For your discussion on mantras:
A number of traditional sources clearly verify that the TM mantras, technically known as bija-aksharas ("indestructible seed-sounds"), are not meaningless but actually have well-defined meanings. In fact there are entire dictionaries of bija mantras like the bija dictionary of Bhairava rishi.
The Brihad-gandharva-tantra (chapter 5) clearly explains:
"The bijas have a meaning. They indicate the Artha or Devata that they are from. What that Devata is, is [supposed to be] taught to the Sadhaka (student), just as the child learns that 'rose' means a certain type of flower, and that rice and milk are the names for a certain type of food and drink he can have."
In any event, here are the meanings of some TM mantras according to the Varada-Tantra to demonstrate:
Aing
[The letter] "Ai" [in the mantra] means Sarasvati. Bindu [the "g" at the end of the mantra] means "dispeller of sorrow". This is the bija of Sarasvati. With it Vani or Sarasvati should be worshipped.
Shring
"Sa" means Mahalakshmi. "Ra" is said to mean "wealth". "I" means "satifaction". Nada is Apara (Ishvara). Bindu means "dispeller of sorrow". This is the bija of Devi Lakshmi. With it this Devi should be worshipped.
Hring
"Ha" means Shiva. "Ra" is said to be Prakriti. "I" means Mahamaya. Nada is said to be Mother of the Universe. Bindu means "dispeller of sorrow". With that Bhuvaneshvari should be worshipped.
etc...
And the second revelation to come in was the fifth and sixth advanced techniques, in response to the earlier post of the first four:
Wow, you only had two to go: shri shri aing aing namah namah and then the same thing in rhythm with the pulsing of the heart.
Enjoy! Don't let your head explode!
