I’ve seen several attempts to solve this conundrum, but these have mainly focused on radial distance – in other words, just drawing a straight line on a map. This doesn’t take into account the geography of Great Britain. In the real world, roads curve and obstacles like rivers and seas block the route – not even The Proclaimers can walk on water. So I attempted to solve the riddle using mathematical graph theory.
Graph theory is the study of networks made up of points (known in graph theory speak as “vertices”) connected by lines or “edges”. Every time you look up a driving route or search for a train journey, graph theory is what lets your computer calculate all the available routes and work out which one is fastest, shortest or cheapest.
To plan the Proclaimers’ route, I need to create a graph of the road network of Great Britain. Fortunately, Ordnance Survey provides an openly licenced vectorised dataset called Open Roads which I downloaded and converted it into an “adjacency matrix” – effectively, a huge table containing all the road junctions and road ends (the vertices) and the road segments connecting them weighted by length in metres (the “edges”).
The song featured on the Proclaimers second album Sunshine on Leith, the Edinburgh suburb where the band originate from, so it’s a reasonable assumption that they started their walk in the town. The Town Hall, which houses Leith Theatre, seems a likely place to start.
Walking 500 miles
So our task is to traverse every walkable road in Great Britain, without doubling back on ourselves, to find points exactly 500 miles from Leith Town Hall, without using any public transport. Luckily, the OS Open Roads dataset contains the road type attribute so I can filter out motorways and other non-pedestrian roads – after all, they walked, not drove, those 500 miles.
It’s a sizeable graph consisting of 3,078,131 vertices and 7,347,806 edges so represents a significant mathematical challenge, so I used Graphics Processing Unit (GPU) computing. GPUs are the powerful parallel computation engines contained in graphics cards, which are normally used to render 3D graphics for video games but can also be used to perform mathematical calculations.
I used NVIDIA’s new open source accelerated data science platform, RAPIDS, and an NVIDIA Quadro GV100 GPU, to perform the computation which uses a parallel algorithm to solve the Single-Source Shortest Path (SSSP) problem.
I then built the graph, applied SSSP, and found all results exactly 500 miles from Leith Town Hall, which took less than three seconds in RAPIDS.
This yields two possible destinations, both in Cornwall, the first of which is a remote farm 3 miles from Mevagissey which appears an unlikely destination.
The second result is the appropriately named Lusty Glaze Road in Newquay.
Given the urban location, overlooking the beautiful Lusty Glaze Beach, this would appear to be the most likely destination to fall down at her door.
The walk would have taken The Proclaimers through all three constituent countries of Great Britain, passing through central Edinburgh, Peebles, crossing into England north on Longtown, Carlisle, Penrith, Kendal, Lancaster, Preston, Wigan, Warrington, Whitchurch, Shrewsbury, Ludlow, Hereford, entering Wales at Monmouth, Chepstow, crossing the River Severn back into England via the M48 pedestrian bridge, Avonmouth, Bridgewater, Taunton, Tiverton, Okehampton, Bodmin and St Columb Major before finally arriving in Newquay.
Walking 500 more
But perhaps, having walked all that way to Newquay, the woman wasn’t to be found so they had to walk 500 more in order to find her.
This yielded 11 possible destinations across Southern Scotland: Glenwhilly, Kilmarnock, Strathaven, two destinations in the Rutherglen area of Glasgow, Livingston, Haymarket in Edinburgh and four destinations in Leith, including the Victoria Swim Centre, Leith Walk, the Tesco superstore and the Town Hall and theatre where they originally started.
Conclusion
So I would suggest the most likely explanation is that the Proclaimers looked for the woman at Leith Town Hall & Theatre where they were performing, mistakenly thought she’d gone to Newquay, and walked all the way there.
However, it looks like the woman had simply popped round the corner, maybe for a walk, a swim or to shop in Tesco, so they had to walk all the way back to find her.
If you’d like to try this for yourself, I’ve made the Python Notebooks, together with links to the source data, freely available on GitHub.
