Assuming the alien generation is as long as ours, this would take about 1200 years. If the galaxy is about 12 billion years old (if may be 15, or more), then that's only 0.00001% of history. Not much. Consider what Earth would be like today if civilization started only 5,000 years earlier than we did. We'd have been to the moon by the time the Egyptians built the Pyramids in our timeline. Imagine where we'd be today.
Of course, this makes zero sense, given that the Galaxy happens to be a few tens of thousand light-years across and that you would have to go 'around' the core to reach to the other side.
Species and civilization might evolve and turn into themselves by using nanotechnology and creating virtual worlds. Why go to another star system if everything you want you can create?
Assuming the alien generation is as long as ours, this would take about 1200 years.
Actually, the author means a generation in the following sense:
We establish a colony on a more-or-less earth-like planet, with perhaps 100 or 1000 people. Very possibly less earth-like. Those people begin to hard-scrabble out a life on that planet. They establish a civilization, multiply, build a population, etc. It could be a thousand years, or thousands of years, before they decide they can spare enough resources to take on the large project of sending out another colonization ship, if they ever do.
So 38 generations of colonists could be a pretty long time.
Sure, but we are where we are. We each get 26,000 days. Some more, some fewer. It might be interesting to live on Alpha Leonis, but then we would wonder if it might be better to live on Sol.
If we inhabited every star in the galaxy, who would have time to read the list of Imperial planets. Just read the list, not even to look at a picture of each one. Could the list be read in a lifetime? Would such a life be considered well-spent, a success?
Don't take this to mean I wouldn't be personally interested in going on an expedition to another star. I would want to bring a few books. During the journey there might even be time to figure out what the heck Husserl was going on about unless the ship needed constant maintenance.