I know, two weeks isn't long. We did Chicago, New York, back to Chicago, which is not all of America or even typical of the country. But you do notice things. We arrived in the evening, in the snow. For the briefest of moments it seemed like that was going to be pretty cool.
We've been shovelled off the 19-hour flight into O'Hare, once the largest airport in the world, into an arrivals concourse that cannot be right. Great drifts of people, everything closed, little signage, everyone looking lost. You think O'Hare will be a well-oiled machine but it's just the place where they dump you.
It's Sunday night and outside it's snowing and nearly dark. The ride-share cars arrive in streams, four, five lanes of them, while the people wait, strung along the front of the terminal, peering hopelessly into the swirling gloom. Cars in Chicago don't have to display a front licence plate and many don't.
There's a man with a whistle, going at it hysterically, but he isn't keeping order. The cars just drift along and you, and they, take your chances. It's like they've never had to cope with crowds before. Never expected there would be such a thing as snow.
Our car doesn't come. Each time I call, the service is friendly, apologetic and insistent the car is there already. After half an hour they switch to "three minutes away", which will become our magic number, full of hope and signifying nothing. I get through to the driver and he tells me the same thing, but it turns out he doesn't even know where to go.
After 90 minutes, they arrange another car. The hire service texts later to hope everything went well and asks me to rate them. Should have caught the train. Should have come to a first-world country.
Friendness. It's a national characteristic. Once upon a time New York was a dangerous city and friendliness was a signal: Everyone on the sidewalk, in the 7-11, making it clear they're not going to hurt you. That fear is gone now but the friendliness persists. People seem proud of it: This is me, this is us; despite how everything's gone so wrong, we can still be good people.
The friendliness is not always useless and lying. Every single bus driver we met in both Chicago and New York was helpful, concerned, naturally ready to brighten their passengers' day as we were invited to brighten theirs. They were like care workers.
For all Americans, everything has gone wrong. If you're appalled by Trump, it's obvious: Your bustling, high-minded democracy has become a sinister parody of itself and made you the laughing stock of the world. If you're for Trump, you're outraged every day at the elites who won't accept it and want to take you down.
If you don't care, your world has been filled with the bile and brutality of everyone who does. They are the only news. They are the only reality.
Following the news is like being in two parallel universes. On CNN and the main broadcast channels, the country is in the grip of a wretched crisis and there's much brow-furrowed analysis of how close Trump is to impeachment.
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Over on Fox, they carry on as if even the thought of crisis, let alone impeachment, hasn't occurred to them. Their news is all about the strong economy, falling unemployment and crowds who love their President.
It's not just the analysis that's different – even the topics don't match up. In a Venn diagram of what CNN and Fox cover, the two circles would barely overlap. Within each circle, they acknowledge the other in order to sneer and fume, and mainly to laugh.
You can see it's stressful. Dom Lemon, an African-American journalist on CNN, completely lost it one night when a white woman he was interviewing told him his experience of racism wasn't really racism. The repercussions of that played out over several more nights.
The anti-Trump media believe it surely can't last, but why not? Support for the President has barely moved since the election. And come 2020, when he sets out to destroy his opponent, does anyone think there's a line he won't cross? Well, he won't shoot them in the face. Maybe that's the line.
The theatres are in the thick of the action. Network has opened on Broadway – not a revival but a brand-new stage version of the 1970s movie about a broadcaster called Howard Beale who goes troppo on live TV. Breaking Bad's Brian Cranston has the role, and may be the reason most people go to see it, and he's very good. As for the show itself, it's prescient, disturbing, very energetic. Madcap pacing as metaphor for life as we know it.
There's a famous line: "I'm mad as hell and I'm not going to take it any more!" Beale encourages his viewers to go to their windows and yell it into the street, setting off a spontaneous uprising of angry citizens.
Back in 1976, two years after the Watergate scandal forced Richard Nixon from office and one year after the Vietnam War ended, that seemed like a left-wing cry of rage. Now, it's the cry of the Trumpian base.
The medium is the message? Beale learns that's wrong. Television wasn't the problem then any more than social media is now. The medium is a means to an end. The power is in ideas.
It's so Trumpian. They don't have to be true ideas. They shouldn't be, because ideas based on fear are not susceptible to rational objection. They resonate too deeply.
Executives swirl around Beale, trying to stop him, steer him, seduce him. They're the liberal elite and he thinks they're his enemy – until the chairman of the board appears to him on high, like God.
Howard, says the chairman god, it's the corporate shareholders, we are the ones you should be frightened of. In the end, they have him shot on live TV.
Howard Beale has become an avatar for the Trump base. Furious at the machinations of the elite, manoeuvred by forces more powerful than he can imagine, impotent except in his capacity for self harm and, ultimately, dispensable.
Broadway is such a great window on to America. Frozen was playing! And the biggest show in town was Hamilton, the story of Alexander Hamilton and the rest of the Founding Fathers, brilliantly stood on its head by the device of casting non-white actors.
We couldn't get tickets for love or money in New York so we saw it in Chicago, where the theatre was packed with people who started cheering the moment the curtain came up. Hamilton was written before Trump ascended but now has a special political ferocity.
"Immigrants," says one of the characters, channelling the show's creator Lin-Manuel Miranda, "we get the job done." Big cheer.
The climactic song is "Who lives, who dies, who tells your story", and in this play full of men it's sung by a woman. History has been written by the victors but other people are writing it now.
We know now that American democracy is rubbish in every formal sense, but the life of it still seethes in the culture. Vice-President Mike Pence came to see Hamilton, which was brave, and even claimed to like it, but that was surely a lie. The show burns to the ground everything he represents.
Late at night in Times Square, there were acrobats with big elaborate routines, living statues wherever you looked, great drifts of people. It was frantic, everyone was antsy, even the statues looked hyped. A barker for a comedy show had a good line: "Who likes comedy and black people?"
For a few years there, everyone in Manhattan said you have to walk the High Line. Now, you have to think twice about it.
This disused 3.7km stretch of elevated railway has been converted to a walkway with great planting and art, and even on a cold day in April it was packed. Come summer, the whole thing gets like a crowded railway carriage, the press of bodies keeping you upright even if you pass out. Bloody tourists.
As if oblivious to this ruination of a once-wonderful idea, the city has supercharged the commerce at both ends. To the north, the brand new towers of Hudson Yards, with a vast new shopping mall and thousands of residents and office workers above. To the south, Chelsea Market and the bars and boutiques of the meatpacking district, the sidewalks all around converted to pedestrian plazas.
The American way. Invent a good thing and then just keep going until you have too much of it.
Chicago has a more fun option - the 606, or Bloomingdale Trail, 4.3km of shared pathway busy with locals out for their constitutionals, and hardly any tourists at all. Bike hire is all you need.
In Chicago the thing is to do an architectural tour on the Chicago River, which winds through the central city. They're proud of the buildings, and rightly so, but it's hard to be on that river because it's horrible.
The city grew by pumping its waste into it, while the skyscrapers turned their backs. Even when the threat of typhoid and cholera became too great, they didn't clean it up. Instead, in 1900 they reversed the flow, channelling the waste away from the lake, which holds their drinking water plants, to the Mississippi, where it could become someone else's problem. A great American solution.
This century, the city leaders looked at the beautiful River Walk through San Antonio in Texas and said to themselves, why didn't we think of that? Now, if you're building or renovating on the river's edge you must provide a public walkway; slowly, awkwardly, they're cleaning up the river.
Ludwig Mies van der Rohe defined the mid-century style with his black marble and glass monoliths. Today, Studio Gang, led by architect Jeanne Gang, has produced the best response. Sleek, beautiful, sometimes the colour of water, her skyscrapers ripple and bulge with a sinuous, off-kilter energy, curving far into the sky.
The new central library is a different kind of response: A fortress of rich red adobe, parapets on top, like some warlord's stronghold in the Nevada desert. Yes, it is a library. It even won a competition.
There is also, naturally, a Trump Tower, commanding a corner spot on the river, with more angles and panes of reflective glass than you might think strictly necessary, but actually it looks pretty good. A vast building, with no visible gold trim.
The sprawling, formal gardens along the foreshore ignore them all. They date from the 1920s but were designed in an 19th-century Parisian style, complete with heroic neo-classical statues, as if Napoleon had annexed the midwest. America does confidence so well.
It's doing discovery now, too. The Birmingham Project is a series of dual photographic portraits by Dawoud Bey, showing in a gallery just near that Napoleonic park, commemorating the lives of the black children killed when white supremacists bombed a Baptist church in Birmingham, Alabama, in 1963.
Each photo shows a child exactly the age of one of the victims, with an adult in their sixties, the age they would be now. They stare at you, the adults with all that lived experience, the children less certain, some of them angry.
The Birmingham Project was first shown in 2013, before the rise of Trump and Black Lives Matter. It would have been powerful then; it's supercharged now.
Every street corner in downtown Chicago has an elderly African-American, a veteran, begging on it. That's less common in New York. Downtown Manhattan has the 9/11 Memorial, two enormous rectangular holes in the ground, on the sites of the World Trade Centre buildings. In each, water streams down the walls into a shallow lake and then falls again into another rectangular hole.
The reverse of a monument. We were there in the rain and even then the crowd was thick all round the edges, peering over the low walls, which carry the names of all 2977 people who died, peering into the dark, seemingly bottomless hole.
You know it will affect you but you're not prepared for how much. People finger the names. Stare down at the disappearing water, endless, flowing on all sides. Those giant rectangles speak of elegance and order, also humility. The water flows over all, infinite. Humanity brought close to something far bigger.
Someone in front of us as we walked away dropped a tissue and it lay there, crumpled, white, an affront to the place. I picked it up and walked around with it forever: there are no rubbish bins anywhere near Ground Zero.
The Middle East was everywhere. At the Metropolitan Museum, an exhibition called The World Between Empires showcased a tiny alabaster statue of a naked goddess, with gold jewellery and rubies for eyes, from Babylon around the time of Christ. Sometimes, the power and beauty of a culture stops you dead.
There were several steles, or grave markers, from Petra in what is now Jordan. Faces of the gods, except they were almost blank: the concept of not looking directly at the mystical, rendered in stone.
PS1, formerly Public School No 1 in Long Island City, is an art gallery and outpost of MoMA, the Metropolitan Museum of Modern Art. It was showing Works and Days, room upon room of small sculptures by the Syrian artist Simone Fattal. Barely human forms, the clay squeezed roughly into upright shapes, some just a pair of legs, or a crude horse, or a house with its roof stove in.
Life reduced by war to primordial anguish. And reinforced by ancient texts of the misbegotten adventuring of scoundrel kings: Homer's Odyssey, the Mesopotamian Epic of Gigamesh. I've hardly ever seen art so unsettling, so eloquent in its silent record of horror. It felt like a betrayal to leave.
The Metropolitan Opera, meanwhile, has revived its 2012 production of Rigoletto, set in Las Vegas but very conventionally told. Rigoletto is a story of how bullies and bloated egos ruin everything good, but three years after the ascension of Trump, the Vegas setting, even with a real stripper, felt anaemic. They missed a trick there.
Out on the grand foyer staircase during the break, Napoleon and his attendants moved among the crowds, looking for all the world like young men from expensive schools doing dressups.
The next day, a Saturday, Madison Ave filled up with Sikhs, a sea of glowing orange turbans. It was Sikh Day, when everyone comes out for a Nagar Keertan or "meditation celebration", their ceremonial swords and daggers flashing, their drums banged for hours.
New York, where there is always someone making a noise.
We went for lunch at Manhatta, the new restaurant of star chef Danny Mayer, on the 60th floor of a block near Ground Zero. I had a burger.
Mayer is famous for his burgers. He does them cheap for Mets fans at Citi Field in Queens. He's got mid-range outfits churning them out, and now the seriously upscale Manhatta. I'll give him this, it was probably the best burger I've eaten.
It was raining the day we went and you couldn't see a thing out the windows. Just an empty grey sky. Should ask for our money back?
We sat down, the mist cleared a little, and there, right outside the window I was facing, the glittering, pyramidal art deco top of a skyscraper appeared. Hovering in the sky, metres away, mist below and mist all around.
And then it faded away. And another appeared, off to the left, and another, another, and suddenly you're looking down on that beautiful landscape of spires and rooftop gardens and water tanks, all of them round, on stilt legs with a conical hat. And then it's gone again.
Through the lunch the mist came and went, and so did the Hudson and East rivers, the Brooklyn bridge, the skyscrapers stretching far away to Harlem and the Bronx, the Jersey Shore, the ships, the smokestacks, the steel and glass, and Wall St filled with scurrying insects, right there under our feet, far, far below.
Tucked away at the top of the Field Museum in Chicago there's a Ngati Porou wharenui, in a large empty room with a kindly American woman who explains its provenance.
Destitute iwi sold it to a rapacious American collector, and later, when it needed repair, fixed it up too. It has picnic tables inside, that was a first. And no photos, and all the tukutuku is the same. It's real and not real. The guide did not seem aware that anything might be wrong. She, the Field Museum, America, were doing the world a service.
The hotel restaurant sold Chicago food. A mountain of fatty meat and cheese, vegetables buried in it, potatoes, fried bread. They seemed quite proud of this. You can get that meal anywhere in the city, any time of the day. Upmarket, downmarket, it's always the same. They sell it at the health-food breakfast bar.
I honestly do love America. The toe-tapping, hip-grinding, soul-melting culture. The intellectual exuberance, all the good their belief in opportunity brings.
But something's gone wrong. It's fanciful to think this, but easy too: You see it in so many faces. Despite the friendliness it's as if they've been afflicted, like some confusing experience has harmed them inside. For some, it's always been like this. For many more, it's new. They know it wasn't like this before.
We left, from the same Chicago airport we arrived in, during more snow. The concourse was filled with a sea of people, all hoping to get through a single set of doors. Time passed, so much time, and when you eventually got close you could see there was a zigzag queue, but many people were just moving straight past, leaving everyone else stuck for even longer.
The officials were friendly, of course they were, but no one seemed to think there might be a way to do it better.
It was as if nobody from the airport had ever been anywhere else to see how they do it, because what could the rest of the world teach America? It was like it hadn't occurred to them that the weather might cause them any problems at all.