Updated 7:20 a.m. |

Good morning on this sticky Monday.

Times Square, that hourglass-shaped patch of our metropolis, has lived many lives: as a lackluster commercial district, a swanky cultural hub, a bustling agora, a sanctuary of sleaze, a core of crime, and a billion-watt neon circus.

Its iconography is just as varied, from the jubilation of Alfred Eisenstaedt’s V-J Day kiss to the bleak opening sequence of “Taxi Driver.”

It wasn’t even always called Times Square. That moniker came in 1904, when a certain newspaper moved into the neighborhood.

“Its meanings have changed,” the author James Traub once wrote of Times Square, “but the sense of its centrality has not.”

On Times Square’s busiest days, more than 460,000 pedestrians pass through the area sometimes called “the heart of the world.”

Still, the square may transform again: Mayor Bill de Blasio is considering digging up its pedestrian plazas and banning its topless models, who are known as desnudas.

The Times’s critic Michael Kimmelman described the mayor’s campaign as “prudish grandstanding” and a “harebrained scheme.”

It might take some political acrobatics from Mr. de Blasio on this one. Perhaps he could take a cue from Harry Houdini, who once unbound himself from a straitjacket while dangling from a crane above Times Square.

What do you make of the potential changes to Times Square? Let us know in the comments.

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Updated 11:00 a.m.

Good morning on this mucky Friday.

New Yorkers aren’t shy about much, least of all their dance moves.

There are lots of hideous dancers (hello, Elaine Benes) and people who would do us a favor by not dancing (are you listening, mom and dad?), but the city is otherwise alive with endless forms of creative movement.

From sidewalks to subway cars, you never know where you might happen upon the next impromptu stage.

This weekend is as good a time as any to join the light-footed masses.

You could learn to tap, salsa, or pirouette at classes offered across the city.

Or perhaps you could draw inspiration from New York-based dance movies like “Fame,” “West Side Story,” and “Saturday Night Fever.”

During one scene in “Fame,” hordes of revelers spontaneously break into dance in the middle of Times Square, flooding the street and leaping on top of cars.

If you’re not feeling quite so limber, you can leave it to the experts.

Here are some free dance shows worth checking out this weekend:

• The Battery Dance Festival comes to an end on Friday with a night of international dance.

• A weeklong residency showcases its work in Long Island City, at the Socrates Sculpture Park on Saturday.

• Dancing in the Streets presents two site-specific performances at parks in the Bronx, on Friday and Sunday.

As the writer Samuel Beckett is known to have said, “Dance first. Think later.”

Perhaps heeding those words, one pair broke it down this week at NewYork-Presbyterian/Allen hospital’s second annual Senior Prom. The ambitious duo makes an appearance in our Week in Pictures Slideshow.

What are you favorite spots for dancing in the city? Tell us in the comments.

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Updated 10:00 a.m.

Good morning on this murky Thursday.

Let other parks have their carousels of dancing horses, galloping around in an endless circle.

Today, the Battery gives us a new menagerie: The SeaGlass Carousel opens to the public.

Inside a glass pavilion, not unlike a fish tank, are 30 fiberglass fish, ranging in size but every one large enough to hold both an adult and a small child. They whirl and spin in a panoply of riotous color, all accompanied by music.

The experience sounds a little overwhelming.

David W. Dunlap, a columnist and critic for The Times, spent some time riding the carousel.

He liked it.

“Just to be sure, I tried SeaGlass a half-dozen times one evening last week before I was finally talked off the ride by adult supervisors,” he writes.

But the carousel’s path to the Battery was not exactly straightforward.

The idea for it arose after the Sept. 11 attacks, which darkened and devastated the city.

The carousel seemed a joyful way to resurrect a neighborhood in chaos, but it was stymied by Hurricane Sandy.

Almost three years later, it’s here.

So try taking a ride under the sea … kind of.

The carousel will operate from 1 p.m. to midnight today, its opening day. Thereafter it will be open daily from 10 a.m. to 10 p.m., every month except January and February. Rides cost $5.

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Updated 6:27 a.m.

Good morning on this mottled Wednesday.

Things have been a little shaky between Mayor Bill de Blasio and the media.

Over the weekend, The Times wrote about the challenges of the mayor’s second year in office, in which he appeared defensive about his record. On Tuesday, he was all smiles.

When asked about the fairness of the news media’s coverage of his administration, the mayor brushed it off — he had nothing to say, and moved on to the next question.

It was a different tone from Saturday.

He had begun the interview with The Times over the weekend by saying: “Let’s be straightforward here: You’re going to write a piece about how it’s been a bad summer, and you’re not going to talk about our achievements.”

Some of the mayor’s allies have suggested that his administration isn’t doing a good job touting his accomplishments.

But at least one constituent didn’t see it that way.

In a phone call to the Brian Lehrer show on WNYC, a man who identified himself as “Louis in the Village” took the mayor’s side.

“I don’t want a mayor that spends all his time bragging and taking victory laps,” Louis in the Village said.

His voice sounded quite familiar to some.

“Consensus in the control room seems to be that Louis from the Village, who just called to defend the mayor and knock the media, might be a certain Louis from the Village who people have heard of,” Brian Lehrer said moments later. “We will just leave it at that.”

We will, too.

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Updated 9:39 a.m. Good morning on this still-hot Tuesday.

August in Brooklyn: It’s not Oklahoma, but the corn is almost as high as an elephant’s eye.

In at least one tree pit we saw on Sixth Avenue in Park Slope, there is a very, very small farm’s worth of corn.

Corn becomes harvest-ready in July, but it tastes even better in August, when it’s at its sweetest and juiciest.

This is a good week to eat corn — it’s Corn Week at the Union Square Greenmarket, which will feature recipes to make the best of the harvest.

We don’t imagine that their selection will be hyperlocal, as corn doesn’t seem to be too common in city gardens. For one thing, it takes up a lot of space.

Last year, Arthur Bovino, the executive editor of The Daily Meal and a former employee at The Times, tried to grow corn in his East Village garden.

His plants got off to a good start — “They were pretty plants to see waving around in front of the Con Ed plant from our roof” — but despite careful tending, he said, “the corn itself never really progressed beyond those initial stages” and he didn’t plant any this year.

He said he may try again next year.

Or, like Ralph Waldo Emerson, he could just rejoice in the natural splendor: “I expand and live in the warm day like corn and melons,” he wrote in “Nature.”

Do you grow corn in your city garden, or have you surreptitiously planted a few kernels in a city tree pit? What does it taste like? Let us know in comments, on our Facebook page, or on Twitter using @nytmetro.

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Updated 10:01 a.m.

Good morning on this sticky Monday.

Presumably, one of the perks of being president would be a good excuse to get an exemption from jury duty.

But it’s not so easy for candidates. And at 9:07 a.m., Donald J. Trump emerged from a stretch limousine in front of the civil State Supreme Court in Lower Manhattan.

He was greeted, of course by a media throng and asked if he would try to get his jury service postponed.

“No, I’ve got to do it,” he said. “We’ll see what happens.”

James C. McKinley Jr., who covers courts for The New York Times, reports that the candidate proceeded to the fourth-floor Norman Goodman Jury Assembly Room, sat through a motivational video from the state’s chief judge and a long instructional speech from a clerk, and filled out a questionnaire.

Just like everyone else.

“Trump seemed bored as the clerk droned on,” Mr. McKinley writes.

Just like everyone else.

Mr. McKinley said it was unlikely that Mr. Trump would be selected for a jury — in the past, celebrities, including Madonna, have been dismissed because they can be a distraction to the other jurors.

But anything is possible.

Mr. Trump was fined $250 this year for failing to show up a few times for jury duty over the last several years.

(A spokesman for Mr. Trump said that the summonses had been sent to the wrong address and that the fine had been waived.)

Mr. Trump, who is leading in the polls of Republican candidates for president, has been very busy lately, but he’s making time for the civic duty.

On Saturday, Mr. Trump arrived at the Iowa State Fair in a helicopter. Amid the famous butter sculpture and fried food, he made his way through the crowd, wearing a hat with his slogan, “Make America Great Again.”

His campaign also offered free helicopter rides to children at the fair.

And he ate a pork chop.

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Updated, 8:32 a.m.

Good morning on this warmer Friday.

New York City is not widely known for its stargazing.

From the observation deck of the Empire State Building, you’d see less than one percent of the celestial objects that someone in Galileo’s time would have been able to observe without a telescope.

But one cosmic show broke through the glow of light and air pollution this week: the Perseid meteor shower, made up of burning specks of debris from the Swift-Tuttle Comet.

(“Crumbs of matter left behind by the comet scream into the atmosphere and die a breathtaking death,” a Times reporter, Dennis Overbye, wrote of such showers in 2002.)

A crowd of stargazers at Inwood Hill Park appears in our Week in Pictures slideshow.

The meteor shower’s peak has passed, but there will still be a few stray shooting stars tonight. Here are some other chances to study the night sky:

• A sky-viewing party on the Great Lawn of Central Park, starting at 8 p.m. tonight. [Free]

• The Amateur Astronomers Association is observing Saturn from Lincoln Center, part of the group’s schedule of viewings across the city. They also bring their telescopes to the High Line for visitors to enjoy every Tuesday night through October. [Free]

• The astronomy department at Columbia University holds one of its occasional telescope observations tonight, preceded by the Hubble movie in IMAX. [Free]

• And tomorrow urban park rangers will be at Fort Greene Park to talk about the history and folklore of the solar system, one of many astronomy-themed events at city parks.

• If you’re up for exploring, you might visit darker corners of the city, like Floyd Bennett Field in Brooklyn or Great Kills Park on the southeastern shore of Staten Island.

But even when we’re not seeing much in the sky, one of the tristate region’s most famous exports to space, the NASA astronaut Scott J. Kelly, is watching us.

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Updated 9:10 a.m.
Good morning on this positively pleasant Thursday.

“Hamilton” opened on Broadway last week to rave reviews.

“Yes, it really is that good,” was how The Times’s theater critic, Ben Brantley, began his take on the musical.

The show tells the story of Alexander Hamilton and the founding of the United States.

But let’s not forget that Mr. Hamilton spent most of his life in New York.

And he arrived the same way that millions of New Yorkers did: as an immigrant. (He was from the Caribbean.)

In honor of his many contributions to our country and of his Broadway debut, we did a tour of the more particularly Hamiltonian places in and around the city.

• He attended King’s College, now Columbia University, and a statue of him stands outside Hamilton Hall, one of the school’s academic buildings, in Morningside Heights.

• He frequented Fraunces Tavern in Lower Manhattan, where George Washington bade farewell to the Continental Army at the end of the Revolutionary War.

• As Washington’s aide de camp, he spent time at the Morris-Jumel Mansion in Upper Harlem, Washington’s residence and headquarters in New York.

• And he ended his days at his country estate, the Hamilton Grange, in Upper Manhattan.

• He and his wife, Eliza, are buried in the graveyard of Trinity Church in Lower Manhattan.

• He helped found the city of Paterson, N.J., whose Great Falls would play a role in powering a fledgling United States toward economic independence.

• And he wrote this, which isn’t about New York, but is still pretty cool:

“The sacred rights of mankind are not to be rummaged for among old parchments or musty records.

“They are written, as with a sunbeam, in the whole volume of human nature, by the hand of the divinity itself; and can never be erased or obscured by mortal power.”

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Updated 9:22 a.m.
Good morning on this drier Wednesday.

Even though New York and New Jersey don’t always get along, there’s a lot that connects us.

Starting with our tunnels.

Emma G. Fitzsimmons, The Times’s transportation reporter, writes that officials from both states agree that new rail tunnels are desperately needed (especially in light of the snarling delays recently) but that they have clashed over funding.

Senator Chuck Schumer has an idea: to create a nonprofit corporation to plan and fund the tunnels, known as the Gateway project.

Apart from tunnels, other things keep us together, too.

There’s football: Both the New York Giants and the New York Jets play at MetLife Stadium in the Meadowlands.

And basketball: Even though the (formerly) New Jersey Nets moved to Brooklyn three years ago, they haven’t completely abandoned their previous home yet — operations and practices still take place in East Rutherford, N.J.

Jersey City wants to share bikes, with Citi Bike stations set to open there in September.

And last, but most historic: Signal beacons on New Jersey hilltops, stretching from north to south, were used to alert militias in both states when the British were coming.

Their sites, scattered along the mountainous spine of New Jersey, then became Cold War missile bases, and later, Sept. 11 memorials.

Are there any deep-seated bonds we’re missing? Let us know in the comments, on our Facebook page, or on Twitter at @nytmetro.

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