The essential organization of elements within a given frame of time constitutes, authentically, a composition. These “pictures,” in turn, remind us of what we have already experienced in life as well as of those things to which we aspire. Consider that life’s passages are finite in duration, and that if we are fortunate, one day we are single, the next married, the day after a mother, and then, “later in the week,” a savta. Each of the spans through which we pass can and ought to be enjoyed during their season. Living fully means embracing each allocated moment.
As for our dreams, just as we hope to be married and to have children, we likewise hope for all of our children to marry and for them to have their own children. Future-tripping means, in most cases, our previewing the building of generations of family. Occasionally, it means beholding a fourth generation.
A little more than a month ago, my husband and I awaited the arrival, to Israel, of our respective mothers. We were going to greet them, for the first time, as great-grandmothers. Our grandson’s birth constituted an amazing occasion for our family’s matriarchs. Imagine, meriting to marry, meriting to have children, meriting to see those children marry, meriting to see those children have their own children and then, just when life couldn’t get any better, meriting to see those children’s children marry.
To live to witness the existence of grandchildren, let alone to witness their nuptials, is a special height. In His generosity, HaKadosh Baruchu lifted our mothers even higher; He allowed them to experience yet one more level; the introduction to this world of the baby of their babies’ babies. Such a reward, here, on Olam HaZeh, is mind-boggling.
Those people amongst us, who are fairly recent parents, appreciate the miracle that is the presence of life where life didn’t previously exist. It follows that those people amongst us, who have merited seeing their sons and daughters grow, also appreciate the amazing sensation constituted by being able to see them to the chuppah. Finally, those people amongst us, who are fortunate enough to have become grandparents, appreciate the incredible feeling of observing their fruit, itself, bud. I can’t break my mind into enough fractals, though, to contemplate the awe indigenous to becoming a great-grandparenthood. 
The Rebbe, Rabbi M.M., Schneerson, wrote that “[t]his experience, to give life, to watch it grow, to be torn apart by it, to receive pleasure from it and to give life again—for this the soul descended from its ethereal heights…. and when it shall return to there, enveloped in these memories, it will finally know their depth. And with them travel ever higher and higher.” 
I get the gist of what the Rebbe said, I think. We are born into this world and blessed are we whom see generations. Adding to the human chain is the greatest of gifts we can receive.
While I’m not sure how other individuals respond to this sort of heavenly abundance, I know that each and every instance of it in my life has overwhelmed me. For instance, when Missy Older was born, for months, I prayed, I painted, and I wrote my gratitudes. When Older Dude came into this world, I literally danced the joy of having a son in addition to a daughter. When Missy Younger returned home from her second emergency trip to the hospital, in as many weeks of her new life, I morphed into a vessel; I took courses which enabled me to help other young mothers find their passage through their postpartum periods’ trials and tribulations. Finally, when Younger Dude was delivered alive and well, neither state of which, during my very complicated pregnancy with him, had been guaranteed, my husband and I became frum. I rejoiced, albeit differently, at the advent of each of my children.
When, more recently, Missy Older gave birth to her first child, to that precious soul, whom I will henceforth call in public “Baby Baby,” my soul melted. It is one thing to try to reflect on the marvel that is the birth of one’s own a child. It is quiet beyond normal cognitive facility, though, to think of one’s own child’s child. I can not grasp what it would be like to embrace, conceptually, the child of a child’s child.
Try as I might, there is nothing I can do to approximate what my mother and my husband’s mother (and his father) must be feeling. The emotional ebbs and flows that roll within their souls are far beyond my boundaries of contemplation. Simply to become a great-grandparent is to warrant witnessing not only a second or third generation, but a fourth, one, too. Such headiness is past my scope of reflection. IYH, one day I might similarly merit such an experience!