# Discovering Mathematical Tourism

Sometimes you don’t have to go far to find travel inspiration and a change of scenery. In my search of the world for sites of mathematical significance, it turned out I’d been overlooking one practically on my doorstep!

The Union Canal, near Falkirk

In 1822 the Union Canal opened, providing (with the Forth and Clyde Canal) a link between Scotland’s two major cities, Edinburgh and Glasgow. It became known locally as ‘the mathematical river’- by following a natural contour line, the Union Canal maintained a fixed height for its 31 mile course from Falkirk to Edinburgh, removing the need for time-consuming locks. Nor is this its only mathematical claim to fame- in 1834, the scientist John Scott Russell discovered what are now known as soliton waves whilst experimenting on the canal:

“I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat suddenly stopped—not so the mass of water in the channel which it had put in motion; it accumulated round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued its course along the channel apparently without change of form or diminution of speed. I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles an hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height. Its height gradually diminished, and after a chase of one or two miles I lost it in the windings of the channel. Such, in the month of August 1834, was my first chance interview with that singular and beautiful phenomenon which I have called the Wave of Translation.”

As Scott Russell described, such waves are unusual in that they can travel long distances whilst preserving their shape, rather than toppling over or simply flattening out with time. Named in his honour in 1995, The Scott Russell Aqueduct carries the Union Canal over the Edinburgh city bypass, yet the thousands of people who drive underneath it every day have probably never heard of his work- many have probably not even heard of the canal! Yet as well as having added to our understanding of physics, electronics and biology, soliton waves are of great practical importance today for their role in long distance communication with fibre-optics.

It seems that a waterside stroll is often of benefit to the advance of mathematics. Nine years after Scott Russell’s discovery – and several hundred miles away, in Dublin – the Irish mathematician Sir William Rowan Hamilton had a ‘flash of genius’ whilst walking along the Royal Canal. He had realized the equations for the quaternion group and, fearful that he might forget them just as suddenly, promptly carved them into the nearby Broom bridge. The original carving did not survive, but there is now a stone plaque in its place, which has been described as “the least visited tourist attraction in Dublin.”

Despite its clever design, the Union Canal’s importance would be short-lived: within twenty years, trains had overtaken barges as the fastest way to travel. The banks became overgrown and the canal filled with rubbish, and the decline continued after its eventual closure in 1965, as the construction of housing and the M8 motorway caused sections to be cut or filled in. Fortunately, an £85-million project – the millennium link – came to the rescue. The two canals had originally been joined by a series of 11 locks in Falkirk, but as these had not survived, a more spectacular solution was found- the Falkirk Wheel.

This engineering marvel is the world’s only rotating boat lift, capable of transferring boats between the two waterways in minutes – and, thanks to physics, using only as much energy to do so as boiling 8 kettles! The wheel opened in 2002, providing the final piece to restore the link between the two cities, providing ideal opportunities for walking, cycling or boating. I can’t wait to explore it further in the spring!

(First published on the SoSauce travel blog.)