History books and public television documentaries are always trying to tell you all sorts of ''facts'' about New York. That Canal Street used to be a canal. That Bryant Park used to be a reservoir. It's all hokum. I've been to Canal Street, and the only time I ever saw a river flow through it was during the last water-main explosion. Never listen to what people tell you about old New York, because if you didn't witness it, it is not a part of your New York and might as well be Jersey. Although that bit about the Dutch buying Manhattan for 24 bucks might have something to it -- there are and always will be braggarts who ''got in at the right time.''

There are eight million naked cities in this naked city -- they dispute and disagree. The New York City you live in is not my New York City; how could it be? This place multiplies when you're not looking. We move over here, we move over there. Over a lifetime, that adds up to a lot of neighborhoods, the motley construction material of your jerry-built metropolis. Your favorite newsstands, restaurants, movie theaters, subway stations and barbershops are replaced by your next neighborhood's favorites. It gets to be quite a sum. Before you know it, you have your own personal skyline.

Go back to your old haunts in your old neighborhoods and what do you find: they remain and have disappeared. The greasy spoon, the deli, the dry cleaner you scouted out when you first arrived and tried to make those new streets yours: they are gone. But look past the windows of the travel agency that replaced your pizza parlor. Beyond the desks and computers and promo posters for tropical adventures, you can still see Neapolitan slices cooling, the pizza cutter lying next to half a pie, the map of Sicily on the wall. It is all still there, I assure you. The man who just paid for a trip to Jamaica sees none of that, sees his romantic getaway, his family vacation, what this little shop on this little street has granted him. The disappeared pizza parlor is still here because you are here, and when the beauty parlor replaces the travel agency, the gentleman will still have his vacation. And that lady will have her manicure.

You swallow hard when you discover that the old coffee shop is now a chain pharmacy, that the place where you first kissed so-and-so is now a discount electronics retailer, that where you bought this very jacket is now rubble behind a blue plywood fence and a future office building. Damage has been done to your city. You say, ''It happened overnight.'' But of course it didn't. Your pizza parlor, his shoeshine stand, her hat store: when they were here, we neglected them. For all you know, the place closed down moments after the last time you walked out the door. (Ten months ago? Six years? Fifteen? You can't remember, can you?) And there have been five stores in that spot before the travel agency. Five different neighborhoods coming and going between then and now, other people's other cities. Or 15, 25, 100 neighborhoods. Thousands of people pass that storefront every day, each one haunting the streets of his or her own New York, not one of them seeing the same thing.

We can never make proper goodbyes. It was your last ride in a Checker cab, and you had no warning. It was the last time you were going to have Lake Tung Ting shrimp in that entirely suspect Chinese restaurant, and you had no idea. If you had known, perhaps you would have stepped behind the counter and shaken everyone's hand, pulled out the disposable camera and issued posing instructions. But you had no idea. There are unheralded tipping points, a certain number of times that we will unlock the front door of an apartment. At some point you were closer to the last time than you were to the first time, and you didn't even know it. You didn't know that each time you passed the threshold you were saying goodbye.