"A hundred and twenty-three years to Alpha Centauri - five or six generations, more than a long lifetime...
"Enrico Yamatsu, Starward!"
-Poul Anderson, Cold Victory (New York, 1982), p. 32.
I was told at school that a generation was about twenty years - long enough for someone to be born, to grow up and to start having children. Someone else said twenty five years. The fictional Yamatsu effectively says twenty or twenty five years. That is a lot of generations to be born inside a spaceship. But, of course, it is not five or six generations living and dying inside the spaceship. Yamatsu says that one hundred and twenty three years (just under a century and a quarter) is longer than a long lifetime - but it is not very much longer.
Now, in 2016, I remember my maternal grandmother, born in the late nineteenth century, and know children who should live into the twenty second century. Thus, three overlapping lifespans cover more than two hundred years. Therefore, some people who are born and die inside the Pioneer should know many who were born on Earth and many others who will die on a planet of Alpha Centauri. It is strange to think of those intermediate lifespans spent on neither planet.
Robert Heinlein introduced the idea of a generation ship and, I think, has conditioned sf readers to imagine many generations both living and dying inside such a ship. However, the crew of his Vanguard had mutinied and killed their officers. Subsequent generations lost all scientific knowledge and came to regard their enclosed artificial environment as the entire "Universe." Many never went to the front of the large, spinning vessel to look out at the stars. They knew only cabins and corridors and, of course, devised a mythology to account for this environment. No one knows how long they drifted through space. By contrast with this, a generation ship that remains on course should be expected to reach its nearby stellar destination in a few decades and therefore in a manageable number of generations. Anderson's psychotechnicians socially engineer the crew to avoid the fate of the Vanguard.