"In so many ways his family's life feels like a string of accidents, unforeseen, unintended, one incident begetting another"

There are many ways to interpret this quote, and I guess it all comes down to each individual person's view on life.That being said I am looking at this from a complete personal perception. The way I see it is that it is Gogol's final realisation of all the little moments in life that seemed like  complete twists of fate, or even just utterly insignificant, were in fact the string of necessary tragedies, successes, failures, and everything in between that put him where he is in the end. What I guess I'm trying to say is that everyone seems to think that they're working towards each individual goal at a time, but in reality we are slowly moving closer and closer to something much bigger. Let me give you an example; I think one of the main concepts in this novel is the notion of one needing to find their own identity, who they really are. You see that Ashima finally achieves this in chapter twelve, when she states that she is finally representative of her name ("she who has no borders"). But how did she get there? Well it was not easy I can tell you that; this is a woman who left her home, her family, basically everything she has ever known and loved or found comfort in. She left all of that behind to come to America, adopt new customs she did not quite understand, raise children in a difficult time, and eventually she loses her husband. Ashima must have seen it all as absolute calamity at the time. Throughout travelling from Calcutta to Boston I can imagine her dreading that next chapter of her life; having to go through early marriage, pregnancy, the early years of childhood, all without her parents. As her kids grew older and begin to rebel she must have questioned where she went wrong, and how she could undo it. Hearing the news of her husband's death, regret, sadness, and fear would have taken over her mind.  In the end all this makes her stronger, it makes her more independent, she even says to herself that she is no longer afraid. Although it took years, she now knows who she is, and what she is capable of doing and overcoming.
This just goes to show that those moments, or those chapters in your life that seem like they were accidents, as if they were just a string of unforseen and unexpected incidents, whether they were to be celebrated or want to be forgotten are what put you where you are supposed to be.