The duration of a New York Minute varies from person to person and from instance to instance, but should be defined as "The length of time a New Yorker can wait for something without getting impatient or annoyed."
The city is paced like a cinematic device to show the passage of time, a clock in an episode of the Twilight Zone with its hands spinning faster than the eye can follow. Every second is simultaneously precious and unnoticed; there are better things to do than stand still. We are aware in some subconscious way of the passage of time but are conditioned not to count the minutes. We run on instinct. It sounds strange to talk about instinct in a place so far removed from nature, but it's true. Time is as fluid here as it is in greener parts of the world it just moves much, much faster. Take the stalking of a zebra by a lion and speed it up a hundred-fold and you have a fair approximation of what it's like to cross 23rd street at eight in the morning.
A New York Minute isn't a scientific thing, isn't a concrete measure of time in any respect. You can't be somewhere in two New York Minutes - once you're ticked off once, it's all over. It's like a game show, the object being to get from point A to point B without being slowed down by sidewalk congestion, glared at by a hipster or hit up for change or cigarettes by every third person you come across. Don't play this game in Times Square - the table's rigged.
A New York Minute is a deeply psychological truth, a marriage of a person's patience with what's going through their heads. Five (real world) minutes in a deli turns into an amount of time over a New York Minute if the deli guy passes you up to take the order from the suit behind you. Waiting for table service in a restaurant can take as long as it likes provided you've got someone to talk to, you don't need a refill and your waiter looks overwhelmed.
Summer saturdays in Central Park are usually not annoying, therefore enjoyable and therefore less than a New York Minute even if they last til sunset. By contrast, when waiting for traffic to slow up enough to cross a street a New York Minute asymptotically approaches zero.