Hmm... interesting explanation.
However in Buddhism, strictly speaking we do not speak of
'reincarnation' but more of 'rebirth'. Reason being 'reincarnation'
believes that a soul or a self gets reincarnated... but actually
there is no entity called the 'self' which is undergoing change or
incarnation. So the difference between 'rebirth' and
'reincarnation' is more at the 'technical level'... on the teaching
of Anatta (no-self). Conventionally rebirth & reincarnation
appears to be the same concept.. therefore I may use the term of of
reincarnation or rebirth interchangeably.
When a person attains enlightenment, at least the Arhat level - he
is totally freed from the bondange of samsara and afflictions.
Meaning he no longer gets reborned because of his wholesome or
unwholesome karma, or out of ignorance, attachment, defilements,
etc etc. For a Buddha, he may get 'incarnated' again according to
the Lotus Sutra Chapter 16 - Lifespan of the Tathagatha (see
http://web.mit.edu/stclair/www/Lotus16.html).
This is because of his Great Compassion. He gets 'incarnated' to
save sentient beings like us. So although he appeared to enter
Parinirvana, in reality he did not enter Parinirvana and still
dwells within our trichiliocosm*. He may be teaching in another
planet within our trichiliocosm now and has to wait until the next
Buddha, Maitreya Buddha, takes over.
*updated: sinweiy corrected me
that 'san qian da qian shi jie' should be translated as
'trichiliocosm' and not '3000 world system' as it contains three
kinds of thousands rather 3000 world altogether,
equivalent to 1, 000, 000, 000 small worlds.
