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.
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.
Stone Patañjali Mūrti (Idol)
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):
- sthūla-śarīra (gross body) – annamayakośa
- sūkṣma-śarīra (subtle body) – prāṇamayakośa, manomayakośa and vijñānamayakośa
- 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), satyaṃ (truth), ṛtaṃ (morality), mahat (cosmic), and yoga.
The Causal Body (kāraṇa-śarīra)
The internal vibration that hums at the heart (hṛdaya) 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
Hasta Mudra and Nada Meditation
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
- Adopt Jñāna mudra gesture while saying “Sa”
- Adopt Ākāśa mudra gesture while saying “Ta”
- Adopt Pṛthvī mudra gesture while saying “Na”
- Adopt Varuṇa mudra gesture while saying “Ma”
- Sa-Ta-Na-Ma are primal sounds that form the words “satya-nāma” (True Name) meaning the transcendent
- Repeat 3x aloud
- Repeat 3x softly
- Repeat 3x silently
- Repeat 3x softly
- Repeat 3x aloud
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.