The Guru of Maha Rishis and of the Greatest of Yogis..
As the Guru who bestows Jyana, he is Medhaa Dakshinamurthy revealing the knowledge that liberates;
He faces south ( usually inauspicious ) as it is the direction of Death which is something everyone is afraid of, in some form or another.
But he sits facing Death, as one who is also Mahakala, the one who conquers death, and gave Markandeya victory over Death .
Curiously In Ramanashram , the room where Ramanar stayed, he was always facing South too.
Dakshina + Amurthy , Amurthy – he who is without form , Chidswarupa , Chaitanya is Dakshinamurthy..
Dakshina is right , Left side is the physical heart, right side heart ( the heart chakra , which we intuitively point toward the center of our chest ) , hence he who sits inside of us ( Atma Svarupa )
Most don’t know that in the Puranas, after the destruction of Daksha’s Yagya, when the Devas approached Lord Shiva for forgiveness and Upaaya, the form he was in was that of Dakshinamurthy.
Once , the 4 Manasik born Putras of Brahma , the 4 Kumaras , wanted to get Brahma Gyana and so approached their father who was deeply admiring Saraswati Devi’s music.
Annoyed, they left for Vaikuntha..
There Vishnu was asleep, with Lakshmi massaging his feet. This made them even more angry. Thinking of Shiva , remembering he being known to be always in Meditation they approached Kailasha.
At least in Brahmaloka, Brahma was at a distance from Saraswati. And in Vaikuntha, Vishnu was still separate from Lakshmi, though closer.
Here, Shiva was completely one with Devi as Ardhanaareshwara! Disgusted thinking non of the Trimurti are worthy to be their Guru, they left.
The Compassionate Mother, then told Lord Shiva, Swamy , Jyanis can be as however they wish to be , but Shishyas might not be able to understand such Jyanis like you, in that way.
So please take a form that such seekers would be able to accept , that would aid them in their liberation, though forms don’t mean anything to you.
As the 4 Kumaras were walking down a path , under a big banyan tree, Shiva appeared in the form of Lord Dakshinamurthy, in Blazing Glory and Sublime Silence. It is then, the 4 Kumaras knew, they had found their Guru, and sat down at his feet.
And Dakshinamurthi gave them Gyana via his Supreme Silence.
– Excerpts from Nochur Sri Venkataraman Tamil Pravachanam