New York has a new folk hero, the slim, bespectacled young man who was reading a newspaper and minding his own business on a Manhattan subway train early last Saturday afternoon when four young men began to hassle him. According to witnesses, the four, armed with sharpened screwdrivers, approached the rider and "asked" him for money. He stood up, calmly drew a silver revolver from his belt and shot all four. Then he helped a few women to their feet, told the conductor he was not a policeman and disappeared into the subway tunnels. Of the four, all are in the hospital, one paralyzed by the gunman's bullet.

The event has provoked an enormous public response. A columnist speculates that the gunman had seen the current Charles Bronson movie "Death Wish." A hot line set up to receive tips about the man with the gun was deluged by thousands of calls supporting him. Mayor Koch has promised an all-out effort to solve the case, but the joke on the streets is that he just wants to find the gunman before the Republicans nominate him for mayor.

It's easy to understand why New Yorkers are responding in this spirit. Their subway, once a fast, efficient, cheap, 24-hour-a-day transit network that other American cities envied, has fallen on hard times. Much of the equipment is old and constantly breaking down. The cars and the stations are filthy, covered with graffiti and littered with trash. There are thousands of fires in the system each year, most started in refuse strewn on the tracks. But the most frightening element is the crime. The four young men involved in Saturday's incident all had arrest records and appeared to be typical of the toughs who roam the trains, even in midday, terrorizing and robbing passengers.

This is the heart of it. The mayor has put more than 3,000 uniformed police officers on the trains and stations, and Gov. Cuomo has counseled calm. "A very firm, even, tough criminal justice system," says the governor, is the way to fight crime. He's right, of course, but such a system is not in place. When people feel they are not adequately protected, the force of the argument that they should not take their defense into their own hands diminishes.

The subway riders of New York have been sorely provoked. An episode of do-it-yourself law enforcement has undeniable implications of spreading violence and chaos, but it reflects directly upon those in official positions, like the mayor and the governor, who have failed to provide the protection that the citizenry has every right to demand.