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

 

 

 

https://www.lifesloka.com/en/3-granthi-in-kundalini-yoga/

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.

granthi

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.

 

 

https://yogalinda.es/en/blog/the-bandhas-and-the-granthis/

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

 

https://www.lifesloka.com/en/3-granthi-in-kundalini-yoga/

 

Untying the Knots That Bind Us

 

https://yogalinda.es/en/blog/the-bandhas-and-the-granthis/

Maha Vakyas: Great Aphorisms in Vedanta

Maha Vakyas: Great Aphorisms in Vedanta

 

I have always been fascinated by terse short aphorisms of Non dual Vedanta philosophy of Hinduism.

It took me several years to understand meaning of each based on my understanding of several scientific concepts

  • Recursion or Recursiveness
  • Fractal Geometry
  • Cybernetics and Systems Theory
  • Subject Object split to Subject Subject
  • There is no objective reality
  • Part and Whole Relationship
  • Microcosm and Macrocosm
  • Pinde and Brahmande
  • Interconnectedness of all
  • Hierarchy Theory
  • Networks Theory

 

 

Key Words

  • Non Dual Vedanta
  • Dualistic Vedanta
  • Advaita Vedanta
  • Brahman
  • Atman
  • Brahman and Maya
  • Real and Apparant
  • Jivatma and Paramatma
  • Sankhya
  • Yoga
  • Buddhism
  • Tantra

 

 

http://lb.geek.rs.ba/oldstuff/swamij-mirror/mahavakyas.htm

Mahavakyas: The Great Contemplations

Contemplation on the Mahavakyas
gradually reveals their truth
in direct experience.

Introduction

The Great Utterances: The Mahavakyas are the Great Sentences of Advaita Vedanta and Jnana Yoga, and are contained in the Upanishads. Maha is Great, and Vakyas are sentences, or utterances for contemplation. They provide perspective and insights that tie the texts together in a cohesive whole. The contemplations on the Mahavakyas also blend well with the practices of yoga meditation, prayer, and mantra, which are companion practices in Yoga. The pinnacle of the wisdom and practices of the ancient sages is contained in the terse twelve verses of theMandukya Upanishad, which outlines the philosophy and practices of the OM mantra.

See also these articles:
Song of the Self (Atma Shatkam)
Mandukya Upanishad

These make the wisdom more accessible: Seven Mahavakyas are described below. By focusing on these seven Mahavakyas, the rest of the principles of self-exploration described in Vedanta and the Upanishads are more easily accessible. Included with the descriptions below are suggestions on what to do with these seven Mahavakyas.

Validation in the inner laboratory: To truly understand the meaning of the Mahavakyas it is necessary to practice contemplation and meditation in your own inner laboratory of stillness and silence. It means doing a lot of self observation, including the four functions of mind. You may find it useful to learn both the Sanskrit and the English of the Mahavakyas. They are not practiced as blind faith beliefs, but rather are reflected on, so that their meaning is validated in direct experience.

Start by hearing the insights described: Some methods of contemplation give you a principle, a word, on which to reflect, but give no clues of the insights that will come. For example, if you contemplate on the word Truth, that is very broad, and may have many meanings. It might take a long time to even come to a core principle. Sometimes, in school or elsewhere, you have probably seen a study guide that has a list of questions that also includes the answers, in a Q&A format. With the Mahavakyas, it is somewhat like that, in that the Mahavakyas provide the answers, already written down. You still have to do the contemplations, but the journey is much more direct.

Direct experience, not mere belief: In contemplating the Mahavakyas, it is not a matter of merely accepting that the statements are true. In the oral teachings of the sages, it is said that you should never merely believe what you are told or what you read in a book. Rather, it is suggested that you should check it out for yourself in the inner laboratory of direct experience. It also seems true that, while ultimate oneness is the same for all, there is also a coloring of cultural and religious influences that determine the way in which different people will experience the early, or unfolding stages of insight.

Dig deep into the well
of only a few such Mahavakyas.

Dig deep in only a few wells: It can appear that exploring only a few sentences, like these seven, is a mere beginning point, and that one must subsequently learn hundreds or thousands of other sentences. This is definitely not the case. Although in academic circles one may do complex intellectual analysis of many scholarly commentaries, comparing and contrasting viewpoints, the seeker of direct experience digs deep into the well of only a few such contemplations.  In the monastic traditions of the swami order, a monk may contemplate exclusively on a single Mahavakya or maybe several of them. The practice bears fruit by deeply going into one, or a few, rather than memorizing many, or doing only intellectual analysis of the many.

Over and over and over: The passionately dedicated practitioner will contemplate on one or more of the Mahavakyas repeatedly, often, over a long period of time. Mind gradually comes to have a greater understanding, and then becomes still as the contemplation shifts from an observing, reflective process into a deep contemplative meditation. Reflection transforms into insight, which again transforms into the direct experience of the underlying truth or reality of the Mahavakya.

Companion practices: In the oral tradition of the Himalayan sages, the Yoga Sutras, Vedanta, and internal Tantra are companions on the journey to Self-Realization. The practices of the Yoga Sutras stabilize and clear the clouded mind. The Vedanta practices form a philosophical basis and means for discovering the underlying unity of the different aspects of our being. Internal Tantra provides the means for awakening the spiritual energy, so that the absolute, unchanging reality at our core is realized.

Mahavakyas are at the heart of Vedanta: These seven principles below are practices at the heart of the Vedanta part of the triad. Actually, all of these emerged out of the one source of teachings, and now appear to be three separate practices. The higher understanding and direct experience comes from person-to-person listening (written and oral), followed by deep reflection, contemplation, and deep contemplative meditation.

Advaita or Non-Dual Reality: It is popular to speak of Advaita as if it were a brand name of spirituality. It is not. Advaita is exactly what it says, Advaita, which means non-duality, not-two. If this little planet were to fall into the sun and burn up, there would no longer be any religionists or philosophers, but that which truly “is” still “is.” Advaita is exactly what it says it is, Advaita, not-two, which stands alone. Any suggestion that there are things such as Hindu Advaita or Buddhist Advaita or Anything-Else Advaita are games of the mind. To transcend all of the levels of false identity so as to “Be” that Reality of Advaita is the Knowledge or Jnana that is sought. It is only the most sincere and longing of aspirants who seek and Know this in direct experience. For others, it is merely an arena of philosophical and religious debate. For those who Know, Advaita stands alone.

 Stages of Yoga Vedanta Meditation and Contemplation
Swami Rama

Meditation and contemplation are two different techniques, yet they are complementary to each other. Meditation is a definite method of training oneself on all levels – body, breath, conscious mind, and unconscious mind – while contemplation builds a definite philosophy. Without the support of a solid philosophy, the method of meditation does not lead to higher dimensions of consciousness.

Contemplation makes one aware of the existence of the Reality, but Reality can be experienced only through the higher techniques of meditation. In the Vedanta system, meditation and contemplation are both used. When an aspirant tires of meditation because of lack of endurance, then he contemplates on the mahavakyas [great contemplations] and studies those scriptures that are helpful in the path of Self-realization and enlightenment. Contemplation, vichara, complements the Vedantic way of meditation, dhyana.

In Vedanta philosophy, there is a definite method used for contemplation. Ordinarily, the mind remains busy in self-dialogue, entangled in the web of its thought patterns. Because of desires, feelings, and emotions, unmanageable conflicts are created in one’s mental life. But the Vedanta way of contemplating transforms the entire personality of the aspirant, for the statements, mahavakyas, imparted by the preceptor create a dynamic change in the values of his life. These statements are compact, condensed, and abstruse srutis and cannot be understood without the help of a preceptor who is fully knowledgeable of the scriptures and these terse texts. Only a realized teacher can impart the profundity of such knowledge in a lucid language.

The thoughts, feelings, and desires which were once important to the aspirant lose their value, for he has only one goal to attain. The glory of contemplation brings a dynamic transformation to the internal states of the aspirant. This seems to be very necessary, because that which creates a barrier or becomes an obstacle for students loses its strength due to the power of contemplation, which transforms all his internal states.

First, an aspirant attentively listens to the sayings of the Upanishads from a preceptor who is Brahman-conscious all the time.

In the second step, he practices vichara (contemplation), which means that he goes to the depths of the great sayings and determines to practice them with mind, action, and speech.

One-pointed devotion, full determination, and dedication lead him to the higher step called nididhyasana. Here he acquires comprehensive knowledge of the Ultimate Truth. But he has not yet attained the final step of consciousness that leads him to the direct realization of the one self-existent Truth without second.

The highest state of contemplation is called saksatkara. In this state, perception and conceptualization are in complete agreement, and all the doubts from all levels of understanding vanish forever. At this height of knowledge, truth reveals itself to the aspirant, and perfect realization is accomplished, “I am Atman – I am Brahman.” This state of advaita is attained by the process of contemplation. Meditation plays an entirely different role and helps the aspirant make his mind one-pointed, inward, and steady.

Steadiness and stillness are practiced from the very beginning in this meditational method. The method of sitting, the method of breathing, the method of concentration, and the method of allowing a concentrated mind to flow uninterruptedly are subsequent steps that help the aspirant to expand his capacity so that he can contemplate without distraction.

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Meaning of the word brahman

Root of the word: The word brahman comes from the root brha or brhi, which means knowledge, expansion, and all-pervasiveness. It is that existence which alone exists, and in which there is the appearance of the entire universe.

Not subject to change: Brahman means the absolute reality, that which is eternal, and not subject to death, decay, or decomposition. In English, we speak of omnipresence or oneness. This is the principle of the word brahman.

Not a proper name: Brahman is not a proper name, but a Sanskrit word that denotes that oneness, the non-dual reality, the substratum underneath all of the many names and forms of the universe. Brahman is somewhat like the difference between the word ocean, and the specific ocean called Pacific Ocean. The word brahman is like ocean, not Pacific Ocean. Brahman is not a name of God. These contemplations neither promote nor oppose any particular religious concept of God.

Immanance and transcendence: One may also choose to think of brahman in theological terms, though that is not necessary. Within that perspective, the scholars speak of two principles: immanence and transcendence. Immanence is described as the divinity existing in, and extending into all parts of the created world. In that sense, the Mahavakyas can be read as suggesting there is no object that does not contain, or is not part of that creation.

It’s really indescribable, as it is beyond form: However one chooses to hold the word brahman, it is very useful to remember that brahman is often described as indescribable. For convenience sake, it is said that brahman is the nature of existence, consciousness, and bliss, though admitting that these words, too, are inadequate.

Seek direct experience: The real meaning comes only in direct experience resulting from contemplation and yoga meditation.

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1. Brahma satyam jagan mithya
Brahman is real; the world is unreal
(The absolute is real; the world is unreal or only relatively real)

Brahman is real: The way in which brahman is real is like saying that the clay in a pot is real, or the gold in a bracelet is real (metaphorically speaking). The idea is that first there was clay and gold, and when those changed form, there now appears to be a pot and a bracelet.

The world is unreal: However, when the pot is broken, or the bracelet is melted, there is once again only clay and gold. It is in that sense that the pot and the bracelet are not real; they come and go from manifestation. They are not as real as are the clay and the gold. (Remember that these are metaphors, and that obviously, we could also say that clay and gold also come and go, such as when planets are born and die from the nuclear fire of suns. Also, note that using the English words real and unreal for the Sanskrit words satyam and mithya, are not perfect, but they are the best we have to work with.)

Something is more real than the temporary: In saying that the world is unreal, it means to say that literally everything we experience in the external world is, like the pot and the bracelet, in a process of coming, being, and going (so too with all of the objects of the subtle realm). If the Mahavakya stopped there, this might appear to be a negative, or depressing comment. But it does not stop there. It makes the added comment that this absolute reality is, in a sense, more real than the temporary appearances.

Two points: Thus, the Mahavakya does two major things:

  • Reminder of the temporary: First, it serves as a reminder of the temporary nature of the worldly objects.

  • Reminder of the eternal: Second, it serves as a reminder that there is an eternal nature, that is not subject to change.

An invitation to know: In these reminders there is an invitation to come to know, in direct experience, the existence, consciousness, and bliss that is this eternal essence of our being.

Don’t stop living in the world: When practicing contemplation with this, and the other Mahavakyas, it is important to not allow the reflection that the world is unreal to stop you from doing your actions in the external world. To think that the world is unreal, and therefore we need not do anything is a grave mistake. The realization of the unreality of the world and the reality of the essence behind the world brings freedom, not bondage or lethargy.

1. Brahma satyam jagan mithya
Brahman is real; the world is unreal
(The absolute is real; the world is unreal or only relatively real)

What to do: The purpose of contemplation and yoga meditation exercises is to attain Self-realization, or enlightenment, which has to do with knowing or experiencing the deepest, eternal aspect of our own being. By working with this Mahavakya, one increasingly sees the difference between what is temporary and what is eternal.

  • Be mindful of the passing objects: One way to work with this Mahavakya, is to simply be mindful of the world around you. Gradually, gently, and lovingly observe the countless objects that are ever in a process of coming and going.

  • Remember the eternal: Allow yourself to also remember the eternal nature that is always there, enjoying the beauty of how this process ebbs and flows through that unchanging, eternal essence.

Be mindful of your own temporary and eternal: As you witness the external world in this way, allow your attention to shift to your own physical, energetic, and mental makeup. Gradually comes the insight that these more surface aspects are also temporary, and in a sense, are also unreal, or only relatively real. It increasingly allows the mind to see that there is an eternal aspect of our being, and that this is actually the source of the mind itself. The mind comes to see that it must, itself, let go, so as to experience the eternal that is within.

Practice this at daily meditation time: By observing the world in this way, it is then easier to do the same kind of silent observation and contemplation while sitting in the stillness of your meditation time. Over time, the depth of the insights increase, as an inner expansion comes.

The different Mahavakyas work together: In practice, the Mahavakyas work together. This becomes evident by exploring the others, such as the ones that follow below.

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2. Ekam evadvitiyam brahma
Brahman is one, without a second
(There is one absolute reality, without any secondary parts)

No object is truly independent: As our attention goes from object to object, image to image, we keep finding that those objects and images are only relatively real (as discussed above). Gradually, we come to see that no object exists independently from brahman, the whole. Hence, it is said there is one, without a second. Wherever we look, whatever we think or feel, try as we will, we can find no second object or part. Everything is seen as a manifestation of something else.

The objects are made of the same stuff: To speak of one, without a second, is like thinking of thousands of pots or bracelets made from clay or gold. As you look at each of the pots and bracelets, one at a time, you conclude that this pot, and this bracelet is not separate from the whole field of clay and gold. Suddenly you come to the insight that there is not a single pot that is separate from clay, and there is not a single bracelet separate from gold. In other words, you see that there is one field, without a second object, or simply stated, there is one, without a second.

Once again, this can also be viewed in a theological way, wherein immanence(versus transcendence) means the divinity existing in, and extending into all parts all parts of the created world. Thus, there is no object that does not contain, or is not part of that creation.

2. Ekam evadvitiyam brahma
Brahman is one, without a second
(There is one absolute reality, without any secondary parts)

What to do: Keep exploring the latter part of the sentence, the part of being without a second. Consciously look at the objects of the world, and the thoughts that arise in the mind. Observe whether it has independent existence and permanence. It is like asking, “Does this object or thought exist on its own? Does it stay in this form, or does it go away? Is it, therefore a second object in comparison to the whole?”

  • Try to find a second object: One practice is to repeatedly look for some second object, which has independent existence from the whole, from brahman.

  • You’ll find there is none: The aspirant will repeatedly find that there is no second object, which has independent existence, but that all objects derive from some other, like the pots from clay, or bracelets from gold. This brings the increasing awareness of underlying wholeness.

See the beauty of oneness in diversity: If this is approached as a mere philosophical opinion, if we merely believe the principle, then the deep insight that comes from exploration will be missed. Each time that some new object or thought is seen to not be a second in relation to the whole, the personal realization of the truth of the principle will become deeper and more profound. We come to see the beauty in this, to see the joy of wholeness, of the unity within the diversity. The interrelationship between the Mahavakyas will also become clearer.

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3. Prajnanam brahman
Brahman is the supreme knowledge
(Knowing the absolute reality is the supreme knowledge)

Knowledge out of which other knowledge arises: There are many types of knowledge one can attain. However, they all stem from, or are a part of, a higher knowledge. There is one exception, and that is the absolute knowledge, which is the highest. It is called absolute because it is not stemming from something else. Supreme knowledge is the ground out of which the diversity of knowledge and experience grows. The plant, though appearing separate, is made of the stuff of the ground.

Many metaphors for higher knowledge: It is just about impossible to write words describing this notion of supreme knowledge, which is part of the reason that there are so many different descriptions given by many people. Thus, we use metaphor after metaphor trying to capture and communicate the essence of the meaning. This Mahavakya is saying that as you climb the ladder of knowledge, this higher knowledge is to be found at the level of brahman, the oneness of universal consciousness.

Reflect on lower knowledge to find the higher: Reflecting on lower knowledge might give some idea. The knowledge of how to ride a bicycle is a form of knowledge, but it is based on the higher knowledge of how to move your body. The knowledge of complex mathematics is based on the higher, more foundational, prerequisite knowledge that allows the thinking process itself. When you see a person that you recognize as your friend, there was first an ability to see and conceptualize, which is a higher knowledge.

Find the foundation: Intuitively, you come to see that there is consciousness, or whatever term you would like to use, that is higher, more foundational, or prerequisite to the lower knowledge in all of its other forms. The highest rung of the ladder is called supreme knowledge, prajna, and this is said to be one and the same with brahman, the oneness.

Knowing is not mere intellectualizing: It is extremely important to note here, that this is not a process of intellectualizing. Knowledge refers to knowing or awareness, not just a linear, cognitive thinking process. The knowledge here, is more like the knowledge of recognizing an object as a tree, than the process of adding up a list of numbers. There is simply no more straightforward way of saying it, than to say it is a matter of knowing the tree.

Knowing applies to both head and heart people: Also, it is not that some people are intellectual, or head people, while others are emotional, or heart people. While these differences between people might be real, this Mahavakya is talking about a universal principle that applies to all people. The practices themselves are applicable to all people, whether inclined towards the head or the heart, though different people will quite naturally have different experiences leading to the same ultimate realizations.

3. Prajnanam brahman
Brahman is the supreme knowledge
(Knowing the absolute reality is the supreme knowledge)

What to do: In trying to reflect on the nature of supreme knowledge, the eternal substratum of all other knowledge, the mind will present many memories, images, impressions, thoughts, sensations, and emotions. All of these are some form of knowledge, that’s for sure. However, they are not the highest knowledge.

Ask yourself if a knowledge is lower or higher: Simply allow these thought patterns to arise. Then ask yourself, “Is this the higher knowledge?” Repeatedly you will find that the answer is no, that it is not the higher, but is a lower form of knowledge.

Remember there is higher knowledge: This kind of reflection leaves a quietness in which the intuition of the existence of the higher knowledge starts to come. The intuition deepens with practice. This quietness is not one of lethargy or laziness, but rather of clarity and openness. It brings a smile to the face and to the heart, as the field of knowing gradually expands towards the wisdom of the Mahavakya.

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4. Tat tvam asi
That is what you are
(That absolute reality is the essence of what you really are)

That is what YOU are: This Mahavakya is stated as if one person is speaking to the other, saying, “That is what you are!” when referring to brahman. The person speaking is the teacher, and person being spoken to is the student.

It is YOU at the deepest level: Imagine that the teacher has explained to you all of the above Mahavakyas, that you had reflected on these, and that you started to have some sense of the meaning of the oneness called brahman. Imagine that the teacher then pointed a finger at you and explained, “That brahman, that oneness, is who you really are, at the deepest level of your being!” It is like telling a wave in the ocean that it IS the ocean.

You are the person underneath the personality: Often, we hold on to our personal identities, such as being from this or that family, organization, or country. We take on the identity of our roles in our jobs or in our families, such as father or mother, sister or brother, son or daughter. Or, we come to believe that who we are, is our personality traits that have developed through living. We forget our true nature, that is underneath all of these only relative identities.

We continue our duties, holding identities loosely: The realization of this Mahavakya, Tat tvam asi, leads us to see that the relative identities are not who we really are. It does not mean that we drop our duties in the world, or stop acting in service of other people because of this realization. Rather, we become ever more free to hold those identities loosely, while increasingly being able to act in the loving service of others, independent of attachment to our false identities.

4. Tat tvam asi
That is what you are
(That absolute reality is the essence of what you really are)

What to do: As if talking to yourself, direct your attention inward, possibly towards the heart center. Say to yourself, “That is who you are!”

Point a finger at yourself: You might want to even point your index finger at your own chest, the place from where you experience, “I am.” As you hold in awareness the essence of the truth that this brahman, this oneness, is who you reallyare, also observe how you can gently let go of the false identities, seeing that they are only temporary and relativelyme.

Say to yourself, “That is who you are”:When reflecting on the other Mahavakyas, such as brahman is the supreme knowledge, then shift the observation from that truth, directing attention to your own inner being and say, “Tat tvam asi; That you are!”

Remember the inner feeling: Notice the inner feeling that comes from the statement and the realization of your spiritual nature, rather than your more surface level of mental or physical identity.

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5. Ayam atma brahma
Atman and Brahman are the same
(The individual Self is one and the same with the absolute)

The wave and the ocean are one: Is the wave separate from the ocean? Not really, but sometimes we lose sight of that. Imagine that you are standing by the ocean, watching the vastness of the ocean. Imagine that a really big wave starts to come ashore, and that your attention comes to this one wave. You intently notice it, becoming absorbed in the crashing of the surf, and the feel of the salt spray. In that moment, you are only aware of the immensity of this one wave. The ocean itself is forgotten during that time. Then, an instant later, you recall with an inner “Aha!”, that the wave and the ocean are one and the same.

  • Atman refers to that pure, perfect, eternal spark of consciousness that is the deepest, central core of our being.

  • Brahman refers to the oneness of the manifest and unmanifest universe.

It is like saying that atman is a wave, and brahman is the ocean. The insight of Ayam atma brahma is that the wave and the ocean are one and the same.

Atman seems to be here, and brahman there: Notice how the statement Ayam atma brahma (Atman and Brahman are the same) is framed as if you are a separate observer of both Atman and Brahman. It is like standing at the beach, looking out at both the wave and the ocean, and declaring that the wave an the ocean are one. You are observing from a witnessing stance, outside of both of them . Notice how this perspective contrasts with Aham brahmasmi (I am Brahman), which declares that “I am!”, an inner experience, rather than from an observing standpoint (like being on the beach).

Different perspectives for the underlying reality: In this way, each of the Mahavakyas gives a different perspective of the same underlying Reality. Gradually, they are seen as mirror reflections of the same Absolute Reality. That integrated flash of insight touches on the true meaning of the word brahman. It is like gaining different points of view from different viewing points. Together, they converge in a complete understanding.

5. Ayam atma brahma
Atman and Brahman are the same
(The individual Self is one and the same with the absolute)

What to do: Sit quietly and reflect on the inner core of your being, such as by placing your attention in the space between the breasts, the heart center.

Be aware of your center: Don’t visualize anything, but allow your awareness to touch the feeling aspect of the center of your being. Or, if you like to visualize internally, imagine a tiny spark of light that represents the eternal essence your own self, the atman. Hold this attention for a few seconds or minutes.

Shift to awareness of the universe: Then, shift your attention in such a way that you are imagining the breadth of the entire manifest and unmanifest universe, the gross, subtle, and causal realms. Imagine the oneness that permeates all, and is all. Do this in a way that you are aware of the essence in which all exists, like being aware of the gold or the clay described above.

Then be aware of both as separate: Then, allow your attention to hold both the awareness of the spark that is atmanand the universal essence that is brahman. Be aware of atmanalso being within that oneness of brahman. Allow this to bring insight and peace. You might want to internally think the words of the Mahavakya, “Ayam atma brahma; atman and brahman are the same.”

Be aware of both as one: It is a beautiful practice to do the same thing in relation to other people. Think of the people who are closest to you, including family, friends, and coworkers. Allow yourself to notice the surface levels of their actions and speech, their physical features, and their personalities. Be aware of the subtle aspects of their makeup, and of the spark of the eternal that is the center of their consciousness. Be aware of how that spark, atman, is one with the oneness, brahman.

Different insights from different Mahavakyas: Notice the different insights and feelings between the Mahavakyas. The insight from Tat tvam asi (That is who you are) is experienced differently from Ayam atma brahma (This individual Self is one with the absolute). The two simply feel different internally, yet they work together, describing the same fundamental truth about about who we are. By experiencing the separate vantage points, the whole is more completely experienced.

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6. Aham brahmasmi
I am Brahman
(Who I really am, is that absolute reality.)

If a gold bracelet could speak: Imagine two possibilities of what a gold bracelet might say, if it could speak. It might say one of these two things:

  1. “I am a bracelet!”
  2. “I am gold!”

Bracelet is temporary: Which is more true, more everlasting? We might be tempted to say that #1 is more accurate, in that bracelet seems more encompassing, being both bracelet and gold at the same time. However, the bracelet aspect is not eternal. It is temporary. It is only a matter of the particular shape in which the gold was molded. Is bracelet what it really is?

Gold is everlasting: What is always true, is #2, that “I am gold,” everlasting, ever pure, and not subject to death, decay, and decomposition. (One might argue that gold is not everlasting either, but in the metaphor, gold is being only used as an example.)

Bracelet is gold; I am gold: Note that this metaphor may sound similar to the ones above, regarding the impermanence of a bracelet and the permanence of the gold (metaphorically speaking). This is not the case. The realization that, “I am gold!” or “I am brahman!” is an internal experience compared to the statement, “The bracelet is gold!” (which sounds like the bracelet over there). The two insights are separate, though they also come to be the same.

Similarly, it is very different to realize, in direct experience, “I am brahman!” than one of the statements such as, “Brahman alone is real!”:

  • Out there: “Brahman alone is real!” seems to be about the world out there. It is a valid perspective.

  • In here: “I am brahman!” is an inner declaration of who I am, in here. This is also a valid perspecive.

Truth comes in the stillness of intuitive flash: The truth of a Mahavakyacomes through intuitive flash, that is progressively deeper as one practices. It is not merely an intellectual process, as it might appear to be by explaining the gold metaphor. The metaphors are used as a means of explaining the principle, but this is not the end of the process. In a sense, such explanations are only the beginning of the process. The key is in the still, silent reflection in the inner workshop of contemplation and yoga meditation.

After thinking, let go into contemplative insight:The initial insights come somewhat like the creative process when you are trying to solve some problem in daily life. You think and think, and then finally let go into silence. Then, suddenly, the creative idea just pops out, giving you the solution to your problem. The contemplation on the Mahavakyas is somewhat like that at first. Later, it goes into deeper meditation.

Insight comes within your own context: One may experience himself or herself as being like the gold or the clay, or like a wave in an ocean of bliss, that realizes the wave is also the ocean. With all these metaphors used only as tools of explanation, the insight of each person will come in the context of their own culture and religion, and will not seem foreign or unnatural. One’s religious values are not violated, but rather, are affirmed.

6. Aham brahmasmi
I am Brahman
(Who I really am, is that absolute reality.)

What to do: Reflect on the oneness, or brahman, and the meaning, as suggested in the practices above. Allow your attention to focus on the insights from those Mahavakyas, such as Brahman is one, without a second.

Literally ask questions of yourself: Ask yourself, internally, “Who am I? Am I this body, or do I have a body? Am I this breath, or is this breath just flowing? Am I this mind, or is this mind a manifestation of some deeper truth? Who am I, really? Who am I?”

Make your own declarations: Inside the chamber of your own being, declare to yourself, “I am brahman. I am not only a wave, I am made of ocean. I am ocean!” Allow the truth of the statements to expand. Be sure to practice such affirmations only if you have reflected on them, and find truth in them. This is not about selling yourself, but on affirming what you know.

In daily life, when sitting, or resting: As you do these contemplations, you might be right in the middle of your daily life. Or, you might be sitting straight in a formal yoga meditation posture. Or, you might be resting comfortably in a chair, on a sofa, or lying down in a relaxed position. There is a great diversity of settings in which you can do this type of contemplation.

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7. Sarvam khalvidam brahma
All of this is Brahman
(All of this, including me, is that absolute reality)

The various insights are revealed: Gradually, one comes to understand and increasingly experience the deeper aspects of the other Mahavakyas (the six described above):

  • Brahman is real; the world is unreal.
  • Brahman is one, without a second.
  • Brahman is the supreme knowledge.
  • That is what you are.
  • Atman and brahman are the same.
  • I am brahman.

They sing a song together: As one comes to experience the truth of the individual Mahavakyas, it seems they come together in a song, that cries out in joy, “All of this is brahman!” As was said in the beginning, it is a process that comes from person-to-person listening (written and oral), followed by deep reflection, contemplation, and meditation.


(Perspective on “Sarvam khalvidam brahma”)

Realization comes in stages:

  • First, there is cognitive understanding of the meaning.
  • Second, intuition rolls down, revealing deeper meanings.
  • Finally, it is as if the one doing the practice travels upwards to merge in the direct experience, even though there was never any division in the first place.

7. Sarvam khalvidam brahma
All of this is Brahman
(All of this, including me, is that absolute reality)

What to do: Allow your awareness to try to encompass, at one time, the entire manifest and unmanifest universe, the objects and people in the world around you, as well as your own body and mind. Hold these together, as one whole, and reflect on the words, “All of this is brahman! All of this is one!” This builds on the other practices, and expands in its experience.

Mind is set aside in an explosion of awareness: Eventually, in the depth of meditation and contemplation, the entire mind is set aside in an explosion of awareness, in which the truth of the Mahavakyas comes forward, and is seen to have been there all along, ever still, waiting to be discovered in direct experience.

Four traditional Mahavakyas

Four of the Mahavakyas above are most traditional to Vedanta. Some 1200 years ago Adi Shankaracharya assigned one Mahavakya to one of four monastic teaching centers or mutts in India.

Mahavakya Source Mutt/Center

Prajnanam brahman
Brahman is supreme knowledge
Aitareya Upanishad
3.3, of Rig Veda
Puri/Govardhana
East

Tat tvam asi
That is what you are
Chandogya Upanishad
6.8.7, of Sama Veda,
Kaivalya Upanishad
Dwaraka/Sarada/Gujrat
West

Ayam atma brahma
Atman and brahman
are the same
Mandukya Upanishad
1.2, of Atharva Veda
Jyoti/Badrinath
North

Aham brahmasmi
I am brahman
Brihadaranyaka Upanishad
1.4.10, of Yajur Veda,
Mahanarayana Upanishad
Sringeri/Mysore
South

 

 

Please see my related posts

The Pillar of Celestial Fire

The Great Chain of Being

Indra’s Net: On Interconnectedness

On Holons and Holarchy

Recursion, Incursion, and Hyper-incursion

Third and Higher Order Cybernetics

 

 

 

Key sources of Research:

 

Arsha Vidya Gurukulam

arshavidya.org

Talk on The Essence of Vedanta

 

Talk on Vedanta by Swami Sarvpriyananda

Recursion, Incursion, and Hyper-incursion

Recursion, Incursion, and Hyper-incursion

 

How do Past and Future inform the present?

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

Key Terms

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

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

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

X (t+ 1) =f(X(t), X(t-1) …p..)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Please see my related posts

On Anticipation: Going Beyond Forecasts and Scenarios

Autocatalysis, Autopoiesis and Relational Biology

Key sources of Research

 

Computing Anticipatory Systems with Incursion and Hyperincursion

Daniel M. DUBOIS

 

Click to access cd554835f0ae367c3d3e3fa40f3e5e5f5f11.pdf

 

 

 

Anticipation in Social Systems:

the Incursion and Communication of Meaning

Loet Leydesdorff 

Daniel M. Dubois

Click to access casys03.pdf

 

 

 

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

Daniel M. Dubois

 

Click to access dubois.pdf

 

 

 

Non-wellfounded Set Theory

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

Hypersets

  • Jon Barwise &
  • Larry Moss

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

Non-well-founded set theory

https://en.wikipedia.org/wiki/Non-well-founded_set_theory

Knot Theory and Recursion: Louis H. Kauffman

Knot Theory and Recursion: Louis H. Kauffman

 

Some knots are tied forever.

 

Key Terms

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

 

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

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

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

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

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

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

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

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

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

 

LH Kauffman with Trefoil Knot in the back.

LH Kauffman

 

From Reflexivity

A Knot

Screen Shot 2020-01-06 at 12.49.45 PM

 

Trefoil Knot

Tricoloring

 

Screen Shot 2020-01-07 at 6.32.04 AM

 

 

 

From Reflexivity

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

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

 

From Laws of Form and the Logic of Non-Duality

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

From Laws of Form and the Logic of Non-Duality

True Love.  It is a knotty problem.

Screen Shot 2020-01-07 at 9.51.03 AM

 

Wikipedia on Knot Theory

Tabela_de_nós_matemáticos_01,_crop

 

 

Please see my related posts:

Reflexivity, Recursion, and Self Reference

Jay W. Forrester and System Dynamics

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

Second Order Cybernetics of Heinz Von Foerster

Cybernetics Group: A Brief History of American Cybernetics

Cybernetics, Autopoiesis, and Social Systems Theory

Cyber-Semiotics: Why Information is not enough

Ratio Club: A Brief History of British Cyberneticians

Autocatalysis, Autopoiesis and Relational Biology

Feedback Thought in Economics and Finance

Increasing Returns and Path Dependence in Economics

Boundaries and Distinctions

Boundaries and Relational Sociology

Boundaries and Networks

Socio-Cybernetics and Constructivist Approaches

Society as Communication: Social Systems Theory of Niklas Luhmann

Semiotics, Bio-Semiotics and Cyber Semiotics

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

Networks and Hierarchies

 

Key Sources of Research:

 

Home Page of Louis H. Kauffman

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

Recursive Distinctioning

By Joel Isaacson and Louis H. Kauffman

 

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

 

 

Knot Logic – Logical Connection and Topological Connection

by Louis H. Kauffman

Click to access 1508.06028.pdf

 

 

KNOTS

by Louis H. Kauffman

 

Click to access KNOTS.pdf

 

 

 

BioLogic

Louis H. Kaufman, UIC

Click to access BioL.pdf

New Invariants in the Theory of Knots

Louis H. Kaufman, UIC

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

 

 

 

Eigenform – An Introduction

by Louis H. Kauffman

Click to access 2007_813_Kauffman.pdf

 

 

Knot Logic and Topological Quantum Computing with Majorana Fermions

Louis H. Kauffman

 

Click to access arXiv%3A1301.6214.pdf

 

 

Reflexivity

by Louis H. Kauffman

Click to access videoLKss-slides.pdf

 

 

 

Eigenforms, Discrete Processes and Quantum Processes

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

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

 

 

 

Eigenforms — Objects as Tokens for Eigenbehaviors

by Louis H. Kauffman

Click to access 1817.pdf

 

 

 

Reflexivity and Eigenform The Shape of Process

Louis H. Kauffman A University of

 

Click to access ReflexPublished.pdf

 

 

 

FORMAL SYSTEMS

EigenForm

Louis H. Kauffman

 

Click to access Eigen.pdf

 

 

 

EigenForm

Louis H. Kauffman UIC, Chicago

 

Click to access Eigenform.pdf

 

 

Form Dynamics

Click to access FormDynamics.pdf

 

 

Arithmetics in the Form

Click to access ArithForm.pdf

 

 

 

Self Reference and Recursive Forms

Click to access SelfRefRecurForm.pdf

Click to access Relativity.pdf

 

 

 

Laws of Form and the Logic of Non-Duality

Louis H. Kauffman, UIC

 

Click to access KauffSAND.pdf

 

 

 

Laws of Form – An Exploration in Mathematics and Foundations

by Louis H. Kauffman UIC

 

Click to access Laws.pdf

 

 

 

The Mathematics of Charles Sanders Peirce

Louis H. Kauffman1

 

Click to access Peirce.pdf

 

 

 

A Recursive Approach to the Kauffman Bracket

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

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

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

 

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

 

https://www.researchgate.net/publication/266226046_God_in_the_Fractals_Recursiveness_as_a_Key_to_Religious_Behavior

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

Integral Philosophy of the Rg Veda: Four Dimensional Man

Integral Philosophy of the Rg Veda: Four Dimensional Man

 

Meditations Through the Rg veda:  Four Dimensional man was published in 1976.  In 1999, Antonio de Nicholas published a review of his work.  See below.

 

From Forward to the book.

rgvedargveda2

From Infinity Foundations website

Meditations Through The Rg Veda: A Retrospective
(Philosophy East and West. Vol.49. Number 2. April 1999)
by Antonio T. de Nicolas, PhD

Paradigm, Theory, Ritual

It is now twenty five years since Meditations Through the Rg Veda: Four-Dimensional Man was first published in the United States. My earlier work on the Rg Veda was published in 1971 in Bangalore, India. Though the structures of the book were born during my twelve years of consecutive living in India, these structures did not become a paradigm until later. The structures I refer to are the word things and the order of their arrangement I was embodying as I lived there, a context at a time. It was the way the sun rose or the dawn arrived, the slow-motion for the sun to set and the sudden night; the lines of movement, of people, animals, wind or rain; the sudden appearance of forms, by the river, a well, in the sky; the dissolution of familiar and unfamiliar names, in the rhythm of language, Gujarati, Sanskrit, even English or Spanish names; but above all, the new habit of listening with my eyes to the movements in the sky, the forest, the streets, the homes; for the world, and my body, were a musical string plucked at every turn, in every silence , in every sight, sound, smell, touch and movement. Hidden geometries became human flesh, unnoticed. It was a silent world longing to become language, but can a multiplicity of embodied languages be expressed as one? After a while it was life in the twilight; which was the shadow, which the real object? One has to gain distance, and none farthest than an American Ph.D. Nonetheless, dispite the distance, and dispite the academic language, a new paradigm was born, in the Bronx, of all places. The structures I embodied gave way to an experienced, embodied geometry, sustaining all the structures, texts and statements I silently learned in India. Of course, when I set down this paradigm in writing, be it the Rg Veda or the Gita, the actual written text was already a theory, no longer a paradigm, though perhaps the most accurate translation of the paradigm. Those who disagreed kept silent and those who agreed, the majority, repeated my theory as participants in a ritual. In short, the acts by which the paradigm was born in me, or is born in any one giving birth to an original text like the Rg Veda, is not the written text. The act of creation is silent. The text of the Rg Veda, however, as written down is only a theory of itself, an invitation to a ritual. It is not even one text, or one language, but several and can only be expressed in plural linguistic wholes. Paradigms may be tested; they leave invariant epistemologies, but they can never be taught; they are sheer creation. Theories, as short hand of possible paradigms, on the other hand, we learn in the classroom. They are the easy ones to repeat. Those who follow the path of creation, of embodied-vision, follow the path of the gods. The others follow the path of the fathers, the path of pro-creation, the path of ritual, as the Rg Veda indicates. One leads to immortality, the other to rebirth. On which of these two paths stands the author of the text, rsi, commentator, priest or scholar? Besides, the Rg Veda is the sruti (revelation) tradition of India. As such, it is earlier than any other claim of revelation from any of the canonical texts, from the East, Middle East or West. The paradigm of the interpreter, if it coincides with that of the Rg Veda, should also give birth to those gods that gave humans sensation, inspiration and immortality, not just life to a priesthood that changes ritual as the mood strikes, bent on the act of pro-creation for, after all, the immortality of the ritual is more important than the immortality of the soul. Nor is it legitimate while interpreting to disband these earlier gods in the name of a later one, nor the heart-ethics of these original people for the head-ethics of those who came later, and if done it should be made evident. And this is how the “written” Rg Veda began. The priests wrote it down thousands of years later (depending on which initial date you choose). Ideographic language gave way to alphabetic writing, criteria of sound to those of sight, the path of the gods to that of the fathers, the structures of immortality to those of reincarnation, paradigm to theory repeated in ritual. Which Rg Vedic text are we talking about? What is recoverable from such a text? In the end, all we are left with are the technologies by which we recreate either text. Which path do they open for us? Now, once this is said, however, the modern interpreter cannot be blamed for not being a rsi. Let the reader be free to decide between the two paths, and let the interpreter be aware of both.

The Myth of Invariance

The first scholar to find my 1971 edition of the Rg Vedic world “captivating” was Ernest McClain. His interest was my claim that every statement in the oral/aural Rg Veda was tied to a language grounded on musical criteria. Music was once, at the origin of human language, the epistemology of oral cultures. This was all Ernest McClain needed to make a life and a project of his training as a musicologist. We started collaborating, getting together for brunch at the Waldorf Astoria in New York, in 1974. His first book appeared in 1976, The Myth of Invariance: The Origin of the Gods, Mathematics and Music from the Rg Veda to Plato (Nicolas-Hays, N.Y.) In 1978 he brought out with the same publisher, The Pythagorean Plato: Prelude to the Song Itself, and in 1981 Meditations Through the Quran: Tonal Images in an Oral Culture. When we last spoke he had already found confirmation of his work and mine, not only in Greece, but also in Chinese and Biblical texts. In his words: The Rg Veda is the original epistemology upon which humans built knowledge and also immortality. And thus by the hand of music the Rg Veda re-entered human consciousness.

The Artful Universe

At first glance this book is a most welcome addition to Vedic studies. It covers a territory in Indian Studies few dare to tread, and in doing so the author brings to the discussion almost everyone, ancient or modern, who has written anything on the Vedas. The writing style is beautiful and the translations from the Sanskrit have a modern ring that makes the original less intimidating. There is a definitive purpose by the author in the writing and interpreting of these texts! On the one hand, and this is the thesis of the book, the Vedas are the product of the imagination, and on the other this imagination expresses itself as ritual, as the religious imagination of the Vedic religion. Professor William K. Mahoney takes six chapters to develop this thesis. The first two are a preparation to understanding the religious imagination, the third and fourth chapters cover the Rg Veda and the last two the Upanishads. The book, however, does not end here. The Notes that follow these six chapters are yet another book within the book which allow the reader to follow the inner footsteps of Prof. Mahoney in the composition of his book. It is easy here to admire his delicate scholarship and his flare for the happy phrase in translating or interpreting the work of others. While my intention in writing this essay is a celebration of the human effort carried out in getting to the origins of our species, I wish also to sharpen the debate in the hope that “embodied structures” take over where simple or simplistic statements become the origin of the dialogue.

The modern scholar dealing with the Vedic period has several options: Translations of individual hymns under arbitrary categories, as it has been done and can be found in the Bibliography of The Artful Universe; or corrections, very important, as to the date of the Vedas, as In Search of the Cradle of Civilization, as G. Feuerstein, S. Kak and D. Frawley have successfully done, or he/she may try to uncover for us the paradigm and mental faculty through which the Vedic seers “composed” the original hymns. This is what Prof. Mahoney promises us:

“To Vedic visionary poets, the world is – or could be – an integrated whole, a unified structure and process of being in which there are no unbridgeable distances separating the divine, natural, and human worlds” (p.2).

And this world is held together by ” mental abilities or processes associated with what I will call the imagination” (p.5), ” the divine imagination… and the human imagination – especially the poetic, sacerdotal, and contemplative imagination… (and) whether divine or human, it is precisely the imagination that fashions and recognizes the universe as meaningful, abiding, and valuable, that is to say, real” (p. 7).

Here are my first questions. When we take, say the Rg Veda, for examination or commentary, which “text” are we recreating? The oral text the rsis chanted, the written text the priests codified in ten mandalas and became a ritual, or a new mongrel text that repeats a lot of names and quotes but can be used, at most, as the weekend comfort of New Age Evangelicals? And if so, where are the priests in the Upanishads when the Ksatriya instruct them? But above all, if the imagination is the faculty used by the seers in the composition (creation) of the oral, original hymns, which is the faculty that the priests use when they write down the text and when they repeat the same written text in ritual after ritual? But above all, if the imagination is a faculty, how does it work, which are its movements besides naming it, which are its structures, and are these structures the same or different from our own, and if the same why, and if different, how can we understand the Vedic imagination? How many priests does the author know with imagination? Isn’t their job to repeat a ritual imagined by others, deadening thus not only their senses but their faculties too? An imaginative priest is known as a heretic!

These remarks are not to be answered by Prof. Mahoney. He has written his beautiful text. But is this text the Rg Veda, or is it the case that any attempt at writing down one Rg Veda will give us of necessity several texts? It is obvious that this study fluctuates between the “creation” text of the original rsis and the “pro-creation” text of the later, codifying priests. Where once we had sheer power of creation, through an active imagination, giving birth to gods, powers and continuities, very soon we descend to the repetitive ritual of procreation through human semen, and the danger is that this becomes the ritual we celebrate today:

O holy drop!
You are the master of ecstasies!
You are the immortal god’s favorite drink!
Show us the way to success,
as a friend to a friend. (p. 85)

But it is the Rg Veda itself which admonishes us a few hymns later than the one quoted above by Prof. Mahoney (R.V.9.112) to be weary of one single text, be it rituals or anything else:

l. Our thoughts wander in all directions
And various are the ways of men:
The cartwright looks for accidents,
The physician for the sick,
And the brahman for a rich patron.
For the sake of Indra,
Flow, Indra, flow.

4. The horse draws a swift carriage,
The generous host an easy laugh and play.
The penis seeks a hairy slot
And the frog (brahman) hankers for a flood.
For the sake of Indra,
Flow, Indra, flow.

(My translation in Meditations through the Rg Veda).

How does this effort in all of us at producing “one single” text fail when dealing with Indian classical texts, particularly the Rg Veda?

As regards the Notes of this book I have only admiration. It is almost heroic the effort of Prof. Mahoney to footnote his conclusions. It is as if footnoting he were building a path for others to follow. The way he does it, however, may raise serious questions. Is not this the “path of the fathers” leading to the re-incarnation of all ritual, including the ritual of scholarship? Take, for example, part of the footnote he dedicates to my book Meditations through the Rg Veda:

” …The “four dimensions” of the Vedic intentional life outlined by de Nicolas are similar in some ways to the poetic and ritual aspects of the Vedic World I discuss in Chapters Three and Four, below. We overlap most in regards to what de Nicolas calls the “language of embodied vision.” My approach is different from his, however, in that, whereas he concentrates on the linguistic nature of visionary knowledge, I focus my intention on the visionary background of linguistic expression.” (Emphasis mine) (p.238). Does Prof. Mahoney understand that no matter how he “overlaps” me, (ritualizes my writing?) my work antedates his by twenty five years, and supplies him not only with the pertinent Rg Vedic hymns he quotes but also with the secondary sources he needs to gather the community of scholars that will testify to his thesis? Furthermore, was not my book the one to establish not only the “imagination” as a rational intelligence of oral cultures, but also the “moves” it must make to be an imagination in movement, able to keep a diverse society in continuity within the discontinuity of sensation? If this is my thesis where is his? In the ritual of repetition of the original text? I would most probably let this point go were it not for the fact that this “tracing” over other people’s work seems to count these days as scholarship. It seems to be a mind-set of the times. But is this the “text” that gave birth to the Rg Veda? Scholarship is not a ritual, and more so, a thesis is not a ritual. Where is the imagination to get out of other people’s rituals, to rise to ” the path of the gods”? Let’s go on with our conversation. Prof. Mahoney will rejoin us later in the dialogue.

The New Theogony And The Heresy Of Oedipus

” Let us with tuneful skill
Proclaim the origin of the gods,
So that in future generations these origins
May be seen, when these songs are sung.” (R.V. l0.72.1)

Dr. Colavito, in The New Theogony, perhaps the best book on myth written in English, universalizes the “languages” of the Rg Veda, Asat, Sat, Yajna and Rta, to cover the study of all myth.

“What we call “myth”,” she writes “is a fourfold cluster of actions and mental properties that individually and together account for the necessary and sufficient conditions of the mythopoetic worldview, of the nature and workings of the cosmos, and of the individuals and groups of individuals within this cosmos.” For the sake of clarity she summarizes these languages thus: ” These four fundamental acts defining myth are: maia, mythos, mimesis and logos. Each act is a single focus or mental habit; together the four account for the totality of human and divine acts, or mental habits, that have guided the human species to the present shores. Though strictly speaking myth is merely one of the (four) acts in myth making, even this act is incomprehensible unless the other three mental operations are included in the narratives of myth…” She then goes on outline the four “languages”:

“Maia (Gr. midwife) is the term used to signify the bringing forth of action from inaction, cosmos out of chaos, the initial spark that kindles the mind to transform from nothig to something. It is the midwife between the divine realm of immortality and potentiality and the human realm of temporality and human existence. The aspect of maia in the human sphere is represented by the human faculty of imagining. It is the expression of the creative experience; it cannot be described,, it has no form, its proper abode is the midregion between the human and the immortal. Once an individual begins to interpret or reflect upon the experience, maia disappears and the experience receives an existence of its own, outside the real of potentiality, and it is given a form, name, boundary. In short, the reflective act heralds in the aspect of mythos. And with mythos the world moves from chaos to cosmos.

Mythos (from the Gr. delivered by word of mouth) primarily describes the initial reflection of the creative experience. It is the oral transmission of the experience… The first “scream of individuation,” to quote Nietzsche… Mythos, also, represents the original fall from grace, the first act that breaks from the unity of the beginning, from the glory of immortality; for the telling of the experience now has another element, an experiencer, a self, through whom the experience flowed. Thus… the telling of the experience is not the experience… and only those who have had the same experience may truly understand the full import of the teller’s tale…so that communities of experiencers can share common revelations.

Mimesis (Gr. to make a copy) is the aspect that describes the mythopoetic action of re-membering or re-creating… In this manner the story is told with an intent, a moral… What becomes important now is the story not so much as it relates to the original creative experience of individuals, but as it relates to the desire to make a point… The mimetic phase is … the first frozen form: the pictographic mode… geared toward establishing the social mores of the collective group.

Finally, logos, (Gr. the word by which the inward thought is expressed), taking as its origins these mores, completely eradicates the level of personal experience and uses the rules derived from the mimetic to create theories about human action. These mores are founded on human experience, but only on hypothetically universal experience – in other words, experience filtered through the sieve of a collective interpretation. As such, then , no origin in logos has the certainty of an origin in maia… Logos ceases to be a pictographic representation; it transforms into a symbolic or alphabetic system that has only its own correlatives within its own framework, with no derivative capacity from the experiential realm of the individual… Logos has always been the shadow of maia in the mythopoetic world.

This fourfold division is neither a convenient devise for classification, nor an arbitrary tool for interpretation; it is the fabric itself of myth… an abstraction, that, though distinguishable, is inseparable from myth. From a biological perspective this fourfold division is the neurophysiological equipment of the species, its mental habits accumulated through the repetition of the past: imagining, fantasizing, narrating, following the discursive path of logic… )(Thus) while maia stands for an original experience… mythos, mimesis and logos stand for different ways (languages) of making this experience public, either through narrative (mythos), visual forms (mimesis), or… theory…alphabetic substitutions, or conceptual analyses (logos)… Finally, this fourfold system of acts corresponds to the scientific operations functioning within the oral/aural worldview, which has as its verification the ancient science of acoustics.” (pp.6-8)

Using the model of the one dismembering itself or the model of the zero as an addition of objects, Dr. Colavito makes evident the model through which dialogue and understand of myth is possible, and this not in just a few cases, Classical India, Rg Veda, Upanishads, but also the Greek gods and goddesses ending with the education of Pythagoras as imparted on his students, and the acoustic verification in Plato. A breathless trip that ends in the frustrating realization that while simple acts may lead to overwhelming “oceanic” experiences, the unity of maia, once broken, can never be recovered in one single language, but we must learn to move with of plurality of at least four irreconcilable and irreducible languages. Or is this a frustration or a temptation, the temptation to be the shadow of a god, if not god him/her self?

These are very strong claims. If true they may lead to the mobility of the Rta to perform the good act (sukrta), the original act of creation. Can they also lead to reconstructing the original Rg Veda? Where do we find the verification? Dr. Colavito took it upon herself to get to the bottom of the issue. Equipped with two Ph.Ds – one in Comparative Literature and the other in Psychology, her next book, The Heresy of Oedipus and the Mind/Mind Split, introduces us to her “Biocultural Paradigm.” She starts with the Nature/nurture controversy raging in the biological sciences to conclude that neither one nor the other works in isolation, but that nurture opens Nature, and Nature is not activated without nurture. In other words, the neural passages of the brains are open or forever shut if there is not a mutual fecundation. This interaction is limited, and almost chronologically developed in every child from conception to the age of l2; after that, what nurture has not activated in the right hemisphere of the neocortex is forever destroyed, though the left hemisphere, the seat of logic and discourse and the place of the “interpreter module,” keep developing abstract substitutions based on information received by these other brains or by its own conceptual loops, forever. What in her first book was called maia, in the second is the reptilian brain; mythos becomes the limbic brain; mimesis she divides into two: the visual, right hemisphere and the conceptual left hemisphere; and logos is the interpreter module located in the left hemisphere of the neocortex. In this she follows MacLean and Gazzaniga and the latest discoveries in neurobiology. But for the purpose of our discussion, in what way is this relevant to the Vedas and Prof. Mahoney’s or McClain’s books?

Revelation, individual experience, is an affair of the right side of the brains. The left hemisphere can only interpret, translate what the right hemisphere presents as sensation. Thus, while we have five different brains, (not one as Descartes thought and we presume,) only the three of the right hemisphere deal with original experience. And this in different ways. While maia ( the Asat) is the origin, maia is also wired with a geometry capable of letting forms appear, while mythos, the place of gods and heroes, is already a world of forms. However, and this is the point of our discussion, when these two original and originating brains are translated by the right hemisphere of the neocortex they are translated as “visual images;” they are seen as images even if originally they were waves and movement and tactility. In other words, by the time the ritual priests take on the “visual images” to the sacrifice and the ritual, these visual images, originally, were neither images nor visual. Thus by constituting these images as the original text, the followers are removed from the origin, from the source of sensation and are led into a repetition of acts that may crystallize either in a crisis of faith or in a crisis of dogma. The believers may either end up losing faith,( also sensation) or becoming dogmatic preachers in a game of endless logomachy. And the same with any other “text” bound by single language-games, like Western Theology. Thus, according to the Rg Veda it is precisely because of this tendency that the culture calls for cyclical returns to the Asat: to lose all forms, verbal, audial, or visual and break the dragon Vrta open, again. And that excerise, in the Rg Veda, is the true meaning of sacrifice (yajna). The sacrifice is necessary because these languages are invariant biological epistemologies, irreducible to one another.

Dr. Colavito follows up her neurobiocultural bases with studies on myth, Rg Vedic and principally the Oedipus cycle and the whole history of the House of Cadmus, after the mind/mind split took place in the species with the repetition of the technologies developed to introduce alphabetic writing in our mental habits. The paradigm is so explosive that Time magazine (Feb. 1997) could not avoid making a full use of it to describe the early development of the different brains in children, the contrary pole of Dr. Colavito’s thesis as she verified it through earlier cultures, in the infancy of the species. Of special interest in our discussion is her Appendix 2.3 making visible the hidden geometries of the Asat and the two ways of reading those texts: as from the “path of the fathers” or as from the “path of the gods.” How can we overcome the temptation of one single language, and how do we learn to be open to a plurality of four?

The Human Potential

“We can’t put it together; it is together.”

“What we need to understand may only be expressible in a language that we do not know.”

The Encyclopedia of World Problems and Human Potential, is a mammoth ongoing enterprise to cover all human problems ( l2,000 profiles with 120,000 hyperlinks), strategies and solutions (29,500 profiles with 91,000 hyperlinks), human development (4,400 profiles with l5,000 hyperlinks) and human values (1,900 profiles with 23.000 hyperlinks). The Encyclopedia hypertexts are currently edited at the Union of International Associations (UIA) by Nadia McLaren. It is now in its fourth hardback edition, first CD-ROM edition, and is available in demo version on the Web (http://www.uiaorg/homeency.htm/), although all texts have been accessible since l998. Profiles on the Web can be translated through Alta Vista into a variety of major languages.

It is in this global environment that the paradigm of “languages” in the Rg Veda has found a home. The Director of the Union of International Associations, Dr. Anthony J.N. Judge, in article after article, profile after profile, conference after conference has articulated, and compiled in the Encyclopedia, the modern consequences of academic attempts at synthesis when these attempts are expressed in one common language, namely the one engendering the problems in the first place. Dr. Judge’s point of departure is the need to start from the experiential human origins as described in the Rg Veda and then articulate the ensuing insights in the plurality of languages available for their manifestation in the Rg Vedic model. Thus, the model or paradigm, is part of the “answer” proposed by the Editors of the Encyclopedia. Contrary to the position academics take of locating themselves within the “web” of a discipline, research, culture, department or, at times, a simple desk, Dr. Judge travels with ease the “lines of the webs” linking the totality of squares, within which the rest of us seem to be trapped, to a knowledge that seems to come only to those who are able to travel in his manner. He is at home in the East and in the West, in music and in science, in Christianity, Islam, Judaism, Hinduism, Buddhism or the Tao, and he seems to know a “knowledge” that comes only to those who travel the “lines” of the “web,” never squeezed by the particular generalizations of the cubicles within each “web’s square.” His summary of the “languages” of the Rg Veda for contemporary guidance to those looking to solve the problems, individual, communal or global, or contemporary life is appealing to him because it takes into account: ” The interrelated formal languages based on tone; (they lead ) toward reintegrating the individual in action; (make ) this integration embodied: re-imagining man; (take care) of the pluralism through an integration of community dialogue; (guarantee) this integrative renewal through sacrifice (of perspectives); (account) for an integrative vision that is encountered in the movement.” ( ” Liberation of Integration, Universality and Concord through pattern, oscillation, harmony and embodiment.” Originally delivered for the 5th Network Meeting of the United Nations University, project of Goals, Processes and Indicators of Development (Montreal) as a contribution to the discussion on integration of the findings of the Project.) And he includes in his remarks the fact that:

” Integration modelled on sound may be inherently more comprehensible to more people than integration modelled on sight.” (Ibid.) In view of Dr. Colavito’s previous discussed work, this conclusion is not so far fetched since the structures of the Rg Veda are the original embodied structures of the humanity that gave us birth, and as such they are embodied structures, bio-culturally invariant, not only in each of us but also in the earlier cultures that preceeded us.

Conclusion: Regathering The Fragments

The Artful Universe provided the occasion for a round discussion of the earliest structures of human “languages” we carry in our genes.

Any one particular language joining the discussion does not only show us the empirical grounding of their speech, experience, academic construction, but also the imperialistic tendency of such mono-linguistic speech universalizing itself. Contemporary discoveries in neurobiology and the paradigm based on them of Dr. Colavito make it clear that life, that is, human life, is life in community. This community is formed through interaction or dismemberment of a sensorium that is plural by its very bio-culture base and becomes integrated through dialogue. All dialogue, all language carries with it the possibility of sharing in the embodied vision of a paradigm that has been with us from the beginning, since through it we had to break through the “experience of separating earth and sky.” In this manner there is no need, as Prof. Mahoney does in one of his initial footnotes with a humility rarely present in Sanskrit scholars, to apologize for not being ethnically Indian while interpreting the Vedas. Interpretation, like everything else, is biocultural not ethnical. We are dealing with neural equipment, genes, receptors and transmitters, not the color of one’s skin, or the geography of one’s birth. And finally, if there is any hope in preserving the integrity of the University or returning it to its original call, especially in the humanities, this hope resides in the work of scholars like Profs. Mahony, Colavito and Judge who through their work in the classical myths were able to avoid the “empiricist languages” of the present Academic fashion and return to us the memories of our distant progenitors with the structures that made them live in innovation and continuity in the company of the gods. If we form the communities to carry these traditions forward, we might be able to share in the glory and celebration of life that once was ours. I am glad and grateful that Meditations Through the Rg Veda was an inspiration to them. But even more so the reiteration that our human makeup is larger, deeper and more full of sensation in the plurality we are than in the oppression of one single language-community-creed.

This is what William Irwin Thompson called, commenting on my work: “the planetization of the esoteric.”

References:

The Artful Universe: An Introduction to the Vedic Religious Imagination.
by William K. Mahoney , Ph.D.
SUNY Press, Albany N.Y. l998

The New Theogony: Mythology for the Real World.
by Maria M. Colavito, PhD
SUNY Press, Albany, N.Y. l992

The Heresy of Oedipus and The Mind/Mind Split: A Study of the Biocultural Origins of Civilization.
by Maria M. Colavito, PhD
The Edwin Mellen Press, Lewiston,N.Y. l995

Encyclopedia of World Problems and Human Potential.
Edited by The Union of International Associations
4th. Edition, K.G. Saur Verlag, Munchen, New Providence,
London, Paris l994-95

The Myth of Invariance: The Origin of the Gods, Mathematics and Music from the Rg Veda to Plato.
by Ernest McClain, Ph.D.
Nicolas-Hays Ltd. N.Y. 1976

The Pythagorean Plato: Prelude to the Song Itself.
by Ernest McClain
Nicolas-Hays Ltd. N.Y. 1978

Meditations Through the Quran: Tonal Images in an Oral Culture.
by Ernest McClain
Nicolas-Hays Ltd. N.Y. 1981

Coming Into Being: Artifacs and Texts in the Evolution of Consciousness
by William Irwin Thompson
St. Martin’s Press, New York , 1996. (p.187)


Antonio T. de Nicolas was educated in Spain, India and the United States, and received his Ph.D. in philosophy at Fordham University in New York. He is Professor Emeritus of philosophy at the State University of New York at Stony Brook.

Dr. de Nicolas is the author of some twenty- seven books, including Avatara: The Humanization of Philosophy through the Bhagavad Gita,a classic in the field of Indic studies; and Habits of Mind, a criticism of higher education, whose framework has recently been adopted as the educational system for the new Russia. He is also known for his acclaimed translations of the poetry of the Nobel Prize-winning author,Juan Ramon Jimenez, and of the mystical writings of St. Ignatius de Loyola and St. John of the Cross.

A philosopher by profession, Dr. de Nicolas confesses that his most abiding philosophical concern is the act of imagining, which he has pursued in his studies of the Spanish mystics, Eastern classical texts, and most recently, in his own poetry.

His books of poetry: Remembering the God to Come, The Sea Tug Elegies, Of Angels and Women, Mostly, and Moksha Smith: Agni’s Warrior-Sage. An Epic of the Immortal Fire, have received wide acclaim. Critical reviewers of these works have offered the following insights:

from, Choice: “…these poems could not have been produced by a mainstream American. They are illuminated from within by a gift, a skill, a mission…unlike the critico-prosaic American norm…”

from The Baltimore Sun: “Steeped as they are in mythology and philosophy these are not easy poems. Nor is de Nicolas an easy poet. He confronts us with the necessity to remake our lives…his poems …show us that we are not bound by rules. Nor are we bound by mysteries. We are bound by love. And therefore, we are boundless”

from William Packard, editor of the New York Quarterly: ” This is the kind of poetry that Plato was describing in his dialogues, and the kind of poetry that Nietzsche was calling for in Zarathustra.”

Professor de Nicolas is presently a Director of the Biocultural Research Institute, located in Florida.

 

Please see my related posts:

 

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

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

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

Sounds True: Speech, Language, and Communication

Mind, Consciousness and Quantum Entanglement

Semiotics, Bio-Semiotics and Cyber Semiotics

Systems and Organizational Cybernetics

Society as Communication: Social Systems Theory of Niklas Luhmann

 

Key sources of Research:

 

 

Meditations Through The Rg Veda: A Retrospective

(Philosophy East and West. Vol.49. Number 2. April 1999)

by Antonio T. de Nicolas, PhD

https://www.infinityfoundation.com/mandala/i_es/i_es_denic_retrospective_frameset.htm

 

 

 

https://o-meditation.com/2009/11/01/the-four-dimensions-of-man-osho/

 

 

 

Antonio de  Nicolás

http://www.svabhinava.org/hinduchrist/AntonioDeNicolas/index.php

 

On Anticipation: Going Beyond Forecasts and Scenarios

On Anticipation: Going Beyond Forecasts and Scenarios

 

From Anticipation.Info of Mihai Nadin

A Second Cartesian Revolution

For about 400 years, humankind, or at least the western world, has let itself be guided by the foundation set by Descartes and Newton. The cause-and-effect, deterministic model of the machine became so powerful that every thing and every being came to be considered a machine. As a description of the material world and as an expression of the laws governing its functioning, deterministic-based physics and Cartesian reductionism (of the whole to its parts) proved to be extremely powerful instruments in the overall progress of humankind. But neither Descartes nor Newton, nor most of their followers, could have envisioned the spectacular development of science in its current depth and breadth.

The physicist Erwin Schrödinger concluded that organisms are subject to “a new physics,” which he did not produce, but rather viewed as necessary. This new physics might well be the domain of anticipation. Indeed, from within physics itself—that is, quantum mechanics—a possible understanding of some aspects of anticipation can be derived.

The realization that the world is the unity of reaction and anticipation is not new. What is new is the awareness of the limits of our understanding a dynamics of change that transcends the deterministic view. The urgent need for such an understanding is probably best expressed in the spectacular development of the life sciences.

The perspective of the world that anticipation opens justifies the descriptor “a second Cartesian Revolution.” Instead of explaining complexity away, we will have to integrate it into our existence as the informational substratum of rich forms through which anticipatory processes take place.

 

From Anticipation.Info of Mihai Nadin

Anticipation: Why is it a subject of research?

Anticipation occurs in all spheres of life. It complements the physics of reaction with the pro-active quality of the living. Nature evolves in a continuous anticipatory fashion targeted at survival. The dynamics of stem cells demonstrate this mechanism. Through entailment from a basic stem cell an infinite variety of biological expression becomes possible.

Sometimes we humans are aware of anticipation, as when we plan. Often, we are not aware of it, as when processesembedded in our body and mind take place before we realize their finality. In tennis, for example, the return of a professional serve can be successful only through anticipatory mechanisms. A conscious reaction takes too long to process. Anticipation is the engine driving the stock market. Creativity in art and design are fired by anticipation.

“The end is where we start from,” T. S. Eliot once wrote. Before the archer draws his bow, his mind has already hit the target. Motivation mechanisms in learning, the arts, and all types of research are dominated by the underlying principle that a future state—the result—controls present action, aimed at success. The entire subject of prevention entails anticipatory mechanisms.

 

From Anticipation.Info of Mihai Nadin

Research into anticipation revealed various aspects that suggested a number of definitions.

Robert Rosen, Mihai Nadin, Daniel Dennett and others who approached particular aspects of anticipation contributed to some of these definitions. Mihai Nadin (cf. Anticipation – A Spooky Computation) attempted an overview of the various angles from which anticipation can be approached if the focus is on computation. This overview is continued and expanded in the integrated publication (book+dvd+website) to which this website belongs. The following 12 definitions, or descriptions, of anticipation should be understood as working hypotheses. It is hoped and expected that the knowledge community of those interested in anticipation will eventually refine these definitions and suggest new ones in order to facilitate a better understanding of what anticipation is and its importance for the survival of living systems.

  • An anticipatory system is a system whose current state is determined by a future state. “The cause lies in the future,”. (cf. Robert Rosen, Heinz von Foerster)
  • Anticipation is the generation of a multitude of dynamic models of human actions and the resolution of their conflict. (cf. Mihai Nadin)
  • An anticipatory system is a system containing a predictive model of itself and/or of its environment that allows it to change state at an instant in accord with the model’s predictions pertaining to a later instant. (cf. Robert Rosen)
  • Anticipation is a process of co-relation among factors pertaining to the present, past and future of a system. (cf. Mihai Nadin)
  • Anticipation is an expression of the connectedness of the world, in particular of quantum non-locality. (cf. Mihai Nadin)
  • Anticipation is the expression of natural entailment. (cf. Robert Rosen)
  • Anticipation is a mechanism of synchronization and integration. (cf. Mihai Nadin)
  • Anticipation is an attractor within dynamic systems. (cf. Mihai Nadin)
  • Anticipation is a recursive process described through the functioning of a mechanism whose past, present, and future states allow it to evolve from an initial to a final state that is implicitly embedded in the mechanism. (cf. Mihai Nadin)
  • Anticipation is a realization within the domain of possibilities. (cf. Mihai Nadin)
  • Anticipatory mechanisms can be reinforced through feedback. Feedforward and inverse kinetics are part of the integrated mechanism of anticipation. (cf. Daniel Dennett, Daniel Wolpert, Nadin)
  • Anticipation is a power law-based long-range interaction. (cf. Mihai Nadin)

 

From An Introduction to the Ontology of Anticipation

Recent years have witnessed the growth of significant interest in theories and methodologies which seek to foresee the future development of relevant situations. Studies of the future fall under many different denominations, and they employ a huge variety of techniques, ranging from forecasting to simulation, from planning to trend extrapolation, from future studies and scenarios to anticipatory systems. Widely different conceptualisations and formalisations have been proposed as well.1 This remarkable variety may be partly simplified by making explicit the main underlying assumptions of at least some of them. Two of these assumptions are that (1) the future is at least partly governed by the past, and (2) the future can be better confronted by opening our minds and learning to consider different viewpoints. According to (1) the future is part of a structured story whose past and present are at least partially known. The claim is defended that the forces that have shaped past and present situations will still be valid while the situation under consideration unfolds. The core thesis is that the future is embedded in the past; it is the projection of the past through the present. Time series analysis, trend extrapolation, and forecasting pertain to this family. Any of the mentioned methodologies may be further supplemented by computer-based simulations. On the other hand, instead of directly addressing the problem of searching for the seeds of the future in the past, (2) considers the different problem of preparing for the unforeseeable novelties awaiting us in the future. Learning about widely different outcomes is now the issue: one must be ready to consider and address possibly unfamiliar or alien scenarios. The main outcome of this exercise is an increased capacity to distinguish among possible, probable, and preferred future scenarios. These activities come under the heading of future studies, while scenario construction is the best known methodology adopted by practitioners. For now on I shall refer to (1) and (2) as respectively the forecasting and the scenario viewpoints. Forecasts and scenarios are not contradictory one to the other. They may and usually do coexist, since they address the future from two different standpoints. Furthermore, experience shows that both are useful. This paper introduces a third, different viewpoint, here termed the viewpoint of anticipatory systems, which can be profitably synthesized with forecasts and scenarios; i.e. it is not contradictory with the claims of either the forecasting or scenario viewpoint. Recent years have witnessed the growth of significant interest in anticipation.2 Anticipatory theories have been proposed in fields as different as physics, biology, physiology, neurobiology, psychology, sociology, economy, political science, computer science and philosophy. Unfortunately, no systematic comparison among the different viewpoints has so far been developed. It is therefore fair to claim that currently no general theory of anticipation is available. Generally speaking, anticipation concerns the capacity exhibited by some systems to tune their behaviour according to a model of the future evolution of the environment in which they are embedded. Generally speaking, the thesis is defended that “An anticipatory system is a system containing a predictive model of itself and/or its enviroment, which allows it to change state at an instant in accord with the model‟s predictions pertaining to a later instant” (Rosen [19: 341]). The main difference between forecasting and scenarios on the one hand, and anticipation on the 1 See, among many others, Adam [1], Bell [4], Cornish [5], Godet [7], Lindgren and Bandhold [8], Retzbach [16], Slaughter [22], Woodgate and Pethrick [23]. 2 Starting from the seminal Rosen [19]. See also [20], [21]. 2 other, is that the latter is a property of the system, intrinsic to its functioning, while the former are cognitive strategies that a system A develops in order to understand the future of some other system B (of which A may or may not be a component element).

 

 

Key Terms

  • Hyper Sets
  • Hyper Incursion
  • Hyper Recursion
  • Recursion
  • Incursion
  • Anticipatory Systems
  • Weak Anticipation
  • Strong Anticipation

 

Key People

  • Roberto Poli
  • Mihai Nadin
  • Riel Miller
  • Robert Rosen
  • John J Kineman
  • Daniel M Dubois
  • John Collier
  • Loet Leydesdorff

 

 

Key Sources of Research:

 

Systems and models with anticipation in physics and its applications

A Makarenko

http://iopscience.iop.org/article/10.1088/1742-6596/394/1/012024/pdf

 

 

Anticipatory Viable Systems

Maurice Yolles

Daniel Dubois

 

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.195.2167&rep=rep1&type=pdf

Click to access 92666ab431a3f68df0ce8139d594aaeb3f87.pdf

 

 

Anticipatory Kaldor-Kalecki Model of Business Cycle

Daniel M. Dubois

 

Click to access emcsr2004_Daniel-Dubois.pdf

 

 

An Introduction to the Ontology of Anticipation

Roberto Poli

 

Click to access read_Poli-An-Introduction-to-the-Ontology-of-Anticipation.pdf

 

 

Towards an anticipatory view of design

Theodore Zamenopoulos and Katerina Alexiou

 

Click to access anticipation.pdf

 

 

The role of anticipation in cognition

Alexander Riegler

Click to access Riegler%20A.%20(2001)%20The%20role%20of%20anticipation%20in%20cognition.pdf

Click to access 7d5ded82973e081a572c79bd76f8188b0ed5.pdf

 

 

SDA: System Dynamics Simulation of Inter Regional Risk Management

Using a Multi-Layered Model with Delays and Anticipation

Daniel M Dubois1, Stig C Holmberg

2012

 

Click to access P1374.pdf

 

 

Anticipatory Modeling and Simulation for Inter Regional Security

Daniel M. Dubois, Viveca Asproth, Stig C. Holmberg

Ulrica Löfstedt, and Lena-Maria Öberg

 

Click to access dubois-C-EMCSR-2012.pdf

 

 

Attentional and Semantic Anticipations in Recurrent Neural Networks

Frédéric Lavigne1 and Sylvain Denis

 

Click to access lavigne-denis-2001.pdf

 

 

Not Everything We Know We Learned

Mihai Nadin

 

http://www.nadin.name/index.html?/publications/articles_b0.html

 

 

Anticipation in the Constructivist Theory of Cognition

Ernst von Glasersfeld

 

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.8.1971&rep=rep1&type=pdf

 

 

The Communication of Meaning in Anticipatory Systems: A Simulation Study of the Dynamics of Intentionality in Social Interactions

Loet Leydesdorff

Click to access 0911.1448.pdf

 

 

Information Systems and the Theory of Categories: Is Every Model an Anticipatory System?

M. A. Heather, B. N. Rossiter

 

Click to access Rossiter_Information%20systems%20and%20the%20theory%20of%20categories.pdf

 

 

Anticipation.Info of Mihai Nadin

http://www.anticipation.info

http://www.nadin.name/index.html?/publications/articles_b0.html

 

 

Institute for Research in Anticipatory Systems

http://www.anteinstitute.org

 

 

Robert Rosen’s anticipatory systems

A.H. Louie

 

Click to access 09e4150cdd961e4a87000000.pdf

 

 

Computing Anticipatory Systems with Incursion and Hyperincursion

Daniel M. DUBOIS

Click to access 559558fe08ae99aa62c720f3.pdf

 

 

Anticipatory Systems: Philosphical Methematical and Methodological Foundations.

Rosen R.

Springer; 2014.

 

 

ROBERT ROSEN’S ANTICIPATORY SYSTEMS THEORY: THE ART AND SCIENCE OF THINKING AHEAD

Judith Rosen

 

http://journals.isss.org/index.php/proceedings53rd/article/viewFile/1249/410

 

 

The Many Aspects of Anticipation

Roberto Poli

University of Trento

Click to access 9b480ac8cd96999f281892caba100baacc79.pdf

 

 

Being Without Existing: The Futures Community at a Turning Point? A Comment on Jay Ogilvy’s “Facing the Fold”

By Riel Miller

Click to access Being-without-existing-The-futures-community-at-a-turning-point-A-comment-on-Jay-Ogilvys-Facing-the-fold.pdf

 

 

THE COMPLEXITY OF ANTICIPATION

Roberto Poli

Balkan Journal of Philosophy. 2009;1(1):19-29.

 

 

The Discipline of Anticipation: Exploring Key Issues

Riel Miller, Roberto Poli and Pierre Rossel

 

Reflexivity, Recursion, and Self Reference

 Reflexivity, Recursion, and Self Reference

 

From Reflexivity and Eigenform The Shape of Process

 

“Reflexive” is a term that refers to the presence of a relationship between an entity and itself. One can be aware of one’s own thoughts. An organism produces itself through its own action and its own productions. A market or a system of finance is composed of actions and individuals, and the actions of those individuals influence the market just as the global information from the market influences the actions of the individuals. Here it is the self-relations of the market through its own structure and the structure of its individuals that moves its evolution forward. Nowhere is there a way to cut an individual participant from the market effectively and make him into an objective observer. His action in the market is concomitant to his being reflexively linked with that market. It is just so for theorists of the market, for their theories, if communicated, become part of the action and decisionmaking of the market. Social systems partake of this same reflexivity, and so does apparently objective science and mathematics. In order to see the reflexivity of the practice of physical science or mathematics, one must leave the idea of an objective domain of investigation in brackets and see the enterprise as a wide ranging conversation among a group of investigators. Then, at once, the process is seen to be a reflexive interaction among the members of this group. Mathematical results, like all technical inventions, have a certain stability over time that gives them an air of permanence, but the process that produces these novelties is every bit as fraught with circularity and mutual influence as any other conversation or social interaction.

 

In such a context, every object is inherently a process, and the structure of the domain as a whole comes from the relationships whose exploration constitutes the domain. There is no place to hide in a reflexive domain, no fundamental particle, no irreducible object or building block. Any given entity acquires its properties through its relationships with everything else. The sense of such a domain is not at all like the set theoretic notion of collections or unrelated things, or things related by an identifiable property. It is more like a conversation or an improvisation, held up and moving in its own momentum, creating and lifting sound and meaning in the process of its own exchange. Conversations create spaces and events, and these events create further conversations. The worlds appearing from reflexivity are worlds nevertheless, with those properties of partial longevity, emergence of patterns, and emergence of laws that we have come to associate with seemingly objective reality.

 

From The march of self-reference

 

One of the main characteristics of social systems as well as individual systems, distinguishing them from many other systems, is indeed their potential for self- referentiality in the latter sense. Concretely, this means not only that the self- knowledge accumulated by the individual in turn affects both his structure and modus operandi, but it also implies – as especially stressed by constructivism – that in self-referential systems like individuals and social systems, feedback loops exist between parts of external reality on the one hand, and models and theories about these parts of reality on the other hand. To a large extent, both individuals and collectivities indeed produce their own world.

While constructivism, as an explanatory paradigm, is focused on individuals, it is certainly valid for social systems as well. Concretely, whenever social scientists systematically accumulate new knowledge about the structure and functions of their society, or about subgroups within that society, and when they subsequently make that knowledge known, through their publications or sometimes even through the mass media – in principle also to those to whom that knowledge pertains – the consequence often is that such knowledge will be invalidated, because the research subjects may react to this knowledge in such a way that the analyses or forecasts made by the social scientists are falsified. In this respect, social systems are different from many other systems, including (most?) biological ones. There is a clearly two-sided relationship between self-knowledge of the system on the one hand, and the behavior and structure of that system on the other hand.

Biological systems, like social systems, admittedly do show goal-oriented behavior of actors, self-organization, self-reproduction, adaptation and learning. But it is only psychological and social systems that arrive systematically, by means of experiment and reflection, at knowledge about their own structure and operating procedures, with the obvious aim to improve these. This holds true on the micro-level of the individual, as in psychoanalysis or other self-referential activities, and on the macro-level of world society, as in planning international trade or optimal distribution of available resources.

For social scientists, the consequences of self-referentiality are interesting not only for gaining an insight in the functioning of social systems, but also for the methodology and epistemology used to study them. There is a paradox here: as stated above, the accumulation of knowledge often leads to a utilization of that knowledge – both by the social scientists and the objects of their research – which may change or even invalidate the validity of that knowledge (Geyer and van der Zouwen, 1988; Henshel, 1990). It is maintained here that this paradox is interesting as well for psychologists, and exists also at the individual level where the individual not only constructs his world, but also continually reconstructs it. This can be seen in a normal life, but is especially visible in several forms of individual therapy, where old self- knowledge is invalidated by new – though not necessarily always better – self-knowledge.

The usual examples of self-referential behavior in social science consist of self-fulfilling and self-defeating prophecies. Henshel (1990) for example, has studied serial self-fulfilling prophecies, where the accuracy of earlier predictions, themselves influenced by the self-fulfilling mechanism, impacts upon the accuracy of the subsequent predictions. In much of empirical social science research. However, self-referential behavior does not loom large – which is rather amazing in view of its supposedly being an essential characteristic of individual human functioning. In this case the research methodology used may be an issue: survey research, where people are asked what they think or feel, offers little opportunity to bring out self-referential behavior, while depth interviews, which concentrate more on the awhyo than the awhato of people’s opinions have a better chance to elicit self-referential remarks in this respect.

 

Key People:

  • Francisco Varela
  • Lois Kauffman
  • Steven J Bartlett
  • Howard Pattee
  • Niklas Luhmann
  • Felix Geyer
  • George Soros
  • Eric D. Beinhocker
  • Stuart A. Umpleby
  • Heinz Von Foerster

 

Key Sources of Research:

 

Reflexivity. A Source-Book in Self-Reference

Steven Bartlett

http://www.willamette.edu/~sbartlet/reflexivity_and_theory%20of_reference.html

ub.eur.nl/pub/7870http://rep7

 

Self-reference: Reflections on Reflexivity

Steven J. Bartlett & Peter Suber (Eds.)

Dordrecht: Martinus Nijhoff, 1987. Now published by Springer Science.

 

Self Reference and Recursive Forms

Lois Kauffman

Click to access SelfRefRecurForm.pdf

 

The Complexity of Self-reference
A Critical Evaluation of Luhmann’s Theory of Social Systems

Roberto Poli

 

Click to access quad50.pdf

 

Reflexivity and Eigenform The Shape of Process

Louis H. Kauffman

 

Click to access ReflexPublished.pdf

 

The march of self-reference

Felix Geyer

 

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.202.9606&rep=rep1&type=pdf

 

Essays on Self-reference

By Niklas Luhmann

 

Evolving Self Reference

Howard Pattee

Click to access 09e4150577eb05a2cd000000.pdf

 

SELF-REFERENCE, PHENOMENOLOGY, AND PHILOSOPHY OF SCIENCE

Steven James Bartlett

Click to access Bartlett_Self-reference,%20Phenomenology,%20and%20Philosophy%20of%20Science.pdf

 

 

Recursivity and Self-Referentiality of Economic Theories and Their Implications for Bounded Rational Actors

 

Marco Lehmann-Waffenschmidt Serena Sandri

Click to access DDPE200703.pdf

 

A Calculus for Self Reference

F Varela

Click to access VarelaCSR.pdf

 

Ouroboros avatars:
A mathematical exploration of Self-reference and Metabolic Closure

Jorge Soto-Andrade, Sebastia ́n Jaramillo ,Claudio Gutie ́rrez and Juan-Carlos Letelier

Click to access 0262297140chap115.pdf

 

Self Reference and Autopoiesis

A Locker

Click to access metatheor-presupp-autopoiesis.pdf

 

Snakes all the Way Down: Varela’s Calculus for Self-Reference and the Praxis of Paradise

André Reichel

 

Click to access 09e4150d0287eebed2000000.pdf

 

Self-Reference and Time According to G. Spencer-Brown 

Andreas Kull

 

http://sfile-pull.f-static.com/image/users/112431/ftp/my_files/sbrown.pdf?id=11014655

 

Reflexivity in Economics: An Experimental Examination on the Self-Referentiality of Economic Theories

By Serena Sandri 2009

Springer

 

Operational Closure and Seif-Reference: On the Logic of Organizational Change

Markus Schwaninger1and Stefan N. Groesser

Click to access 235_Operational%20Closure%20and%20Self-Reference_SRBS%202012.pdf

 

Fallibility, reflexivity, and the human uncertainty principle

George Soros

http://www.tandfonline.com/doi/pdf/10.1080/1350178X.2013.859415

 

Reflexivity, complexity, and the nature of social science

Eric D. Beinhocker

http://www.tandfonline.com/doi/pdf/10.1080/1350178X.2013.859403

 

Reflexivity and Economics: George Soros’s Theory of Reflexivity and the Methodology of Economic Science

http://www.tandfonline.com/toc/rjec20/20/4

 

REFLEXIVITY IN SOCIAL SYSTEMS: THE THEORIES OF GEORGE SOROS

Stuart Umpleby

Click to access 0c9605187eecf06dff000000.pdf

 

Reflexivity, Expectations Feedback and Almost Self-fulfilling Equilibria: Economic Theory, Empirical Evidence and Laboratory Experiments

Cars Hommes

August 14, 2013

http://dare.uva.nl/document/2/156151

 

 Reflexivity, path dependence, and disequilibrium dynamics

Anwar Shaikh

Click to access 2-Reflexivity,%20path%20dependence,%20and%20disequilibrium%20dynamics.pdf

 

Second-Order Economics as an Example of Second-Order Cybernetics

Stuart A. Umpleby

 

Click to access 890.pdf

 

Reflexivity and Equilibria

Francesco Guala

 

Click to access DEMM-2013_16wp.pdf

 

Umpleby, Stuart A.

“Fundamentals and history of Cybernetics.”

World Multi-Conference on Systemics, Cybernetics, and Informatics. 2006.

Click to access videoSUfh-slides.pdf

 

Complexity to Reflexivity: Underlying Logics Used in Science

Stuart A. Umpleby

Click to access 55edc5ad08ae199d47be4b99.pdf

 

EigenForm

Louis H. Kauffman

 

Click to access Eigen.pdf

 

Laws of Form and the Logic of Non-Duality

Louis H. Kauffman

Click to access KauffSAND.pdf

 

EigenForm

Louis H. Kauffman

 

Click to access Eigenform.pdf