beginningless avidyA and transmigration

[Sankaran Panchapagesan]

Hi.
  This is just something regarding avidyA that I discovered, that really
cleared one of my fundamental doubts regarding advaita.  I think most
people on this list would already know it, but anyway, hopefully it would
help at least one other person who is a beginner like me. Also, I am
generally expressing my present imperfect understanding, Please correct me
if I am wrong anywhere.

        I had a question which was, what is transmigration? Till I came
across advaita I was thinking that each person has a soul called AtmA
which transmigrates, i.e. sort of ("physically") passes from one body that
dies to another body that is born. This is basically true of sAMkhya,
jainism, etc. where Atman or purusha is a word for the soul itself that
transmigrates (right?). But in advaita, I learnt, Atman is nothing but
brahman, common to all, which is expresses itself as the pure
consciousness, the 'I' notion in all. What then is transmigration in
advaita?

I came across the answer in "A Thousand Teachings, The UpadeSasAhasrI of
Sankara" translated and edited by Sengaku Mayeda, published by University
of Tokyo Press, C. 1992.

        In the Introduction, there is a chapter on transmigration, the
meaning of samsAra, avidyA, etc. There is quite a lot of discussion. After
that he quotes Sankara (basically the guru in Upad.) from the
UpadeSasAhasrI:

"As knowledge is of the very nature of Atman it is constantly applied
figuratively to the intellect. And the absense of discriminating knowledge
(aviveka) is beginningless; this and nothing else is taken to be
transmigratory existence." (Upad I,16,61).

"Therefore let transmigratory existence be nothing but nescience
(avidyAmAtra) due to the absence of discriminating knowledge. Because of
(the existence) of the immovable Atman, transmigratory existence is always
existent in Atman as it were." (Upad. I,18,45).

Then Sengaku Mayeda says:
"Thus transmigratory existence is said to be nothing but the absence of
discriminating knowledge (aviveka) concerning Atman and non-Atman, or to
be nothing but nescience (avidyA) due to the absence of discriminating
knowledge."

        This clears things up a bit. It is now clear that there is nothing
essentially called the "soul" which transmigrates. The Atman is not the
"soul" in a person.

        To my beginner's mind, it seems as if the problem in advaita is
similar to the one in buddhism, where I read that a specific causal chain
leading to rebirth after death after birth, is called a transmigratory
chain, without there being anything called the soul (or something like
that.), which again ends when the intuitive knowledge of "SunyatA" is
gained. (i.e.  cessation of "avidyA"). As I seem to understand it, finally
both buddhism and advaita deny the existence of a "soul" that
transmigrates. Am I right in having a preliminary understanding that
Buddhism and Advaita are very similar except that one (advaita) talks in a
positive vein by affirming the existence of Atman/Brahman and the other
(buddhism) in a negative vein by either denying the same, or refusing to
speaking about it?

Regards,
Ganesh.