MEDHA DAKSHINAMURTHI MANTRA

"OM HREEM DAKSHINAMURTHAYE' MAHYAM MEDHAAM PRAGNAAM PRAYACCHA SWAHA"

otherwise you can chant this manthra shortly as below

"OM  HREEM  SRI DAKSHINAMURTHAYE  NAMAHA.!"

        

I will give you a Medha Dakshinamurthy Mantram

"OM HREEM DAKSHINAMURTHAYE' MAHYAM MEDHAAM PRAGNAAM PRAYACCHA SWAHA"

However since the beejam "Hreem" is there it is imperative to get Guru initiation and guidance for the mantra.

Dakshina not only means "south" as you are discussing, but it means "right" (opposite of "left") too. Of course, when one faces east, one's right hand side is in the southern direction and that may be why the right hand is called "dakshina hastam".

The Sanskrit word Dakshinamurthy literally means the figure facing south. In every Siva temple the stone image of Dakshinamurthy is installed, facing south, on the southern circumambulatory path around the sanctum sanctorum. Perhaps, of all Hindu Gods, he is the only one sitting facing south. The great seer Ramana Maharshi, has interpreted the name as "Dakshina amurty", meaning one who is capable but without form.

In the iconic form of Dakshinamurthy, Siva is depicted as sitting on a seat under a banyan tree, facing south. His right leg is placed on a demon lying on the ground. His left leg is folded and placed on the seat. Four sages surround Him. He is instructing them on the absolute truth, silently, using only hand gestures.

Yoga Dakshinamurthy

The index finger of His right hand is bent and touching the tip of his thumb. The other three fingers are stretched apart. This symbolic hand gesture or mudra is the Gnana Mudra (or Jnana Mudra or Jana Mudra), a symbol of knowledge and wisdom. He also holds the scriptures in this hand. There is a snake or rosary or both in one hand and fire in the other. The remaining hand is in the Abhaya Mudra, a posture of assurance and blessing. 

Vyakyaana Dakshinamurthy

Dakshinamurthy is portrayed as being in the yogic state of abstract meditation - and as a powerful form brimming with ever flowing bliss and supreme joy. Variations of this iconic representation include Veenadhara Dakshinamurthy, Rishabharooda Dakshinamurthy etc

Veenadhara DakshinamurthyMedha means intelligence. What is the seat of intelligence? Normally we consider the brain as the seat of intelligence. Dakshinaamurthy is dakshina+amurthy. Amurthy means a formless entity. So "Medha Dakshinaamurthy" may be roughly translated as "the formless entity in the right brain". What is it?If we study the basics of yoga and modern neuroscience, this can become clearer.The right half of the brain controls the left part of the nervous system and the left half of the brain controls the right part of the nervous system. There is a cross over in the medulla. Though Lord Medha Dakshinamurthy's name is associated with the right side (dakshina), he is depicted as sitting with his left (vaama) leg up.Modern science says that structured logic is performed by the left half of the brain and inutition and unstructured logic is performed in the right half of brain. The nervous reflexes associated with left part of the body (and hence the right brain) are used by them more pre-dominently and hence the reflexes are more intuitive.In Yoga, the nervous channels of Pingala and Ida are associated with fire and water (Sun and Moon). In terms of modern terminology, they correspond to sympathetic and parasympathetic nervous systems. One system plays a stimulating (fiery) role and the other plays a soothing (watery) role. Structured logic is fiery in nature and unstructured intuition is watery in nature.Medha Dakshinamurthy is depicted as a guru who teaches without speaking a word. He sits in jnaana mudra in silence and knowledge comes automatically. This seems to point at the intuition within us, which taps to the universal source of knowledge! This intuition that contributes to unstructured learning is "the formless entity of the right brain" and it gives us knowledge thru silence. Medha Dakshinamurthy is stationed in our right brain as the formless entity called intuition and teaches us everything.