A century in certain ways is like a life, and as the end of a century approaches, people behave toward that century much as someone who is nearing the end of life does toward that life.
Evidence
A century in certain ways is like a life.
As the end of a century approaches, people behave toward that century much as someone who is nearing the end of life does toward that life.
The Blank (so = Conclusion, just as = Analogy)
So just as people in their last years spend much time looking back on the events of their life, people at a century’s end .
Evaluate
We can tell from the structure "Just as X is true, Y is true" that we're trying to complete the backend of an analogy. The premises already laid out that a century is somewhat analogous to a life.
People behave similarly, when it comes to the end of a century or to the end of one's life.
What is that similarity?
Well apparently, at the end of one's life, you .
Goal
So by analogy, at the end of a century, you "spend much time looking back on the events of that century.