For years, walking into work at the BBC, I would tramp my way across an artwork. World, by the Canadian artist Mark Pimlott, looks like a playful spin on the BBC News title sequence: the laterals and longitudinals of a deconstructed globe, speckled with little place-names, all laid out across the New Broadcasting House plaza. Whereas the names on TV are mainly just capital cities, these names are the ones embedded in our mental world map by memory (Guantanamo, Beslan, Columbine), by history (Lidice, Babi Yar, Alcatraz) and by myth (Troy, Karnak, Shangri-La). Some mornings, fretting about my to-do list, I’d find my sight troubled by one grim pairing in particular: Jonestown, Waco. I’d remember being spooked by reading of the horror at Waco at university, and the shock of the Oklahoma City bombing, two years later to the day. From London, these places seemed as far away as Troy.

Having left the BBC to write a book about American political nightmares, I needed to pay a visit. So I decided to take the train from Oklahoma City, via Dallas, to Austin, to see how much the real Oklahoma and Texas are anything like the version of America we Brits tend to carry around in our heads: a mythic land, supposedly, of incomprehensible extremes.

The flight from New York to Oklahoma City takes over three hours. It’s about 1,300 miles – if you went east that far from London, you might find yourself in Minsk. Along Main Street, boards explain how, in the Land Rush of 1889, the city was suddenly carved out of the plains. And, perhaps something of that remains. What struck me most was how quiet it was. It’s easy to forget, in Manhattan, that you’re on an island; here, even in the centre of the city, you feel as though you’re still amid the landscape. On my way to a café, I had to wait while a freight train clattered past, pulling endless containers marked ‘Prime’ and ‘Walmart’ through the city and back out onto the plains. Waiting for the streetcar on Sheridan Avenue in Bricktown on a Friday morning, I could count the pedestrians on one hand, the cars on the other. There was plenty of space, plenty of time. People were not in too much of a hurry to be friendly. The Oklahoma City National Memorial seemed to emphasise how the 1995 bombing ruptured this, when its explosion shattered the city’s federal office building at 9:02 one April morning. The Field of Empty Chairs, one for each of the 168 people who were killed, is laid out between two rectangular pillars, marked ‘9:01’ and ‘9:03’.

One word often used to evoke all this is ‘heartland’. On the freeway, I passed the Heartland Truck and Sales Service; near my hotel stood an office of Heartland Payment Systems. It’s a resonant term, evoking one of the great mythic ideas of geopolitics. In 1904, and again in the wake of the First World War, the English geographer Sir Halford Mackinder warned that, with the advent of railways, the Eurasian ‘Heartland’ could provide an impregnable resource-rich base for a land power that could come to dominate the world. In 1943, Mackinder traced the emergence of America as another such fortress, foreshadowing the global stand-off of the Cold War. But theory aside, what is a ‘heartland’? What does it look like up close?

From the window of my seat on the ‘Heartland Flyer’, there were times when it was not obviously different from Wiltshire. I wasn’t expecting quite so many trees. We were headed for Fort Worth, Texas, 200 miles south. At one of the few stops, Norman, a young mixed-race couple were saying a relaxed goodbyes to family. When we finally escaped from the vast autoparts yards and identikit estates, the open landscape was far more varied than I expected: rivers, rocky hills, red-brown ploughed fields.

In British minds, rural Oklahoma only really registers through images minted decades ago: the poor, blighted farming families who fled the dustbowl in the Depression, as dramatised in the 1940 movie The Grapes of Wrath, and the upbeat 1943 musical Oklahoma!, recently revived by London’s Young Vic Theatre. Dotted across this landscape, however, are relics of much more recent real-life dramas: little dead oil derricks, left behind by the 1980s oil boom and bust. For a time, $500 cowboy hats and diamond-studded watches, I was told, were very much the thing among the oil workers; then it all fell apart.

Less visible, at least to a Londoner’s eye, was a much bigger calamity that struck the people here soon afterwards. In the late 1970s, farmers were encouraged to borrow big at rock-bottom rates to buy up their neighbours’ farms and consolidate. When the Fed hiked rates a few years later, it flung those farmers into terminal debt crisis. A wave of foreclosures swept across the plains, bringing unbearable shame: losing the family farm, cherished for generations, was far worse than losing a job. Exploring exactly what legacy the Farm Crisis has left today, though, would demand a longer visit.

When we passed into Texas, there was no dramatic moment: I only realised when we reached Gainesville. Some of the grass was yellower now, but the landscape was also busier than Oklahoma’s. A lot of housing hugged the railroad – low beige, with gently sloping grey roofs. There were Walmart lorries, big industrial buildings, and a Discount Boots and Cowboy Outfitter – in the kind of shed you often see from the window of trains in England, but even bigger.

Visually at least, Dallas – another of those resonant names embedded into the plaza at Broadcasting House – is less obviously ‘heartland’ than Oklahoma City. Like New York or London, it’s all-encompassing, with the same clumps of funny-shaped glass-and-steel towers that sprout up in any really big, financialised metropolis. Back on the train and heading for Austin, passing little settlements, laid out on grids, power lines slung between the houses, the design decisions were so visible that I sensed how recently they were superimposed on the landscape. When we stopped in Cleburne, the 1896 Railroad House seemed like an ancient monument.

The closest the train passes to Waco is a tiny place called McGregor. The landscape here looked familiar from documentaries about the siege of the Branch Davidian compound in 1993. For the first time since we left Dallas, the road running alongside the tracks was single lane each way. The occasional solitary house, perched on a bare patch of land; the occasional solitary horse.

No matter how many photos I took, there was no one ‘mythic’ image here. As the hills and fields and trees rolled by, I could sometimes see all the way to the horizon on both sides of the train, I began to feel how unfathomably vast this country is… and it dawned on me that this is really what lies behind the idea of the ‘heartland’, and the notion that these places are somehow mythic. It’s a function of scale. It’s one thing to read about how colossal America is, or glimpse it from the window of a plane; quite another to watch it go by, hour by hour, river by house by farm. As we arrived into Austin at sundown, to more glass-and-steel towers, I realised that this vastness, the distance it puts between people, is the basic American extreme. Yet, at any given point en route, it could hardly be more normal.