The proposals include new ways to keep water out of the stations, like raising ventilation grates off the ground and building steps at subway entrances that would require passengers to walk up before descending into stations but would prevent rain from flowing downward.

The authority said it was also establishing an emergency response center, planning to install new valves in drain pipes to keep out stormwater and developing a system of customized e-mail and text message alerts for each subway line so riders would know about problems.

. . .

The deluge dumped as much as 3.4 inches of rain on parts of the city within a few hours and overwhelmed the transit system.

How could they? How dare they?

John Glendinning, 53, a retired laborer from Brooklyn who goes by Whitey, is so agitated he can’t watch the games without losing his sense of civility. “I get too nervous,” he said. “I start throwing things at the wall.”

But, hey, calm down. Collapses happen.

Indeed, where would the city be without its grandiose collapses? The all-out falls from grace or riches or first place, or even a simple upright position, are a familiar and infuriating and perhaps even necessary part of the New York experience. And while collapses smart, they can also be spellbinding.

These breakdowns, of course, aren’t confined to baseball teams that suddenly forget how to hit or pitch, not to mention catch fly balls. They materialize in every aspect of life.

Roads collapse, stores collapse, financial markets collapse, egos collapse. They’ve all happened throughout New York’s history, again and again. During the 1975 fiscal crisis, in fact, the entire city just about collapsed.

Collapses can be aberrant or telling. They can reveal something about larger societal verities. Or they can be vacant of meaning — simply perversely breathtaking to watch.

Part of what makes these sour episodes so intriguing is the velocity at which they can happen. Part of what makes them so frightening is that they can upend our world, even cause us to root for a different team. People and institutions that we thought we knew and trusted to always be there are — poof — gone just like that.

Then again, one of the worthwhile things about collapses is that they allow the often pleasing challenge of recovery, which isn’t always that hard.

. . .

Infrastructure Collapses are pretty common: Walls go, roads go, especially when no one takes care of them. Thus in May 2005, a 75-foot-high retaining wall collapsed onto the Henry Hudson Parkway in Upper Manhattan, burying parked cars in mounds of debris and dirt. The road, at least, held. Not so in 1973, when an 80-foot section of the West Side Highway fell onto West Street near Canal Street.

Years in the making, the nature walk was one of the community benefits that the Newtown Creek Monitoring Committee (NCMC), a group comprised of local residents that meets regularly with the Department of Environmental Protection (DEP), was able to negotiate as part of the massive Newtown Creek Wastewater Treatment Plant expansion and upgrade.

The visit was part of a five-day tour called Creative Nation, during which Prince Frederik — joined by Danish government and business leaders — aims to showcase and promote Danish business in the United States.

The prince, an officer in several branches of the Danish military, listened intently as Commander Ted Gangsei explained that Fort Wadsworth is home to the largest Coast Guard operational command center in the country.

. . .

Prince Frederik’s visit to the Big Apple is drawing major attention in Denmark, with several radio, television and print media representatives shadowing his every move here. Queen Margrethe, Prince Frederik’s mother, is the figurative head of state, and Prince Frederik is first in line for the throne.

“Opportunities to hear, challenge, and learn from controversial speakers of different views are central to the education and training of students for citizenship in a shrinking and dangerous world,” the dean of SIPA, John Coatsworth, said in a statement. Mr. Coastworth invited Mr. Ahmadinejad to kick off a series of lectures and events about Iran, he said in a statement. The president of Columbia University, Lee Bollinger, is scheduled to introduce Mr. Ahmadinejad on Monday to an audience that will be made up exclusively of Columbia students, faculty, and a few invited guests.