We could go anywhere, he said, but we had to start somewhere, and of all the streets in New York, he picked the corner of Flushing and Lee, opposite the Marcy Projects, on the border of Bedford-Stuyvesant and Williamsburg. Professor Bill Helmreich had walked nearly 10,000 kilometres to tell the city's story. He could stroll a couple more.
The avenue was crowded with families of Satmar Jews, the most observant of the orthodox: women in wigs and hats minding four, six, eight children each while the men worked. A young white couple passed by, baby slung koala-style. Across the street, black kids played basketball in the housing estate Jay Z rapped his way out of. A Guatemalan woman sold tamales - ''pollo picante, two dollars'' - at the corner.
New York is informally segregated but the city Helmreich has spent his life studying is also one in which cultures compete for space, a place defined and redefined by waves of immigration, tiny invasion after tiny invasion into tide.
As a child growing up in Washington Heights, in the far north of Manhattan, Helmreich and his father used to play a game called Last Stop. They would get on a train, ride it to the end of the line - Rockaway Beach, Jamaica, Astoria or Coney Island - and spend the day wandering. They explored the penultimate neighbourhood, then the one before that, and so on, every weekend for about five years.
''He was a fearless man and he taught me not to be afraid,'' Helmreich said. After his first fight, at the age of seven, his dad told him ''don't come home until you've won''. So young Bill took his cap gun, bashed the other boy over the head ''and that was the end of it''.
The sociology course he teaches at City University of New York includes regular excursions into ''the greatest outdoor museum in the world''. To research his book, The New York Nobody Knows, he walked every block in the five boroughs of Manhattan, Brooklyn, Queens, the Bronx and Staten Island.
According to the Metropolitan Transit Authority, there are 6360 miles (10,323 kilometres) of streets in New York. Helmreich's pedometer registered a little less, but he insists he took no shortcuts, literal or figurative, and has the maps to prove it, scored out to the last dead end.
Bill's attitude is, ''You don't ask. You just do.'' We hadn't walked far when he ducked into a Jewish rest home, smiled at the elders hunched over their Talmuds and headed for the toilet, observing that it is the only room without a scroll of verses from the Torah affixed by the door. ''Do you know what this is?'' asked the Rebbe. ''We know,'' Helmreich answered. ''And we support it.'' He gave a vague, regal wave.
New Yorkers have a reputation for rudeness. Helmreich believes this is undeserved. ''I found that if you approach people in a friendly manner, they will almost always respond in kind,'' he said. ''There's nothing mysterious about it.'' In his ''harmless and relentless'' way, he has mapped the whole city: where to eat Guyanese curried duck, where to dance an authentic polka, where the hot dog stands go at night.
He is particularly fond of tales that begin on ''one of the worst streets in the Bronx'', or somewhere else he was warned not to visit. There was the time a pitbull almost took his hand off, the time he hugged a Hells Angel, the time he rolled up to the Louis Pink housing projects - ''where if they don't like the drug deal they throw you out the window'' - and told the toughs ''I'm so happy you're here because I know that as long as you're watching my car, ain't nothing gonna happen to it''. Nothing did.
We returned to his car and drove into Bedford-Stuyvesant, past rows of terraces with barred windows, to the rapidly gentrifying area around the Brooklyn Brownstone School, where upper middle-class families priced out of Park Slope (home to the new Mayor of New York, Bill de Blasio) can still afford a townhouse.
In 1990, there were 2245 murders in New York, many associated with the crack epidemic that devastated poor African-American communities like Bed-Stuy. Last year, there were just 414 homicides recorded in the whole city. ''When people look at everything that's built up in New York city they think it cannot change, but if you've lived through 50 years of changes up and down you know it can happen again,'' said Helmreich. ''We remember 1975, when President Ford told the city to drop dead.''
Back then, he drove a yellow cab to pay his way through college. Like Martin Scorsese's Taxi Driver, Travis Bickle, he took fares all over. ''Those were dangerous times to be driving a cab. A lot of cabbies got killed,'' he said. ''But I was young, brash, brave, bold, reckless, foolish.'' As he spoke, he accelerated towards a changing traffic light, swerved around a parked truck and dared an oncoming car not to back down.
We were approaching Bushwick, an industrial area at the edge of Williamsburg that has been colonised by artists and students. ''We're gonna take a right. This is going to be the most amazing graffiti you've ever seen, I promise you,'' he said.
On block after block, artists had given their imaginations full rein. There was a horse with the skin stripped back to reveal its sinews, a ninja in lipstick, a good cop and his bad cop shadow, bears hiding in a black and white forest, men-monsters in diving helmets and a tribute to the Brooklyn rapper Notorious B.I.G.
Across the street, a sign outside the Anchored Inn read, ''believe it or not, we do have neighbours''. On a bench outside the Newtown cafe, a lone customer struggled to light his cigarette in the wind.
''This is the vanguard of gentrification,'' Helmreich said. Then he drove me to the subway and headed home, to his house in the suburbs, just outside city limits.