[QUOTE=Li’l Pluck]
I think I understand you (up to a point), but it strikes me as odd that someone walking down the street who simply says, “Hey”–just that, not asking for money or anything else–could constitute an intrusion.
And yeah, many of us are in our own little worlds, especially during our daily commutes (between the pressures of school and work, I do that, too), but I guess my thing is this: Is whatever you’re (second person “you”) multi-tasking really so deep that you can’t, when meeting someone else’s gaze (as opposed to just not paying attention to other people), just at least nod a friendly “hey”?
And why am I now hearing Jim Croce, may he rest in peace, singing “New York’s Not My Home”? 
[/QUOTE]
I grew up in NYC, and left for college at the College of William & Mary, which for the uninformed among us in in the Southern part of Virginia.
There was definitely a huge culture shock – in the first year I would often feel… well, kind of scared by total strangers speaking to me on the street in the friendly “hey” way. People who speak to you on the street in NYC generally want something from you. I felt like somehow EVERYONE viewed me as a target.
I don’t know how to put it except that New Yorkers have so very little personal space – sometimes sacrificing all of it just to get by as in a daily commute on a jampacked subway, living with roommates, etc – that I think headspace becomes a precious commodity. Entering the headspace, the only private protected real estate most people enjoy on the island of Manhattan, without a reasonably good reason is an intrusion. If you have a reasonably good reason I truly believe New Yorkers are some of the helpfullest people on Earth.
And if you said “hey” to every person you saw coming the opposite way, there’d be no space left for your own thoughts, it would just be a huge long stream of “heyheyheyheyheyhey.” Because you’re never NOT seeing a flood of people in the other direction, faster than you could even address them.
Edited to add - there are lovely parks outside of Manhattan even! all over NYC. One of the most famous is Prospect Park in Brooklyn. The nearby Brooklyn Botanic Gardens are also very well known and beautiful.