Lowland Scotland is networked with motorways – many of them astonishingly empty. Where my mother-in-law lives, in Motherwell, you can get in the jam jar, and within an hour be in Stirling Castle, or Edinburgh Castle, or clambering up the natural fortification of Ben Lomond. So, you can be forgiven for thinking of the entire statelet as a series of arbitrarily interchangeable visitor attractions. We were zooming up to Stirling when I saw the sign for the Falkirk Wheel.

We'd been meaning to go on the Wheel for yonks, but somehow hadn't got round to it. Boom-boom. Now seemed like the right time: the day was as bright as a political theorist who's just solved the West Lothian question, and the views – I felt confident – would be superb. I diverted on to another empty motorway and drove straight into a filthy fogbank. Still, even if the prospects had dimmed there was still the miracle of engineering itself for us to admire.

The Wheel comes complete with its own tourist infrastructure: glass-roofed café-cum-infopoint, mandatory gift shop. Even in the thick mist the 15-metre long arms, shaped like double-headed axes, which bracket the Wheel looked impressive. Why wouldn't they? The Falkirk Wheel is almost unique: a rotating boat lift that links the restored Forth and Clyde Canal with the Union Canal. It lifts canal boats up to the height of an eight-storey building in two enormous caissons full of water, that are so finely balanced the whole thingamajig uses only as much electricity as boiling eight kettles of water; if, that is, you were minded to boil eight kettles of water.

The boys weren't wound up by the Wheel, but I thought it a finely balanced madness to be in a boat, in a lift, going up to an artificial river, that was itself on a bridge. Frankly, you can't get a more psychotic geography than that! I happily coughed up £21.50 for our family ticket, and we boarded the Archimedes, together with a handful of other wheelies: ginger boys and old girls with skin like foundation.

Our guide for this memorable voyage was a jolly soul who looked a little like Hagrid's younger sister. As the Archimedes ground into its caisson she gave us the spiel: the Wheel was, she trumpeted, a triumph of Scottish engineering. An assertion that was somewhat undermined by her next statement: it was designed and built by a Derbyshire firm, Butterley's. Then she continued, explaining the "Celtic" inspiration of double-headed battleaxe template, and the nuts and bolts of the operation.

I confess, I couldn't concentrate on this deluge of information; I was far more taken by the jerky – and yet oddly fluid – sensation of being on a boat in a lift. The visitor centre fell away below us, while beyond it the mist moiled over the pennants of corporate hospitality marquees; Bosch, I think, or possibly tosh. With a bump and a grind our caisson married with the aqueduct, and then we were off along it heading for the Rough Castle Tunnel, which took us below the main Edinburgh-Glasgow rail line and the remains of the Antonine Wall.

In fairness, you couldn't get a denser layering of the ways: I half expected to see the lost eagle of the Ninth Legion being carried out of a hospitality marquee by James Watt. So, why did I have to be so churlish as to enquire of our guide: "How many canal boats, exactly, have used this since it was all opened in 2002?" She had the figure at her tongue-tip: 4,000. I went on with my churlishness, venturing that this seemed like an awful lot of expenditure to make a couple of thousand Scots retirees happy. (Being the man I am, when I got home I checked the figures: it cost £85m for the Wheel, the aqueduct and the tunnel, making it over 20 grand for each trip.)

Oh no, she said, that wasn't the way to look at it all – besides the Wheel was already paid for by European Union and Lottery Fund money. With logic as inertial as the Wheel itself I kept on: that means we paid for it. Ah, but you don't understand, she persisted, the Wheel has brought myriads of tourists and millions of pounds of inward investment to the Falkirk area. Aha! Investment – I maintained – that could just as easily have been boosted if you'd built a giant tomato, or a 35 metre-high Tunnock's Tea Cake.

But by now the other passengers on the Archimedes were rallying to her defence. There was talk of the greening of Scotland, the restoration of canals, the dawn of a new and gentler age – I was hounded off to the car park along with the hell spawn. As we drove on to Stirling, I ruminated: certainly, we might be headed back to the dawn of the Industrial Revolution, but if society underwent that kind of reversal the only double-headed battle axe that would be required was one actual size.