In our tradition as you well know we give a particular name and form to this aspect of Ishwara as a bestower of Jnana, the Ultimate Guru, as Lord Dakshinamurti.
The symbolism associated with His name and form is well-known as follows:
The entire manifest Universe is represented in His form in a eightfold aspect (yasyaiva murthy ashtakam)
The body or idol itself represents Prthvi or earth.
He has a different earring on each ear representing both the male and female aspects.
The Ganges on his head represents water.
The damaru in one hand represents space or akasha.
The headband bandhana that ties the hair reveals the presence of vayu or wind.
The flame in one hand represents of course fire or agni.
On the head is the Sun one one side representing all the luminous bodies, on the other the crescent moon representing all the planets and satellites.
The four disciples represent Sanaka and other jivas who first receive the teaching.
The vedas on one hand represent the shruti, the pramana, the means of knowledge, and the japamala represents the sadhana for attaining the right preparedness of mind and intellect without which the knowledge cannot take place.
Obstacles (apasmara) to this knowledge (raga,ddvesha,kama,krodha) represent the figure under his foot whom he (effortlesslly) vanquishes.
The chinmudra finally represents "tat tvam asi" - the union of angushtha the thumb representing ishwara and tarjanya the index finger representing the ego.
The angushtha is ever asangah - unassociated with the fingers but without it the functioning of the other fingers is impossible. The three other fingers represent the three gunas (or three avasthas) and the process of the ego dis-identifying himself from them three and instead uniting with parameshwara is what the chinmudra symbolizes.
The halfopen eyes symbolize awareness of both within and without.
Thus in this particular form we have the entire srshti represented as well as a representation of the Ultimate Guru, who gives us knowledge of the Absolute.
There is some question on whether he taught in silence.
The very opening lines of the dhyanastotra to Dakshinamurthy start with "maunavakhyaprakati ta"
But in the stotra itself we are told that he utters "tat tvam asi" ("tat tvam asi iti veda vachasaat yo bodhayat ashritan") How do we reconcile this. Was He silent or did He say tat tvam asi? If He "silently" said "tat tvam asi" then is this really silence?
What is intended to be conveyed is that the silence indicates that the meaning of the (liberating) words He utters "tat tvam asi" is not to be taken in its direct sense(shabdavachyam ) but in an implied sense (shabdalakshyam) . Because right now when someone says "thou" we take the "thou" to be something it is not, and we take "that" to also be something else. Hence, it is not in the direct sense that we are to understand "I am Brahman" but in an implied sense alone.
Even after saying tat tvam asi unless the mind is prepared for the teaching it is mere "words" and "sound" alone; one goes beyond the (literal) words to the "silent" understanding of the truth that is conveyed.
naanaachchhidra ghaTodarasthitahaa diipaprabhaabhaasvaraM
GYaanaM yasya tu chakshuraadikaraNa dvaaraa bahiH spandate .
jaanaamiiti tameva bhaantam anubhaatyetatsamastaM jagat.h
tasmai shriigurumuurtaye nama idaM shriidakshiNaamuurtaye