Deepak, you're right - further to this, if you think about what consciousness is and what "the self" is, it's made up of everything we've ever learned, read, heard, experienced, everyone we've ever known etc. Consciousness doesn't reincarnate the way people think, like a single soul again and again, but more each life form imprints itself upon the present and that ripples into the future, and affects everyone around them, and that then affects THEIR consciousness which then affects MORE consciousnesses etc.

There are some quotes that encapsulate it well:

"I am a part of all that I have met" - Ulysses, Tennyson

"The nature of our immortal lives is in the consequences of our words and deeds, which go on pushing themselves throughout all time" - Cloud Atlas

This can explain "reincarnation" as less a religious concept and more a function of how consciousness moves and shifts and ripples throughout time and between lifetimes.