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Yes, if one reads the Epics of Ramayan and Mahabharat, they are completely based on people being reborn, either to attain salvation or to extract revenge, which too is part of the discourse in the Bhagvad Gita, that the soul remains for ever, it is just the exterior that changes form.
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Of course, both were totally unrelated, both families not connected, but the thought did come across.. Surely there will be families who go through the pain of parting mixed with the Joy of a new addition. What overrides? The sorrow to the one who has lost a partner, or the Joy of another, having a part of one's self entering into the World, with a life that is just starting.
Death and Life or Life and Death (depends on how one views it), are inevitable facets of the cycle of life. Whether walking or flying, all creatures have to succumb to this, some through nature's planned road, some unprepared and sudden. What does remain key, is what we make out of the Life that we get? How well do we use it?
Do we enjoy the little things that we get in Life, or do we cry on what we did not? Some take it seriously, some as it comes, some take it is a joke, some having no value for it. Some always cursing it, some thankful for it, wanting it, waiting for it to come, wanting to contiune for ever.
Life followed by Death, or Death followed by Life. Sounds like the "A Light at the end of a Tunnel" or Every Dark Cloud has a Silver Lining"....... For me it is Death followed by Life.. How about you?