 55), “Whatever the nature of a hierarchic organisation, its constituent holons are defined by fixed rules and flexible strategies” (emphasis in the original). So Koestler’s holons are posited and “fixed” only out of the relational rules and strategies that help us make sense of reality.

Because holons are defined by the structure of a hierarchy each identified holon can itself be regarded as a series of nested sub-hierarchies in the same way that a set of Russian dolls is an inclusive series of dolls contained within each other. Holons are, then, both parts and wholes because they are always parts of larger hierarchies and they always contain sub-hierarchies. Holons simultaneously are self-contained wholes to their subordinated parts, and dependent parts when seen from the inverse direction. Hence, holons can be seen as reference points in hierarchical series or holarchies.

Russian dolls

Koestler also recognised that holons are the representative stages or nodal structures that define the developmental hierarchies. As he says (1967, p. 61),

the different levels represent different stages of development, and the holons … reflect intermediary structures at these stages.It is this crucial stage-like characteristic of holons that Wilber takes up, expands and utilises in his spectrum model of human growth and later in his quadrants framework for describing Kosmic development. It is interesting to note that Koestler also recognised that the stage-like nature of hierarchies that existed in the inorganic world and in “the interplay of cohesive and separative forces in stable inorganic systems, from atoms to galaxies”.

So, we see that Koestler not only introduced the nomenclature of holons but he also described their place in developmental theory and saw how they could be used to overcome many of the philosophical problems that were plagued the social and psychological sciences of the early twentieth century. Even more than this, Koestler developed a very detailed set of holonic principles that actually defined a new theory of social development and general evolutionary theory. These principles are outlined in an appendix to “The Ghost in the Machine” and are titled “General Properties Of Open Hierarchical Systems (O.H.S.)”. Many of these principles have been taken up and expanded on by Ken Wilber in his holonic tenets but there are many that have not. Before comparing Koestler’s OHS properties with the twenty tenets of Wilber I will give a brief overview of how Wilber has adopted the holon and how it fills a central role in his most recent writings on Integral theory.

Ken Wilber’s Holonic Tenets

Sex, Ecology, Spirituality

 

Wilber adopted Koestler’s holon construct during, what Wilber has called, the phase-2 period in the development of his philosophy. This phase, which occurred around the late seventies and early eighties, is characterised by a focus on the spectral transcend-and–include nature of all developmental structures. It is no surprise that Wilber would be drawn to the holon as a construct given his developmental interests and particularly his revolutionary pre/trans theorem which is so useful to unravelling the boundary stages of growth. So, it was quite early on that the holon construct was incorporated into the basic theoretical scheme Wilber’s writings as a way of emphasising the hierarchical/holarchical nature of reality. To my knowledge, the first reference that Wilber makes to the holon construct is in his 1983 book, “Eye to Eye” but he may well have been aware of the term for some time. This was at least 15 years prior to the great expansion of his ideas that culminated in 1995 in the publication of “Sex, Ecology, Spirituality” (SES) which introduced the Four Quadrants of Kosmic evolution (Wilber’s Phase-4). From 1995 the holon and its various defining qualities have held an increasingly important position in Wilber’s writings.

Wilber holonic theory or as he refers to it “the twenty tenets” were first laid out in the opening chapters to SES. They provide the foundation for his mapping out of the All Quadrants, All Levels framework (AQAL). It is clear from the very beginning of SES that Wilber now regards the idea of the holon as the primary explanatory unit in his AQAL framework. This is conveyed in his famous statement that,

“Reality as a whole is not composed of things or processes, but of holons”.

This groundbreaking statement sets the holon construct at the very heart of Wilber’s whole explanatory endeavour. And, I believe, that this marks a major turning point in the history of Western philosophy of science and in our more general attempt to develop scientific explanations of social phenomena. The reason for this is because in clearly identifying the holon as the central unit of explanation Wilber provides a basis for connecting all fields of scientific and cultural knowledge.

Wilber’s AQAL framework and the Holon

As with Koestler, Wilber uses the holon theory to, “undercut the traditional argument between atomism .. and wholism”. For Wilber to incorporate holonic theory into the theoretical structure of the AQAL framework was easy at one level because both theories were founded on the idea of hierarchical inclusion. The difference between them was that Wilber’s AQAL framework was a way of seeing the whole developmental and evolutionary nature of all relative knowledge, experience and activity. Wilber took Koestler’s holon to its logical end and, placing within the AQAL framework, saw the holon as a way of analysing all aspects and domains of reality. The subtitle of SES is “The Spirit of Evolution” and to my mind the book is an attempt to bring evolutionary theory out of its traditional biological home and to apply to all levels of existence – from matter to spirit. Wilber does this through the identification of the holon as his core explanatory device. This is the absolutely crucial part that holons play in his model.

In taking up Koestler’s wonderful theory of holons, Wilber too has stressed the sliding and contextual, yet hierarchical, nature of holons. Wilber has creatively used the holon construct to highlight the holarchical nature of his AQAL framework. The framework is derived from an immense amount of scientific, cultural and experiential knowledge. In adopting the holon construct the AQAL model becomes more than just a new way of connecting existing fields of knowledge in a developmental overview. It is also a new way of looking at the referential “units” of that knowledge – holons. Built into the heart of the model is the concept that all developmental phenomena can be viewed as aspects of dynamic, holonic events that are nested within a holarchy of evolving/involving structural patterns.

The holons construct is so critically important to the utility of the Integral model because it enables the AQAL framework to be focused on any point in the holarchy or, to put it another way, it enables any developmental event to be analysed in terms of an Integral methodology. As such, the concept of the “holon” does away with the endless quest of trying to find the fundamental parts or wholes that constitute reality and it releases us from the basis mythologies inherent in materialistic, mentalistic, animistic, relativistic, or idealistic conceptions of reality. Quantum physics, that most advanced of all natural sciences, now overtly recognises the completely mythological nature of “matter” (Davies & Gribble, 1992), and of ideas that regard reality as simply permutations of solid substance, empty space, and linear time. The AQAL model, when it is used as an interpretive schema, extends this demythologising awareness across all explanatory systems (including itself) and brings to the fore the holarchic and developmental nature of reality. With the idea of a nested holarchy of holons, Wilber has opened a vision of reality that does not fall into the errors associated with various forms of reductionism, elevationism or relativisim. In bringing Koesler’s holon concept into his model, Wilber has not only opened up the possibility of a truly open-ended Theory of Everything but also a systematic theoretical approach towards any thing/process/event.

The holon – Integral theory’s unit of analysis

The development of the human, in both its personal and social forms, is the most complex phenomena that we yet know about in the Kosmos. To understand this process in any sort of detailed and valid fashion is, to put it mildly, a big task. It is my opinion that Ken Wilber’s Integral theory is the only philosophical/epistemological/theoretical framework that attempts to present a comprehensive understanding of the complex and multi-layered reality that we see about us. One of the most attractive central features of Integral theory is that it does not rely on ontological reductionism to simplify that complexity, as do many other branches of science. The neurologist and the medical specialist reduce the human to the biochemical with their unit of study being the chemical compound. The behaviourist reduces the human to physical action with their unit of study being the behavioural stimulus-response cycle. The cognitivist reduces the human to the world of behaviour and thought with their basic unit of explanation being the pattern of thought, belief or feeling. The evolutionist reduces it to reproductive advantage with the locus of explanation being the adaptive interaction between environment and phenotype. The sociologist reduces the human to the world of interpersonal relations and group dynamics with their focus of explanation being the social event. The humanist reduces the human to the world of being and identity with authenticity in word and deed being their centre of interest. The transpersonalist reduces, or more correctly elevates, the human to the world of spirit and finds explanation in the analysis of the mystical event.

All these disciplines simplify human complexity to find something of certainty, something that is true, something that will have lasting validity. And, in their own way, each of the main perspectives on human reality does contribute unique knowledge to the quest for understanding that so occupies us. As Wilber has often pointed out, all these contributions are partially correct. The human can be understood and explained through the study of the physical, the chemical, the animal, the social, the political, the cognitive, the existential, the spiritual, and the historical. Once this partiality is recognised, we are then faced with the problem of truly integrating the valid and the true of each and bringing them into some semblance of coherency. And the very first task that is required for this integrative endeavour to be successful is to identify a unit of analysis or explanation that does not privilege any of the units of analysis or explanation associated with partial views.

In my opinion it is one of Wilber’s greatest insights that he has been able to identity an explanatory reference point that avoids the ontological pitfalls that have so plagued all previous explanatory elements. In so doing Wilber allows Integral theory to transcend (and integrate) all the reductionisms of the partial views to boldly propose that the true locus of explanation does not reside in any particular level of reality and cannot be limited to any single domain of investigation. The basic unit of analysis for Integral theory is not the atom, or the molecule, or the mathematical unit, or the interpretive perspective, or the cognitive pattern, or the historical event, or the spiritual revelation. For Integral theory the unit of analysis, it’s basic point of explanation, analysis, reference and “measurement” is the holon. This is why students of Wilber work, if they are to understand what Integral theory/philosophy, the AQAL framework and IMP’s are truly about, will have to have a good grounding in holon theory.

The reductive research paradigm has been immensely successful for investigating physical and chemical phenomena. More recently holistic approaches like the various systems theories, humanistic disciplines, and developmental theories have been successfully applied to social phenomena. The holon, the “part-whole”, has a built in non-reductive perspective that allows for the simultaneous recognition that anything can be studied holistically and anything can be analysed reductively at the same time. This combination of holistic and reductive methodologies also introduces a new element and immensely important capacity for explanatory methodologies that utilise this part-whole focus of explanation. It now means that the various types of reductive science can now be carried out in relational context. The disciplines of physics, chemistry, biology, psychology, the humanities, sociology, theology, and cultural studies can now be pursued within a cross-disciplinary framework that connects and situates their disparate findings and truths instead of juxtaposing them. By allowing for both holistic and reductive methodologies, the holon framework introduces an integrative dimension of implementing those approaches that no other approach can claim. This new capacity lies at the heart of Wilber’s (2002) recent call for a revolutionary Integral Methodological Pluralism (IMP) – “a project of synthesis”.

Holism, reductionism and pluralism

The holon is the holarchic (i.e. hierarchic plus heterarchic) reference point through which the various principles of the AQAL model can be applied. This is the real point behind Wilber’s first tenet of holons, “Reality as a whole is not composed of things, or processes, but of holons”. He is really pointing out here that holons permit an analytical holism that can evade the reductive errors that result from explanations that rely on some fundamental thing or process. Unfortunately the wording of this tenet suggests that holons themselves are building block composites that in some way fit together to make up Kosmic reality. But this is not at all Wilber’s intended reading for this tenet. The holon construct allows Integral theory and it’s AQAL methodology to step away from and the methodological battles engaged in by other disciplines and to avoid the reductive pitfalls that abound wherever science seeks to understand complex phenomena. The use of the holon as the means for applying Integral theory also allows the many other truths that have been uncovered by human knowledge quests to be honoured and rightfully situated within a non-reductive context. It is not just that the holon in conjunction with the AQAL principles can investigate systemic and elemental aspect of reality but that it can also, as Wilber says, “acknowledge, honor, and include all authentic modes of human inquiry ” (and their valid findings). In short, the full integration of the holon and the AQAL model enables Integral theory to overcome the traditional reductionist propensity to privilege very biased methodologies for gathering observations and experiences and very narrow modes of explanation for understanding them. As Wilber (2002) has recently said:

AQAL, then, is a metatheory that attempts to integrate the most amount of material from an integral methodological pluralism, thus honoring the primary injunction of an integral embrace: Everybody is right.

Everybody, i.e. all major theorists, philosophies and stores of cultural knowledge, are right (within context) and it is the holon construct that allows Integral theory to move without prejudice around these vast domains of human knowledge and pursue its agenda of holistic exploration and analysis. This process of acknowledging the validity and value of established personal and cultural knowledge quests can be viewed from a broader perspective than simply that of Wilber’s integral theory. Wilber has recently termed any such endeavour as Integral Methodological Pluralism (IMP). Integral theory is an example of such an approach to the investigation of events, experiences, and knowledge. But I believe that any such method will need to be based on the holon construct in some form because it is the only explanatory concept that can accommodate the three definitive criteria for an IMP.

Similarities and Differences

I have pointed out that Koestler has proposed a quite detailed set of holonic principles and shown that the holon construct has a very wide application. Wilber, in turn, has placed the holon construct firmly at the centre of his comprehensive integrative framework for connecting knowledge. Wilber has expanded holon theory into a new approach to understanding the relationship of many different knowledge domains. It should, however, be noted that Koestler provided Wilber with much more than just a new term to label the “building blocks” of his Integral theory/AQAL framework. Koestler’s principles of Open Hierarchical Systems (OHS) and Wilber’s twenty tenets are clearly very related and the following table shows the correspondences between the two types of holon theory.

Table 1: Correspondences between Koestler’s OHS principles
and Wilber’s twenty Holonic Tenets
Wilber’s Twenty tenets Koestler’s OHS principles*
1: Reality can be seen in terms of an endless series of holonic relations 1.3 Parts and wholes in an absolute sense do not exist in the domain of life. The concept of the holon is intended to reconcile the atomistic and holistic approaches. “The [holarchy] is open-ended in the downward, as it is in the upward direction”
2a: Holons have agency, individuality, deep autonomy. 4.1 Every holon has the … tendency to preserve and assert its individuality as a quasi-autonomous whole; 9.2 the holon’s agency is that which controls the part from the next higher level.
2b: Holons have communality, mutuality, and collective relationships 4.8 The canon of a social holon represents not only constraints imposed on its actions, but also embodies maxims of conduct, moral imperatives and systems of value.
2c: Holons have a capacity for self-transcendence, and active transformation into greater wholes 5.6 A holon on the n level of an output-hierarchy is represented on the (n+ I) level as a unit, and triggered into action as a unit. A holon, in other words, is a system of relata. which is represented on the next higher level as a relatum.
2d: Holons have a capacity for self-immanence, and the active integration of its parts 4.1 Every holon has the tendency to function as an integrated part of an (existing or evolving) larger whole.
4.1 a holon’s Integrative (INT) tendencies are inherent in the concept of hierarchic order and a universal characteristic of life. The INT tendencies are the dynamic expression of the holon’s partness.
3: Holons emerge creatively and indeterminately 8. Holons on successively higher levels of the hierarchy show increasingly complex, more flexible and less predictable patterns of activity. while on successive lower levels we find increasingly mechanised stereotyped and predictable patterns.
4: Holons emerge holarchically, i.e. through dynamics between hierarchy and heterarchy 6.1 Hierarchies can be regarded as ‘vertically’ arborising structures whose branches interlock with those of other hierarchies at a multiplicity of levels and form ‘horizontal’ networks
5: Each emergent holon transcends but includes its predecessors “A hierarchy of holons should rightly be called a holarchy”
8: Each successive holon level within a holarchy produces greater depth and less span 2.2 The number of levels in a hierarchy is a measure of its “‘depth”, and the number of holons on any given level is called its “span”.
12a: Evolution displays increasing complexity 8.4 Each upward shift is reflected by a more vivid and precise consciousness of the ongoing activity; and, since the variety of alternative choices increases with the increasing complexity on higher levels, each upward shift is accompanied by the subjective experience of freedom of decision. (“We find [holons] in an ascending order of complexity” )
Holarchies possess interiority and consciousness 8.6 Consciousness appears as an emergent quality in phylogeny and ontogeny, which, from primitive beginnings, evolves towards more complex and precise states.

* All direct quotes from “The Ghost in the Machine”

Table 1 shows the clear concordances between Koestler’s OHS principles and Wilber’s twenty tenets. I have pointed out these overlaps to show that Wilber’s extended use of the holon construct clearly builds on Koestler’s quite extensive and detailed explications of holon theory and that therefore the two models should be seen as a single continuum of development in the theory. Wilber has taken the foundational theorems laid down by Koestler and greatly extended their theoretical and practical application. As a whole holon theory needs to be seen as a new and very promising philosophy of knowledge that may well open up an entirely new and genuinely integrative understanding of the natural and social worlds and how they relate to each other.

There are several aspects of Koestler’s theory that have, as yet, not been explored by Wilber or any other Integral theory writers. These include the concept of holonic exchange/input-output systems which looks at the way holonic outputs are triggered and how holons scanners and filter inputs. Koestler’s concepts of “arborisation”, “reticulation” and “regulation channels” also show promise as ways of seeing how holons can relate to each other. There is also the issue of holonic health and how holons change and Koestler’s principles on holonic equilibrium, disorder and regeneration offer fertile ground for further study.

Holons and the Future

I noted earlier that Ken Wilber (2002b) has recently suggested some principles that define, what he calls, an Integral Methodological Pluralism (IMP). This idea refers to the broad characteristics of a discipline that can be considered to be an integral approach to a topic. Wilber maintains that any future over-arching model of knowledge will have posses the main principles that define an IMP. These principles are non-exclusion, enfoldment/unfoldment, and enactment. Wilber defines non-exclusion as follows:

Nonexclusion means that we can accept the valid truth claims (i.e. the truth claims that pass validity tests for their own paradigms in their own fields, whether in hermeneutics, spirituality, science, etc.) insofar as they make statements about the existence of their own enacted and disclosed phenomena, but not when they make statements about the existence of phenomena enacted by other paradigms. (2002b, ¶52)

This principle refers to the acceptance of partial but valid knowledge that has been gleaned by disciplines focusing on particular aspects of holons. Much of this knowledge has been the result of reductionist paradigms (disciplinary matrices/methodologies). The second principle, enfoldment/ unfoldment is defined as:

nonexclusion often discloses an unfoldment that is enfoldment: in any particular developmental stream, successive waves transcend and include their predecessors, and thus each wave is adequate, each succeeding wave is more adequate. (2002b, ¶73)

In short, in healthy unfolding, each wave is holistic, each succeeding wave is more holistic. (2002b, ¶81)

The unfoldment/enfoldment principle refers to the acceptance of the holistic and developmental nature of knowledge and methods. This principle relates to the idea that all knowledge bases and methods are connected and can illuminate each other. Wilber’s third principle, the Enactment principle is explained as follows:

Putting all of these modes of inquiry together, as an enactment and disclosure of turquoise cognition, results in what we are calling integral methodological pluralism, which embodies the more practical side of an Integral Post-Metaphysics (Wilber 2002a, ¶64)

phenomena are enacted, brought forth, and disclosed by practices, then we realize that what appeared to be “conflicting phenomena” or experiences are simply different (and fully compatible) experiences brought forth by different practices. (2002b, ¶89)

So enactment refers to the novel capacity of an IMP to situate and provide a new integrative context for all other partial approaches be they reductionist or holistic. It is precisely these three IMP capacities that are made available when the holon is seen as the unit of analysis for Integral theory. This leads to what Wilber calls Integral indexing or conferencing.

“AQAL indexing” (“integral indexing” or “holonic conferencing” [see below]) allows individual paradigms to be seated next to each other at the integrative table, in such as a way that each individual paradigm is honored and acknowledged. (2002b, ¶75)

Richard Slaughter, in an essay on the possibilities of an Integral Futures discipline, has pointed out that any futures studies practitionsers will not only need to understand the potentials and limitations of their own worldviews but will also need to be “proficient in exploring other perspectives” and the relationships that come out of the meeting of different perspectives. There seems to be an imperative here for scholars who deal with Big Pictures to take on the IMP framework. As part of this move, I would further add that the holon construct and holon theory may well be an essential aspect of any IMP. I say this simply because the holon framework presents a methodological basis for the IMP principles. The holon construct allows for the discriminative analysis of phenomena through non-exclusion, it allows for the inclusion of holistic and developmental through unfoldment/unfoldment, and it allows for the active discovery of insight and connective knowledge through its capacity to generate the enactment of integrative practices. The holon is the core unitary construct that will define any IMP approach to investigating, experiencing and analysing the human encounter with our world.

Conclusions

The holon construct and it associated theory has the potential to play a crucial role in the movement to combine and synthesise scientific and cultural knowledge about psychological and social realities. While there is a long tradition of attempts to derive a comprehensive philosophy for understanding human realities it is only with the 19th and 20th centuries contributions of evolutionary theory and developmental models of human growth that this synthesising project has really come of age. In many ways holon theory is the culmination of this integrative movement and its development comes at a time when such connective knowledge and holistic approaches are most needed. The global systems that threaten the development of healthy and sustainable social development require systemic and integrative modes of imagination and action. Holon theory as an example of an IMP provides the scope and insight that global crises demand.

It is not by accident, I believe, that the two founders of holon theory have both come from outside of academia. One from the world of journalism and real politic and the other from the world of contemporary spirituality and the human potential movement. Out of their visionary thinking these two writers/philosophers have forged a new approach to seeing the breadth and depth of reality and the challenges that are inherent in it. Koestler and Wilber’s lives and writings are very different but also in a deep way very complementary. One comes from the experience of war and revolution in continental Europe while the other comes from a secluded life of inner journeys. One writes fiction as a way of wrestling with the world of human suffering the other writes non-fiction as a way of mapping out the potential for life. One is immerses himself in the psychologies and philosophies of the western tradition and the other follows contemplative paths of Eastern spirituality. Together they bring a new vision to how we and our realities are connected to each other. In the chapter which introduces the neologism “holon” for the first time, Koestler quotes the writer L.L. Whyte who said that, “fertile vistas may open out when commonplace facts are examined from a fresh point of view.” In my view the holon, and its associated theoretical principles, will open up the richest and most crucial fields of scientific and cultural endeavour in the 21st century.

References

Koestler, A. (1967) The ghost in the machine. London: Arkana

Wilber, K. (1995) Sex, ecology and spirituality: The evolution of spirit. New York: Shambhala.

Wilber, K. (2002) Excerpt B: The Many Ways We Touch -Three Principles Helpful for Any Integrative Approach

Please see my related posts:

 

Levels of Human Psychological Development in Integral Spiral Dynamics

Multilevel Approach to Research in Organizations

The Great Chain of Being

Boundaries and Networks

Hierarchy Theory in Biology, Ecology and Evolution

Networks and Hierarchies

Consciousness of Cosmos: A Fractal, Recursive, Holographic Universe

Truth, Beauty, and Goodness: Integral Theory of Ken Wilber

Boundaries and Relational Sociology

Reflexivity, Recursion, and Self Reference

 

Key Sources of Researches:

 

 

 

Holon (philosophy)

WIKIPEDIA

https://en.wikipedia.org/wiki/Holon_(philosophy)

 

 

 

Holons and Holarchy of Arthur Koestler

 

Arthur Koestler

 

Click to access holarchy-holons-koestler.pdf

 

 

 

 

The Holonic Revolution Holons, Holarchies and Holonic Networks. The Ghost in the Production Machine

Piero Mella

https://www.researchgate.net/publication/270338868_The_Holonic_Revolution_Holons_Holarchies_and_Holonic_Networks_The_Ghost_in_the_Production_Machine

 

 

 

Holons and agents

A. Giret

https://www.researchgate.net/publication/226808580_Holons_and_agents

 

 

 

 

A Brief History of Holons

Mark Edwards

Click to access Edwards-Mark-A-Brief-History-of-Holons.pdf

http://www.integralworld.net/edwards13.html

 

 

 

 

 

The Holonic View of Organizations and Firms

 

Rolf Sattler

 

Eastern Roots of Russia’s most famous Toy

The Great Chain of Being

The Great Chain of Being

 

 

‘Yat Pinde tad Brahmaande’

“As above, so below.” The ancient Vedas and Upanishads say, “Yatha pinde, tatha Brahmande”, translated as: “As is the atom, so is the universe. As is the microcosm, so is the macrocosm.” i.e., The individual is truly cosmic.

 

‘To see a world in a grain of sand and heaven in a wild flower,
hold infinity in the palm of your hand and eternity in an hour.’
William Blake

 

Key Ideas

  • Hierarchical Nested Levels
  • Vertical Chain of Being
  • Multi-Levels Thinking
  • Multi Scale Thinking
  • Fractal (Self Similar) Structure
  • Holographic Brain, Holographic Universe
  • Hierarchy, Heterarchy, and Holarchy
  • Parts and Whole ( Part in Whole, Part is the Whole, Whole in the Part)
  • Hyper Sets
  • Nested Platonic Solids
  • Connectivity (Interconnected) Hypothesis
  • Myth of Invariance
  • Invariance in Time and Space
  • Levels of Consciousness
  • Sheaths of Being (Kosha)
  • 14 Lokas (worlds) in Hinduism
  • 11 headed Chenrezig (Tibet Buddhism)- Chenrezig in Tibet / Avalokiteshvara in India/ Kuan-yin in China/ Kannon in Japan.
  • Virat Swarup of Krishna (Bhagvat Geeta)
  • Realms in Norse Mythology
  • Shiva (10), Rudra (18), Bhairav (64)
  • Shri Yantra Geometry
  • Vasu (8), Rudra (11), Aditya (12),
  • Hyper Cube (Tessarat) / Hyper Sphere
  • 14 Parts of Maha Vishnu
  • Microcosm and Macrocosm
  • Theory of Correspondences
  • 7 Chakras of Human Body
  • Involution and Evolution
  • Immanence and Transcendence
  • Ascent and Descent
  • Jacob’s Ladder
  • Continnum
  • Jhini Jhini Chaddariya (Songs of Kabir)
  • Jambu Dwipa to Pushkar Dwipa
  • Board Game of Saap-Seedhi / Snakes and Ladder
  • Bhu/Bhuvah/Svah (Terrestial to Celestial)
  • Flatland (book)
  • Square and Circle / Squaring the Circle
  • Three Gunas – Sattva, Rajas, Tamas
  • Pancha Bhuttas ( Five Elements)
  • Philosophy of Astrology
  • Relations of Nakshatras with Gunas
  • 72,000 Nadis in Human Body – 14 main Nadis – Pingala, Ida, Sushumna
  • Three Doshas – Kapha, Pitta, and Vata in Ayurveda
  • Jain Cosmology/Buddhist Cosmology/Hindu Cosmology
  • 14 Rajju – Height of Universe in Jain Cosmology
  • Three Granthies (Knots) – Brahma (Base of Spine), Vishnu (Heart), Rudra (Between Eyebrows)
  • 14 Verses of Maheshvara Sutras (Panini)
  • Bhuvneshvara – Lord of 14 Lokas – Bhuvans – Levels
  • 14 Parts of Osiris in Egypt (Misr) Myths
  • 14 Years Exile of Ram, Lakshman, and Sita in Ramayan
  • Three Bodies – Gross, Subtle, Causal
  • Three States – Waking, Dreaming, Sleeping
  • Man in the Universe, Universe in Man
  • Mind in Man, Man in the Mind
  • Mind Only School of Mahayana Buddhism (Yogachara)

 

 

Great Chain of Being

Great Chain of Being, also called Chain of Being, conception of the nature of the universe that had a pervasive influence on Western thought, particularly through the ancient Greek Neoplatonists and derivative philosophies during the European Renaissance and the 17th and early 18th centuries. The term denotes three general features of the universe: plenitude, continuity, and gradation. The principle of plenitude states that the universe is “full,” exhibiting the maximal diversity of kinds of existences; everything possible (i.e., not self-contradictory) is actual. The principle of continuity asserts that the universe is composed of an infinite series of forms, each of which shares with its neighbour at least one attribute. According to the principle of linear gradation, this series ranges in hierarchical order from the barest type of existence to the ens perfectissimum, or God.

The idea of the chain of being was first systematized by the Neoplatonist Plotinus, though the component concepts were derived from Plato and Aristotle. Plato’s “idea of the good” in the Republic, eternal, immutable, ineffable, perfect, the universal object of desire, is fused with the demiurge of the Timaeus, who constructed the world of becoming because “he was good, and in one that is good no envy of anything else ever arises.” Aristotle introduced a definition of the continuum and pointed out various graded scales of existence. Thus, in the words of Plotinus, in his Enneads,“The one is perfect because it seeks for nothing, and possesses nothing, and has need of nothing; and being perfect, it overflows, and thus its superabundance produces an Other.” This generation of the many from the one must continue until all possible varieties of being in the descending series are realized.

The scale of being served Plotinus and many later writers as an explanation of the existence of evil in the sense of lack of some good. It also offered an argument for optimism; since all beings other than the ens perfectissimum are to some degree imperfect or evil, and since the goodness of the universe as a whole consists in its fullness, the best possible world will be one that contains the greatest possible variety of beings and so all possible evils. The notion died out in the 19th century but was given renewed currency in the 20th by Arthur O. Lovejoy (The Great Chain of Being: A Study of the History of an Idea, 1936).

 

General Characteristics of the Renaissance

The Great Chain of Being

Among the most important of the continuities of the Renaissance with the Classical period was the concept  of the Great Chain of Being. Its major premise was that every existing thing in the universe had its “place” in a divinely planned hierarchical order, which was pictured as a chain vertically extended.  (“Hierarchical” refers to an order based on a series of higher and lower, strictly ranked gradations.) An object’s “place” depended on the relative proportion of “spirit” and “matter” it contained–the less “spirit” and the more “matter,” the lower down it stood. At the bottom, for example, stood various types of inanimate objects, such as metals, stones, and the four elements (earth, water, air, fire). Higher up were various members of the vegetative class, like trees and flowers. Then came animals; then humans; and then angels.  At the very top was God. Then within each of these large groups, there were other hierarchies. For example, among metals, gold was the noblest and stood highest; lead had less “spirit” and more matter and so stood lower. (Alchemy was based on the belief that lead could be changed to gold through an infusion of “spirit.”)  The various species of plants, animals, humans, and angels were similarly ranked from low to high with in their respective segments. Finally, it was believed that between the segments themselves, there was continuity (shellfish were lowest among animals and shaded into the vegetative class, for example, because without locomotion, they most resembled plants).

Besides universal orderliness, there was universal interdependence. This was implicit in the doctrine of “correspondences,” which held that different segments of the chain reflected other segments. For example, Renaissance thinkers viewed a human being as a microcosm (literally, a “little world”) that reflected the structure of the world as a whole, the macrocosm; just as the world was composed of four “elements” (earth, water, air, fire), so too was the human body composed of four substances called “humours,” with characteristics corresponding to the four elements. (Illness occurred when there was an imbalance or “disorder” among the humours, that is, when they did not exist in proper proportion to each other.)  “Correspondences” existed everywhere, on many levels. Thus the hierarchical organization of the mental faculties was also thought of as reflecting the hierarchical order within the family, the state, and the forces of nature. When things were properly ordered, reason ruled the emotions, just as a king ruled his subjects,
the parent ruled the child, and the sun governed the planets. But when disorder was present in one realm, it was correspondingly reflected in other realms. For example, in Shakespeare’s King Lear, the simultaneous disorder in family relationships and in the state (child ruling parent, subject ruling king) is reflected in the disorder of Lear’s mind (the loss of reason) as well as in the disorder of nature (the raging storm). Lear even equates his loss of reason to “a tempest in my mind.”

According to the chain of being concept, all existing things have their precise place and function in the universe, and to depart from one’s proper place was to betray one’s nature. Human beings, for example, were pictured as placed between the beasts and the angels. To act against human nature by not allowing reason to rule the emotions–was to descend to the level of the beasts.

 

From From the Great Chain of Being to Postmodernism in three Easy Steps

 

Chain of Beingchain of Being 2chain of being 3chain of being 4Chain of being 5Chain of Being 6

 

The 14 Lokas Of Hinduism –

The concept of the 14 Lokas of Hinduism state that they are divided into 7 upper worlds or Vyarthis and the 7 lower ones, known as the Patalas.

The 7 Vyarthis –

1 Satya-loka: Brahma’s loka. Satya-loka planetary system is not eternal. Abode of Truth or of Brahma, where atman are released from the necessity of rebirth.

2 Tapa-loka: Abode of tapas or of other deities. Ayohnija devadas live here.

3 Jana-loka: Abode of the sons of God Brahma.

4 Mahar-loka: The abode of great sages and enlightened beings like Markendeya and other rishies.

5 Svar-loka: Region between the sun and polar star, the heaven of the god Indra. Indra, devatas, Rishies, Gandharvas and Apsaras live here: a heavenly paradise of pleasure, where all the 330 million Hindu gods (Deva) reside along with the king of gods, Indra.

6 Bhuvar-loka (aka Pitri Loka): Sun, planets, stars. Space between earth and the sun, inhabited by semi-divine beings. It is a real region, the atmosphere, the life-force.

7 Bhur-loka: The Vishnu Purana says that the earth is merely one of thousands of billions of inhabited worlds like itself to be found in the universe.

The 7 Patalas –

1 Atala-loka: Atala is ruled by Bala – a son of Maya – who possesses mystical powers. By one yawn, Bala created three types of women – svairiṇīs , who like to marry men from their own group; kāmiṇīs, who marry men from any group, and the puḿścalīs.

2 Vitala-loka: Vitala is ruled by the god Hara-Bhava – a form of Shiva, who dwells with attendant ganas including ghosts and goblins as the master of gold mines. The residents of this realm are adorned with gold from this region.

3 Sutala-loka: Sutala is the kingdom of the pious demon king Bali.

4 Talatala-loka: Talātala is the realm of the demon-architect Maya, who is well-versed in sorcery. Shiva, as Tripurantaka, destroyed the three cities of Maya but was later pleased with Maya and gave him this realm and promised to protect him.

5 Mahatala-loka: Mahātala is the abode of many-hooded Nagas (serpents) – the sons of Kadru, headed by the Krodhavasha (Irascible) band of Kuhaka, Taksshaka, Kaliya and Sushena. They live here with their families in peace but always fear Garuda, the eagle-man.

6 Rasatala-loka: Rasātala is the home of the demons – Danavas and Daityas, who are mighty but cruel. They are the eternal foes of Devas (the gods). They live in holes like serpents.

7 Patala-loka: The lowest realm is called Patala or Nagaloka, the region of the Nagas, ruled by Vasuki. Here live several Nagas with many hoods. Each of their hood is decorated by a jewel, whose light illuminates this realm.

 

 

Koshas and Lokas in Hinduism

chain of being

 

greatchain2

 

 

greatchain3

 

The Five Koshas

Swami Satyananda Saraswati

 

Satsang in Toulon, France, June 9, 1984

In philosophy, the body, mind and spirit are understood as one continuity, but in fact eastern and western thought were never in agreement with each other. Western philosophy originated from Greece while eastern philosophy originated in India. Greek philosophers in general and western philosophers in particular spoke about the object. Indian philosophers in general and in particular spoke about consciousness, and for many centuries western thinkers could never accept anything beyond object as tangible: here is the object, I can see it, I can touch it, therefore it is.

However, in yoga and in vedanta, object and consciousness are interrelated. In fact, modern science, what you call physics, speaks in exactly the same way as yoga. Both modern physics and ancient yoga move absolutely parallel to each other in explaining the reality of matter and consciousness.

Body, mind and spirit are interconnected, interrelated and interpenetrating. Therefore, a person is a combination of three things: firstly, the gross body, secondly, the subtle or astral body and thirdly, the causal body or unconscious. These three bodies constitute you, me and everyone, but they are gross divisions, broad classifications.

Each body has a dimension and a layer. You can call it a field. Just as you say electromagnetic field or radioactive field, in exactly the same way there are fields in your body. In vedanta, they are known as koshas which means ‘sheaths’. These koshas are five in number: annamaya, pranamaya, manomaya, vijnanamaya and anandamaya, and are further sub-divisions of the three bodies, which represent the three states of your daily experience.

Every day you have three types of experiences. One is the waking experience in which you experience through your senses and mind. The second experience is dream. In dream you do not experience through the senses, but through your subconscious mind. The third experience is sleep in which there is no knowledge of time and space, no knowledge about yourself or about anything in sleep, but when you get up in the morning, you know that you slept well the night before.

So every day the individual self undergoes these three experiences alternately. These experiences relate to a particular field. Whenever your individual self goes to one particular realm, it has one experience, and as your individual self changes the field, realm or dimension, it has another experience. For example, if you go to the North Pole, you will feel cold, or if you go to a tropical country, you will feel hot.

Annamaya kosha

The first kosha is annamaya, the physical body. Annamaya kosha can be sattwic, rajasic or tamasic. The word sattwa means harmony, balance and tranquillity, where you create a balance between activity and peace. Rajas means dynamic, active, violent. Tamas means dull and inert. Through the hatha yoga shatkriyas, you develop a sattwic annamaya kosha and when annamaya kosha becomes sattwic, then the bouncing of energy is much greater.

In modern science it is said that all the time, the whole day and night, atomic energy is bouncing in and out from this physical body like a pendulum. Of course, you cannot see it, but scientifically it has been seen that just like a pendulum swings from left to right, left to right, in the same manner everybody is emitting or throwing away these atoms. The sattwic body creates a longer bouncing, a tamasic body perhaps no bouncing at all, while a rajasic body has a bouncing but it has no limitation.

Now when these atoms or atomic particles bounce off your body and come back, there is a period of rest. That period of rest is always in the pendulum also. When it goes to the left and then turns to the right, there is a moment of rest. In the same way, when you do pranayama, in between inhalation and exhalation there is a point of rest. That is called timelessness and it is very short. Sometimes it can be a one-thousandth part of one second and sometimes a ten-thousandth part of a second. In that short period, the body transmits energy which is sattwic, rajasic or tamasic. Therefore, annamaya kosha, which is the container of the other koshas, is tackled through the practices of the hatha yoga shatkriyas.

Pranayama kosha

The second kosha is pranamaya, the kosha composed of prana, or life force. This prana is a part of cosmic life. Each and every creature, each and every thing in this world is a part of cosmic life. Prana is the force or energy for all kinds of motion. Prana is a Sanskrit word meaning movement, motion or vibration.

Pranic energy is in constant motion throughout life. It is not only in human beings, animals, herbs or trees, not only in oceans and mountains, minerals and bacteria. The tiniest part of an atom has prana. This prana is both visible and invisible. We need not talk about invisible prana now. Visible prana is manifesting before you. Wherever there is prana there is movement, growth, change and activity and where there is no prana there is no activity. When we die the body dissipates because it has become completely bereft of prana.

Prana is one item of your total composition and should also be dealt with in yoga. If the pranas are agitated or there is a pranic imbalance, there is imbalance everywhere. To understand prana you need to know a little about positive and negative atoms. The pranas are in the atmosphere in the form of positive and negative ions, which keep on bouncing, migrating and reintegrating. A balance has to be created between them.

If you study the science of the behaviour of positive and negative ions, you will understand the importance of balancing the prana in the body, because prana represents the positive energy in the body, and mind represents the negative energy. When there is a balance between positive and negative energy, then you can see illumination and everything is in harmony.

This prana is responsible for the action of the karmendriyas, the organs of action, just as electrical energy is responsible for the functioning of a microphone or light bulb. If the electricity which is being supplied somewhere in 220 volts becomes 440 volts, everything will burn. If the electricity becomes 120 volts, then there will also be a crisis. Therefore, the electricity has to be adjusted according to the capacity of the microphone or the bulbs. Similarly, there has to be coordination between the prana and the indriyas or sense organs. If there is too much prana, then your children are sometimes hyperactive. Hyperactivity in the body is due to hyperactivity of the prana.

There are five karmendriyas: feet, hands, vocal cords, urinary and excretory systems. Indriya means vehicle, tool or sense. Karma means action. Through these five karmendriyas you perform five gross actions. Prana is the force behind them. You have seen how old people become slow due to lack of prana. Pranamaya kosha is the energy in annamaya kosha.

There are five main pranas: prana, apana, udana, samana and vyana. These forms of prana control various functions in the physical body. For example, urination, excretion, insemination and childbirth are consequences of apana. Then there are five auxiliary or secondary pranas.

Prana is not a mechanical outcome of the body as it is understood in modern medical science. According to the classical tradition prana enters the womb in the fourth month of pregnancy. When an embryo is developed in the mother’s womb, it is part of the mother’s body and prana. After the third month, the independent or individual pranas manifest in the foetus. That is to say, from the fourth month, the mother’s prana and the prana of the embryo become two different pranas. Therefore, remember that prana is universal energy.

Pranamaya kosha is purified through the practice of pranayama, because pranayama makes the pranic energy penetrate into each and every cell and fibre of the body. Pranayama does not literally mean breathing exercise. The word pranayama is composed of two ideas, prana and ayama, meaning field, dimension or area. Pranayama means extending the field of prana. In this physical body you have a field of prana. It is the subtle form of energy and can be measured. This prana shakti can also get blocked. It can be in excess in some parts of the body and sometimes there is an imbalance in the prana.

Manomaya kosha

The third kosha is manomaya, the kosha composed of the mind. Mind is consciousness. It is a field of energy by itself. Even as prana is the positive field of energy, mind is the negative field of energy. In Sanskrit, the mind is known as manas, and has three dimensions. In fact, in Samkhya philosophy, they say that the mind has ten dimensions. Here they mean the mind of everyone, not only of human beings but of lower animals, the vegetable kingdom, the mind of each and everything in this world.

There are ten stages in the evolution of the mind from the most crude to the most fine. If you want to study those ten stages, you should read the Samkhya Sutras. However, out of those ten stages of mind, three are known to human beings: the conscious mind, the subconscious mind and the unconscious mind. Now these three stages are divisions of the human mind. The literal meaning of manas is ‘that by which you cognize, perceive and understand’. Perception, cognition and understanding are the basic and primary qualities of the mind.

This mind is connected with time, space and causality. What are past, present and future? They are the three so-called divisions of the same mind. What is the form of the mind? It is said that the mind moves at the greatest speed. Do you know the speed of an object? French trains run at 240 kilometres per hour. You know the speed of sound and of light, but do you know the speed of the mind. If only you could create a mental train! The mind is a very subtle unit and when it goes to the subconscious level, it begins to go into the unknown past.

Carl Jung used to talk about archetypes, dreams and visions. He said there is no known source of these things. Whether they are transferred to you from your parents or from a super space, from your previous incarnations or from some unknown transmissions, there is a primitive stock of archetypes within you. This is called samskara. It is known as the seed body or the unconscious. These are the three broad divisions of the mind.

Now this mind can be brought closer, that is to say, time, space and causality can be brought closer. When we are on the external conscious plane, the distance between time, space and causality is long and when you are in meditation, then the gap between time, space and causality is very short. In fact, if the mind can sometimes stop, time stops. A lot of work has been done on this by modern physicists.

The mind which I am talking about is part of the cosmic mind. Of course, I think that I have an individual mind. Everyone thinks this, but it is ignorance because we do not know, just like an ignorant person may feel that the light burning in the light bulb is individual, but another person understands that the energy is coming from the powerhouse. In the same way, this mind is part of the universal mind. How can we put this mind in touch with the cosmic mind? Through raja yoga practices.

Vijnanamaya kosha

The fourth kosha is vijnanamaya. Vijnana means psyche. Vijnana is a Sanskrit word from the prefix vi and jnana meaning knowledge or awareness, inner perception or experience. Vijnana has two meanings: external science and also inner experience. Therefore, whenever you have any experience which is subjective in nature, it is a consequence of vijnanamaya kosha. Whatever you are dreaming is a projection of vijnanamaya kosha, and in your meditation, concentration or mantra yoga, when you see lights and flowers, figures, angels or saints, smell perfumes or hear sounds, it is the consequence or result of vijnanamaya kosha.

Vijnanamaya kosha is related to a very unknown part of the universe and it is a link or sutra between the conscious mind, the individual mind and the universal mind. Universal knowledge comes to the conscious mind through vijnanamaya kosha or the psychic mind. Vijnanamaya kosha does not depend on time, space and causation factors.

You may not have seen Peking, but vijnanamaya kosha can give you a complete film of Peking because it is not limited by time past, present or future. The mind has its eyes on the object, but vijnanamaya kosha has its eye on the universe, and therefore Hindus say that vijnanamaya kosha has a thousand heads and a thousand eyes, a thousand hands and a thousand feet. This means it can see anywhere and think anything.

How can it be developed? It can be developed through tantra because tantra is related to vijnanamaya kosha. The tantric practices act as a catalyst because it is in you, just as curd and butter are in milk, but cannot be seen as separate unless they are released. Matter has energy in it, but when you look at matter, can you see the energy? No, you cannot. Even if you believe that there is energy in matter, still you cannot see it. Then you adopt a method to separate the energy from the matter. That is what nuclear energy is. All energy is inherent in matter. In the same way, vijnanamaya kosha is inherent within you but it is hidden in you like butter is hidden in milk. You have to separate it; you have to release your vijnanamaya kosha.

Anandamaya kosha

The fifth organism is anandamaya kosha. It is not possible to translate the word ananda. Some translate it as bliss or happiness, but ananda is when there is no happiness and no unhappiness. In happiness you are jumping, in unhappiness you are dull – sometimes low, sometimes high. So your mind is swinging. In ananda there is no swinging. There is unified experience and that experience does not change.

Death cannot change that experience; birth cannot change it; love and hatred cannot make your experiences swing. When your mind has become steady in experience and does not fluctuate under any condition, that is ananda. So we call it homogenous experience. The experience which you have in your life every day is not homogenous. It is divided and that is why swamis have ananda in their name, to remind them that they must achieve the state of mind where there is no swinging. So, anandamaya kosha means the kosha which comprises homogenous experience.

In many books, anandamaya kosha is translated as the blissful sheath. But I have thought about ananda for many years and have come to the conclusion that there is a state of mind which does not change, despite anything that happens in life. With that state of mind you can live with all the conditions of life. You can live with a good partner or a bad partner, prosperity or poverty, disease or death, in a discotheque, on a beach, a hotel, everywhere, because nothing affects you. You are where you are, firmly rooted in your own self, but at the same time you can interact with everyone. You can even fight, but still not be affected.

The three gunas

You are composed of these five sheaths or koshas, but you are not that. These five koshas belong to the lower existence, not to the range of supreme knowledge. They are controlled by the three gunas: sattwa, rajas and tamas. Guna means quality, faculty or attribute. The three gunas belong to nature. In this context nature does not mean beautiful places, mountains and hills.

In philosophy nature means prakriti, the universal law. There is a universal law which controls all, from biggest to tiniest, and it is inherent in the thing itself. Take a tree, for example. It is controlled by the laws inherent in the tree. In the same way every human being and every animal is controlled by a law which is inherent in it. My controller is inherent in me and that is the law. That is prakriti, and it controls, maintains or manages each and every law by the three gunas.

These three gunas again control the five koshas. The three gunas work in unison. Nothing is controlled by one guna. The body is controlled by tamoguna, but there is also a little bit of rajas and sattwa. In the same way, anandamaya kosha is controlled by sattwa guna, but there is a trace of the other two gunas. The mind is controlled by rajoguna, but there is a trace of the other two gunas. The three gunas control the five koshas in cooperation with each other. They all have a share. In one kosha, one guna may have a major share and in the others a very minor share, but the proportion changes from time to time.

Where can we place yoga here? First of all, the various practices of yoga purify the mechanism of these koshas. Thereby they can change the quantum of the gunas in each kosha. For example, the body is predominantly tamasic, but by the practices of hatha yoga, sattwic food and a good daily program, you can increase sattwa guna in the body. In the same way you can change the quantum of the gunas in each kosha.

When you change the quantum of the gunas in these five koshas through the yoga practices, a balance is created and when balance is created, then greater awareness takes place. These five koshas are separate classifications. You can experience them during your yoga practice. When you meditate, you pierce through or penetrate each and every kosha.

There are many books on the koshas. One is Vivekachudamani, a very famous book by Adi Shankaracharya, the second is Panchadashi, a very famous book in fifteen chapters dealing with terminologies in yoga and vedanta, and the third is Samkhya Sutras. These three are authentic classical texts.

The five koshas, five tattwas, three gunas and various forms of yoga should be studied in conjunction with each other because they are related to everyone. Even animals have koshas, but the nature of evolution is different. Animals have a well developed annamaya kosha and pranamaya kosha, but their manomaya kosha is in a rudimentary state of evolution, while their anandamaya kosha is not at all manifest. In little insects, annamaya kosha is there but pranamaya kosha is not fully developed and manomaya kosha is unmanifest there.

So the five koshas are not the sole property of human beings. Anything in this universe which has a body has five koshas, but as it goes on evolving then the later koshas become more and more prominent. A yoga practitioner has a developed vijnanamaya kosha while one who has achieved the result of yoga has anandamaya kosha fully developed. But beyond these five koshas is the absolute self. The purpose of existence is to experience that cosmic self and in order to understand and experience that cosmic self, you have to first understand these five koshas and then separate them.

 

 

From http://www.yogamag.net/archives/2007/isep07/vij1.shtml

Awakening the Vijnanamaya Kosha (Part 1)

Swami Satyasangananda Saraswati

Satsang to Iranian yoga students at Rikhia, 24th January 2007

Please tell us about vijnanamaya kosha and the practices to awaken it.

Shalom! Salamalekam! Shabahkher! Swagatam! Namaskar! Namo Narayan! and welcome to the land of yoga. Although yoga by virtue of being a science is the universal birthright of mankind, which necessarily implies that it does not belong to any sect or group of people, nor to any country or even religion, yet I would not be wrong in saying that India is the land of yoga because it is here that this knowledge was preserved. It was in this land that this knowledge was kept alive for centuries amidst the ravages of war and turbulence of history, and for that we have to thank those great souls, the rishis and munis, who were the original scientists on this planet.

Scientists are those who, with complete freedom of mind, without any bias or preconceived notions, explore and probe deeply into the underlying mysteries of the universe and life therein. In that sense, these rishis were scientists because they devoted their entire lives to exploring the mysterious terrain of inner life. With utmost honesty, courage, sincerity and dedication they spent their time unravelling the deeper layers of the mind and consciousness, discovering its mighty potential and the source from which it has sprung. Yes, the credit for this discovery goes entirely to these ancient scientists of the vedic era, just as the credit for unravelling the mysteries of matter goes to the scientists of the modern era.

Of course, in those times they were not known as scientists. Instead they were known as rishis, which means seer, or munis, which means sage, or sannyasins, which means one who has entrusted himself to the divine will. Although they are often mistaken to be priests or religious sectarian pontiffs, that is not the case. They may have been born into a particular religion, just as you and I have been born into the Hindu, Muslim or Christian religion, but that did not in any way influence their quest for the mystery called ‘life’. Who knows what religion they followed in those prehistoric vedic times? We cannot say for sure because we know so little about it and what the historians tell us is mere speculation.

Just as the only reality the scientists of today know and believe in is that of matter, the only reality these ancients believed in was that of consciousness. Their entire quest was in this direction for they believed that the purpose of life was to discover the infinite, that reality which is not subject to death or decay. The finite perishes and after so much spent energy, one finally realizes that the source of this finite world is what one should be able to capture, for in that lies the ability to be master of both the finite as well as infinite worlds.

It was this magnificent quest so full of difficulties and perils that led them to the awakening of the vijnanamaya kosha, and it is on account of their discoveries and the records that they left behind that today we can sit here and discuss this important subject. Otherwise we would not even know that we have a vijnanamaya kosha!

The five koshas

According to the science of yoga, there are five koshas which surround this body in much the same way as the inner core of an onion is covered by layers of skin. Only, in the case of koshas, each subsequent kosha is more subtle and unperceivable to the naked eye than the one preceding it. One can say that these koshas can only be realized with the opening of the inner eye, in the state of meditation.

Annamaya kosha

The first is annamaya kosha, which is the physical sheath made from food. Anna means food. The grain which you eat is called anna and the body which is composed of food is one that you can touch, see and feel. It is the substratum for the subtler koshas, which also assume the shape and size of the body.

Pranamaya kosha

Subtler than that which is not visible to the naked eye is the pranamaya kosha, which instead of food is made of prana or energy. You ought to know that your body is enveloped by this field of prana and when you leave this room, you will carry it out along with your body. Although you can’t see it, the pranamaya kosha follows you wherever you go.

However, if you raise your awareness by the practices of yoga, then you will see the pranamaya kosha in the form of an aura which surrounds the body. Many people are born with this natural gift, where they are able to read the aura of people and determine what is in store for them, because this aura keeps changing all the time according to the state of health you are in at that time. Even your moods influence the pranic aura. The phrases ‘green with envy’ or ‘red with rage’ are just a few indications of the vibrations emitted by the aura according to our mental state.

Manomaya kosha

Beyond the pranamaya kosha, this physical body is surrounded by a more subtle energy which is purely mental in nature, known as the manomaya kosha. It is at the level of manomaya that the chatushtaya antahkarana, comprising manas or mind, buddhi or intellect, ahamkara or ego, chitta or memory spring up and begin to perceive, cognize, record, understand, rationalize, discriminate, accept, reject, compare, to name only a few of the myriad functions that it performs effortlessly in our lives. Without the manomaya kosha we would be no better than the vegetables sitting on your kitchen shelf!

This kosha is the seat of para or empirical knowledge. It beholds the world around and although an instrument of inner consciousness, it has the capacity to externalize the awareness as well as withdraw it inwards. When it is under the sway of the senses, it is fully occupied with the external impulses that it receives from the world of smells, sounds, lights, colours, touch and taste. But there are times when, dissatisfied with the finite nature of these experiences, the mind propels inwards, and at that time it receives the impulses of the self which recharge and rejuvenate the manomaya kosha.

This happens in the state of meditation too, and that is why meditation broadens the horizons of the mind, sharpens the intellect, brings the ego in tune with nature and strengthens the chitta.

Vijnanamaya kosha

Beyond manomaya or mind is the sheath of intuition or vijnanamaya kosha, and needless to say it is subtler than all the preceding koshas. The Taittiriya Upanishad elucidates the existence of the vijnanamaya kosha in the following manner: “Separate from the self comprised of mind, there is another inner self comprised of intuitive knowledge. This one is also like the shape of a person like the preceding koshas. Faith is its head, Tasye shraddhaiva shiraha; righteousness its right wing and truth its left wing, hritam dakshinah pakshaha satyamuttarah pakshaha; yoga is its soul, yoga atma, and maha its foundation, maha puchham pratishtaha.”

Koshas and lokas

Interestingly, by stating that maha is the foundation of vijnanamaya, we derive a clue as to how the koshas are also linked to the lokas, which are planes of consciousness one experiences as the awareness gains ascent from annamaya to pranamaya to manomaya to vijnanamaya. The sapta or seven lokas are bhu, bhuvar, swar, maha, jana, tapo and satya. While bhu, bhuvar and swar, the earthly, intermediate and divine planes, are related to annamaya, pranamaya and manomaya, maha, the plane of siddhas, jana, the plane of rishis and munis, and tapo, the plane of liberated souls, relate to awakening, stabilization and illumination of vijnanamaya.

Satya loka, the plane of ultimate bliss, corresponds to anandamaya kosha, which is none other than pure consciousness. The Taittiriya Upanishad defines anandamaya kosha as having the shape or form of a person with love as its head, joy as its right wing and delight as its left wing, bliss as its trunk and Brahman as its support or foundation.

Maha loka, the plane of siddhas and saints, is the foundation or support of vijnanamaya kosha. It is from here onwards that the superstructure of heightened awareness is constructed. If the foundation is shaky, in other words if the siddhis which begin to manifest become the object of focus or enjoyment, then the siddha will surely fall back to lower planes of consciousness. However, if he does not allow them to distract the awareness, especially when he is in a state of samadhi, then ascent of awareness to higher lokas known as jana, the realm of rishis and munis, and tapo, the realm of liberated souls, the jivanmuktas and videhamuktas, is definitely assured.

From vijnanamaya to anandamaya

The above is such an important stage in the ascent of awareness that the Raja Yoga Sutras of Patanjali has devoted an entire section to this mega event, when the consciousness is able to perceive the four dimensions of time, past, present, future and eternity. Patanjali has termed this event when siddhis manifest as vibhooti. He calls it the accomplishment of yoga and has cautioned the aspirant against becoming distracted by this accomplishment. It is the state equivalent to paroksha anubhuti, or awareness of only one point without consciousness of one’s own self. Deepening awareness of paroksha anubhuti leads the practitioner to aparokshanubhuti, which correlates to the bliss of anandamaya kosha.

So you can say that vijnanamaya is the doorway to anandamaya. The experiences of vijnanamaya give you glimpses of what is in store for you as your awareness begins to experience pure bliss, but the experience again drops due to the appearance and disappearance of distractions and one-pointedness of mind. All siddhas and saints must have passed through this stage before they attained enlightenment. The tales about Buddha, where prior to nirvana he encountered the demons and bewitching damsels, as well as the forty days and forty nights when Christ encountered temptation before he experienced God, point a finger in this direction.

When there is awakening in vijnanamaya kosha, siddhis begin to manifest. The practitioner becomes clairvoyant and telepathic; he begins to know many things about people and events before they happen, which come to him in the form of dreams, thoughts or visions. He may be able to appear at many places to many people at the same time. He develops the power to read others’ thoughts and also to change them. Or else he may develop healing powers. His words, touch or glance can heal the deadliest of diseases which no doctor can cure. In some exceptional cases, depending on the extent of his advent into the level of vijnanamaya kosha, he may even be able to resurrect life or enter another person’s body. A person exhibiting such powers could easily be mistaken for God, which perhaps many did who were unaware of the manifestation of siddhis through the power of yoga when there is awakening in vijnanamaya kosha.

Yoga has boldly declared that you are not just the body you perceive with the eyes, nor are you just blood, bones, marrow, muscles, nerves and the different organs that keep you alive. You are much more than that. In fact, what you see of yourself with the eye is sustained by what you cannot see. If the unseen part of you ceased to exist, the seen part of you would wither and die. This unseen part of you is composed of the five koshas as mentioned above. The aim of all the practices of yoga, without exception, is to energize and awaken these koshas until ultimately you experience awakening in vijnanamaya kosha. That alone is the purpose of yoga.

Koshas and shariras

Now, you ought to know that these five koshas belong to or co-relate with three bodies that constitute your being. These three bodies, which are known as sthula or gross, sukshma or subtle and karana or causal, along with the koshas also influence each and every experience and reaction you face or evoke throughout your life. For example, the experiences related to annamaya kosha belong to the sthula sharira or gross body, whereas the sukshma sharira or subtle body is the arena for the experiences of pranamaya and manomaya koshas. The most subtle body, known as karana sharira or causal body, which stores all of our karmas, samskaras and impressions of many, many incarnations is the one we encounter when we speak about awakening in vijnanamaya kosha.

As life evolved through 84 lakh yonis or incarnations, from an amoeba to a bacteria or virus and then on to insects, plants, fish, birds, animals and finally to the human being, it carried the impressions of its experiences. All of these experiences, pleasant and unpleasant, are stored in the vijnanamaya kosha. In order to step into the arena of spiritual ecstasy, you have to pass through this zone and face what is stored there eye to eye. You simply cannot avoid it, just as you cannot avoid your thoughts or your feelings and dreams. The practices of yoga can accelerate this process and accomplish this in a systematic and graded manner. It is only when the awakening occurs in vijnanamaya and that experience is stabilized, that the transcendental experiences of ecstasy and bliss related to anandamaya kosha arise in the consciousness.

In modern psychology, the causal body or karana sharira is known as the realm of the unconscious. You may even term it as the psyche of man. It is the mythical Pandora’s Box, virtually the skeleton in the closet. You cannot know what is stored there until there is awakening in vijnanamaya kosha. When you experience awakening in manomaya kosha, you are still within the realm of buddhi or intellect. Everything that you experience will be within the fold of logic and reason and thus there is a degree of control of the experiences and their outcome.

The dimension of intuition

Vijnanamaya kosha transcends intellect and enters into the dimension of intuition, where the mind does not work. This mind of yours which you are familiar with does not function in vijnanamaya kosha; nor does the intellect. Each one of us operates at the level of instinct, intelligence, intellect and intuition. Till the level of intellect you are under the influence and in the field of manomaya kosha. But when you are able to transcend this intellect, even for a second, you will experience an intuitive flash about something or other that has been on your mind. All of us have at some time in our life experienced this intuition, which comes in flashes due to a sudden contact with the vijnanamaya kosha. But they drop. You get intuitive, but you are not able to hold on to that state of awareness and once again you regress to the hold of intellect and intelligence.

The aim of yoga is not just to induce these abilities. More than that, the focus of yoga is to attain mastery or control of these supernormal powers that belong to the realm of intuition. That intuition should act as a tool in your hands, just like your intellect, mind or intelligence. All the practices of yoga are designed to take you to this point. And each one of us has to find a way for ourselves, because each one of us has a different temperament and each one of us has our own dharma which determines our own individual needs.

(To be continued in the next issue)

 

From http://www.yogamag.net/archives/2007/koct07/vig2.shtml

Awakening the Vijnanamaya Kosha (Part 2)

Swami Satyasangananda Saraswati

 

In the journey to awaken vijnanamaya kosha, first of all, you have to find out exactly where you are standing at this present moment. What exactly is your temperament? Are you tamasic, rajasic or sattwic? While it is true that each individual is a combination of these three gunas or qualities that belong to the realm of prakriti or nature, still one or the other is predominant in us. Are you by nature a procrastinator, lazy, dull and negligent in your duties and responsibilities; if you are, then you are tamasic by nature. Of course, we are all lazy at some time of the day, but tamasic individuals are unable to rise above these tendencies, no matter how hard they try. On the other hand, predominantly rajasic people are always on the go, trying to accomplish and achieve something, having a lot of desires and passions. Or are you sattwic, full of knowledge, peace and tranquillity? Is that the point where you are going to start your journey to the awakening of vijnanamaya kosha?

Preparing for the awakening

After discovering your temperament, you have to prepare the vehicle which is this body, annamaya kosha. The journey starts from the body because it is through this vehicle that you can reach that point of intuition. The next thing you have to gear up is the fuel to move this vehicle to higher states of experience which are beyond the gross and mundane. Just as you need refined high octane fuel to drive your Mercedes Benz, Bentley or Rolls Royce, in the same way you need high octane fuel to drive this body and mind out of the clutches of the sensorial experience into the state of meditation.

According to yoga, that fuel is known as prana. Prana is not oxygen, nor is it the breath. Prana is the energy which flows in the breath. It is the vital energy, the source of life. So first of all you have to prepare the vehicle, and you also have to see that the quantum of prana which is flowing in the body is sufficient to take you to that heightened state of awareness. If there is an insufficient flow of prana in the body, then you simply cannot meditate. You may be able to meditate for a short period, but again the awareness drops. But to awaken vijnanamaya kosha you have to have enough fuel to allow unhindered and uninterrupted meditation.

So you have to find ways to increase as well as conserve the quantum of prana which is being dissipated and lost in the myriad activities you engage yourself in throughout the day. Prana is depleted in the digestion of food; you also lose prana when you talk, sing or dance. In fact everything requires prana, from blinking the eyelids and sneezing to thinking and contemplating. A lot of prana is wasted when you are worried, anxious, frightened or upset, which means you have to also learn the mental disciplines of yoga so that you don’t waste prana in useless thoughts, but instead are able to conserve it for meditation. This means that along with the vehicle and the fuel, you also have to take care of the driver, which is the mind. You have to keep the mind in order if you want to dive into the experiences of vijnanamaya kosha. By mind, I mean the totality of mind which constitutes the conscious, subconscious and unconscious.

The path of yoga

Good health or a beautiful body is not the aim of yoga. Fitness, beauty and youth are a by-product or side effect of yoga, not its final goal. Just as modern medicines produce side effects – for example, long usage of aspirin results in peptic ulcers or some other drug results in night blindness or vertigo or stiff joints – yoga too has a side effect. The difference is that the side effects of yoga are not detrimental; instead, they always have a positive and beneficial influence on the body and mind. You derive good health and attain clarity and focus of mind. Your intellect and memory are sharpened and your capacity to take correct decisions improves. You acquire confidence, poise and grace. These are only some of the side effects of yoga, but they are certainly not the aim or purpose of yoga.

The purpose of yoga is far more sublime. It is to prepare you for that ultimate state of meditation or transcendental experience. Through the practice of asana you first of all purify the entire physical structure and organs which constitute the body. The heart, lungs, liver, kidney, endocrine, nervous and circulatory systems are purified and the body is brought to an optimum condition. Then through the practice of pranayama you increase the level of prana, which increases the flow of blood to all the organs of the body and also to the brain, which is the most vital organ for meditation.

When all the organs are functioning properly and the flow of prana is unobstructed, then calmness and a peace descend on you, which is essential for meditation. In fact, peace of mind is a prerequisite and not a consequence of meditation as we normally tend to think. Unless you have attained peace of mind you cannot ever meditate, because the distractions of mind will simply not allow you to reach that heightened state. Instead of concentration, the mind will be wandering everywhere.

Asana and pranayama are practised to induce a balance and harmony between the body and mind, or you may say the physical and mental activities. Asanas do not just influence the organs, they influence your emotions as well. Together they play an important part in regulating the turbulent emotions which influence your attitude, responses and perception of the events in your life.

Through the practices of asana and pranayama you can directly instigate an immediate influence on the quantum of prana which flows through 72,000 channels or nadis throughout your entire body. Although all the nadis are to be purified, for this there are three which are most important, known as ida, pingala and sushumna.

Ida nadi, which corresponds to the sympathetic nervous system, is responsible for your mental activity, and pingala nadi, which corresponds to the sympathetic nervous system, is responsible for your physical activity. Originating at the root of the spine, they wind their way upwards, intersecting at a few junction points from where they send offshoots to all the different parts of the body, conveying prana right from your head down to your toes. An imbalance in the flow of these two nadis not only results in physical or mental sickness, but also obstructs awakening of the third nadi, sushumna, which corresponds to the autonomic nervous system.

The practices of yoga are intended to create a balance between the flow of these two nadis, which carry physical and mental energy to every part of the body, as that paves the way for the grand awakening of sushumna. Because it is only with the awakening of sushumna that experiences of vijnanamaya kosha begin to take place. Unless and until you are able to awaken sushumna through the balance of ida and pingala, you will not have the experience of vijnanamaya kosha. That is the sum and substance of what you have to do for awakening of vijnanamaya kosha.

Stages of awakening

This awakening takes place in three stages, which yoga terms as pratyahara, dharana and dhyana. As you become proficient in the practices of asana and pranayama and attain a balance in the flow of ida and pingala, you will find your mind becoming more and more introverted and that suddenly it is easier for you to withdraw your awareness from the external to the internal. That awareness, which is deeply attracted by the sense perception of sound, taste, smell, sight and touch, is able to transcend the influence of the senses and turn inwards. In other words, you are able to shut off the external world for some time and enter into the inner dimension. This is known as pratyahara and mastery of this state is essential before you can progress any further to the next stage. There are several ways prescribed to induce pratyahara, but pranayama is one of the most effective ways to perfect it, no matter whether you are temperamentally tamasic, rajasic or sattwic.

In the brief moments when you find that you are able to achieve this enormously difficult feat of sense withdrawal or pratyahara, you will need to fix that awareness on an inner point so that the concentrated energy that you are directing inwards does not dissipate, scatter or diminish. This inner focus or fixed concentration on a point is known as dharana. As you build your proficiency in these two practices with regular practice, the third stage of dhyana or meditation occurs. There are no rigid barriers between pratyahara, dharana and dhyana. Perfection of one spontaneously leads to the other.

When you do the practices of asana and pranayama, particularly pranayama, you may at any time spontaneously experience the state of pratyahara. If this state of pratyahara continues for some time, the mental energy will automatically become concentrated and dharana will occur. And as soon as the mind is concentrated, the internal state of dhyana or meditation simply happens, which is none other than the experience of awakening in vijnanamaya kosha, and glimpses of the experience of bliss and ecstasy related to anandamaya kosha begin to filter through.

Experiencing vijnanamaya kosha

The most important thing you have to know is that vijnanamaya kosha is the realm of your unconscious mind or psyche. It is a world of signs and symbols, colours and lights. And your unconscious is a part of the collective unconscious. It is directly linked to the collective unconsciousness or hiranyagarbha, the cosmic womb, that holds everything that has ever come into existence or is waiting to come into existence. It is the cosmic storehouse to which the unconscious mind of each and every individual is linked. That is why when you have experience of vijnanamaya kosha you become intuitive, because you begin to perceive things which belong to the four dimensions of time, the past, present, future and beyond that to eternity.

When your mental frequencies transcend time, space and object to attain a heightened frequency, that knowledge becomes available to you. The collective unconscious is a definite reality, where everything that has happened, everything that is happening and everything that will happen is stored. You can say it is a bank of unlimited knowledge. For example, it does not have the limitation of country. It is not Indian knowledge, nor is it American knowledge. Nor does it have the limitation of religion, because religions are man-made. This knowledge is universal. It is the knowledge of existence. It is not restricted to time and space.

Therefore, if you want to enter this realm of your being which is mystical and psychic, it is important that you should try to know a bit about your past: what is your ancestry, where do you come from, what is your heritage? Each one of us has a lineage, a heritage and a tribe from which we have descended. I may be an Indian, but that is not my tribe. That may be my national identity, but it does not indicate my tribe. The identity each one of us holds dear to ourselves of nation, religion and sect is fabricated or stitched so neatly around us that ultimately we are reduced to that and cease to be nothing more than that.

Eventually we fit into that mould, but undoubtedly there is something more to us than that. So each one of us has to go through this process of self-discovery which will take us beyond the confines of caste, country and religion back to our origins from where we descended. Who were those people from whom you descended? What was their tribe? What were their beliefs? Which rituals did they follow? What mantras did they chant? What methods did they employ to alter the consciousness?

You may be American by birth, but you may belong to a tribe that has its roots in India. From the North Pole to the South Pole, from Peru to Alaska, there are many, many thousands of tribes that have existed since time immemorial, who later congregated in different countries, different sects, different beliefs and different religions. In the course of time, they lost that tribal identity, but that does not alter the fact nor change the reality that those tribal influences will remain embedded in their psyche.

For instance, an Indian belonging to the Santhali tribe of Jharkhand will have a different psychic influence to an Indian belonging to the Toda tribe of the Niligiris. To reach the roots of your ancestry is important if you want to delve into mystic practices, because knowledge of that will help in ascertaining the practices that will yield quick results for you. This is because every tribe has its own set of mystic practices that are peculiar to them. Some tribes used mantras and mystic sounds to reach that mystical state, others used fire rituals, still others had knowledge of herbs or music and dance.

There is not one but thousands of rituals practised by different tribes, which they preserved as long as they maintained their tribal identity. Once they lost that identity, these rituals may have gradually ceased to exist in the conscious mind, but they would certainly have retained their roots somewhere in the unconscious as memory. It is this unconscious memory in the form of symbols and sounds, colours, lights and visions that comes to the fore in mystical practices and generates an altered state of consciousness.

As long as you want to develop the mind, intellect and intelligence, it is perfectly in order that you resort to the knowledge which is available according to the place where you live and your surroundings. But if you want to delve into the mystic practices that will awaken vijnanamaya kosha and develop your intuition, you will need to correlate yourself with your primitive and instinctive origins. That will give you very good results.

Instinct and intellect

Although instinct and intuition are very similar in expression, they are not the same. However, even though they are not the same, they are deeply linked and you may say that they are two sides of the same coin. At one level the consciousness expresses itself as instinct, as it does in the animal kingdom, and at the other end it expresses itself as intuition in humans.

If you observe birds and animals closely, you will find that they know of natural calamities in advance. Is that instinct or intuition? Not only that, they can know of distant events; leave some tasty meat outside in your courtyard and see the swarm of birds and animals that descend there in just a matter of seconds. This is the instinct of survival which perhaps we have inherited from them, which in the course of time can evolve to intuition if we know how to transform it. The difficulty we face is that we have lost sight of our instincts because we rely solely on our intellect and intelligence to survive. The intellect and intelligence is so highly developed in us that it has simply erased the innate instinctive responses and reactions that are still alive in animals. You have to restore that connection with your primeval past if you want to transform your instinct into intuition. Unfortunately, you have sacrificed your instinct at the hands of intelligence and intellect, which in a sense has corrupted your natural responses and led you away from your inner self.

That self, which becomes apparent as there is awakening in vijnanamaya kosha, cannot be realized through the mind. This mind which is responsible for your present experiences has to be separated and thrown out of its present field or range of experience. It is not this mind that illumines your experiences beyond manomaya kosha, but the self that illumines your path.

Intuition is born when the mind is transcended. So long as you function in this mental state of logic, reason and intellect, your intuition will not reveal itself to you. Intuition has no logic, it is pure feeling. It comes to you with amazing clarity as if that event is occurring right before you. For example, once a lady had come to meet my guru and as she entered the room I saw her in a white sari, although she was wearing a bright red one. It was just a flash of a vision and I did not give it much importance until I learnt a few days later that she had become a widow due to a tragic accident. Imagine my amazement when, two weeks after her visit, she again returned for my guru’s blessings, this time in the white sari which I had seen her in. That was intuition working.

This is an important point as well, for intuition first of all reveals calamities, destruction, fatal events, sickness, tragedy and all that is negative. This why the sage Patanjali in ‘Vibhooti Pada’ of the Raja Yoga Sutras has clearly warned against the use, or should I say misuse, of siddhis that arise as a consequence of awakening in vijnanamaya kosha. In fact, he has called them obstacles in the path of yoga – Te samaadhavupasarga vyutthane siddhayah (3:38). To an ordinary person they are a welcome achievement, one that he can boast about and maybe use to earn money, name and fame, but for a serious aspirant they act as hindrances. For if he begins to use them, in time they will disappear and leave him bankrupt. Even if you do not want the siddhis, they will come to you as you progress on the path of yoga, because awakening of vijnanamaya kosha grants vibhootis (divine attainments) and brings out the inherent pratibha (inner light, intuition) in an individual.

Beyond the mind

To awaken vijnanamaya you have to transcend the influence of mind and intellect. The easiest and quickest way to influence the analytical mind and logical intellect is to provide it with a set of practices that defy all logic. Amazingly, according to yoga and tantra, this really works. Mystic practices, involving mantras, rituals, worship, music as well as dance as in the case of the whirling dervishes and Sufi traditions which have been utilized since time immemorial by millions of races and tribes throughout the world, are a very important heritage which we can delve into. Of course, if you don’t have knowledge of your ancestral past, you can still use the practices of yoga. Because, as I said at the very beginning, yoga is universal, it belongs to mankind. And all mystic practices, all practices dealing with the esoteric, have some link with yoga. So you can easily use the practices of yoga, such as asana, pranayama, mudra, bandha, mantra, pratyahara, dharana and dhyana, to awaken vijnanamaya kosha.

 

From https://www.swami-krishnananda.org/moksha/moksh_09.html

The Moksha Gita by Swami Sivananda Commentary by Swami Krishnananda

Chapter 9: The Five Sheaths

 

1, 2. The Guru said: This Annamaya sheath or food sheath is made up of the five elements. It has a beginning and an end. It is inert and full of parts. It is an effect of the five elements. It is full of impurities. Therefore you are not this physical body or the Annamaya sheath. You are the witness of this body. Understand, therefore, “I am not the body. I am Brahman.”

The physical body is the grossest form of thought. The food consumed by the parents is converted into Sukla (semen) in men and Sonita in women and by the combination of these the physical body is formed. After birth, the body grows by suckling the milk which is only a transformation of the food consumed by the mother. The body is further developed by taking food. It gets dissolved in earth which is another form of food. The body is itself a food for other creatures. Hence it is called the food sheath, the material body or the earthly encagement of the soul. The food sheath is an object of perception. The Atman is the cogniser and the body is the cognised. Hence the Self is different from the body. In dream and deep sleep there is no consciousness of the body.

The five elements constitute the physical body. These modifications of Maya are not the Truth, the body and its Dharmas, size, form, birth and death are not actual modifications of the Self. Varnashrama, name and class differ in different births. They are mere accidental attributes of the body. There is no physical body either before birth or after death. Hence it is non-eternal.

Existence, birth, growth, modification, decay and death are the six Vikaras of the physical body. Just as the ether in a pot is not affected in any way by the destruction of the pot, so also the Atman is not at all affected by the destruction of the body or the Annamaya Kosha. Atman is unattached. Ether is subtle, but the Atman is still subtler. Atman is formless, changeless, birthless, deathless, free from old age. It is neither born nor is killed. Hence one should meditate on this Atman or Brahman.

 

3, 4. The Pranamaya Kosha or the vital sheath is a product of Rajoguna. It also has a beginning and an end. It is inert. It is an effect. Therefore you are not the Pranamaya Kosha. You are the witness of this sheath. Understand, therefore, “I am not the Pranamaya Kosha. I am Brahman.”

The Pranamaya Kosha consists of the five Pranas and five Karma-Indriyas or organs of action. Though the Prana is waking when one is sleeping, it does not invite a friend and entertain him; it cannot stop a thief who tries to remove the articles in a house. Therefore it is insentient. The Self is a mass of Intelligence. It is Chaitanya-Swarupa. It is entirely different from the Prana. The Self is the knower, seer and witness of this sheath.

Prana is only the active working of the mind. A pure-hearted man breathes rhythmically. The breath of an evil-minded person is disturbed. When the mind is controlled the Prana is automatically controlled. The Vedantic aspirant does not practise Pranayama, because his breath is automatically regulated and Kumbhaka naturally follows when the mental Kumbhaka or concentration and meditation are practised. The Pranas are the Rajasic manifestations of the dynamic mental force which with their ups and downs maintain the balance of individual existence even as the bicycle is kept in balance when its wheels are vigorously turning. When there is a break of this movement, the bicycle falls down and when the Prana is inhibited the individualising mind together with the ego breaks down and dies.

Hence there should be no identification with the Pranamaya Kosha and the aspirant should assert the Self-existent Atman distinct from it.

 

5, 6. The Manomaya Kosha or the mental sheath is a product of Sattwa Guna. It also has a beginning and an end. It is inert. It is an effect. Therefore you are not the Manomaya Kosha. You are the witness of this sheath. Understand, therefore, “I am not Manomaya Kosha. I am Brahman.”

The Manomaya Kosha consists of the mind and the five Jnana Indriyas. It is a means of enjoying pleasure and pain. The mind causes egoism in the body and “mine”-ness in house, sons, wife, wealth, etc., and passes outside through the avenues or channels of these five Indriyas. It is the internal instrument for gaining the experiences and knowledge of this world. Mind is associated with the Vrittis or waves of lust, anger, etc., and is a terrible objectifying agent. Mind is a Vikari, it constantly changes itself.

The Self is a witness of the Manomaya Kosha. The Self is Nirvikari. The mind is not the Self. The Self is the Atman or Brahman, unblemished, eternal and changeless, and one should meditate on it as such.

 

7, 8. The Vijnanamaya Kosha or this Buddhi sheath is a product of Sattwa Guna. It has also a beginning and an end. It is inert. It is an effect. Therefore you are not the Vijnanamaya Kosha. You are witness of this sheath. Understand, therefore, “I am not the Vijnanamaya Kosha. I am Brahman.”

The Vijnanamaya Kosha consists of the intellect in conjunction with the five organs of knowledge or the Jnana-Indriyas. During sleep it gets involution or Laya along with Chidabhasa or the reflection of Pure Consciousness. During waking state it is the doer. It is an effect like a jar and is inanimate. It shines in borrowed feathers. It borrows its light temporarily from its source, just as the moon borrows its light from the sun. It is not the eternal Self.

The Pranamaya, Manomaya and the Vijnanamaya Koshas constitute the subtle body. The subtle body is composed of the five unquintuplicated elements. There is neither breathing nor talking, neither seeing nor hearing in the dead body. There is also no warmth. The self-cognitions such as “I speak; I hear; I am hungry; I am thirsty;” and the like appear distinctly in the subtle body. The subtle body operates in the waking and the dreaming states. Ghosts and apparitions are the manifestations of the subtle body only.

The ego is hidden in the intellect and the memory (Chitta) is hidden in the mind. The subtle body thus, contains nineteen principles or Tattwas. It is also called the “Puri-Ashtaka” or the eightfold city. The five organs of sense, the five organs of action, the five vital breaths, the five subtle primary elements, the fourfold Antahkarana, ignorance, desire and action are the eightfold city of the subtle body.

The physical body is only an instrument in the hands of the subtle body. When the subtle body is disciplined through Pranayama, abstraction and concentration, the physical body also becomes very healthy and strong. Whatever the subtle body is, that the physical body also becomes. The mind which is the ruler of the subtle body gets fattened by worldly affections, by avarice for wealth, by the acquirement of women and gold and by attachment to the external fleeting forms of beauties. The mind is thinned out by eradication of the Vasanas and egoism.

The subtle body is the distracted expression of the self through Avidya, the causal sheath. Therefore it is not the Truth. Truth is Brahman and all else is false. One should meditate that he is not the subtle body and that he is the self-effulgent Atman.

 

9, 10. The Anandamaya Kosha or this bliss sheath is Avidya or ignorance, a modification of Prakriti. It is the effect of past deeds. It is endowed with changing attributes. It is Jada or insentient. Therefore you are not the Anandamaya Kosha. You are the witness of this sheath. Understand, therefore, “I am not the Anandamaya sheath. I am Brahman.”

The Anandamaya Kosha is made of Mula-Ajnana. It is the Karana Sarira or the causal body which is the substratum of all other sheaths which are external to it. Its three attributes or Dharmas are Priya, Moda and Pramoda, affection, delight and intense happiness. It is the indescribable beginningless Avidya, the nescience of the Atma, and is composed of Malina Sattwa. It is inanimate, beginningless, but has an end in Atma-Jnana.

The ignorance of the real nature of the Self constitutes this causal body or seed-body. It contains the potentialities or the seeds for the subtle and gross bodies. It projects the appearance of the whole universe through the subtle sheath. It is the food of ignorance for the hungry ego. The mind has come out of this ignorance and gets involved in it during deep sleep. In the sleeping state there is a vigorous functioning of this ignorance in which everything is lost as in pitch darkness. The Karana Sarira screens the Satchidananda Brahman.

He who knows the ignorance or the negation of the existence of the Atman and the denial of its appearance is the true Self, the Atman. He who knows the effects of ignorance, such as “I am a man, I am the doer and enjoyer, I am happy, I am miserable,” is the witness and the Atman. Hence in reality the Self is the seer, knower and the witness of the causal body or the ignorance. The Self is the Knowledge and the Light itself.

As the light that enlightens the jar is different from it, so is the Self different from the bodies witnessed by it. Therefore the Self is Consciousness itself and not the bodies.

The aspirant should endeavour to rise above the five Koshas to realise the identity with Pure Consciousness. Just as one draws out the thin stalk from the Munja grass by stripping off its upper layers one by one, so also one should take out the innermost essence of the Atman from all objects of perception, i.e. the five Koshas, by the “neti, neti” doctrine of negating unreality. Just as butter is removed from milk by churning the mixture of curd, so also the butter of the Atman should be taken from the mixture of the five Koshas by the churning of constant meditation on the Immortal Brahman which fictitiously appears as the sheaths, the world, etc. When the identification with the sheaths ceases, the self realises the Infinite Being and gets liberated beyond death.

 

Above Dhruvaloka by 10,000,000 yojanas is Maharloka, above Maharloka by 20,000,000 yojanas is Janaloka, above Janaloka by 80,000,000 yojanas is Tapoloka, and above Tapoloka by 120,000,000 yojanas is Satyaloka. Thus the distance from the sun to Satyaloka is 233,800,000 yojanas, or 1,870,400,000 miles. The Vaikuṇṭha planets begin 26,200,000 yojanas (209,600,000 miles) above Satyaloka. Thus the Viṣṇu Purāṇa describes that the covering of the universe is 260,000,000 yojanas (2,080,000,000 miles) away from the sun.

SB 5.23.9, Translation and Purport:

The body of the Supreme Lord, Viṣṇu, which forms the Śiśumāra-cakra, is the resting place of all the demigods and all the stars and planets. One who chants this mantra to worship that Supreme Person three times a day—morning, noon and evening—will surely be freed from all sinful reactions. If one simply offers his obeisances to this form or remembers this form three times a day, all his recent sinful activities will be destroyed.

Summarizing the entire description of the planetary systems of the universe, Śrīla Viśvanātha Cakravartī Ṭhākura says that one who is able to meditate upon this arrangement as the virāṭ-rūpa, or viśva-rūpa, the external body of the Supreme Personality of Godhead, and worship Him three times a day by meditation will always be free from all sinful reactions. Viśvanātha Cakravartī Ṭhākura estimates that Dhruvaloka, the polestar, is 3,800,000 yojanas above the sun. Above Dhruvaloka by 10,000,000 yojanas is Maharloka, above Maharloka by 20,000,000 yojanas is Janaloka, above Janaloka by 80,000,000 yojanas is Tapoloka, and above Tapoloka by 120,000,000 yojanas is Satyaloka. Thus the distance from the sun to Satyaloka is 233,800,000 yojanas, or 1,870,400,000 miles. The Vaikuṇṭha planets begin 26,200,000 yojanas (209,600,000 miles) above Satyaloka. Thus the Viṣṇu Purāṇa describes that the covering of the universe is 260,000,000 yojanas (2,080,000,000 miles) away from the sun. The distance from the sun to the earth is 100,000 yojanas, and below the earth by 70,000 yojanas are the seven lower planetary systems called Atala, Vitala, Sutala, Talātala, Mahātala, Rasātala and Pātāla. Below these lower planets by 30,000 yojanas, Śeṣa Nāga is lying on the Garbhodaka Ocean. That ocean is 249,800,000 yojanas deep. Thus the total diameter of the universe is approximately 500,000,000 yojanas, or 4,000,000,000 miles.

 

From http://www.vedicworld.org/vedic-cosmology-the-planets-of-the-material-universe/

Vedic Cosmology – The Planets of the Material Universe

The cosmology and cosmography of the ancient Vedas is awe inspiring to say the least. The more “modern” of the Vedic texts are known to originate from approximately 3000 B.C., thus being the oldest scientific and religious doctrines known to man. The descriptions of our solar system and what modern astronomy has discovered of the visible universe corresponds with the ancient Vedic knowledge, proving that man has had advanced knowledge of astronomy for thousands of years before our modern civilization began. This article describes the Vedic version of planetary systems from the topmost, eternal planets down through the temporary planetary systems within innumerable universes of this material world.

When saying “cosmic manifestation” we speak of two separate worlds, the spiritual and the material. The spiritual planetary systems are eternal, beyond the limits of the material universes, and belong to a “super dimensional” or “anti-material” dimension. These are beyond the limitations of material time and space and therefore beyond our vision, or powers of perception. In these planetary systems there is no occurrence of creation or dissolution, and these planets are unlimited, indestructible, and eternally existing. There are descriptions of these spiritual planets in the vedic literatures, but this article concentrates on those within the material universe.

The material planetary systems are created at some point in time and will be destroyed at another. They are bound by the influences of time and space. Both of these energies (spiritual and material) are of the same divine source called “brahmajyoti”, the spiritual light. About 1/4th of this brahmajyoti is covered by the “mahat-tattva”, the material energy, where are found innumerable material universes. The 3/4th portion is the eternal spiritual sky. In the spiritual world are two realms of existence, “Goloka-dhama” and “Hari-dhama”. The material world has one realm called “Devi-dhama”.

Goloka-dhama is the topmost planet and residence of the Supreme Godhead Sri Sri Radha-Krishna. Below this is Hari-dhama where the spiritual planets of the Vaikunthalokas are situated. Below the Vaikuntha planets is “Mahesh-dhama” (also called Sadasivaloka, or the abode of Lord Siva). This is the realm dividing the spiritual from the material universes. Below Mahesh-dhama is Devi-dhama, the realm of the material universe. It is said that the systems of yoga offer different destinations. Bhakti yoga directs one toward entering Hari-dhama or Goloka-dhama. Jnana yoga directs the aspirant toward entrance to Mahesh dhama, and karma yoga directs one to remain in Devi-dhama, experiencing repeated birth and death in the material worlds.

The Planetary Systems of Devi-Dhama

In the Bhagavad-Gita we find a statement that there are three divisions of material planets in our universe. They are “urdhva-loka” (highest), “madhya-loka” (middle), and “adho-loka” (lower). Above the urdhva-lokas are the coverings of the material universe beyond which lie the eternal realms of existence. Within these three spheres of existence are 14 main planetary systems with different standards of life and duration of existence. The residents of the upper three systems have almost no disease or aging of the body, and they have no sense of fear. As the planetary systems progress downward there is lesser duration of life and standard of living, as well as a greater manifestation of disease and anxiety.

The 14 planetary systems are named as follows, from highest to lowest:

1) Satya-loka

2) Tapa-loka

3) Jana-loka

4) Mahar-loka

5) Svar-loka

6) Bhuvar-loka

7) Bhur-loka

8) Atala-loka

9) Vitala-loka

10) Sutala-loka

11) Talatala-loka

12) Mahatala-loka

13) Rasatala-loka

14) Patala-loka

In one of the Vedic scriptures called the “Hari-vamsa” there is a description as follows: “Above the planetary systems where humans live is the sky. Above the sky is the orbiting sun, which is the entrance point of the heavenly planetary systems. This is the middle of the universe where begins the planets of those elevated by great austerities and penances. The planets above these, up to Satya-loka are the residences of those advanced in spiritual knowledge. All these planets are within the material world and under the control of Devi (Goddess Durga), and therefore called Devi-dhama.”

The term “amara” (deathless) is often used to describe the residents of the heavenly planets because their span of life is inconceivable to us, but although they live for millions of years by our calculation, none within the material worlds can live here eternally. In Bhagavad-Gita there is given a description for the life span of those living on Satyaloka. One day is equal to 4,300,000,000 solar years. On other heavenly planets the day is considered to equal six months of our time, and the night also equal to six months on earth. These souls live in their bodies for 10 million of their years.

Time duration such as day, night, months, and years are different in different planetary systems, and there are also different types of human beings, animals, trees, and vegetation. Some of the planets that are visible to us are considered heavenly planets with different timings. Jupiter, Venus, and the Moon are examples of planets where one day is equal to six months on earth. How can that be, one may ask, when we can see these planets orbiting the Sun?

One point of reference that may be difficult for some to understand is crucial to this realization. All planets have different dimensions surrounding them. The dimension of existence visible to our eyes gives us the impression that the other planets in our solar system are mostly devoid of life. In actuality astronomers have found proof of intelligent life on other planets, regardless of the fact that little is yet public knowledge. The purview discernable by our physical eyes, though, cannot enter into the heavenly spheres of these planets where devas, angels, and higher beings exist, nor even that of humans who enjoy an existence far superior to what is obtainable on our planet earth.

Just as on and surrounding earth there are realms of existence inhabited by ethereal beings invisible to our eyes, some highly advanced and others bound by unfortunate circumstances (such as ghosts), all planets have different spheres of existence. We can never gain knowledge of the multi-dimensional reality on earth with our physical eyes, so how could we possibly expect to enter into the higher realities of other planets with them?

There are also different types of oceans on different planets in the material world. “Siddhanta-siromani”, an ancient vedic astrological text describes them as being of seven varieties:

1) an ocean of salt water

2) an ocean of milk

3) an ocean of curd

4) an ocean of ghee (clarified butter)

5) an ocean of sugar cane juice

6) an ocean of liquor

7) an ocean of sweet water

Our minds may balk at such a conception of different types of oceans, but why should any of these be more fantastic than the ocean of salt water that we have here on earth?

There are also some eternal planets seemingly situated within this material universe, but they are always inaccessible for human beings. The text “Laghu-Bhagavatamrita” describes these eternal planets as follows: “Above Rudraloka, the planet of Lord Siva, is the planet called Vishnuloka. It is 400,000 miles in circumference, and inaccessible for any mortal living being. Above that Vishnuloka is a golden island called Maha-Vishnuloka in the ocean of salt. Brahma and other demigods sometimes go there to meet Lord Vishnu. Lord Vishnu lies there with Lakshmi (the goddess of fortune). East of here is the “ocean of milk” where within is the island of Svetadvipa, where Lord Vishnu also resides with Goddess Lakshmi. His transcendental island is 200,000 square miles and covered with desire trees for the pleasure of the Supreme Lord.”

This planet is called “Dhruvaloka” and we see it as the polestar. It is said to be 3,800,000 yojanas above the sun (one yojana is equal to 8 miles). Above Dhruvaloka by 10,000,000 yojanas is Maharloka. Above Maharloka by 20,000,000 yojanas is Janaloka, a further 80,000,000 yojanas lies Tapaloka, and above by 120,000,000 yojanas is Satyaloka. The Vaikuntha planets begin 26,200,000 yojanas beyond Satyaloka.

The scripture “Vishnu Purana” describes that the outer covering of the universe begins 260,000,000 yojanas above the sun. About 70,000 yojanas below the earth begin the seven lower planetary systems of Atala, Vitala, Sutala, Talatala, Mahatala, Rasatala, and Patala. Below these planets 30,000 yojanas is the Garbhodaka Ocean where Sesa Naga lies. This ocean is 249,800,000 yojanas deep. This gives an approximate diameter of the universe as 500,000,000 yojanas or 4,000,000,000 miles. These distances are calculated according to the distances between the planetary “planes” of existence. Actual distances between planets may be more.

The higher planetary systems are the realms of devas, demigods, and angels. Bhuvarloka is the abode of ghostly spirits, and the lower planets are populated by those of demoniac consciousness as well as the snakes known as “Nagas”. Development of higher consciousness, which also includes advanced intellectuality, starts with human beings and further increases among the denizens of higher planetary systems. The earth is situated close to the middle of these planetary systems.

Descriptions of the Planetary Systems
Satyaloka

This is the abode of Lord Brahma, the progenitor of this material universe. Here there are airplanes controlled by mantra, not by any mechanical means. The residents have mind and intelligence, but no material gross bodies. They feel compassion for those suffering in the lower regions, but do not suffer fear, old age, or death. At the time of final dissolution of the material planets the residents here transform their subtle bodies into spiritual bodies and enter the eternal Vaikuntha planets. Great yogis finally reach this highest planet through the Milky Way, which is the “highway” to this most elevated planet where the duration of life is calculated as 15,480,000,000,000 years.

Tapaloka

This is the abode of the four Kumaras named Sanat, Sanaka, Sanandana, and Sanatana. In this world many great sages also reside due to their advancement through spiritual austerity. The enjoyment available to the residents is inconceivable to us as it is beyond anything of our experience. When there is annihilation of the material universe the residents here also transform their subtle bodies to spiritual and enter the spiritual sky.

Janaloka

This planet, still above the heavenly realms, is another abode of great saints and sages. This planet is populated by mystics who move to higher planets, and eventually transform their subtle bodies to spiritual, when the fire of devastation consumes the material planets. These residents can move between any planets within the material universe as mystic “spacemen” at speeds unthinkable to us.

Maharloka

When fully purified from material desire and contamination through sacrifice, penance, and charity one can reach the heavenly planets, and if advancing further can pass through the higher orbits to reach Maharloka. The greatest of sages, such as Bhrigu Muni, live in this place. It is situated beyond the “Sisumara”, which is the pivotal point for the turning of the universe. Advanced yogis reach this planet and live here for 4,300,000,000 solar years. When the fire of devastation almost reaches this planet the residents transport themselves to Satyaloka where they live further before this highest of planets is destroyed. They then transform their subtle bodies to spiritual and enter the spiritual realms.

Dhruvaloka

In every material universe is one Vaikuntha planet with an ocean of milk where Lord Vishnu resides on an island called Svetadvipa. This planet is Dhruvaloka. Living here are completely pure personalities. In our universe this planet is seen as the polestar and is situated above the planets of the Seven Rishis. As it is a spiritual planet, it is eternal and therefore remains when all other planets within the material universes are destroyed. It is said that this planet is the pivot for all material stars’ and planets’ orbits. All planets travel at high speeds in orbit, including the sun, which travels 16,000 miles per second in its orbit around Dhruvaloka. The planets of the seven sages are stars just below this planet that also orbit Dhruvaloka. They are always concerned with the welfare of the living entities within this material world and send emissaries to bring spiritual knowledge at various times and circumstances.

Sanaiscara (Saturn)

Saturn is considered an inauspicious planet astrologically, as he gives painful lessons to us here on earth. It is situated 1,600,000 miles above Jupiter and passes through one sign of the zodiac every 30 months.

Brihaspati (Jupiter)

Jupiter is considered a most auspicious heavenly planet and is generally considered favorable astrologically, depending on placement at the time of our births here on earth. It is a planet of devas, and situated 1,600,000 miles above Mars.

Angaraka (Mars)

Mars is considered to be a malefic planet, which creates lack of rainfall on earth and almost always is capable of creating unfavorable influences here. It is situated 1,600,000 miles above Mercury.

Buddha (Mercury)

Mercury is said to be the son of the moon and is 1,600,000 miles beyond the planet Venus. As does Venus, he sometimes moves behind the sun, sometimes in front, and sometimes along with it. Generally the influence of Mercury is said to be auspicious astrologically, except when not moving with the sun. At such times this planet causes great storms on earth.

Shukra (Venus)

Venus is considered a most auspicious and favorable planet, and is also of the heavenly planets. Venus is said to bring rainfall, another reason for it being considered auspicious to life on earth.

Chandraloka (Moon)

The Moon is one of the four most important residences of the demigods. Those who worship the demigods through sacrifice aimed at great material enjoyment are promoted to the Moon. Here the celestial, intoxicating beverage called “soma” is available. It is not possible to enter into or even see the actual heavenly dimensions of this planet with our present eyes. The Moon passes through the entire zodiac in approximately one month. He influences the growth of vegetation and therefore considered the life-giver for all living beings on earth.

Surya (Sun)

The Sun is the source of light and heat for our universe. Modern science considers many stars to also be suns, but in the vedic literature they are considered to be planets of varying material elements, but not the center, as is the Sun. Surya, the sun god, is considered an expansion of Narayana (a form of Lord Vishnu). He controls the seasons here on earth. It is situated between Bhuloka and Bhuvarloka, rotating through the time circle of the zodiac. Yogis practicing hatha or ashtanga yoga, or those performing agnihotra sacrifices, worship the sun for their benefit. The demigods residing on the sun planet have bodies made of fire, necessary for life here.

Rahu

Rahu is said to be an invisible planet, which is situated 80,000 miles below the sun. It causes solar and lunar eclipses, as Rahu, along with Ketu, are the north and south nodes of the moon respectively.

Siddhaloka, Caranaloka, & Vidyadharaloka

These planets are 80,000 miles below Rahu. The residents of these planets are born with natural mystic powers, including the ability to fly without mechanical means, even to other planets. They have all the mystic siddhis, and being materially perfect beings can control gravity, time, and space. Their arts, culture, and sciences are far superior to that knowledge possessed by we here in the earthly realm.

Yakshaloka & Rakshashaloka

Beneath these higher planetary systems, in the sky called “antariksha”, are the residences of the Yakshas, Rakshashas, Pisachas, ghosts, and other etheral beings. This realm extends as far as the wind blows and clouds float in the sky. Above this there is no air.

Bhu-mandala (Middle Earth)

The planetary systems of middle earth (Bhumandala or Bhuloka) are abodes of both standards of living such as we enjoy on our planet, as well as some heavenly abodes where living beings may “stop” on the way to, or from, births in the heavenly planetary systems. There are seven planetary systems, which are divided by seven oceans. The names of the planetary systems are Jambu, Plaksha, Salmali, Kusha, Krauncha, Shaka, and Pushkara. Each system is twice as large as the one preceding it, and each ocean between the systems are made respectively of salt water, sugarcane juice, liquor, ghee, milk, emulsified yogurt, and sweet water.
Bhumandala is shaped like a lotus flower and the seven planetary systems are in the whorl of the lotus. The radius of Bhumandala extends as far as the sunshine, and the limits of our vision here to see the stars and moon. As the sunshine reaches earth from a distance of 93,000,000 miles, this is the radius of the plane of Bhumandala.

Lower Planetary Systems

Below the earth are seven other systems called Atala, Vitala, Sutala, Talatala, Mahatala, Rasatala, and Patala. These lower planetary systems are the same size as the earth planet, and begin 560,000 miles below earth. Sunshine does not reach these planets and light comes from jewels on the hoods of serpents. These planets are populated by persons of great power and opulence, yet of demoniac consciousness, who have reached here through austerity aimed at material enjoyment without spiritual development. They do not become old and diseased and fear only the time factor, which ultimately must destroy their abodes. Therefore they are given the name of “bila-svarga”, or subterranean heavenly planets.

The residents here enjoy a standard of material comfort more opulent than even the higher planets due to their desires for high standards of sensual enjoyment, wealth, and influence. The residents are known as Daityas, Danavas, and Nagas and are all engaged in illusory material enjoyment with no thought of spiritual liberation. There are incredible feats of architecture in their cities bedecked with valuable jewels in houses, gardens, compounds, etc. All residents drink juices and bathe in herbal elixirs which free them from any anxiety or physical disease, as well as any sign of physical aging. The visual beauty of these artificial heavens surpasses that of the higher planets and this sensual atmosphere completely captures the mind, allowing no thoughts but those directed toward sensual pleasure and happiness. Since time is not divided into days and nights due to no sunshine reaching these planets, they have no fear produced by time. Only at the time of dissolution does anxiety and fear consume them.

Narakaloka, the Hellish Planetary Systems

Beneath the planet Patalaloka, and slightly above the water of the Garbhodaka ocean, are the Naralokas, or the hellish planetary systems. These planets are of different degrees of suffering for those who must endure life there. Here on earth we can see many hellish circumstances of suffering for people, but nothing like what is experienced on these planets. They are said to be a place of rectification for those who commit the most abominable actions while living as humans on the earthly plane. Although life here seems like it goes on for an eternity, in actual fact the duration of one’s “karmic sentence” here may be only seconds or moments. There are 28 different hellish planets described in the Vedic literatures.

These descriptions of the material creation, as well as the spiritual planets, may be found in several Vedic literatures to a far greater depth. I have out of necessity greatly abbreviated the information given here.

All of the planetary systems in the material world will in time be annihilated. This annihilation takes place in two ways. Partial annihilation occurs every 4,300,000,000 solar years, or at the end of each day on Satyaloka. This extends from the hellish planets through all lower planetary systems up to the heavenly planets. The highest planets are not annihilated at this time. The entire cosmic manifestation is wound up in the universal form of God every 8,600,000,000 x 30 x 12 x 100 solar years. The spiritual world, which is never annihilated, simply absorbs the material creation. It is described that before the destruction there is no rain for hundreds of years. Everything dries up and dies due to continuous sunshine. The sun becomes 12 times as powerful as was previously. Then there are horrendous rains that absorb everything into water.

The mortal bodies of living entities, including all vegetation, merge into the earth. The earth merges into its subtle sensation of fragrance. Fragrance merges into water, and water merges into its quality of taste. That taste merges into fire, which merges into form. Form merges into touch and touch into ether. Ether finally merges into the sensation of sound. The senses all merge into their origins, the presiding devas and demigods, then they merge into the controlling mind, which merges into ego in the mode of goodness. Sound becomes one with ego in the mode of ignorance, and ego (the first of all the physical elements), merges into the total nature. The total material nature dissolves into the modes (goodness, passion, and ignorance). These modes then merge into the unmanifest form of nature, and that unmanifest form merges into time. Time merges into the Supreme Godhead, present as Maha-Vishnu, the original creator of the cosmic manifestation. The origin of all life merges into God, the unborn Supreme Soul who remains one without a second, and from whom all creation and annihilation takes place. This annihilation of the material world is the exact reverse of the process of creation. Everything ultimately rests within the Supreme Absolute.

 

 

Please see my related posts:

Networks and Hierarchies

Consciousness of Cosmos: A Fractal, Recursive, Holographic Universe

Boundaries and Networks

Hierarchy Theory in Biology, Ecology and Evolution

Geometry of Consciousness

Mind, Consciousness and Quantum Entanglement

Process Physics, Process Philosophy

Reflexivity, Recursion, and Self Reference

 

 

 

Key Sources of Research:

 

 

 

THE GREAT CHAIN OF BEING

Click to access THE%20GREAT%20CHAIN%20OF%20BEING.pdf

 

 

 

 

Early modern cosmology (Introduction)

Click to access Cosmology-2.pdf

 

 

 

Worldview: The Great Chain of Being

Click to access The%20Great%20Chain%20of%20Being.pdf

 

 

Gaia and the great chain of being

Click to access 2745204.pdf

 

 

 

Translations, Notes, and Questions for A. O. Lovejoy’s Great Chain of Being

Click to access Lovejoy.pdf

 

 

 

General Characteristics of the Renaissance

Click to access great-chain-of-being.hnd.pdf

 

 

 

MACROCOSM/MICROCOSM

John Henry

 

Click to access MACROCOSM-MICROCOSM_HISTORY%20OF%20SCIENCE%20AND%20RELIGION%20IN%20THE%20WESTERN%20TRADITION.pdf

 

 

 

From the Great Chain of Being to Postmodernism in three Easy Steps

Ken Wilber

Click to access FromGC2PM_GENERAL_2005_NN.pdf

 

 

 

 

Man the microcosm, Universe the macrocosm

https://auromere.wordpress.com/2009/08/18/man-the-microcosm-universe-the-macrocosm/

 

 

 

Plato used Hindu Microcosm and Macrocosm!

Plato used Hindu Microcosm and Macrocosm!

 

 

 

The Microcosm: The World of Quantum Mechanics

VV Raman

Click to access World%20of%20Quantum%20Mechanics_Resonance__Aug2012_Vol17_no_8.pdf

 

 

Aitareya Upanishad: Origin of the Universe & Man

Click to access Aitareya-Upanishad.pdf

 

 

 

 

Eternal Dance of Macrocosm

Click to access EternalDanceMacrocosm.pdf

 

 

 

MICROCOSM and MACROCOSM

http://www.iranicaonline.org/articles/microcosm-and-macrocosm

 

 

 

Microcosm and Macrocosm

http://www.newworldencyclopedia.org/entry/Microcosm_and_Macrocosm

 

 

Hindu Temple and the Structure of Human Body: Comparison

https://www.surya-world.org/hindu-temple-and-the-structure-of-human-body-comparison/

 

 

The Philosophical Foundations of Jyotish

http://www.puja.net/Pages/Jyotish/JyotishPhilosophy.htm

Hierarchy Theory in Biology, Ecology and Evolution

Hierarchy Theory in Biology, Ecology and Evolution

 

I have always been intrigued by multi-level thinking whether it is in organizations, biology, ecology, and evolutionary theory.

  • Plant – Division – Corporate – Industry – Macro-economy
  • Molecules – Organelles – Cells – Tissue – Organs – Whole body
  • Organism – Populations – Communities – Ecosystem –  Bio-Sphere

 

How does human body forms from Molecules?  Is it all evolutionary?  or is there a role for Vitalism?

How to integrate decision making in organizations at multi levels?  From Corporate level to Plant Level.

How does an Individual fits in Groups, Communities, Society, and Ecosystem?

What is the role of fractals thinking in Evolutionary Biology?

 

A SUMMARY OF THE PRINCIPLES OF HIERARCHY THEORY

The Hierarchy theory is a dialect of general systems theory. It has emerged as part of a movement toward a general science of complexity. Rooted in the work of economist, Herbert Simon, chemist, Ilya Prigogine, and psychologist, Jean Piaget, hierarchy theory focuses upon levels of organization and issues of scale. There is significant emphasis upon the observer in the system.

Hierarchies occur in social systems, biological structures, and in the biological taxonomies. Since scholars and laypersons use hierarchy and hierarchical concepts commonly, it would seem reasonable to have a theory of hierarchies. Hierarchy theory uses a relatively small set of principles to keep track of the complex structure and a behavior of systems with multiple levels. A set of definitions and principles follows immediately:

Hierarchy: in mathematical terms, it is a partially ordered set. In less austere terms, a hierarchy is a collection of parts with ordered asymmetric relationships inside a whole. That is to say, upper levels are above lower levels, and the relationship upwards is asymmetric with the relationships downwards.

Hierarchical levels: levels are populated by entities whose properties characterize the level in question. A given entity may belong to any number of levels, depending on the criteria used to link levels above and below. For example, an individual human being may be a member of the level i) human, ii) primate, iii) organism or iv) host of a parasite, depending on the relationship of the level in question to those above and below.

Level of organization: this type of level fits into its hierarchy by virtue of set of definitions that lock the level in question to those above and below. For example, a biological population level is an aggregate of entities from the organism level of organization, but it is only so by definition. There is no particular scale involved in the population level of organization, in that some organisms are larger than some populations, as in the case of skin parasites.

Level of observation: this type of level fits into its hierarchy by virtue of relative scaling considerations. For example, the host of a skin parasite represents the context for the population of parasites; it is a landscape, even though the host may be seen as belonging to a level of organization, organism, that is lower than the collection of parasites, a population.

The criterion for observation: when a system is observed, there are two separate considerations. One is the spatiotemporal scale at which the observations are made. The other is the criterion for observation, which defines the system in the foreground away from all the rest in the background. The criterion for observation uses the types of parts and their relationships to each other to characterize the system in the foreground. If criteria for observation are linked together in an asymmetric fashion, then the criteria lead to levels of organization. Otherwise, criteria for observation merely generate isolated classes.

The ordering of levels: there are several criteria whereby other levels reside above lower levels. These criteria often run in parallel, but sometimes only one or a few of them apply. Upper levels are above lower levels by virtue of: 1) being the context of, 2) offering constraint to, 3) behaving more slowly at a lower frequency than, 4) being populated by entities with greater integrity and higher bond strength than, and 5), containing and being made of – lower levels.

Nested and non-nested hierarchies: nested hierarchies involve levels which consist of, and contain, lower levels. Non-nested hierarchies are more general in that the requirement of containment of lower levels is relaxed. For example, an army consists of a collection of soldiers and is made up of them. Thus an army is a nested hierarchy. On the other hand, the general at the top of a military command does not consist of his soldiers and so the military command is a non-nested hierarchy with regard to the soldiers in the army. Pecking orders and a food chains are also non-nested hierarchies.

Duality in hierarchies: the dualism in hierarchies appears to come from a set of complementarities that line up with: observer-observed, process-structure, rate-dependent versus rate-independent, and part-whole. Arthur Koestler in his “Ghost in The Machine” referred to the notion of holon, which means an entity in a hierarchy that is at once a whole and at the same time a part. Thus a holon at once operates as a quasi-autonomous whole that integrates its parts, while working to integrate itself into an upper level purpose or role. The lower level answers the question “How?” and the upper level answers the question, “So what?”

Constraint versus possibilities: when one looks at a system there are two separate reasons behind what one sees. First, it is not possible to see something if the parts of the system cannot do what is required of them to achieve the arrangement in the whole. These are the limits of physical possibility. The limits of possibility come from lower levels in the hierarchy. The second entirely separate reason for what one sees is to do with what is allowed by the upper level constraints. An example here would be that mammals have five digits. There is no physical reason for mammals having five digits on their hands and feet, because it comes not from physical limits, but from the constraints of having a mammal heritage. Any number of the digits is possible within the physical limits, but in mammals only five digits are allowed by the biological constraints. Constraints come from above, while the limits as to what is possible come from below. The concept of hierarchy becomes confused unless one makes the distinction between limits from below and limits from above. The distinction between mechanisms below and purposes above turn on the issue of constraint versus possibility. Forget the distinction, and biology becomes pointlessly confused, impossibly complicated chemistry, while chemistry becomes unwieldy physics.

Complexity and self-simplification: Howard Pattee has identified that as a system becomes more elaborately hierarchical its behavior becomes simple. The reason is that, with the emergence of intermediate levels, the lowest level entities become constrained to be far from equilibrium. As a result, the lowest level entities lose degrees of freedom and are held against the upper level constraint to give constant behavior. Deep hierarchical structure indicates elaborate organization, and deep hierarchies are often considered as complex systems by virtue of hierarchical depth.

Complexity versus complicatedness: a hierarchical structure with a large number of lowest level entities, but with simple organization, offers a low flat hierarchy that is complicated rather than complex. The behavior of structurally complicated systems is behaviorally elaborate and so complicated, whereas the behavior of deep hierarchically complex systems is simple.

Hierarchy theory is as much as anything a theory of observation. It has been significantly operationalized in ecology, but has been applied relatively infrequently outside that science. There is a negative reaction to hierarchy theory in the social sciences, by virtue of implications of rigid autocratic systems or authority. When applied in a more general fashion, even liberal and non-authoritarian systems can be described effectively in hierarchical terms. There is a politically correct set of labels that avoid the word hierarchy, but they unnecessarily introduce jargon into a field that has enough special vocabulary as it is.

A SHORT ANNOTATED BIBLIOGRAPHY OF HIERARCHY THEORY.

This bibliography is in chronological order, so that the reader can identify the early classics as opposed to the later refinements. If you must choose just one book to read, turn to the last reference in this bibliography, Ahl and Allen, 1996. Simon, H.. A. 1962. The architecture of complexity. Proceedings of the American philosophical society 106: 467-82. This is the foundation paper of hierarchy theory originating from an economist. It was a re-published in “Sciences of the Artificial” by Simon. It introduces the idea of near-decomposability. If systems were completely decomposable, then there would be no emergent whole, because the parts would exist only separately. The “near” in near-decomposable allows the upper level to emerge from the fact that the parts anre not completely separate.

Koestler, Arthur. 1967. The ghost in the machine. Macmillan, New York. This is a long hard look at human social structure in hierarchical terms. The notion of holon first occurs in this work. This is a classic work, but is easily accessible to the lay public.

Whyte, L.. L.., A. G. Wilson and D. Wilson (eds.). 1969. Hierarchical structures. American Elsevier, New York. This is a classic collection of early scholarly works by some of the founders of hierarchical thinking.

Pattee, H.. H. (ed.) 1973. Hierarchy theory: the challenge or complex systems. Braziller, New York. This edited volume has some classic articles by Pattee, Simon and others.

Allen, T. F. H. and T. B. Starr. 1982. Hierarchy: perspectives for ecological complexity. University Chicago Press. This book has a significant ecological component but is much more generally about hierarchical structure. It is abstract and a somewhat technical treatment but has been the foundation work for the application of hierarchy theory in ecology and complex systems theory at large.

Salthe, S. 1985. Evolving Hierarchical Systems: their structure and representation. Columbia University Press, New York. This book has a strong structural bias, in contrast to the process oriented approach of Allen and the other ecologists in this bibliography. Salthe introduces the notion of the Triadic, where there is a focus on 1) the system as both a whole above the levels below and 2) a part belonging to another level above, 3) not forgetting the level of the structure itself in between. While much biological hierarchy theory takes an anti-realist point view, or is at least reality-agnostic, wherein the ultimate reality of hierarchical arrangement is left moot, Salthe’s version of hierarchy theory is concerned with the ultimate reality of structure. The anti-realist view of structure is that it is imposed by the observer, and may or may not correspond to any ultimate reality. If structure does correspond to ultimate, external reality, we could never know that to be so. Salthe’s logic is consistent but always takes a structural and ontological position.

O’Neill, R. V., D. DeAngelis, J. Waide and T. F. H. Allen. 1986. A hierarchical concept of ecosystems. Princeton University Press. This is a distinctly ecological application of hierarchy theory, making the critical distinction between process functional ecosystem approaches as opposed to population and community relationships. It is an application of hierarchy theory to ecosystem analysis.

Allen T. F. H. and T. Hoekstra. 1992. Toward a unified ecology. Columbia University Press. This book turns on hierarchy theory, but is principally a book about ecology. It goes beyond the O’Neill et al book, in that it makes the distinction between many types of ecology (landscape, ecosystem, community, organism, population, and biomes) on the one hand, and scale of ecology on the other hand. It ends with practical applications of hierarchy theory and ecological management.

Ahl, V. and T. F. H. Allen. 1996. Hierarchy theory, a vision, vocabulary and epistemology. Columbia University Press. This slim a volume is an interdisciplinary account of a hierarchy theory, and represents the shallow end of the pool. It is the primer version of Allen and Starr 1982. It is full of graphical images to ease the reader into a hierarchical perspective. It makes the distinction between levels of organization and levels of observation. It takes a moderate anti-realist point of view, wherein there may be an external reality, but it is not relevant to the discourse. We only have access to experience, which must of necessity involve observer values and subjectivity. There are examples from a wide discussion of many disciplines. Included are examples from psychology, ecology, the law, political systems and philosophy. It makes reference to the global and technological problems facing humanity, and offers hierarchy theory as one tool in the struggle. The summary of hierarchy theory in the opening paragraphs above comes from this book.

This summary was compiled by

Timothy F. Allen, Professor of Botany,
University of Wisconsin Madison,
Madison Wisconsin 53706 — 1381.
Email – tfallen@facstaff.wisc.edu

 

 

Key People:

  • James Grier Miller
  • Howard Pattee
  • Stanley Salthe
  • T F Allen
  • Herbert Simon
  • NILES ELDREDGE
  • CS Holling

 

 

Key Sources of Research:

 

A SUMMARY OF THE PRINCIPLES OF HIERARCHY THEORY

T Allen

http://www.isss.org/hierarchy.htm

http://www.botany.wisc.edu/allenlab/AllenLab/Hierarchy.html

 

 

Hierarchy Theory

Paweł Leśniewski

 

Click to access 2006-06-28_-_Hierarchy_Theory.pdf

 

 

Summary of the Principles of Hierarchy Theory

S.N. Salthe

 

Click to access Summary_of_the_Principles_o.pdf

 

 

HOWARD PATTEE’S THEORETICAL BIOLOGY:

A RADICAL EPISTEMOLOGICAL STANCE TO APPROACH LIFE, EVOLUTION ANDCOMPLEXITY.

Jon Umerez

 

Click to access umerez.pdf

 

 

 

Hierarchy Theory as the Formal Basis of Evolutionary Theory

 

Click to access HierarchyTheoryastheFormalBasisofEvolutionaryTheory.pdf

 

 

The Concept of Levels of Organization in the Biological Sciences

 

PhD Thesis Submitted August 2014 Revised June 2015

Daniel Stephen Brooks

 

http://d-nb.info/1082033960/34

 

 

A spatially explicit hierarchical approach to modeling complex ecological systems: theory and applications

Jianguo Wu , John L. David

 

Click to access Wu_David_2002.PDF

 

 

What is the Hierarchy Theory of Evolution?

 

Click to access What-Is-The-Hierarchy-Theory.pdf

 

 

HIERARCHICAL ORGANIZATION OF ECOSYSTEMS

Jackson R. Webster

 

Click to access 274.pdf

 

 

Ecological hierarchies and self-organisation – Pattern analysis, modelling and process integration across scales

Hauke Reutera,, Fred Jopp, José M. Blanco-Morenod, Christian Damgaarde, Yiannis Matsinosf, Donald L. DeAngelis

 

Click to access Reuter_etal_BAAE%202010.pdf

 

 

Levels of organization in biology: on the nature and nomenclature of ecology’s fourth level

William Z. Lidicker, Jr

 

Click to access Artigo4.pdf

 

 

Chapter 24

Hierarchy Theory: An Overview

Jianguo Wu

 

 

 

Recent progress in systems ecology

Sven E. Jørgensena, Søren Nors Nielsenb, Brian D. Fath

Click to access 55f1782708ae199d47c2624c.pdf

 

Click to access Jorgensen%20et%20al%202016.pdf

 

 

Heterarchies: Reconciling Networks and Hierarchies

Graeme S. Cumming

https://www.researchgate.net/publication/303508940_Heterarchies_Reconciling_Networks_and_Hierarchies

 

 

Evolutionary Theory

A HIERARCHICAL PERSPECTIVE

EDITED BY NILES ELDREDGE, TELMO PIEVANI, EMANUELE SERRELLI, AND ILYA TEMKIN

 

 

Holons, creaons, genons, environs, in hierarchy theory: Where we have gone

Timothy Allen, Mario Giampietro

http://www.sciencedirect.com/science/article/pii/S0304380014002993

 

 

The Evolutionary Foundations of Hierarchy: Status, Dominance, Prestige, and Leadership

Mark van Vugt & Joshua M. Tybur

Click to access Handbook_of_Evolutionary_Psychologymvv2014rev.pdf

 

 

The Microfoundations of Macroeconomics: An Evolutionary Perspective

Jeroen C.J.M. van den Bergh

John M. Gowdy

 

Click to access 00021.pdf

 

 

Understanding the complexity of Economic, Ecological, and Social Systems

C S Holling

Click to access Holling_Complexity-EconEcol-SocialSys_2001.pdf

 

 

Hierarchical Structures

Stanley N. Salthe

 

Click to access 5768411408ae7f0756a2248c.pdf

 

 

Two Frameworks for Complexity Generation in Biological Systems

Stanley N. Salthe

 

Click to access A-life_Conf_paper_Word.pdf

Click to access _publ_classified_by_topic.pdf

 

 

Spatial scaling in ecology

J. A. WIENS

 

Click to access Spatial%20scaling%20in%20ecology%20v3%20n4.pdf

 

 

The Spirit of Evolution

by Roger Walsh

An overview of Ken Wilber’s book Sex, Ecology, Spirituality: The Spirit of Evolution (Shambhala, 1995).

http://cogweb.ucla.edu/CogSci/Walsh_on_Wilber_95.html

Growth and Form in Nature: Power Laws and Fractals

Growth and Form in Nature: Power Laws and Fractals

 

There are several instances of power laws found in nature and in society.  Some of the well known ones are:

  • City Sizes (Zipf’s Law)
  • Firm Sizes
  • Stock Market Movements
  • Income and Wealth (Pareto’s Law)
  • Metabolic Rate and Body Mass (Kleiber’s Law-3/4 or Rubner’s Law-2/3)

 

Power laws and Scaling in Biology

After 1997 paper by West et all, many publications have analyzed  empirical evidence as to what the correct exponent is and what is the fundamental theoretical basis for power law.

West found 3/4 as exponent, others have reported 1/4, 2/3, 4/5 etc.

Animals and Mammals follow 3/4 exponent.  Plants follow 2/3.

The Metabolic Theory of Ecology

Scaling in biology has a rich and important history. Typically body mass, or some other parameter relating to organism size, is related to anatomical, physiological, and ecological parameters across species. Quite remarkably, diverse organisms, from tiny microbes to the earth’s largest organisms are found to fall along a common slope, with a high degree of variance explained. The beauty of such scaling ‘‘laws’’ has been the generality in biotic organization that they suggest, and the challenge (for ecologists) has often been interpreting their mechanistic bases and ecological consequences.

Scaling laws have thus far inspired scientists in at least three major areas. First, scaling laws may illuminate biology that is otherwise shrouded. For example, if scaling relationships can account for variation in a parameter of interest, the residual variation may be much more easily examined because the major influence of some trait, say, body size, is removed. Second, some scientists have taken an interest in ‘‘the exponent’’—essentially the exponential scaling values that produce the allometric relationship. What are the precise values of these exponents? Are they all from a family of particular values (quarter powers) for many different biological relationships? This area seeks to define the generality of patterns in nature and to explore the empirical robustness of the relationships. Third, from a mechanistic perspective, if scaling laws are mechanistic and truly general, then this suggests some underlying common biological process that forms the structure and function of species and ultimately generates biological diversity. The mechanistics of scaling from metabolism and the currently favored fractal network model of resource acquisition and allocation may allow scientists to understand the laws of how life diversified and is constrained. Perhaps more importantly, such a mechanistic understanding should allow the successful prediction of evolutionary trends, responses of organisms to global change, and other basic and applied biological problems.

The Ecological Society of America’s MacArthur Award winner, James H. Brown, working together with colleagues for over a decade on scaling in biology, has arrived at an outline for a metabolic theory of ecology—a proposal for a unifying theory employing one of the most fundamental aspects of biology, metabolism. This metabolic theory incorporates body size, temperature (metabolic kinetics described by the Boltzmann factor), and resource ratios of the essential elements of life (stoichiometry). Indeed, this bold and visionary proposal is likely to inspire ecologists and provoke much discussion. My goal in assembling this Forum was to work toward a balanced discussion of the power and logic of the metabolic theory of ecology. I have asked both junior and senior scientists to evaluate the ideas presented in the metabolic theory and to go beyond the listing of strong and weak points. As such, this collection of commentaries should be viewed neither as a celebration of the theory nor as a roast of Jim Brown. It should, however, serve as a springboard for future research and refinements of the metabolic theory.

Several themes and axes of admiration and agitation emerge from the forum. The focus on metabolism, and metabolic rate in particular, is an advance that most agree is the fundamental basis for the processes of acquisition of resources from the environment and, ultimately, survival and reproduction of organisms. The combination of size, temperature, and nutrients has compelling predictive power in explaining life-history traits, population parameters, and even broader-scale ecosystem processes. The key point here is that Brown et al. are making a direct link between factors that affect the functioning of individuals and the complex role that those individuals play in communities and ecosystems. Although what we have before us is a proposal for a unified theory of ‘‘biological processing of energy and materials’’ in ecosystems, Brown et al. embrace the unexplained variation and acknowledge other areas of ecology that may not be subject to metabolic laws.

The commentaries presented in this Forum are unanimous in their admiration of Brown et al.’s broad theoretical proposal and its clear predictions. Yet, points of discussion abound and range widely: What really is the correct exponent? Does the scale at which scaling is applied affect its explanatory power? Are the laws really based on mechanism or phenomena? How does the addition of temperature and resource limitation enhance the power of scaling relationships? And, is scaling up from the metabolic rate and body mass of organisms to population dynamics, community structure, and ecosystem processes possible? This Forum ends with Brown’s response to the commentaries. Although there will be continued debate over the correct exponent, the data at hand from the broadest taxonomic groups support quarter powers. There is general agreement over the issue of scale and the fact that, depending on the scale of interest, metabolic theory may have more or less to offer. Finally, nutrient stoichiometry is the most recent addition to metabolic theory, and all agree that further research and refinement will determine the role for such nutrient ratios in the ecological scaling. The benefits of a metabolic theory of ecology are clear. The authors of this Forum have outlined some of the future challenges, and tomorrow’s questions will evaluate these theses.

 

Metabolism provides a basis for using first principles of physics, chemistry, and biology to link the biology of individual organisms to the ecology of populations, communities, and ecosystems. Metabolic rate, the rate at which organisms take up, transform, and expend energy and materials, is the most fundamental biological rate. We have developed a quantitative theory for how metabolic rate varies with body size and temperature. Metabolic theory predicts how metabolic rate, by setting the rates of resource uptake from the environment and resource allocation to survival, growth, and reproduction, controls ecological processes at all levels of organization from individuals to the biosphere. Examples include:

(1) life history attributes, including development rate, mortality rate, age at maturity, life span, and population growth rate;

(2) population interactions, including carrying capacity, rates of competition and predation, and patterns of species diversity;

(3) ecosystem processes, including rates of biomass production and respiration and patterns of trophic dynamics.

Data compiled from the ecological literature strongly support the theoretical predictions. Eventually, metabolic theory may provide a conceptual foundation for much of ecology, just as genetic theory provides a foundation for much of evolutionary biology.

 

 

Key Terms

  • Power Laws
  • Multi-scale
  • Fractals
  • Allometric Scaling Laws
  • Kleiber Law
  • Metabolic Ecology
  • Zipf Distribution
  • allometry
  • biogeochemical cycles
  • body size
  • development
  • ecological interactions
  • ecological theory
  • metabolism
  • population growth
  • production
  • stoichiometry
  • temperature
  • trophic dynamics

 

 

 

Key Sources of Research:

 

The Origin of Universal Scaling Laws in Biology

Geoffrey B. West

 

Click to access gbwscl99.pdf

 

 

Life’s Universal Scaling Laws

Geoffrey B. West and James H. Brown

 

Click to access Life’sUniversalScalingLaws.pdf

 

 

A General Model for the Origin of Allometric Scaling Laws in Biology

Geoffrey B. West, James H. Brown, Brian J. Enquist

 

Click to access West_Brown_Enquist_1997.pdf

 

 

Power Laws in Economics: An Introduction

Xavier Gabaix

 

Click to access pl-jep.pdf

 

 

 

The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure and organization

Geoffrey B. West, James H. Brown

Click to access 1575.full.pdf

 

 

 

A general model for ontogenetic growth

Geoffrey B. West, James H. Brown & Brian J. Enquist

 

Click to access OntogeneticGrowth.pdf

 

 

 

Plants on a different scale

Lars O. Hedin

 

Click to access nature_news_views_06.pdf

 

 

 

The Fourth Dimension of Life: Fractal Geometry and Allometric Scaling of Organisms

Geoffrey B. West, James H. Brown, Brian J. Enquist

 

Click to access S1999_West.pdf

 

 

 

TOWARD A METABOLIC THEORY OF ECOLOGY

JAMES H. BROWN,

with JAMES F. GILLOOL Y, ANDREW P. ALLEN, VAN M. SA V AGE, AND GEOFFREY B. WEST

 

Click to access Brown_JH_MA.pdf

 

 

 

Complexity and Transdisciplinarity; Science for the 21st Century(?)!

GEOFFREY WEST

 

Click to access Geoffrey%20West.pdf

 

 

 

Scaling Laws in Complex Systems

 

Click to access ma_scaling_laws.pdf

 

 

 

A General Model for the Origin of Allometric Scaling Laws in Biology

Geoffrey B. West, James H. Brown,* Brian J. Enquist

Click to access Science-1997-West.pdf

 

 

 

Effects of Size and Temperature on Metabolic Rate

James F. Gillooly,1* James H. Brown,1,2 Geoffrey B. West,2,3 Van M. Savage,2,3 Eric L. Charnov

 

https://dspace.unm.edu/bitstream/handle/1928/1656/science2001.pdf?sequence=2&isAllowed=y

 

 

 

Growth, innovation, scaling, and the pace of life in cities

Luís M. A. Bettencourt, Jose ́ Lobo, Dirk Helbing, Christian Kuhnert, and Geoffrey B. West

 

Click to access zpq7301.pdf

 

 

 

Urban Scaling and Its Deviations: Revealing the Structure of Wealth, Innovation and Crime across Cities

Lu ́ıs M. A. Bettencourt1,2*, Jose ́ Lobo3, Deborah Strumsky4, Geoffrey B. West1,2

Click to access pone.0013541.pdf

 

 

 

URBAN DYNAMIC LAWS AND OUR DEGREES OF FREEDOM FOR DEVELOPMENT

Francisco J. Martínez

 

Click to access Francisco-Martinez_Urban-dynamic-laws.pdf

 

 

 

Allometric Scaling Laws and the Derivation of the Scaling Exponent

Marcel Grunert

 

Click to access grunert.pdf

 

 

Cities, Markets, and Growth: The Emergence of Zipf’s Law

Jeremiah Dittmar

August 10, 2011

 

Click to access Zipf_Dittmar.pdf

 

 

Self-similarity and power laws

 

Click to access komulainen.pdf

 

 

The fractal nature of nature: power laws, ecological complexity and biodiversity

James H. Brown1,2*, Vijay K. Gupta3, Bai-Lian Li1, Bruce T. Milne1, Carla Restrepo1 and Geoffrey B. West

 

Click to access Fractal-Nature.pdf

 

 

Metabolic Rate and Kleiber’s Law

https://universe-review.ca/R10-35-metabolic.htm

 

 

Patterns in Nature

http://www.patternsinnature.org/Book/PowerLaws.html

 

 

Zipf, Power-laws, and Pareto – a ranking tutorial

Lada A. Adamic

http://www.labs.hp.com/research/idl/papers/ranking/ranking.html

 

 

The Power of Power Laws

http://www.the-scientist.com/?articles.view/articleNo/14689/title/The-Power-of-Power-Laws/

 

 

Re-examination of the 3/4-law of Metabolism

P. S. DODDS, D. H. ROTHMAN- AND J. S. WEITZ

 

Click to access Dodds%20et%20al%202001.pdf

 

 

Fifth dimension of life and the 4/5 allometric scaling law for human brain

Ji-Huan He, Juan Zhang

 

Click to access he2004a.pdf

 

 

Lack of Evidence for 3/4 Scaling of Metabolism in Terrestrial Plants

Hai-Tao LI1*, Xing-Guo HAN2 and Jian-Guo WU

 

Click to access W020090624623546294020.pdf

 

 

Is West, Brown and Enquist’s model of allometric scaling mathematically correct and biologically relevant?

J. KOZLOWSKI and M. KONARZEWSK

 

Click to access FE.pdf

 

 

Evidence against universal metabolic allometry.

Folmer Bokma

 

Click to access bokma2003u.pdf

 

 

An evaluation of two controversial metabolic theories of ecology

 

Click to access Louw2011.pdf

 

 

ASSESSING SCALING RELATIONSHIPS: USES, ABUSES, AND ALTERNATIVES

Karl J. Niklas1, and Sean T. Hammond

 

http://www.journals.uchicago.edu/doi/pdfplus/10.1086/677238

 

 

􏱂􏱅Network Allometry

Click to access network%20allometry.pdf

 

 

A critical understanding of the fractal model of metabolic scaling

José Guilherme Chaui-Berlinck

 

Click to access 3045.full.pdf

 

 

 

Allometric scaling of metabolic rate from molecules and mitochondria to cells and mammals

Geoffrey B. West*†‡, William H. Woodruff*§, and James H. Brown

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