Luminosity and Chromaticity: On Light and Color

Luminosity and Chromaticity: On Light and Color

Key Terms and Ideas

  • Luminosity and Chromaticity
  • Light and Color
  • Diwali (Festival of Light) and Holi (Festival of Colors)
  • Rama and Krishna
  • Non Dual Vedanta and Trika Philosophy
  • 1 and 3
  • Verticalism and Horizontalism
  • Vedic and Tantric
  • Flute of Krishna and Shiva Jyotir Linga
  • Bow and Arrow of Ram
  • Ram Parivar and Shiv Parivar
  • Shiv Ratri
  • Plato and Aristotle
  • Sun, Moon, Earth and Mars
  • Rods and Cones in Retina
  • Color Temperature
  • Lok and Kosh
  • Seven Chakra
  • Trishool
  • Ram, Lakshman, Sita, Hanuman
  • Achromatic and Chromatic
  • Grey scale and Color Primaries
  • Mind and Moon
  • Moon and Emotions
  • Tone Circle
  • Color Circle
  • Pythagoras
  • 3 and 7
  • 137
  • 007
  • Prism
  • Seven Colors
  • 4 + 3 = 7
  • 4 x 3 = 12
  • Pentatonic
  • Heptatonic
  • Diatonic Scale
  • Chromatic Scale

Newton’s Color Circle


Color Circle in Opticks of I.Newton

Source: Reprint of Opticks by Project Gutenberg

Color Sensation

Source: Understanding color & the in-camera image processing pipeline for computer vision

Electromagnetic Spectrum

Source: Notes for the course of Color Digital Image Processing

Color Temperature

Source: Understanding color & the in-camera image processing pipeline for computer vision

Color Temperatures of the Stars

Luminosity Function

Source: Understanding color & the in-camera image processing pipeline for computer vision

CIE 1931 XYZ

Source: Understanding color & the in-camera image processing pipeline for computer vision


Source: Human Vision and Color

Brightness, Lightness,Hue, Saturation, and Luminosity

Source: The Brightness of Colour

Brightness has been defined as the perceived intensity of a visual stimulus, irrespective of its source. Lightness, on the other hand, is defined as the apparent brightness of an object relative to the object’s reflectance. Thus increasing the intensity of light falling on an object will increase its apparent brightness but not necessarily its apparent lightness, other things being equal [1]. Saturation is a measure of the spectral ‘‘purity’’ of a colour, and thus how different it is from a neutral, achromatic stimulus. Hue is the perception of how similar a stimulus is to red, green, blue etc. Luminous efficiency, or luminosity, measures the effect that light of different wavelengths has on the human visual system. It is a function of wavelength, usually written as V(l) [2], and is typically measured by rapidly alternating a pair of stimuli falling on the same area of the retina; the subject alters the physical radiance of one stimulus until the apparent flickering is minimised. Thus luminance is a measure of the intensity of a stimulus given the sensitivity of the human visual system, and so is integrated over wavelength [3]. Luminance is thought to be used by the brain to process motion, form and texture [4].

Clearly, brightness is monotonically related to luminance in the simplest case: the more luminant the stimulus is, the brighter it appears to be. However, the Helmholtz-Kohlrausch (HK) effect shows that the brightness of a stimulus is not a simple representation of luminance, since the brightness of equally luminant stimuli changes with their relative saturation (i.e. strongly coloured stimuli appear brighter than grey stimuli), and with shifts in the spectral distribution of the stimulus (e.g. ‘blues’ and ‘reds’ appear brighter than ‘greens’ and ‘yellows’ at equiluminance) [1; 5–6].

The HK effect has been measured in a variety of psychophysical studies [7–8] and is often expressed in terms of the (variable) ratio between brightness and luminance. 


Source: Human Vision and Color

Human Eye

Source: Human Vision and Color

Human Retina

Source: Human Vision and Color

Rods and Cones Photoreceptors

Source: Human Vision and Color

Color Receptors

Source: Human Vision and Color

Tristimulus Color

Source: Color/CMU

Visual Sensitivity

Source: Human Vision

Light and Color (Photometry and Colorimetry) I

Source: Interactive Computer Graphics/UOMichigan

Light and Color (Photometry and Colorimetry) II

Source: Interactive Computer Graphics/UOMichigan

Two Types of Light Sensitive Cells

Source: Interactive Computer Graphics/UOMichigan

Cones and Rod Sensitivity

Source: Interactive Computer Graphics/UOMichigan

Distribution of Cones in Retina


Types of Color Stimuli

Source: Perceiving Color.

Color Perception

Source: Perceiving Color.


Source: Human Vision and Color

Luminance and Chromaticity Space

Source: Understanding color & the in-camera image processing pipeline for computer vision

1931 CIE Chromaticity Chart

CIE 1931 Chromaticity Diagram

Source: Human Vision and Color

Source: Notes for the course of Color Digital Image Processing

Additive Colors

Source: Human Vision and Color

Subtractive Colors

Source: Human Vision and Color

Color Mixing

Source: Human Vision and Color

Color Appearance Models
  • RGB
  • CMY
  • CIE xyY
  • Hunter LAB
  • HSB
  • HSV
  • HSL
  • HSI
  • YIQ for NTSC TVs in USA
  • YUV for PAL TVs in EU
  • YCbCr for digital TVs
  • Munsell Color System

Color Models are device independent. For discussion of device dependent color spaces, please see my post Digital Color and Imaging.

LMS, RGB, and CIE XYZ Color Spaces

Source: Color/CMU

HSV Color Space

My Related Posts

Reflective Display Technology: Using Pigments and Structural Colors

Color Science and Technology in LCD and LED Displays

Color Science of Gem Stones

Nature’s Fantastical Palette: Color From Structure

Optics of Metallic and Pearlescent Colors

Color Change: In Biology and Smart Pigments Technology

Color and Imaging in Digital Video and Cinema

Digital Color and Imaging

On Luminescence: Fluorescence, Phosphorescence, and Bioluminescence

On Light, Vision, Appearance, Color and Imaging

Understanding Rasa: Yoga of Nine Emotions

Shapes and Patterns in Nature

Key Sources of Research

What Are The Characteristics Of Color?

Birren Color Theory

by ADMIN on MARCH 11, 2012

Light, Color, Perception, and Color Space Theory

Professor Brian A. Barsky

Computer Science Division
Department of Electrical Engineering and Computer Sciences University of California, Berkeley

Understanding Color Spaces and Color Space Conversion

The Human Visual System and Color Models

Click to access Carmody_Visual&ColorModels.pdf

Defining and Communicating Color: The CIELAB System

Color Vision and Arts



A short history of color theory

Let’s Colormath

Understanding the formulas of color conversion

A History of Human Color Vision—from Newton to Maxwell

Barry R. Masters

Optics and Photonics January 2011—from_newton_to_max/

The Difference Between Chroma and Saturation

Munsell Color

Charles S. Peirce’s Phenomenology: Analysis and Consciousness

By Richard Kenneth Atkins

The Evolution of Human Color Vision/ Jeremy Nathans

Jeremy Nathans Lecture on Color Vision




The Genes for Color Vision

Jeremy Nathans


A Short History of Color Photography

Photography  |  Angie Kordic

Blue: The History of a Color (2001)

followed by Black: The History of a Color (2009) and then Green: The History of a Color (2014), all produced by the same publisher. A fifth, devoted to yellow, should come next. 

Historic Look on Color Theory 

Steele R. Stokley

The evolution of colour in design from the 1950s to today

Francesca Valan

Journal of the International Colour Association (2012): 8, 55-60

Greek Color Theory and the Four Elements

J.L. Benson

University of Massachusetts Amherst


History of Color System

The Origins of Modern Color Science

J D Mollon

Click to access MollonColorScience.pdf

The History of Colors

Tobias Kiefer

Click to access Assignment_History_of_Colors.PDF

Notes for the course of Color Digital Image Processing

Edoardo Provenzi

Understanding color & the in-camera image processing pipeline for computer vision

Dr. Michael S. Brown

Canada Research Chair Professor York University – Toronto

ICCV 2019 Tutorial – Seoul, Korea

Chapter 2
Basic Color Theory

Click to access t3.pdf

Color Science

CS 4620 Lecture 26

Click to access 26color.pdf

Color Image Perception, Representation and Contrast Enhancement

Yao Wang
Tandon School of Engineering, New York University


Arne Valberg, Bjørg Helene Andorsen, Kine Angelo, Barbara Szybinska Matusiak and Claudia Moscoso

Norwegian University of Science and Technology Trondheim, Norway

A Primer to Colors in Digital Design

Archit Jha

Jul 16, 2017


Click to access 07_additive-color.pdf


Matthias Zwicker Universität Bern Herbst 2016


Click to access ColorPerception.pdf

Introduction to Computer Vision

The Perception of Color

In: Webvision: The Organization of the Retina and Visual System [Internet]. Salt Lake City (UT): University of Utah Health Sciences Center; 1995–.2005 May 1 [updated 2007 Jul 9]

Visual Pigment Gene Structure and Expression in Human Retinae 

Tomohiko Yamaguchi,  Arno G. Motulsky,  Samir S. Deeb

Human Molecular Genetics, Volume 6, Issue 7, July 1997, Pages 981–990,

The Difference Between Chroma and Saturation


Number by Colors

A Guide to Using Color to Understand Technical Data
  • Brand Fortner
  • Theodore E. Meyer

Chapter 5 Perceiving Color

The Practical Guide To Color Theory For Photographers

History of the Bauhaus

The Digital Artist’s Complete Guide To Mastering Color Theory

byLeigh G


Anthony Holdsworth

Molecular Genetics of Color Vision and Color Vision Defects

Maureen Neitz, PhDJay Neitz, PhD

Arch Ophthalmol. 2000;118(5):691-700. doi:10.1001/archopht.118.5.691

Color Theory: Introduction to Color Theory and the Color Wheel

Color Spaces and Color Temperature

The Brightness of Colour

David Corney1, John-Dylan Haynes2, Geraint Rees3,4, R. Beau Lotto1*

EECS 487: Interactive Computer Graphics



Basics of Color Theory



Color Matching and Color Discrimination

The Science of Color


1.3 Color Temperature

Color Spaces and Color Temperature

Digital Camera Sensor Colorimetry

Douglas A. Kerr

Click to access Sensor_Colorimetry.pdf

Chromatic luminance, colorimetric purity, and optimal aperture‐color stimuli

DOI: 10.1002/col.20356

Title: A Review of RGB Color Spaces …from xyY to R’G’B’

The CIE XYZ and xyY Color Spaces

Douglas A. Kerr

Click to access CIE_XYZ.pdf


Wallace B. Thoreson and Dennis M. Dacey

Department of Ophthalmology and Visual Sciences, Truhlsen Eye Institute, University of Nebraska Medical Center, Omaha, Nebraska; and Department of Biological Structure, Washington National Primate Research Center, University of Washington, Seattle, Washington

Physiol Rev 99: 1527–1573, 2019 Published May 29, 2019; doi:10.1152/physrev.00027.2018

Human Vision

Introduction to color theory


Human Vision and Color


Click to access 121.pdf


Andrew Stockman

Department of Visual Neuroscience UCL Institute of Opthalmology London, United KIngdom

David H. Brainard

Department of Psychology University of Pennsylvania Philadelphia, Pennsylvania



Click to access lecture15.pdf

What Are The Characteristics Of Color?


A Guide to Color

Guide C-316
Revised by Jennah McKinley

A History of Color

The Evolution of Theories of Lights and Color
  • Robert A. Crone

The Brilliant History of Color in Art

Victoria Finlay

A History of Light and Colour Measurement
Science in the Shadows

Sean F Johnston

University of Glasgow, Crichton Campus, UK

Color codes: modern theories of color in philosophy, painting and architecture, literature, music and psychology

Charles Riley

Chapter 6 Colour

History of Color Systems

Knots in Yoga

Knots in Yoga



Key Terms

  • Granthies or Knots
  • Bandha or Locks
  • Chakra or Energy Centers
  • Nadis
  • Kundalini shakti
  • Tantra
  • Yoga
  • Knots
  • Triplicity
  • Tribhang
  • Trefoil Knot
  • Dhumra Linga, Bana Linga, Itara Linga
  • Brahma, Vishnu, Rudra Knots
  • Tamas, Rajas, Sattva Gunas

3 Granthi in Kundalini Yoga


In Kundalini Yoga, it is said that there are three Granthi can be responsible for preventing prana from rising up through Sushumna Nadi. This Granthi three knots prevent one’s full potential from Kundalini rising energy. These three knots are Brahma Granthi, Vishnu Granthi and Rudra Granthi. They also relate to the Prakritis three Gunas (Tamas, Rajas and Sattva).

Some yogis in yoga see Granthi as a bamboo tree, where each segment is a barrier or barrier to the increase in kundalini energy.

The chakras in the psycho-physical human body at the dormant state form complex intertwined structures, called Granthi, or knots, as they are “link” matter and spirit, enhancing the sense of ego. There are three main granthis in the human body, which make the trinity of Brahma, Vishnu, and Shiva respectively, and they are called Brahma Granthi, Vishnu Granthi and Rudra Granthi.
In any practice to achieve success in the process of Kundalini awakening it is important to open these psychic knots. However, it is quite difficult because of granthi inextricably connected with all that we are accustomed to thinking of our personality, our habits, qualities, desires.

Three granthis together constitute the unconscious complexes (samskara) woven by illusion, and the weight and rigidity of the past is strong opposition to the passage of spiritual power.

The three Granthi are :

  1. Brahma granthi. it covers the area of Mulahara and Svadhisthan chakras. Some call it the perineal knot. It relates to the Tamas Guna (Mulahara and Svadhishthana) the universal destructive power.
    In both the Jabal and the Yogashikha Upanishad state that this granthi is located in the Muladhard chakra. However, most tantric scriptures place it in the Manipura chakra.
  2. Vishnu granthi (doing and prana). It covers the area between Manipura, Anahata and Vishuddi chakras. Sometimes it is known as the navel knot. It relates to the Rajas Guna (Manipura and Anahata) – the universal power of motion and activity.
    Vishnu granthi is said to be located in the area of Anahata chakra (the heart center), which is also the seat of prana. The heart is also the major knot chakra. So, to take the Kundalini Shakti into the passage of the Sushumna through Anahata chakra is also not very easy.
  3. Rudra granthi (Jnana, true knowledge). It covers the areas of Ajna and Sahasrara chakras. It is also known as the forehead knot. Unlike the other five chakras, the Ajna chakra is not connected to the spinal cord. So, the Rudra granthi is blocking the flow of prana beyond the sixth chakra between the eyebrows, Ajna chakra, upwards toward Sahasrara. It relates to the Sattva Guna (Vishuddha and Ajna), the universal creative power.

The Brahma granthi separates the first two chakras (Mulahra and Suadhisthana chakras) from the Manipura chakra. The sympathetic chain is continuous, however, at the upper level of the splanchnic nerves, the presynaptic system changes to the post-synaptic system. So, one can say the Vishnu Granthi is between the Manipura and the Anahata chakras.

Brahma Granthi is the first major block that sadhaka need to transcend. This granthi keeps a person under the illusion of the material benefits, physical pleasures, lethargy, ignorance, and uncertainty.
Among all the most powerful is an illusion of physical pleasure. This granthi plays an important role because it is responsible for the material man’s thinking. It creates a kind of attraction in the nature of the human mind.

Brahma granthi is covered by the essence it produces. This essence is called as “Kledam”. It is colorless and smells as a lotus flower. It is like a mixture of ‘Kapha’ which covers the entrance of Sushumna and also lubricates the Nadi connected. This lubrication helps the pulses of Nadi.

This Kledam is a thick mixture and thickens when we get older if we don’t practice yoga. With the power of Yoga can penetrate this barrier and go up through Sushumna through each barrier.

In short, anatomically the Granthis exist due to either the change of systems from sympathetic to parasympathetic, the separation of Vagus nerve from the Sacral nerve, or the changes from presynaptic fibers to postsynaptic fibers.

The philosophy of Kundalini Yoga is associated with the flow of energy in the channels called Ida and Pingala, (the female and male channels of the astral body, comparable to the sensory and motor nerves of the physical body) and its criss-cross centers in the spinal canal called Sushumna Nadi called chakras.

The three major intersections in the central Sushumna Nadi are at Muladhara (pelvic region), Anahata (chest region) and Ajna chakras (between the eyebrows) are interpreted as Granthi because the exchange energies of physical and mental levels occur at these three places and named after the Trinity.

Granthi means a knotted area which prevents the free flow of energy (Prana) from rising upwards. The concept and explanations related to granthi is a vague term that deals with very internal issues of undoing it and hard to give a figurative expression in a stone medium because they are levels of awareness where the power of Maya, ignorance, and attachment to material things are especially strong.

According to ancient spiritual science, every human has a gross physical body, the subtle astral body, and mind as its counterpart which is linked to each other. Though mind resides and interacts in the physical body, it cannot be given proof for its structure nor location in the body, but the mind influences the astral body also. The energy for the physical body is through external aids, but, energy for the astral body is dependent on the calm state of mind which can be achieved by getting out of the worldly entanglements termed as granthi.

The Ida and Pingala Nadi that are like spirals of opposite poles of the central axis intertwine and unlock while passing through the seven chakras. Psychic knots of granthis are like protective blockages for the gradual change in awareness and open only with the purification of mind and balance between the two Nadi. The purpose of granthis is to block the sudden upward flow of prana, are like circuit breakers to protect the overload that may occur to the practitioner in case of a spontaneous ascension. The display of ‘granthis’ is associated with the ‘Trinity’ as the three main deities (Tri Murti).

They are visualized like psychic knots or obstacles on the path of the awakened kundalini, (The power of awareness) which is difficult to pass through for every human, as it brings about a change in personality. Each aspirant must transcend these barriers to make a clear passageway for the ascending kundalini. In tantra based sculptures, the two major components Nadi, Ida and Pingala of kundalini as are pictured in anthropomorphic form as male and female human figures and crisscross is indicated as in contact or the hand positioned in the specific region of chakra.

In sculptural representations of this topic, the figures, since it is related to mind, the core of ‘Chitta’, are usually presented in a nude form, as the bare body represents the unadorned form of mind. In symbolic representations, they are like male and female snakes coiling at three places. The psychic Knots of granthi is depicted in the symbolized form as the Shiva Linga symbol. Different temples use different motifs to convey this topic in sculptures. The two sculptural representations are:

  • Symbolic representation of granthi, through the Linga and snakes.
  • Representation of grant in the human body in a personified form.

Kundalini yoga, a classification under tantra yoga is the form of subtle energy that flows in tubular channels called Nadis towards the conductor. The conductor is nothing but the nerve energy in the physical body that is encased in the spinal canal and called Sushumna. The intersections are recognized as chakras, seven in number, where the two nadi crisscross. At every chakra, a perfect balance and harmony must be established between the two Ida, Pingala Nadi or otherwise the energy of kundalini cannot progress to higher levels in the central channel of Sushumna.

In sculptural representations of tantra yoga depictions, the mind was projected as the female deity and prana as the male deity. Some sculptures depict the two male and female figures to be in contact at three or five regions like the foot, knee, genital place (Muladhara), heart (Anahata) and the tip of the nose (that is connected to Ajna chakra). Some schools recognize the chakras to be sixteen starting from foot, knee, palm, and so on. The contact at the foot and knee is suggestive of the lower points from which the Ida and Pingala (Female and male Nadi) arise and proceed. The contact at the foot is suggestive of the initial phase of activating the Ida and Pingala Nadi.

To clear Brahma granthi is to establish in totality, clearing Vishnu granthi is perceiving the existence of universal life principle and to clear Rudra granthi is to attain a non-duality of realization of oneness and universal awareness.


Brahma Granthi

Brahma Granthi at Muladhara chakra is represented by the Dhumra Lingam. Dhum means smoky. The linga is represented smoky and ill-defined (some Lingas made of Sphatika – a crystalline form of quartz stone) as a Symbol of the physical world. It is also called Svayambhu linga- the self-created linga. It signifies the establishment of life principles in totality.

Brahma granthi functions in the base region of the Muladhara chakra at the genital area and hence a display of organs. It implies the entanglement with physical pleasures, material objects, and excessive selfishness or a sense of fear. It also implies the ensnaring power of tamas – negativity, lethargy, and ignorance. Such negative qualities act as hindrances and stop the serpent power kundalini from awakening. Once this blockage is removed from the energy instincts of the deep rootedness with worldly affairs, the realm of consciousness gets awakened and the trapped serpent power energy is released. The kundalini or primal energy is thus able to rise beyond Muladhara and Swadhisthana without bogged down by the attractions to which our consciousness is hooked. On breaking open the Brahma granthi, the practitioner feels relaxed and enjoys bliss arising from the void.

The figures related to the granthis are nude because they are related to the state of mind ‘Chitta’ and personal. Muladhara relates to, Ajna chakra as the starting and release points of prana, which is indicated in the sculptures as contact points. Muladhara has a direct link to Ajna chakra – situated in midbrain but indicated as above the nose, between the eyebrows. The subtle energy of these two Ida-Pingala currents crosses over to connect with the right and left hemispheres of the brain.

Brahma granthi is the manifest force of the energy of life and creation, depicted in sculptures as the pleasure of touch. It is known as blockage of Brahma because it holds the consciousness at the level related to physical dimensions like sensuality or procreation. Once this blockage is overcome, the consciousness of deep rootedness to worldly pleasures is released. The kundalini can rise above, crossing this knot.

Vishnu Granthi

Vishnu Granthi in Anahata chakra (between Manipura and Ajna chakra) is represented as Bana Linga. The linga is depicted red or gold-colored as a Symbol of the subtle world. Clearing Vishnu knot is to perceive the existence of universal life principles.

The contact at the chest is the second stage of awareness at Vishnu granthi – to detach from emotions related to bondage. Vishnu granthi operates in the region of the Anahata chakra in the heart region. It is associated with the bondage of emotional attachment and attachment to people and inner psychic visions. It relates to the qualities of rajas – the tendency towards passion, ambition, bondage and assertiveness, individual ego and power. Once the blockage at Vishnu granthi is removed, the practitioner feels great bliss. The sustenance energy undergoes a change from the localized centers of the physical level to the universal level which means the energies of the body become harmonious with the energies of the cosmos. The interaction between the individual personality and the cosmos begins to happen naturally & spontaneously, enhancing the quality of compassion.

The position of placement of chakra wheel as balls suggests that she is activating the Ida and Pingala in legs as well as in hand with the acupressure or chakra ball. It also gives a hint that opening out of Vishnu granthi is not a spontaneous act. It begins from the hand and leg Nadi, followed by the opening of Brahma granthi at Muladhara. In the right hand, as she is holding the ball, highlighting the thumb as the starting point of Nadi in hands. Activating the center of hands and feet is beneficial to health.

The freedom from the knotty – worldly problems and the freedom from knotty congestion in her meridians that restricts the flow of bioenergy at her mental and physical levels – are viewed as obstacles, the root cause for problems and indicated as the cloth around the breasts called ‘kanchuka’ with a knot. Philosophically, clearing the knot of kanchuka means liberation – freedom from ignorance, bondage, commitments due to obligations of bondage, power are the obstacles project as knotty problems in life. The aspirant is constantly advised to dissociate from all limitations and identify oneself with all the pervading, blissful, non-duality spirit of the Brahman.

Rudra Granthi

Rudra Granthi in Ajna chakra is called Itara or Itakhya Linga. The linga is black, well defined with a very consolidated outline. Here, in Ajna, the awareness of ‘what I am’ is more sharply defined and various capacities are being awakened. The Dhumra and Bana Linga are depicted in lotus petals and only Itara linga is well defined. It signifies a state of non-duality. Clearing of Rudra granthi promotes spiritual vision. Awareness goes at the transpersonal level with super consciousness.

The loving gaze was used as a simile in tantra based sculptures to explain the abstract concept that mind (female) and prana (male) are harmonizing and mind is coming under the control of prana, in other words, mind is one with the object concentrated upon enjoying supreme bliss and super consciousness called ‘samadhi’.

The third contact at nose tip is related to crossing the hurdle of Rudra granthi – restraining from the thoughts of pride that comes sometimes from service to others or as the knower of knowledge. The pride prevents one from uniting with all with a non-dual thought. The three granthis when crossed, open the doors of Sahasrara chakra promoting spiritual vision and super consciousness. The Ida Pingala Nadi first intersect at the base of the spine and ends at the third eye center indicated at the apex of the nose. At the third eye center, these two currents cross over to connect with the right and left hemispheres of the brain.

The nose of the two male and female figures touch to symbolize the revitalization of memory and concentration of intuitive knowledge or cognition. Physiologically, the nasal nerves of olfactory bulb travel directly to the limbic area of the brain which controls the unconscious intuition of memory and sexuality. It functions in the region of Ajna chakra governing the Ajna and Sahasrara chakras. It represents the transformation of an existing form, idea or concept into the universal aspect. It is associated with the attainment of siddhis, a psychic phenomenon but still attached to and the concept of self as the power. In a psychological perspective, though serving others is a completely satisfactory way to spend one’s life at this stage, this service could create resentment against others, and view them as lesser beings as the pride of acquiring knowledge sometimes gains an upper hand. One must surrender the sense of individual ego and transcend duality to make further spiritual progress and then complete the circle by bringing that consciousness into compassionate actions.

With awareness, yoga practitioners ascend towards the Sahasrara chakra where the final merging of the individual Soul or Atman with the universal cosmic soul takes place to achieve the realization of oneness.

Awakening of Kundalini Shakti

Rshi Patanjali said “it is very difficult to walk on this Yoga path (Kundalini) like walking in the eyes of a knife that is very sharp, wrong or slipped a little too wounded” also walked to meet Him like doing a masterpiece project, all obstacles and obstacles we must be able to overcome only with determination. , disciplined and diligent practice.

So far we leave Him to approach him is something that requires extra energy. The energy that drives the realization of the Yoga goal is Kundalini Energy. Energy is power, power, shakti, power or whatever the term all of this already exists within us and also outside ourselves. Enormous energy that lies dormant in the form of a 3.5-circle snake with his head facing down around Linga swayambhu Siwa.

If the Kundalini energy is able to be raised, this energy will push someone to reach his life goal or his Yoga goals. The increase in Kundalini’s energy will cleanse every chakra that is passed then activate the chakras and various Siddhas will be felt even though it is still only a moment. The increase in Kundalini will be very helpful, especially to increase self-awareness and the vitality of the body is also increased, for example, to help self-healing or even become a healer.

But what needs to be considered is not only the benefits that are very useful, but also how we deal with every problem caused by the rise in Kundalini. Because the increase in kundalini will clean and open the knot chakra because kundalini is only limited to energy so this energy will play just breaking down, so we need to know the knowledge and directing techniques so that nothing happens that is desired. Many spiritual aspirants have fallen ill because of Him without realizing that the cause is Kundalini (kundalini syndrome).

Everyone has this Energy hidden in our body. Kundalini energy is very large energy like nuclear energy in the body. It can be imagined how much energy is in our bodies if this energy we are able to generate. To generate Kundalini energy you need sufficient knowledge, especially regarding the Main Chakra. In addition to this knowledge, a guide who really knows about the awakening of Kundalini or a spiritual teacher is very much needed.

Kundalini is the mother who protects us, the mother of the universe is often referred to as Mrs. Durga (Hyang Nini Bagawati), Mrs. Gayatri and Mrs. Saraswati. To awaken this Sakti Energy there are various ways and with certain training.

If the awakening of Kundalini towards this negative direction will have unfavorable consequences, there are several things that are affected that can hurt the physical body, this can be really real or will change the nature, emotions, behavior, and others towards the negative.

Kundalini is more commonly interpreted as a scroll, a power is in “Kunda” which is a quadratic place or mandala (Muladhara chakra), encircling the “Linga” three half circles that are above the “Yoni” Kundalini in the form of a snake resides in the cakra Muladhara and in in Muladhara there is linga and yoni this is where Kundalini as a power of silence. Kundalini is also known by various names including Mrs. Durga, Mother at times, Mrs. Bhuta, Mother Universe, Mrs. Bagawati and so on, all Mother’s names are Himself. She is also referred to as Ibu Prana, the inner Power of the Mother or latent energy whatever the name refers to her. I offer my devotion to the Great Mother … Energy Mother …

The negative polarities will flow towards the positive polarity, and the positive polarity is in the fontanel in Sahasrara Cakra where the Supreme Lord is located. Passive Shiva who is silent but whose vibrations spread to meet nature. Single Shiva (Eka) and many (various) at the same time. Shiva who lives in Sahasrara means that the vibrations of his silence dwell in each person’s Sahasrara. He sits in his favorite siddhasana, he whose body is bright as the reflection of sunlight on a snow mountain, whose hair is neatly woven, which flows holy Ganga water, surrounded by beautiful crescent moons, wears snakes as His necklace, blue-necked, body covered with weed, His two hands lifted up to give blessings and deliver from all fears, adorned with tiger skins as His garments, who sat on a lotus of thousands of golden leaves, whose smiles emit vibrations of peace.

The awakening of the Kundalini energy flow is determined by our level of consciousness, or in other words, we process it, we are the controller.

The thing to consider is that energy is still energy, He will follow our own consciousness, follow our mindset if we think towards virtue

Purification of Karma through 3 Granthi

In each bulkhead, vertebrae are stored with positive and negative karma as long as humans life. Every action or result of mental karma will be placed according to the place that caused it.

For example karma as a result of:

  • Material things, rough emotions, supernatural powers, magic, etc. are stored at the bottom (Muladhara).
  • Desires, desires and low egos are stored in Swadistana.
  • Subtle emotions, dynamism, strength, etc. are stored in the central node of the Manipura chakra (Stomach).
  • Feelings, love, envy, sadness, happiness, will be stored in the heart’s central node (Anahata),
  • The ego is more subtle, including the highest ego that wants to reach God stored in the Wisudhi chakra.
  • Mental instability, ignorance, wisdom, weigh and decide right and wrong, good and bad, mental balance, are stored in Ajna before heading for Enlightenment (in the Sahasrara chakra), … etc … according to the causes of chakra activeness and its consequences.

The two way of Oneness and Karma Melting through this method (granthi) :

  1. From top  (Sahasrara chakra) heading down through Sushumna. The meeting was in the deepest depth of Ajna. While experiencing calm, it will release fluid from the pineal gland, producing a form of fluid / Tirta Amritha which then drips into Sushumna, penetrates and removes impurities in each segment.
    This method is considered safer, and the risk is minimal. Although safe, it does not mean without obstacles and mental obstacles that need to be overcome. The effect is cold and some even feel like ice water flowing in each segment to the lower end until it merges with the power of Kundalini (Shiva-Shakti).
  2. From bottom (Muladhara chakra) by awakening the power of Kundalini. This Kundalini fire breaks through and increases the burning of karma in each of its ascension paths until it experiences unification in Sahasrara (Shiva-Shakti).
    In every process of ascension ranging from the most subtle (the heat) to the magma fire, the perpetrator will experience many obstacles to significant changes in mental effects and the temptation to get siddhi.

Being aware of every moment of attitudes and mental changes or the like is very necessary to get to the next level, as well as efforts to unleash the power of the siddhis obtained. Giving up the siddhi that is obtained does not mean that it will disappear when the higher attainments all of the things below will also be followed and controlled (included).

Both unity from above and taking the road from the bottom produced “Amritha / Tirta Kundalini”. The effect of this will result in peace, calm, silence, towards Samadhi.

In Bali, this meaning is also poured into the song Wargasari Down the Tirta so sublime … etc. Where this is the way from above (Requesting) the union of Shiva and Durga / Shakti (Kundalini).

In Kanda pat he the power that results in the purification of Tirta seeps through the bamboo cavities, arteries and the like depending on the experience he sees,

This result is also a Tirta “wiping out” (negative melting) released through saliva (vaguely inserted in a glass of water for Tirta by some Balinese healers). While some possessed (kerauhan) he came out through a kind of mucus through the nose when possessed.

Untying the Knots That Bind Us








March, 2015

The Sanskrit word granthi means “knot” or “doubt” and also means “an especially difficult knot to untie.” People in India wearing a sari or dhoti cloth will form a small pouch to hold money, and close it by knotting the fabric – this tightly knotted purse is called a granthi. Granthi in spiritual practice are psychological or psychic barriers to total freedom. Granthi prevent prana from moving freely up sushumna nadi. Granthi bind the soul; they lock us to our misperception of reality (avidya) and self (asmita). They hold us to our preferences (raga and dvesha) and root us in fear of death (abhinivesha). Knowledge (jnana) is a key component to transcend fear, and together with action (karma) they give wings to our spiritual desires – the rise of Kundalini.

The hathayoga methods for untying these knots are the bandhas, or energy locks. By focusing the pranas in Sushumna Nadi the bandhas increase the potency of the rising Kundalini allowing us to transcend normal restrictions of thinking and acting.

Brahma Granthi is located at the base of the spine between Muladhara Chakraand Svadhisthana Chakra where primitive brain functioning like the “fight or flight reflexes” guarantee survival. Fear of death, anxiety about food, shelter or clothing, or general lack of grounding, all manifest as Brahma Granthi. When you experience fear in an asana like handstand or split, and the fear itself prevents success, this is Brahma Granthi. Lack of spare time can be part of this knot. When your bills and rent payment keep you at work and away from yoga, that is Brahma Granthi.

Mula (Root) Bandha is the first consolidation of Prana and Apana, piercing Brahma Granthi. Vitality, thought, breath, and speech are joined in pursuit of truth. This root lock can be applied all the time transforming every thing we do into a holy act.

Vishnu Granthi knots energy between Manipura Chakra and Anahata Chakra. This Granthi is a knot of individual ego and power. Our clinging to ego, self-cherishing and the quest for personal power can slow spiritual success. Fear of being ignored or of loosing prestige may plague our spiritual growth. This is a knot of power and manipulation, but it is also the knot of accumulation. Accumulation of power, possessions, and fame, all tie us to this level of consciousness. In order to transcend this level of consciousness we must “give up the love of power, for the power of love!” The degree of vulnerability that we show in life – the ability to put our façade aside and challenge our own status quo, unties Vishnu Granthi.

Uddiyana (Flying up) Bandha is the second consolidation of Prana, Apana, and Samana vayus.

Applied together with Mula Bandha, this lock pierces Vishnu Granthi. The individual is able to transcend individuality. The whole abdomen is drawn in and up – symbolizing the renunciation of accumulation and concentration of energy upward toward Anahata Chakra.

Rudra granthi is knotted between the Anahata and Ajña chakras. The attractiveness of heart centered action and the experience of serving others can distract the yogi who desires to “Be Love” – not just experience it. Serving others is a completely satisfactory way to spend your life, but this service could become your cross to bear, where you hold resentment against others, and view them as lesser beings. We must strive to transcend otherness and experience the “oneness of being” in the highest levels of consciousness, and then complete the circle by bringing that consciousness into our compassionate actions. When we are free from the illusion of otherness our actions emerge spontaneously from Love. Jalandhara Bandha enables this leap of consciousness.

The consummate consolidation of prana is Jalandhara Bandha (Cloud Catching Lock or Net Lock – for the network of nadis in the neck) when Prana, Apana, Samana and Udana vayu in Sushumna Nadi loosen Rudra Granthi, and the veil of separation is lifted.

Teaching Tips

  • The yoga practices reveal where we are stopped by granthi, psychological knots, and give us tools for negotiating and loosening those limitations. The granthi are pierced through asana, meditation, pranayama, samyama, virtuous acts, purification of diet, good intention, yama and niyama, mudra, and through nada techniques like chanting and mantra.
  • Practice each bandha separately.
    • Mula: This bandha can be applied while breathing and moving freely.
      The two parts of this lock are a) contraction of the interior of the perineal body on men, or the vaginal walls for women, and b) the area from the pubic bone to navel draws inward and upward slightly.
    • Uddiyana: The diaphragm moves toward the throat drawing the entire abdomen in and up. This lock is only practiced on exhale retention when breathing is not possible and movement is internalized.
    • Jalandhara: Can be applied after inhale or exhale, bringing chest to chin. The spine should stay relatively straight and the chin should rest in the cleft between the clavicle bones.
  • Teach all bandha applied simultaneously in Mahamudra. See Hathayogapradipika Chapter 3, Verses 10-13
  • Investigate the psychological barriers to freedom that are embodied in the granthi, from fear of death and anxiety about survival (Muladhara,) to the accumulation of power and prestige (Manipura,) to the “feel good” effect of helping others, rather than serving others (Anahata.)
  • Teach about the Pranamaya Kosha and it’s component vayus. Asana practice most directly affects the Pranamaya Kosha and consolidates the energy of consciousness into a force of enlightenment.

In Bhagavad Gita 7.1 there is a reference to granthi as doubt, and refuge of the Lord as freedom from that doubt. In Srimad-Bhagavatam 1.2.17-21, bhakti-yoga severs the granthi (hard knot) of material affection and enables one to come at once to the stage of asamsayam-samagram.

The Bandhas and the Granthis


Bandhas are inner body locks that engage both the physical and the energetic body. They provide inner support during asana practice, stimulate the flow of prana and help to release the granthis, which can be understood as energy blockages or psychological knots.

By combining the action of opposing muscles, the bandhas can be activated. Their use during asana practice increases strength, stability and mental focus. Their use during pranayama intensifies its cleansing effect by directing agni or the internal fire to burn the waste matter that has settled and blocks the flow of energy.

Often referred to as locks, the bandhas help to balance two important energies within the body: the prana vayu and apana vayu. If prana is associated with drawing in that which nourishes us, apana is associated with letting go of that which is potentially toxic. Prana is connected to the inhalation and apana to the exhalation. The meeting of these two opposing energies at the base of the spine awakens the Kundalini energy.

There are three main bandhas: Jalandhara, Uddiyana and Mula bandha. Activating all three of these bandhas at the same time is referred to as Mahabandha or main lock.

The Bandhas


The Bandhas

Jalandhara Bandha: the throat lock. Jalandhara bandha can be applied by contracting the front muscles in the neck when tucking the chin towards the sternum. This bandha is naturally activated in some asanas like Sarvangasana (Shoulder Stand) or Halasa (Plough Pose). It is subtly activated during Ujjayi pranayama in which the glottis (the area where the vocal cords are located) is gently contracted.
This bandha focuses the mind on the fifth or throat chakra and contains the upward-flowing movement of prana past the throat. It also seals off the downward movement of “nectar” from the sahasrara or crown chakra, which is said to preserve youth and vitality.

Uddiyana Bandha: the abdominal lock. Uddiyana bandha is applied by contracting the upper abdominal muscles (just below the solar plexus). This bandha is naturally activated after each exhalation when the lungs are emptied and the diaphragm rises. During asana practice it is especially useful to apply this bandha to support the lumbar region in back bends. When used together with Mula bandha, it strengthens the abdominal muscles. While performing asanas it is not possible to fully engage this bandha as it would constrain breathing. This bandha focuses the mind on the third chakra and directs prana up towards the sixth chakra.

Mula Bandha: the root lock. Mula bandha is applied by contracting the pelvic floor and elevating the inner organs in this region like the bladder and genitals. Other groups of muscles, like the upper leg adductors (by slightly pressing the knees together), can intensify this bhanda. If engaged during asana practice it is said to “provide an extra lift, which is especially useful when jumping”. This bandha focuses the mind on the first chakra, and directs prana from the pelvic region upwards, providing energy to the whole body and stopping it from flowing downwards out of the body.

Activating the bandhas can also help to unblock the three granthisor knots that prevent prana from freely circulating within the Sushuma nadi. These knots can block the chakras and keep us tied to negative attitudes and emotions, preventing us from fully experiencing the richness of life.

The Granthi

The Granthi


The Bramha or Vital Granthi is associated with the first three chakras (root, sacrum and solar plexus). This granthi blocks us by feeding our attachment to physical comfort, material wealth and accumulation. It can be unblocked by activating Mula bhanda. To regulate the energy in these vital chakras and granthi, Patanjali recommends self discipline.

The Vishnu or Love Granthi is associated with the fourth and fifth chakras (heart and throat). This granthi blocks us by feeding our attachment to emotional excitement, self-centeredness and lack of receptivity to others’ needs. It can be unblocked by activating Uddyiana bandha. To boost the energy of the love chakras and granthi, Patanjali recommends devotion and commitment.

The Rudra or Light Granthi is associated with the last two chakras (third eye and crown of the head). This granthi blocks us by feeding our attachment to our opinions, prejudices, fantasies and intellectual pride. It can be unblocked by activating Jalandhara bandha. To dissolve pride and “dark” mental patterns, Patanjali recommends self-knowledge.



Please see my related posts

Knot Theory and Recursion: Louis H. Kauffman

Interconnected Pythagorean Triples using Central Squares Theory

The Great Chain of Being

Indra’s Net: On Interconnectedness





Key Sources of Resources


Untying the Knots That Bind Us

Recursion, Incursion, and Hyper-incursion

Recursion, Incursion, and Hyper-incursion


How do Past and Future inform the present?

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

Key Terms

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


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

X (t+ 1) =f(X(t), X(t-1) …p..)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Please see my related posts

On Anticipation: Going Beyond Forecasts and Scenarios

Autocatalysis, Autopoiesis and Relational Biology

Key sources of Research


Computing Anticipatory Systems with Incursion and Hyperincursion

Daniel M. DUBOIS


Click to access cd554835f0ae367c3d3e3fa40f3e5e5f5f11.pdf




Anticipation in Social Systems:

the Incursion and Communication of Meaning

Loet Leydesdorff 

Daniel M. Dubois

Click to access casys03.pdf





Daniel M. Dubois


Click to access dubois.pdf




Non-wellfounded Set Theory


  • Jon Barwise &
  • Larry Moss

Non-well-founded set theory

Knot Theory and Recursion: Louis H. Kauffman

Knot Theory and Recursion: Louis H. Kauffman


Some knots are tied forever.


Key Terms

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

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

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

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

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

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

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

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

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


LH Kauffman with Trefoil Knot in the back.

LH Kauffman


From Reflexivity

A Knot

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Trefoil Knot



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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.

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Wikipedia on Knot Theory




Please see my related posts:

Reflexivity, Recursion, and Self Reference

Jay W. Forrester and System Dynamics

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

Second Order Cybernetics of Heinz Von Foerster

Cybernetics Group: A Brief History of American Cybernetics

Cybernetics, Autopoiesis, and Social Systems Theory

Cyber-Semiotics: Why Information is not enough

Ratio Club: A Brief History of British Cyberneticians

Autocatalysis, Autopoiesis and Relational Biology

Feedback Thought in Economics and Finance

Increasing Returns and Path Dependence in Economics

Boundaries and Distinctions

Boundaries and Relational Sociology

Boundaries and Networks

Socio-Cybernetics and Constructivist Approaches

Society as Communication: Social Systems Theory of Niklas Luhmann

Semiotics, Bio-Semiotics and Cyber Semiotics

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

Networks and Hierarchies


Key Sources of Research:


Home Page of Louis H. Kauffman

Recursive Distinctioning

By Joel Isaacson and Louis H. Kauffman


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



Knot Logic – Logical Connection and Topological Connection

by Louis H. Kauffman

Click to access 1508.06028.pdf




by Louis H. Kauffman


Click to access KNOTS.pdf





Louis H. Kaufman, UIC

Click to access BioL.pdf

New Invariants in the Theory of Knots

Louis H. Kaufman, UIC




Eigenform – An Introduction

by Louis H. Kauffman

Click to access 2007_813_Kauffman.pdf



Knot Logic and Topological Quantum Computing with Majorana Fermions

Louis H. Kauffman


Click to access arXiv%3A1301.6214.pdf




by Louis H. Kauffman

Click to access videoLKss-slides.pdf




Eigenforms, Discrete Processes and Quantum Processes

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




Eigenforms — Objects as Tokens for Eigenbehaviors

by Louis H. Kauffman

Click to access 1817.pdf




Reflexivity and Eigenform The Shape of Process

Louis H. Kauffman A University of


Click to access ReflexPublished.pdf






Louis H. Kauffman


Click to access Eigen.pdf





Louis H. Kauffman UIC, Chicago


Click to access Eigenform.pdf



Form Dynamics

Click to access FormDynamics.pdf



Arithmetics in the Form

Click to access ArithForm.pdf




Self Reference and Recursive Forms

Click to access SelfRefRecurForm.pdf

Click to access Relativity.pdf




Laws of Form and the Logic of Non-Duality

Louis H. Kauffman, UIC


Click to access KauffSAND.pdf




Laws of Form – An Exploration in Mathematics and Foundations

by Louis H. Kauffman UIC


Click to access Laws.pdf




The Mathematics of Charles Sanders Peirce

Louis H. Kauffman1


Click to access Peirce.pdf




A Recursive Approach to the Kauffman Bracket

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

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


Law of Dependent Origination

Law of Dependent Origination


Linear Causality – Independent Variables – Regression Analysis

Mutual Causality – Feedbacks – Dynamic Modeling – Systems Dynamics – Non Linear Sys – Circular Causality – Reciprocity.

Connected – No Boundaries – Interconnectedness – Entanglements – Action at a distance



Key Terms

  • Codependent Origination
  • Interdependent Origination
  • Interconnectedness
  • Mutual Causality
  • Linear Causality
  • Cause and Effect
  • Joanna Macy
  • Paticca Samuppada
  • Pratitya Samutpada
  • Dependent Co-arising
  • Buddhism
  • Theravada Buddhism
  • Mahayana Buddhism
  • Indira’s Net
  • Great Chain of Being
  • Four Noble Truths
  • Twelve Nidanas
  • Eightfold Path



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Paticca Samuppada : Dependent Co-arising

Joanna Macy, in World As Lover, World As Self , made this concept clear to me. It’s not a common idea in Western religious talk, because it makes a divine Authority unnecessary for a moral imperative. She comes to it from systems theory, where it does have a Western parallel.

From page 54, here’s a taste:

According to Western religious thought, ethical values derive from divine commandment. A supernatural source is necessary to provide moral sanction. Without the ontological security of belief in an absolute, everything seems awash, with no clear guidelines, and it’s every man for himself. This assumption is so pervasive in the West that many noted scholars judged Buddhism’s moral teachings to be weak, since they do not issue from belief in any God. It is true that the Way the Buddha taught is freed from the necessity to believe in any supernatural authority. Indeed when he was asked by what authority he spoke, he cited again and again the law of dependent co-arising; not any entity ruling our world, but the dynamics at work within our world. He cited the interdependence of all phenomena. What did he mean by that? How can radical relativity serve as a moral grounding?

Her answer to that question, a description of the vigil under the Bodhi tree, takes too much space to quote at length here, but it begins (p. 540) with…

With fascination I studied the early Buddhist texts. I read how the perception of paticca samuppada dawned on the Buddha the night of his enlightenment, and featured in his discourses. I saw how it underlay everything he taught about self, suffering, and liberation from suffering. I noted how it knocked down the dichotomies bred by hierarchical thinking, the old polarities between mind and matter, self and world, that had exasperated me as a spiritual seeker and activist, and as a woman.

…and includes, on p. 56...

Tracing thus the sources of suffering, he did not find a first cause or prime mover, but beheld instead patterns or circuits of contingency. The factors were sustained by their own interdependence.

…and on p. 58…

According to this apparently simple set of assertions, things do not produce each other or make each other happen, as in linear causality; they help each other happen by providing occasion or locus or context, and in so doing, they in turn are affected. There is a mutuality here, a reciprocal dynamic.

I left out the narrative parts and the quotations from original sources. The argument hangs together better with them, and is more interesting. When I read it I felt I’d been given a great gift: how to understand morality as implicit in the basic nature of the universe, without pinning it on divinity. Instead of being subject to a top-down authority structure, we participate in an interdependent web of being Ñ which enfolds us, dancing with the endless exchange of energy which is our dependent co-arising, our giving and receiving of the life force, of compassion and service, of the dharma.

25 November 1998


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Click to access Dependent+Origination-Macy.pdf

Dependent Co-Arising

Joanna Macy

When the Buddha taught, he was said to turn the Wheel of the Dharma. Indeed, his central doctrine is like a wheel, for through it he taught the dependent co-arising of all things, how they continually change and condition each other in interconnections as real as the spokes in a wheel.

I have been deeply inspired by the Buddha’s teaching of dependent co-arising. It fills me with a sense of connection and mutual responsibility with all beings. Helping me understand the non- hierarchical and self-organizing nature of life, it is the philosophic grounding of all my work.

The recognition of our essential nonseparateness from the world, beyond the shaky walls erected of our fear and greed, is a Dharma gift occurring in every generation, in countless individual lives. Yet there are historical moments when this perspective arises in a more collective fashion and when, within Buddhism as a whole (if we can even talk of “Buddhism as a whole”!), there is a fresh reappropriation of the Buddha’s central teaching. This seems to be occurring today. Along with the destructive, even suicidal nature of many of our public policies, social and intellectual developments are converging now to bring into bold relief the Buddha’s teaching of dependent co-arising–and the wheel of the Dharma turns again.

This is happening in many ways. I see it in the return to the social teachings of the Buddha, in the revitalization of the bodhisattva ideal, in the rapid spread of “engaged Buddhism,” be it among Sarvodayans in Sri Lanka, Ambedkarite Buddhists in India, or Dharma activists in Tibet, Thailand, or Southeast Asia. Western Buddhists, too, are taking Dharma practice out into the world, developing skillful means for embodying compassion as they take action to serve the homeless, restore creekbeds, or block weapons shipments. The vitality of Buddhism today is most clearly reflected in the way it is being brought to bear on social, economic, political, and environmental issues, leading people to become effective agents of change. The gate of the Dharma does not close behind us to secure us in a cloistered existence aloof from the turbulence and suffering of samsara, so much as it leads us out into a life of risk for the sake of all beings. As many Dharma brothers and sisters discover today, the world is our cloister.

Here new hands and minds, aware of the suffering caused by outmoded ways of thinking and dysfunctional power structures, help turn the wheel. Strong convergences are at play here, as Buddhist thought and practice interact with the organizing values of the Green movement, with Gandhian nonviolence, and humanistic psychology, with ecofeminism, and sustainable economics, with systems theory, deep ecology, and new paradigm science.

In his teaching of Interbeing, Vietnamese Zen master Thich Nhat Hanh captures the flavor of this turning. Not only does he model the many bodhisattva roles one life can play–scholar, activist, teacher, poet, meditator, and mediator; he opens as well through the concept and practice of Interbeing a wide gate into the Buddha’s doctrine of dependent co-arising.

Now we see that everything we do impinges on all beings. The way you are with your child is a political act, and the products you buy and your efforts to recycle are part of it too. So is meditation–just trying to stay aware is a task of tremendous importance. We are trying to be present to ourselves and each other) in a way that can save our planet. Saving life on this planet includes developing a strong, caring connection with future generations; for, in the Dharma of co-arising, we are here to sustain one another over great distances of space and time.

The Dharma wheel, as it turns now, also tells us this: that we don’t have to invent or construct our connections. They already exist. We already and indissolubly belong to each other, for this is the nature of life. So, even in our haste and hurry and occasional discouragement, we belong to each other. We can rest in that knowing, and stop and breathe, and let that breath connect us with the still center of the turning wheel.

Wikipedia on Pratitya Samutpada


Hua Yen school

The Huayan school taught the doctrine of the mutual containment and interpenetration of all phenomena, as expressed in Indra’s net. One thing contains all other existing things, and all existing things contain that one thing. This philosophy is based in the tradition of the great Madhyamaka scholar Nagarjuna and, more specifically, on the Avatamsaka Sutra. Regarded by D.T. Suzuki as the crowning achievement of Buddhist philosophy, the Avatamsaka Sutra elaborates in great detail on the principal of dependent origination. This sutra describes a cosmos of infinite realms upon realms, mutually containing one another.

Thich Nhat Hanh

Thich Nhat Hanh states, “Pratitya samutpada is sometimes called the teaching of cause and effect, but that can be misleading, because we usually think of cause and effect as separate entities, with cause always preceding effect, and one cause leading to one effect. According to the teaching of Interdependent Co-Arising, cause and effect co-arise (samutpada) and everything is a result of multiple causes and conditions… In the sutras, this image is given: “Three cut reeds can stand only by leaning on one another. If you take one away, the other two will fall.” In Buddhist texts, one cause is never enough to bring about an effect. A cause must, at the same time, be an effect, and every effect must also be the cause of something else. This is the basis, states Hanh, for the idea that there is no first and only cause, something that does not itself need a cause.[34]

Tibetan Buddhism

Sogyal Rinpoche states all things, when seen and understood in their true relation, are not independent but interdependent with all other things. A tree, for example, cannot be isolated from anything else. It has no independent existence, states Rinpoche.[130]

Joanna Macy

Joanna Rogers Macy (born May 2, 1929), is an environmental activist, author, scholar of Buddhism, general systems theory, and deep ecology. She is the author of eight books.[1]


  • 1 Biography
  • 2 Key Influences
  • 3 Work
  • 4 Writings
  • 5 See also
  • 6 References
  • 7 External links


Macy graduated from Wellesley College in 1950 and received her Ph.D in Religious Studies in 1978 from Syracuse University, Syracuse. She studied there with Huston Smith, the influential author of The World’s Religions(previously entitled The Religions of Man). She is an international spokesperson for anti-nuclear causes, peace, justice, and environmentalism,[1]most renowned for her book Coming Back to Life: Practices to Reconnect Our Lives, Our World and the Great Turning initiative, which deals with the transformation from, as she terms it, an industrial growth society to what she considers to be a more sustainable civilization. She has created a theoretical framework for personal and social change, and a workshop methodology for its application. Her work addresses psychological and spiritual issues, Buddhist thought, and contemporary science. She was married to the late Francis Underhill Macy, the activist and Russian scholar who founded the Center for Safe Energy.[citation needed]

Key Influences

Macy first encountered Buddhism in 1965 while working with Tibetan refugees in northern India, particularly the Ven. 8th Khamtrul Rinpoche, Sister Karma Khechog Palmo, Ven. Dugu Choegyal Rinpoche, and Tokden Antrim of the Tashi Jong community. Her spiritual practice is drawn from the Theravada tradition of Nyanaponika Thera and Rev. Sivali of Sri Lanka, Munindraji of West Bengal, and Dhiravamsa of Thailand.

Key formative influences to her teaching in the field of the connection to living systems theory have been Ervin Laszlo who introduced her to systems theory through his writings (especially Introduction to Systems Philosophy and Systems, Structure and Experience), and who worked with her as advisor on her doctoral dissertation (later adapted as Mutual Causality) and on a project for the Club of Rome. Gregory Bateson, through his Steps to an Ecology of Mindand in a summer seminar, also shaped her thought, as did the writings of Ludwig von Bertalanffy, Arthur Koestler, and Hazel Henderson. She was influenced in the studies of biological systems by Tyrone Cashman, and economic systems by Kenneth Boulding. Donella Meadows provided insights on the planetary consequences of runaway systems, and Elisabet Sahtourisprovided further information about self-organizing systems in evolutionary perspective.


Macy travels giving lectures, workshops, and trainings internationally. Her work, originally called “Despair and Empowerment Work” was acknowledged as being part of the deep ecology tradition after she encountered the work of Arne Naess and John Seed [2], but as a result of disillusion with academic disputes in the field, she now calls it “the Work that Reconnects”. Widowed by the death of her husband, Francis Underhill Macy, in January 2009, she lives in Berkeley, California, near her children and grandchildren. She serves as adjunct professor to three graduate schools in the San Francisco Bay Area: the Starr King School for the Ministry, the University of Creation Spirituality, and the California Institute of Integral Studies.[cit


See also

  • David Korten, a collaborator with Macy on the Great Turning Initiative


External links



Please see my related posts:

Indra’s Net: On Interconnectedness

On Synchronicity

Key Sources of Research:


Dependent Origination: The Twelve Links Explained


Dependent Origination: The Twelve Links Explained




The Co-arising of Self and Object, World, and Society:

Buddhist and Scientific Approaches

William S. Waldron

Middlebury College

Click to access waldron_co-arising_of_mind_and_world0.pdf




Dependent Origination and the Buddhist Theory of Relativity

By Kottegoda S. Warnasuriya

Click to access 134f4e6d2088df76fb7cf033299efb3cf27a1058.pdf




Lama Tsongkhapa’s In Praise of Dependent Origination


Click to access The-Full-Commentary-In-Praise-of-Dependent-Origination-Final.pdf




The Significance of Dependent Origination in Theravada Buddhism

Nyanatiloka Mahāthera

Click to access wh140.pdf

Click to access the_significance_of_dependent_origination__nyantiloka_mahathera.pdf




Nagarjuna’s Seventy Stanzas: A Buddhist Psychology ofEmptiness

David Ross Komito

Translation and commentary on the Seventy Stanzas on Emptiness by Venerable Geshe Sonam Rinchen, Venerable Tenzin Dorjee, and David Ross Komito.


Click to access nagarjuna_seventy-stanzas.pdf




Chapter XXIV

Examination of the Four Noble Truths


Click to access nagarjuna_middleway24.pdf




From Grasping to Emptiness – Excursions into the Thought-world of the Pāli Discourses (2)

Click to access from-grasping.pdf


The Doctrine of Dependent Origination as Basis for a Paradigm of Human-Nature Relationship of Responsibility and Accountability

 Joanna Macy, Buddhism and Power for Social Change

Caiti Schroering


Paticca Samuppada : Dependent Co-arising

Wikipedia on Pratitya Samutpadaītyasamutpāda

Mutual Causality in Buddhism and General Systems Theory
The Dharma of Natural Systems

By Joanna Macy




Dependent Co-Arising

Joanna Macy


Click to access Dependent+Origination-Macy.pdf




A brief history of Interdependence.


Click to access 10McMahan.pdf




Beyond Nature\Nurture Buddhism and Biology on Interdependence

W.S. Waldron. Middlebury College


Click to access waldron_beyondnaturenuture0.pdf




 World as Lover, World as Self

Courage for Global Justice and Ecological Renewal

By Joanna Macy · 2007


Toward a Buddhist Systems Methodology 1: Comparisons between Buddhism and Systems Theory

Systemic Practice and Action Research


Considering Causality

Click to access 52247.pdf


Indira’s Net


On Synchronicity

On Synchronicity

There are invisible ties between us.


Click to access Synchronicity2010.pdf

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

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



Key Terms

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


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

Serendipity: Horace Walpole (1717-1797)


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

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

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

Seriality: Paul Kammerer (1880-1926)


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

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

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

Synchronicity: Carl Jung (1875-1961)

Psychologist Carl G. Jung

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

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

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

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


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

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

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

Please see my related posts:

Interconnected Pythagorean Triples using Central Squares Theory

Indra’s Net: On Interconnectedness

The Great Chain of Being

On Holons and Holarchy

Mind, Consciousness and Quantum Entanglement

Geometry of Consciousness

Systems View of Life: A Synthesis by Fritjof Capra

Consciousness of Cosmos: A Fractal, Recursive, Holographic Universe

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

Shape of the Universe

Reflexivity, Recursion, and Self Reference

Key Sources of Research


Synchronicity: Nature and Psyche in an Interconnected Universe

Joseph Cambray



Synchronicity and Healing



Click to access 18-Beitman-Chap18.pdf




An Acausal Connecting Principle

CG Jung





Christopher Jargodzki


Click to access Synchronicity2010.pdf

Synchronicity, Mind, and Matter

Wlodzislaw Duch




Synchronicity: did Jung have it right?

Kurt Forrer


Click to access bb26804cdc465b355e2f2e09c574d50dc4bb.pdf




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


Click to access Limar.Synchronicity.pdf

Synchronicity: The Bridge Between Matter and Mind

F. David Peat
Bantam Books (1987)

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

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

By Robert Aziz

Jung on Synchronicity and the Paranormal

By Carl Gustav Jung



Synchronicity and Emergence


Click to access Cambray.pdf

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

Synchronicity: Science, Myth, and the Trickster

Allan Combs
Marlowe & Co. (1996)

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

By Victor Mansfield

Synchronicity: Nature and Psyche in an Interconnected Universe

By Joseph Cambray

Rituals | Recursion | Mantras | Meaning : Language and Recursion

Rituals | Recursion | Mantras | Meaning : Language and Recursion


Key Terms

  • Rituals
  • Recursion
  • Mantras
  • Japa
  • Puja
  • Prayer
  • Psychological Development
  • Meaning
  • Meditation
  • Yoga
  • Vedas
  • Tantra
  • Hindu Vedic Rituals
  • Hindu Tantric Rituals
  • Language and Recursion
  • Speech
  • Communication
  • Organizing principle
  • Cognitive science
  • Linguistics
  • Panini
  • Pingala
  • Sanskrit
  • Act of walking and Talking
  • Take a walk
  • Vedic Meters
  • Gayatri Mantra
  • Grammer
  • Panini’s Asthadhyayi
  • Univarsal Grammer
  • Noam Chomsky
  • Frits Staal
  • Subhash Kak
  • Word and World
  • Structure of a Mantra
  • Structure of a Ritual
  • Prose and Poetry
  • Gadya and Padya
  • Fractals
  • Holarchy
  • Holons

Why Language and Thought Resemble Russian Dolls

Michael Corballis is a professor emeritus at the University of Auckland, who has written extensively on the evolution of language and the origins of thought.


Michael Corballis is a professor emeritus at the University of Auckland, who has written extensively on the evolution of language and the origins of thought. In his 2011 book The Recursive Mind, he wrote about how the structure of human language allows for recursion—in which ideas are nested within each other: “He thinks that I think that he thinks.” Recursion allows the construction of sentences of of theoretically unlimited complexity

The main argument of The Recursive Mind is that recursion applies to thought processes and actions that are not limited to language itself, but characterize other aspects of human thought, such as our ability to imagine ourselves in the past or future. I queried Corballis on some of these ideas. An edited transcript follows:

You wrote a book in the last few years called The Recursive Mind. What is recursion and why is it important?

Recursion can refer to a procedure that references itself or similar procedures, or to a structure that contains an embedded structure of the same type. It is important because it allows one to build entities of theoretically unlimited complexity by progressively embedding structures within structures.

Some scholars think that language may be built on the use of recursive building blocks. Isn’t that a fundamental tenet of the modern linguistics pioneered by Noam Chomsky.

Yes, Chomsky’s view of language is that it is recursive, and this gives language its potential for infinite complexity—or what he has also called “discrete infinity.” In recent formulations, this is achieved through an “unbounded Merge,” in which elements are merged, and the merged elements can then themselves be merged—a process that can be repeated without bounds. To Chomsky, though, language is essentially internal thought, a mental monologue, known as I-language, and not a means of communication. The structure of language is therefore a by-product of internal thought. This implies a common structure, called “universal grammar,” that underlies all languages. But there is growing doubt as to whether such a structure exists.

Wasn’t one of the flaws of Chomsky’s work that he thought that the recursion as found in internal self-talk was not linked in any way to natural selection and evolution

Yes, I think so. In Chomsky‘s view, the recursive principle emerged in a single step—a “great leap forward”—at some particular point in human evolution, probably within the time span of our own species. This is contrary to Darwinian evolution, which postulates that change occurs in small, incremental steps, implying that something as complex as language could not have occurred in a single step. Chomsky also argues that language could not have evolved through natural selection because the elements of language are fundamentally symbolic, with no direct reference to the external world, and could not have been “selected” by natural events.

I think these are flawed arguments. The idea of a single step is based in part on evidence of a sudden appearance of symbolic thought in the archeological record, but one can just as easily make a case for a gradual rise. Apes and dogs can fairly easily learn to respond meaningfully to spoken words, suggesting that they, like humans, have innate, mental concepts, to which words are easily attached. Even in humans, the apparently abstract nature of language might well have arisen from more iconic or even pantomimimed representations used as forms of communication that have become “conventionalized” through the generations, sustained through culture rather than biological endowment

I would argue instead that recursive thought may have origins in our ape-like forebears over 6 million years ago, but gained increasing complexity during the Pleistocene, dating from over 2 million years ago, largely as an adaptation toward increasing social complexity. Language depended on this broader recursive capacity, but also owed its earlier origins to manual gesture, perhaps developing a more complex structure through pantomime, with the iconic structure eventually replaced by vocal gestures (speech) or the more arbitrary signs of signed languages.

Hasn’t more recent work extended the idea of recursion? Isn’t it thought that recursive behaviors may actually precede language—and may have led to the emergence of language?

To some extent Chomsky’s view can be seen as consistent with this, since recursion applies to what he calls I-language, which is the language of thought rather than of communication. Communicative language can then regarded as a means of externalizing thought so that we can share our thoughts with others. It may have emerged after the “great leap forward” that gave us I-language, although Chomsky does not, as far as I know, suggest that thought and communicative language arose in sequence.

My own view is that recursive thoughts preceded language in broader ways. So-called theory of mind (“I know what you’re thinking”) or mental time travel (mentally reliving what I did yesterday, or foreseeing what I will do tomorrow) involve the embedding of thoughts within thoughts, and otherwise seem quite independent of what we understand as language. Navigation may be another example, as we embed maps within maps (my office in my house in my city in my country in the world). As I understand it, I-language is based on the structuring of internal symbols, whereas the extended examples I have given are more spatial or iconic than abstract, and therefore have a more direct relation with the external world. It is entirely plausible that they could have emerged through natural selection, which rescues language evolution from the “miracle” of a sudden great leap forward.

Since writing the book, I have moved further from the Chomskyan notion that language is uniquely human to finding the basis of mental time travel even in the ability of rats to “replay” and perhaps “preplay” trajectories in spatial environments. The aim of researchers should be to develop an account of the evolution of thought and language through natural selection, and not through some miraculous event within the past 100,000 years. .

Why are the origins of human language, considered to be one of the hardest problems in science?

The reason is that grammatical language, with its recursive structure, is considered unlike any other form of animal communication, and is restricted to our own species. Part of the difficulty is that we have no historical evidence to go on, since we are the only remaining species among the 20 or so hominins that split from the line leading to the great apes, and even the great apes closest to us do not appear to have grammatical language.

My sense is that we now have enough information from fossil evidence, primate communication, ancient DNA, and the structure of human cognition to begin to construct plausible Darwinian scenarios of how language might have evolved over the past 6 million or so years, and perhaps even earlier, without having to postulate a one-off miracle within the past 100,000.

From Art and Cosmology in India


General equivalences

The view that the arts belong to the domain of the sacred and that there is a connection between them is given most clearly in a famous passage in the Vishnudharmottara Purana in which the sage Markandeya instructs the king Vajra in the art of sculpture, teaching that to learn it one must first learn painting, dance, and music:

Vajra: How should I make the forms of gods so that the image may always manifest the deity?

Markandeya: He who does not know the canon of painting (citrasutram) can never know the canon of image-making (pratima lakshanam).

Vajra: Explain to me the canon of painting as one who knows the canon of painting knows the canon of image-making.

Markandeya: It is very difficult to know the canon of painting without the canon of dance (nritta shastra), for in both the world is to be represented.

Vajra: Explain to me the canon of dance and then you will speak about the canon of painting, for one who knows the practice of the canon of dance knows painting.

Markandeya: Dance is difficult to understand by one who is not acquainted with instrumental music (atodya).

Vajra: Speak about instrumental music and then you will speak about the canon of dance, because when the instrumental music is properly understood, one understands dance.

Markandeya: Without vocal music (gita) it is not possible to know instrumental music.

Vajra: Explain to me the canon of vocal music, because he, who knows the canon of vocal music, is the best of men who knows everything.

Markandeya: Vocal music is to be understood as subject to recitation that may be done in two ways, prose (gadya) and verse (padya). Verse is in many meters.

Please see my related posts

Sounds True: Speech, Language, and Communication

Reflexivity, Recursion, and Self Reference

Society as Communication: Social Systems Theory of Niklas Luhmann

Consciousness of Cosmos: A Fractal, Recursive, Holographic Universe

On Holons and Holarchy

Indra’s Net: On Interconnectedness

The Great Chain of Being


Key Sources of Research

God in the Fractals: Recursiveness as a Key to Religious Behavior

in Method & Theory in the Study of Religion

Eternal Recursion, the Emergence of Metaconsciousness, and the Imperative for Closure

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.




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)


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.


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.


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)





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




Holons and agents

A. Giret





A Brief History of Holons

Mark Edwards

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






The Holonic View of Organizations and Firms


Rolf Sattler


Eastern Roots of Russia’s most famous Toy

Consciousness of Cosmos: A Fractal, Recursive, Holographic Universe

Consciousness of Cosmos: A Fractal, Recursive, Holographic Universe

From Consciousness in the Universe is Scale Invariant and Implies an Event Horizon of the Human Brain

 Our brain is not a “stand alone” information processing organ: it acts as a central part of our integral nervous system with recurrent information exchange with the entire organism and the cosmos. In this study, the brain is conceived to be embedded in a holographic structured field that interacts with resonant sensitive structures in the various cell types in our body. In order to explain earlier reported ultra-rapid brain responses and effective operation of the meta-stable neural system, a field-receptive mental workspace is proposed to be communicating with the brain. Our integral nervous system is seen as a dedicated neural transmission and multi-cavity network that, in a non-dual manner, interacts with the proposed supervening meta-cognitive domain. Among others, it is integrating discrete patterns of eigen-frequencies of photonic/solitonic waves, thereby continuously updating a time-symmetric global memory space of the individual. Its toroidal organization allows the coupling of gravitational, dark energy, zero-point energy field (ZPE) as well as earth magnetic fields energies and transmits wave information into brain tissue, that thereby is instrumental in high speed conscious and sub-conscious information processing. We propose that the supposed field-receptive workspace, in a mutual interaction with the whole nervous system, generates self-consciousness and is conceived as operating from a 4th spatial dimension (hyper-sphere). Its functional structure is adequately defined by the geometry of the torus, that is envisioned as a basic unit (operator) of space-time. The latter is instrumental in collecting the pattern of discrete soliton frequencies that provided an algorithm for coherent life processes, as earlier identified by us. It is postulated that consciousness in the entire universe arises through, scale invariant, nested toroidal coupling of various energy fields, that may include quantum error correction. In the brain of the human species, this takes the form of the proposed holographic workspace, that collects active information in a ”brain event horizon”, representing an internal and fully integral model of the self. This brain-supervening workspace is equipped to convert integrated coherent wave energies into attractor type/standing waves that guide the related cortical template to a higher coordination of reflection and action as well as network synchronicity, as required for conscious states. In relation to its scale-invariant global character, we find support for a universal information matrix, that was extensively described earlier, as a supposed implicate order as well as in a spectrum of space-time theories in current physics. The presence of a field-receptive resonant workspace, associated with, but not reducible to, our brain, may provide an interpretation framework for widely reported, but poorly understood transpersonal conscious states and algorithmic origin of life. It also points out the deep connection of mankind with the cosmos and our major responsibility for the future of our planet.

Key Sources of Research:

The Folding of Life Proteins: On the role of long- and short range electromagnetic pilot mechanisms

Dirk K.F. Meijer* and Hans (JH) Geesink

Click to access The-Folding-of-a-Life-Proteins-On-the-role-of-long-and-short-range-electromagnetic-pilot-mechanisms.pdf



Nature Unites First, Second and Third Harmonics to Organize Coherent Electromagnetic Frequency Patterns that are Crucial for Health and Disease

A Soliton Algorithm with Discrete Frequencies for Ordering and Therapeutic Restoration of Life Processes

Hans (J H) Geesink and Dirk K F Meijer




Bio-Soliton Model that predicts distinct non-thermal Electromagnetic Radiation Frequency Bands, that either Stabilize or Destabilize Life Conditions

J.H. Geesink and D.K.F. Meijer


Click to access 2016_Bio-Soliton_Model_that_predicts_distinct_non-thermal_Electromagnetic_Radiation_Frequency_Bands.pdf



Phonon Guided Biology: Architecture of Life and Conscious Perception Are Mediated by Toroidal Coupling of Phonon, Photon and Electron Information Fluxes at Discrete Eigenfrequencies

Dirk K. F. Meijer and Hans J. H. Geesink

NeuroQuantology | December 2016 | Volume 14 | Issue 4 | Page 718-755


Quantum Wave Information of Life Revealed: An Algorithm for Electromagnetic Frequencies that Create Stability of Biological Order, with Implications for Brain Function and Consciousness


Hans J. H. Geesink and Dirk K. F. Meijer




The Universe as a Cyclic Organized Information System: John Wheeler’s World Revisited


Dirk K. F. Meijer




The Extended Brain: Cyclic Information Flow in a Quantum Physical Realm

Dirk K. F. Meijer



Immortality: myth or becoming reality? On the conservation of information

Dirk K.F. Meijer


Click to access 2013-eng-3-04.pdf


Information: what do you mean? On the formative element of our universe

Dirk K. F. Meijer


Click to access 2013-eng-3-01.pdf



Quantum Physics in Consciousness Studies

Dirk K. F. Meijer and Simon Raggett

Click to access 56e0121478004572db4d42edc9ec6555fa33.pdf



Quantum modeling of the mental state: the concept of a cyclic mental work space

Dirk K. F. Meijer and Jakob Korf


Click to access 2013-eng-1-1.pdf



Consciousness in the Universe is Scale Invariant and Implies an Event Horizon of the Human Brain

Dirk K.F. Meijer, Hans J H Geesink
2017 Vol 15 no 3

Mind, Consciousness and Quantum Entanglement

Mind, Consciousness, and Quantum Entanglement


From Quantum Physics in Consciousness Studies

We can conclude that consciousness is a quantum mechanical entity that can have an independent existence. It can localize in the human brain when the electron is in a particle state. This provides the necessary quantum mechanical base conducive for it to interact with and function in the brain. When the state changes to that of a wave, consciousness takes flight and starts floating. It takes away with it at least a part of the contents of the memory. It possesses the ability to acquire visual, auditory and olfactory information in spite of the fact that there are no sense organs associated with it. This information is produced by the consciousness projection of a different reality caused by the change in state of the electron, which one may interpret later as a dream or hallucination that comes from an altered perception of reality.

The major stumbling block in solving the brain-mind problem is how does the brain-mind bind together millions of dissimilar neuron activities into an experience of a perceptual whole. How does the “I” or “self” or the perceived wholeness of one’s world emerge from a system consisting of so many parts, billions of neurons. What creates the “Oneness” of thought processes? What creates individuality and I-ness or “self”? What creates feelings, free will, and creativity? The eternal consciousness.

No mechanistic system consisting of separate interacting parts could give rise to the above. What are the structures in the brain that create the property which grant us access to the quantum realm? This is a good question and once this is known by all mankind, mankind will change. It has become clear that to explain this theory, one has to consider the most highly ordered and highly unified structures possible in the universe. The structure that possesses both characters, the most highly ordered and most highly unified is the Bose-Einstein condensate.

In classical science, the most ordered structure that we can find is the crystal. Crystals are rigid, immovable structures. In Bose-Einstein condensates, the quantum properties allow both a “fluid” order and a high degree of unity. Each particle in a Bose-Einstein condensate fills all the space and all the time in whatever container that holds the condensate. Many of their characteristics are correlated. They behave holistically as one. The condensate acts as one single particle. There is no “noise” or interference between separate parts. This is why super fluids and super conductors have their special frictionless qualities and lasers become so coherent. Super conductors, super fluids, and lasers are Bose-Einstein condensates. The photons of a laser beam overlap their boundaries and behave as one single photon and the whole system can be described by a single equation. Hence, the part always includes the whole like in fractal geometry.

Super conductors, super fluids, and lasers are either very low temperature or very high energy systems. Super conductors and super fluids loose their quantum coherence long before they reach room temperature. Quantum coherence at body temperature in body cells was found by Herbert Frohlich. Prior to that, quantum physicist Fritz Popp discovered that biological tissue emits a weak glow when stimulated at the right energy levels.

Cell walls of biological tissue contain countless proteins and fat molecules which are electrical dipoles. When a cell is at rest, these dipoles are out of phase and arrange themselves in a haphazard way. But when they are stimulated they begin to oscillate or jiggle intensely and broadcast a tiny microwave signal. Frolich found that when the energy flowing through the cell reaches a certain critical level, all the cell wall molecular dipoles line up and come into phase. They oscillate in unison as though they are suddenly coordinated. This emergent quantum field is a Bose-Einstein condensate and has holistic properties common to any quantum field (Fig.50). Consciousness may work in a similar matter.


Key Concepts:

  • Non-locality
  • Information Field
  • Classical-Quantum Divide
  • Akashic Field
  • Holographic Brain
  • Holographic Universe
  • Quantum Consciousness
  • Entangled Minds
  • Morphic Resonance
  • Implicate Order
  • Decoherence-Coherence
  • Wave-Particle Duality
  • Quantum Entanglement
  • Superpositions
  • Quantum Tunneling
  • Fractal Universe
  • Quantum Biology
  • Relational QM
  • Biofield



Key People:

  • Anton Zeilinger
  • Markus Arndt
  • Koichiro Matsuno
  • David Bohm
  • Rupart Sheldrake
  • Roger Penrose
  • Ervin Laszlo
  • Deepak Chopra
  • Subhash Kak
  • Karl Pribram
  • Amit Goswami
  • David Chalmers
  • Ralph Abraham
  • Stuart Hameroff
  • Ken Wilber
  • Dean Radin
  • S Grof
  • Stuart Kaufman
  • Dirk K. F. Meijer
  • Simon Raggett
  • Hans J H Geesink
  • Max Tegmark
  • Menas C. Kafatos



Key Sources of Research:


Crucial Role of Quantum Entanglement in Bulk Properties of Solids


Click to access 0410138.pdf


The Oxford Questions on the foundations of quantum physics

G. A. D. Briggs, J. N. Butterfield, A. Zeilinger

Click to access 20130299.full.pdf


Studies of Quantum Entanglement in 100 Dimensions

Mario Krenn  Marcus Huber, Robert Fickler, Radek Lapkiewicz, Sven Ramelow, Anton Zeilinger

Click to access 00463520400b3307c2000000.pdf




Click to access oct2012_zeilinger.pdf


Organic Molecules and Decoherence Experiments in a Molecule Interferometer

M. Arndt, L. Hackermu ̈ller, K. Hornberger, and A. Zeilinger


Click to access 2004-14.pdf


The wave nature of biomolecules and fluorofullerenes


Lucia Hackermu ̈ller, Stefan Uttenthaler, Klaus Hornberger, Elisabeth

Reiger, Bj ̈orn Brezger,∗ Anton Zeilinger, and Markus Arndt


Click to access 0309016.pdf


 Quantum interference experiments with large molecules

Olaf Nairz, Markus Arndt, and Anton Zeilinger


Click to access (2003)_Quantum%20interference%20experiments%20with%20large%20molecules.pdf


Interferometry with Macromolecules: Quantum Paradigms Tested
in the Mesoscopic World

Markus Arndt, Olaf Nairz, Anton Zeilinger


Click to access 2002-02.pdf


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