Labor Day weekend marks the end of the peak summer moving season—the American Moving and Storage Association estimates some 40% of the 17.1 million families who move each year do so between mid–May and September. Americans move a lot—on average, it's commonly estimated, every five years. But the move my family and I have just finished is our first in more than 30. Thus I expected no small sense of disruption and dislocation—especially in moving from Boston to New York, given, just for starters, the Red Sox–Yankees rivalry. It has turned out, however, that I have experienced something even deeper than that, something that has me thinking about immigration—and what we owe the wave of new immigrants among us.

We tend to focus on what one gains from a move—job opportunity, most often. But the losses are substantial. In the town where I lived for 37 years, neither my wife nor I could walk down the street without meeting someone we knew—and perhaps whose parents or children we knew as well. They were people who'd been at our wedding and seen our kids grow up. That's what being involved in local politics (as I have been) or running a local small business (my wife helped manage a pottery studio) will do. Indeed, one has to wonder what prompts us to give up such a dense web of connection. Such is American life, I suppose, with its combination of ambition, zeal for new experience and willingness to move on in search of new work. But many, I know, would never make such a trade.

I was prepared, at least intellectually, not to recognize people on the street, not to have people wave or call out my name. It turns out, however, that I've lost something more, which I didn't quite expect. One might call it a sixth sense.

In my old neighborhood, I could place the mundane in context. If a student of high–school age was sitting on a bench across from the school early Saturday morning, that meant the drivers' ed class was about to meet (although some days it could mean SATs were to be administered). If cars were parked across from the recreation complex before dawn, that meant the municipal swimming pool had been repaired and had reopened. If the park was ringed by cars on a Wednesday evening, that meant the summer outdoor concert series was once again under way.

In a new community, one has a form of blindness—one sees such things but has no way to make sense of them. More is involved, however, than simply knowing the routines of neighborhood life. For instance, in the town I have left, if a large police bus stood in front of the station on a Saturday, it was likely there would be anti–abortion demonstrations at local clinics—and possibly large–scale arrests that would fill the bus. That, in turn, reflected the fact that the town permitted so many such clinics to do business—and was closely associated with left–liberal politics, in part because it had been home to a pro–choice Democratic Party presidential nominee. The presence of the bus meant, too, that the town might face budget problems, balancing police overtime against snow removal and such.

Similarly, the American flags that would be put up on telephone poles around a park in early June presaged the surprising annual Flag Day carnival—an event that reflected the local cultural divide between affluent liberals and "townies" whose families had lived in the municipality for generations and did not share the former's disdain for patriotism. Flag Day was the concession secured by one local politician, since deceased, in the wake of a failed effort to require the recitation of the Pledge of Allegiance at the annual town meeting.

There were hundreds of other sights and sites—a local funeral home, a memorial marker in a small park, the modernist town hall—that evoked similar cultural, political and historical associations. They are, collectively, a reminder of the depth and value of localism in the U.S.—of residents who run their own schools and other local services and invest themselves seriously in the process. In a new community, it's as if three dimensions have been reduced to one—as if one sees only the surface and is left to speculate on what's beneath.

This, inevitably, must be what immigrants experience, albeit in a far more extreme way. Of course, today there may be some continuities even for immigrants, just as there are for me. My longtime supermarket has a branch near my new home, and my discount card still works. The same could conceivably be true for the immigrant: Wal–Mart is a major retailer in Mexico now. But so much must be so mystifying. Streets named for historical figures, headlines in the newspaper, holiday celebrations. NPR last year broadcast an oral history in which a Chinese immigrant family recalled being terrified by Halloween. One can only wonder how many have no way to understand the significance and deep feelings associated with Thanksgiving or the other occasions associated with the American civil religion, whether the birthday celebrations of Lincoln or Martin Luther King.

Which is why we owe it to those whom we permit to settle here to administer a thoughtful test for citizenship and to make sure local adult education centers, community colleges and latter–day settlement houses offer preparation courses. It's a way to both encourage civic participation and enrich the lives of newcomers. We can help them learn the meaning of what they see—as I must do for myself.

Mr. Husock is vice president of the Manhattan Institute and a contributing editor of its City Journal.