# From Transcendental Ratios to Euclidean Geometry to the Composite Body to Hasta Mudra and Nada Meditation: A Discourse

Abstract

My class discussion relates the axioms of Euclidean transcendental geometry to the dogmatic expressions of the tri-fold and five-fold models in the verses of the Rg-Veda and Upaniṣad. Particularly, I refer to the Tattva-prakṛti (microcosm-macrocosm) including the pañča mahabhūta model. I allow the prevailing theme of Tattvic cosmic energy to flow into the closing Yogi Bhajan practice of kirtan kriya, which consolidates our knowledge and awareness of prāṇa, the subtle body, the five bhūtas, and the transcendent, through the use of hasta mudra techniques and nada meditation.

Introduction

From the Invocation to Patañjali,

śańkha čakrasi dhariñām

the juxtaposition of a circle (čakra) and a conch shell (śańkha) in the verse, on one hand, indicates an affinity to the celestial, solar (čakra) signs of jyotiṣa (astrology) and, on the other, religious symbolism of traditional Vedic rituals.

On further analysis, intrigued by the conceit of transcendental ratios, I offer another layer of interpretation: the circle represents the transcendental number π, whereas the Valampuri conch shell represents the transcendental number ϕ.

Transcendental Ratios

Transcendental ratios represent the bases for the arcane studies in Sacred Geometry and Numerology, which attempt to relate microcosm and macrocosm. The orbits of planets and natural satellites are defined by π, whereas the geometric proportions and symmetries in nature are defined by the Golden Section or Golden Ratio, denoted by the Greek letter φ:

The geometric proportions of a conch shell can be defined mathematically by a linear recurrence equation,  called the Fibonacci Sequence or Mātrāmeru (Number Mountain).

The Fibonacci numbers for , 2, … are 1, 1, 2, 3, 5, 8, 13, 21, …

A golden spiral is created by drawing circular arcs connecting the opposite corners of the squares in the Fibonacci tiling:

Tri-fold and pentagonal Euclidean symmetries

In Euclid’s Elements, a collection of thirteen books on geometry, the golden mean is defined and applied to the construction of a regular pentagon, an icosahedron and a dodecahedron. Proportions in two dimensions are understood by viewing pentagonal geometries and the rule of thirds.

Composite body or śarīra

Tri-fold models are not uncommon in doctrines. For example, in Christianity, the Holy Trinity, represented by the celtic triquetra symbol as illustrated below, is used in conjunction with the ritual blessing by the sign of the cross.

In the Vedic model of śarīra (composite body) as described in the Taittirīya Upaniṣad of the Yajurveda, the five parts or proportions comprise of the head, the right wing, the left wing, the trunk, and the tail. Tri-fold models are mapped onto overlapping layers of the five-fold model to aid the śruti learning of dogmatic knowledge.

In the Vedic model, we apply the following tri-fold deconstruction of the composite body, in relation to five sheaths (kośaḥ):

1. sthūla-śarīra (gross body) – annamayakośa
2. sūkṣma-śarīra (subtle body) – prāṇamayakośa, manomayakośa and vijñānamayakośa
3. kāraṇa-śarīra (causal body) – ānandamayakośa

Nara refers to the misalignment of the five sheaths.

The Subtle Body (sūkṣma-śarīra)

The sheath of vital life force, or prāṇamayakośa, represents the system that governs the distribution of the vibration/energy of nutrition (anna) throughout the body. The breath (vāyu) model divides the body into:

Prāṇa vāyu: inward movement of energy

Apāna vāyu: outward excretion of energy

Samāna vāyu: balancing air at the seat of digestive fire (navel)

Udāna vāyu: upward-moving energy that promotes mental clarity and acute sensory function

Vyāna vāyu: outward-moving wind that processes the intake of food and circulates the entire body

The sheath of cognition (manas), or manomayakośa, comprises of knowledge, or vidya. The following diagram illustrates the arrangement of the four canonical collections of Vedic Sanskrit literature and the commentaries, brāhmaṇa.

Intuition and wisdom (jñāna) represent the deeper sheath of the intellect, vijñānamayakośa, comprising of śraddhā (faith), satya (truth), ṛtaṃ (morality), mahat (cosmic), and yoga.

The Causal Body (kāraṇa-śarīra)

The internal vibration that hums at the heart (hdaya) of all human consciousness – kāraṇa-śarīra, represents the causal body conceived as ānandamayakośa, comprising of priyam (love), moda (joy), pramoda (delight), ānanda (bliss) and īśvara (the transcendent). Strung by the energies of karma (action and relationship), this is the vibration within you that directs you towards owning your bhāva (pure intention).

Vedic Five Element (pañča mahabhūta) model

The Universal Cosmic microcosm-macrocosm (Tattva-prakṛti) vibration currents rotate from Ether (Ākāśa), to Air (Vāyu), to Fire (Agni), to Water (Jala), to Earth (Pṛthivī).

Solar signs (rāśiḥ) in Vedic astrology grouped into four elements of three

The following hasta mudra and nada meditation practice is popularly named “kirtan kriya” by Yogi Bhajan, even though it is not contemporary bhakti kirtan and it is also not a kriya technique. The intention of the practice is to purify the mind through sound (nada) meditation.

When you intend to practice this meditation technique, you must first prepare to start from calm attentiveness. Mudra techniques engage the subtle body, so you must be ready to experience the subtle aspects of the practice, otherwise your mind will simply be distracted by large movements. I describe the use of mudra techniques in this manner as analogous to controlling the sails of your boat while you are at the mercy of winds and ocean currents.

This meditative technique engages and stabilizes the healing power of the biorhythmic electromagnetic currents in the subtle body, and allows you to notice the thin spaces within.

Jñāna mudra: Thumb to index finger, increases the Air Tattva in the body

Ākāśa mudra: Thumb to middle finger, balances the space within the body

Pṛthvī mudra: Thumb to ring finger, increases the Earth Tattva in the body

Varuṇa mudra: Thumb to little finger, increases the Water Tattva in the body

Instructions:

1. Adopt Jñāna mudra gesture while saying “Sa”
2. Adopt Ākāśa mudra gesture while saying “Ta”
3. Adopt Pṛthvī mudra gesture while saying “Na”
4. Adopt Varuṇa mudra gesture while saying “Ma”
5. Sa-Ta-Na-Ma are primal sounds that form the words “satya-nāma” (True Name) meaning the transcendent
6. Repeat 3x aloud
7. Repeat 3x softly
8. Repeat 3x silently
9. Repeat 3x softly
10. Repeat 3x aloud

Afterword

Mystery is a necessary part of the living condition. Without mystery in life, there would be no motivation for human beings to seek out new ways to distinguish and define their own particular human characteristics and purpose in life. It is by becoming involved in playing with the mystery that contributes to the meditation of the living condition, conveying human consciousness from darkness towards dawn. In Sanskrit, gu (गु) means darkness and ru (रु) means light, while sandhyā is a special word that refers to the transition between the darkness of gloom and the dawn of joy and knowledge. I bow down in gratitude for the wisdom in these teachings that were transmitted to me according to Yoga parampara.

# Haṭhayoga

It irks me that the current usage in the Yoga community of the sanskrit term “Haṭha Yoga” (हठयोग) is taken to mean a gentle (sometimes restorative) style of Yoga.

Haṭha means persistence or force. In Haṭha Yoga Pradīpikā, the author sage Svātmārāma ascribes the traditional methods of persistence or force to the austerities (or self-torture) performed on the physical body in preparation for Yoga.

In Siddhasiddhant Paddhati, Gorakshanath relates the word to the spiritual union of Shakti with Shiv (God Principle), where ha (ह) refers to Shivabija (breathing through the right channel), and ha (ठ) refers to Vahnibija (breathing through the left channel)Haṭha definitely does not mean sun-moon in sanskrit, despite what every Yoga teacher thinks or says!

In modern times, Haṭha Yoga, the post-modern revival of a diasporic culture, popularized by the celebrity appeal of the imagery of body beautiful and of physical culture, presents itself as a lifestyle choice and recreational activity for those who can afford the luxury.

The diverse range of Yoga brands and styles are living testament to the exoteric modernity of the tools of Yoga, no longer provincial to the esoteric few. Without the base of ancient traditions and lineage to ground and direct, Haṭha Yoga educators can choose to separate what they want out of the practice (e.g. health aspect), omit what they do not want (e.g. religious aspect), and draw on inspiration to add new ideas (e.g. Hot Nude Yoga).

Is it any wonder that some people think that Haṭha Yoga is Evil dressed in lambskin?

# Hathayoga Nādi Purification and Mudra Techniques Lesson

This is my self-study of a particular combination of alternate nostril pranayama and mudra exercises as taught by Yoga Therapist Leigh Blashki at the Yoga Australia 2012 conference, which I attended. If you would like to try these advanced hathayoga nādi exercises, please be aware that the efficacy of psychic healing from practicing simple movements with breath cannot be validated, except by one’s own personal experience. Do practice mindfully with gentle intention.

In the yogas of hathayoga and Tantra, it is believed that pranic energy flows through a complex maze of tributaries called nādis in the subtle, or energy, body. The pranayama method of nādi śodhana restores balance to the flow of prana in the subtle body, by using alternate nostril breathing to bring awareness to both left (ida) and right (pingala) polarities of the nādis, while each round of breath engages the Autonomic Nervous System.

The word nādi comes from the Sanskrit root nād, meaning “channel” or “flow”.

Mudra represents a technique for directing vitality to particular behaviours/humours of the subtle body by closing the circuit of the pranic current in the body.

In the esoteric study of the pancha mahābhūta, the subtle or energy body is divided into five Tattvic alchemical phases or humours, which are represented externally in the Universe (tat – macrocosm) as it is internally (tvam – microcosm). Prana, or life force, is said to be composed of the five Tattvas, flowing from spirit to Air, to Fire, to Water, to Earth. Psychic healing is based on the belief that it is the flow of the pranic currents that revitalizes the energy body, which is the subject of this study/lesson.

Each digit on a hand represents one of the five humours or Tattvic phases:

Fire: tejas or agni

Air: vāyu

Ether (Void): ākāśa (or śūnya)

Earth: pṛthvī

Water: āpas or jala

Nādi śodhana is usually practiced with mrigi/nasikagra/nasagra mudra (deer seal), but in this exercise, we replace that mudra with one of the five Tattvic mudras, each of which has an influence on one of the five Tattvic phases:

Jñāna mudra: Thumb to index finger, increases the Air Tattva in the body

Ākāśa mudra: Thumb to middle finger, balances the space within the body

Pṛthvī mudra: Thumb to ring finger, increases the Earth Tattva in the body

Varuṇa mudra: Thumb to little finger, increases the Water Tattva in the body

1. Begin in a comfortable sitting pose and centre yourself. Check that your seat is the right height. To avoid experiencing groin pain, maintain your hips higher than your knees. Be mindful of your lower back (Check that your lower back is not leaning forward or your upper body is rounded forward).
2. Calm your breath. Take long, slow, gentle breaths.
3. Inhale, circle arms from the sides, over your head, and bring palms to touch. Pause. Exhale, bring palms to heart centre.
4. With both hands, adopt Jñāna mudra.
5. Imagine that you are holding on to an invisible thread and you can feel the line of energy between the fingertips, as you separate your hands.
6. Rest left hand on left knee. Hold right hand up, palm facing forward in mudra, and place the mudra over the nose cartilage for one round of nādi śodhana.
7. Lower the hand. Inhale, circle arms from the sides, over your head, and bring palms to touch. Pause. Exhale, bring palms to heart centre.
8. Imagine that you are holding on to an invisible thread and you can feel the line of energy between the fingertips, as you separate your hands.
9. Rest right hand on right knee. Hold left hand up, palm facing forward in mudra, and place the mudra over the nose cartilage for one round of nādi śodhana.
10. Lower the hand.
11. Repeat the exercise with ākāśa, pṛthvī, and varuṇa mudras.
12. To teach this exercise to students, add progressions to what is essentially the same, repetitive exercise that combines nādi śodhana with Tattvic mudras.
13. Contemplate (and share) your individual experience at the time.

“With the inhalation, imagine drawing in pure, cleansing, relaxing energies. And with each exhalation, imagine expelling all obstacles, stress, and negative emotions.”

– Geshe Tenzin Wangyal Rinpoche, The Tibetan Yogas of Dream and Sleep, 2004

# Prāṇa and I

Prāṇa and I maintain an intimate, unfailing relationship. It seems that Prāṇa touches everything that I live with and cannot live without. Nonetheless, I do not measure the dimensions of my Prāṇa, let alone monitor every nuance of its movement. There is nowhere to submit my complaints if it stops working, but I rest assured that it never stops working from the moment that I was born. I am bemused by my attempts to quantify it as a separate resource from my body and mind, as if to suggest that I can be depleted of it, or that I can mine more of it. Such irony is present in the phrasing of ‘I’ve lost my mojo!’ and ‘I’ve got my mojo back now’. How can the sap of life be removed from my body, mind and spirit? Can a circle in spatial geometry have its locus extracted out of its periphery? In yoga (union), I focus on my intimate, unfailing relationship with prāṇa because the locus of the self is sarām (essence), and the essence of life is prāṇa.

Prāṇa as living energies

Prāṇa is a concept espoused by the ancient yogins and yoginīs to explain the dynamics and vibration of the psyche, the body and the relationship with the external environment (including nature and culture) that support well-being and life.

Prāṇa, unlike the fundamental forces of physics, is described as psychic vibrations, based on psychology, metaphysics, and phenomenology. New Age exploration of psychic energy, however, tends towards the propagation of pseudoscientific myths based on superstition, magic and beliefs that support a placebo effect. Moreover, there is no tool that can physically measure psychic energy, aside from an individual’s own subjective experience, in a manner of speaking. Thus, literature and practices that make claims of some miracle or magic panacea under the auspices of the placebo effect to treat a wide range of symptoms – hair loss, sexual dysfunction, weight loss, etc. – should be viewed with a reasonably high amount of skepticism.

Prāṇa in the metaphysical model of existence (Vedānta psychology)

Historically, the concept of prāṇa first appeared in ancient gnostic scriptures called the upaniṣads, as part of a metaphysical framework of existence that describes structures of experience or consciousness.

The Vedic sages’ ascetic discipline of the psychology of experience was a precursor to the twentieth century phenomenology of Edmund Husserl, Martin Heidegger, Maurice Merleau-Ponty, Jean-Paul Sartre, et al., which involves the study of appearances rather than reality.

In particular, the taittirīya upaniṣad illuminates the underlying phenomenological concept as illusion (maya) – by presenting its model of the experience of prakṛti (nature) in terms of five layers. From the gross to the causal, the layers are named annamaya, prāṇamaya, manomaya, vijñāṇamaya (or buddhimaya) and ānandamaya. Each of these mayaḥ represents the phenomena (Greek phainomenon, appearance) or manifestations of things, or things as they appear in our experience, or the ways we experience things.

Within the annamaya (food) layer of the physical body (sthūlaśarīra), the prāṇamaya layer represents the vitality of the subtle body (liṅgaśarīra or sūkṣmaśarīra).

The word ‘kośa’ (sheath) was not used in the taittirīya upaniṣad, and it might have entered the lexicon through Ādi Śaṅkarācārya’s commentary on the ten principle upaniṣads. The model (illustrated) is popularly known as the pancamaya kośaḥ, where ‘kośa’ is commonly used as a synonym for ‘layer’.

The term ‘kośa’ is not used in the Krishnamacharya-Desikachar lineage when describing the five layer model of experience, because it suggests compartmentalization within the layers, instead of conveying the pervasive, unbounded nature of human consciousness and experience.

Five forms of prāṇa

The five forms of prāṇa are also described in the taittirīya upaniṣad,

Adhyātma (inner spiritual self or spirit) | prāṇa, vyāna, apāna, udāna & samāna

These five forms are also known as the pañčavāyuḥ, or five airs, which localize prāṇa activity in various parts of the body:

1.       prāṇavāyu: responsible for the beating of the heart and breathing.

2.       apānavāyu: responsible for the elimination of waste products from the body through the lungs and excretory systems.

3.       udānavāyu: responsible for producing sounds through the vocal apparatus.

4.       samānavāyu: responsible for the digestion of food and cell metabolism (and also directly affects jaṭhara agni).

5.       vyānavāyu: responsible for the expansion and contraction processes of the body, e.g. the voluntary muscle system.

Metabolic fire or Jaṭhara agni

Fire (agni), as the earthly manifestation of the power of the Sun, is sacred in Hindu rituals, and its symbolism in the work of haṭhayoga connotes the oblations of the temple that is the energy body, and its prāṇa (vital energies) – leading to transformation to a higher level of being.

In the context of prāṇa, the catabolism (breakdown) of food for samānavāyu (digestion, metabolism) is represented by the imagery of fire in the jaṭhara (Japanese hara, belly). By inference, the dynamics of the belly function as the centre or heart of the subtle body system. In other words, the symbol of agni represents the hṛdaya (heart) or sarām (essence) of prāṇa.

Prāṇa Balance

Sometimes I feel moody, overworked or tense in some parts of my mind-body but lethargic or sluggish in other parts of my mind-body.

In Āyurvedic terms, the state of vikṛti, or imbalance of bodily humours or dośaḥ in the body depends on my relationship with prāṇa.

The practice of yoga (union) is to bring the subtle psychic energies back into a sense of balance, by drawing the downward-moving psychic flow of apānavāyu up towards the navel (psychic energy centre referred to as ‘maṇipūra’, or city of jewels), and the upward-moving psychic flow of prāṇavāyu down towards the navel.

# Śitali Pranayama

At Yoga Synergy (Bondi), I learned a basic prāṇāyāma technique called Śitali (Tongue Hissing), a cooling and detoxifying breath to curb fever, anxiety, and control appetite. This is in contrast to the Ujjayi Prāṇāyām (Victorious or Cobra Breath), an ocean breath that builds internal heat.

In Śitali Prāṇāyām, air is inhaled through the protruding tongue that is curled into a tube. As air passes over the moist tongue during inhalation, it cools and refreshes the throat.

Other yogic breathing techniques include Bhramari Prāṇāyām (Humming Black Bee Breath) and Śitkari Prāṇāyām (Teeth Hissing Breath).