An Irishwoman's Diary
ON October 16th, 1843 – a Monday – the mathematician William Rowan Hamilton was walking along the banks of the Royal Canal at Broombridge with his wife. They were chatting idly about this and that, enjoying the bright autumn morning. Then, without warning, Hamilton experienced what he later described as “an electric current closing in his brain”.
It was what we would call an “aha” moment, in which Hamilton had solved a mathematical problem with which he had been wrestling for years. He had created four-dimensional numbers, or quaternions. And if you’re thinking, uh oh, dusty old maths, think again. Without quaternions we wouldn’t have the classic computer game Tomb Raider, and its up-front heroine Lara Croft – not to mention many of the 3D special effects we now take for granted at the cinema.
Back at the canal bridge, Hamilton did a celebratory special effect of his own; he got out his pocket knife and carved his “aha” formula into the stones. It must have been more of a scratch than a carving, because it vanished a long time ago; Hamilton himself, searching for it in later years, couldn’t track it down. A plaque now marks the spot, however, and every October 16th the great mathematician is commemorated with a walk along the banks of the canal he loved so much. Participants retrace Hamilton’s steps by starting at Dunsink Observatory, then strolling down to meet the Royal Canal at Ashtown train station.
The walk continues along the canal to the commemorative plaque at Broombridge in Cabra. It takes about 45 minutes, and attracts about 200 people from diverse backgrounds – from Transition Year students to Nobel Laureates. The physicists Murray Gell Mann and Steven Weinberg have participated in recent times and in 2005, Hamilton’s great-great-
grandson, Mike O’Regan, also walked the walk. There is, apparently, something of a carnival atmosphere in the area on the day, with a banner on the bridge itself and stalls along the canal walk.
William Rowan Hamilton was born in Dominick Street in Dublin in 1805; his father was a solicitor and his mother came from a coachbuilder’s family in Summerhill. In 1823 he went to Trinity College, Dublin and was appointed professor at Dunsink – effectively the Astronomer Royal of Ireland – while still an undergraduate. He married, had three children, and lived at Dunsink Observatory for the rest of his life.
This quiet man was also a published poet who was friendly with the poet Samuel Taylor Coleridge and intrigued by the philosophy of Emmanuel Kant. While on a tour of engineering sites in England in 1827 Hamilton met Wordsworth and invited the great man – then 57 – to come and visit Dunsink, which he duly did. There is more than a hint of Wordsworth’s influence, not just in Hamilton’s poetry, but in his approach to mathematics as well. “Mathematics,” he once wrote, “is an aesthetic creation, akin to poetry, with its own mysteries and moments of profound revelation.” It’s a position with which Fiacre Ó Cairbre, senior lecturer in mathematics at NUI, Maynooth and the current organiser of the annual Hamilton walk, is in agreement. Mathematics, he says, is all about ideas. He offers an analogy with music. “In music,” he says, “the sheet of notes on the page is important – but it’s nowhere near as interesting, powerful or beautiful as the music. In maths, symbols are important and useful – but they’re nowhere near as interesting, powerful or beautiful as the ideas they represent. If you get too hung up on the symbols on the page, you may miss the ideas. But once you look for the ideas behind the symbols you may have a whole new perception of mathematics.
“Hamilton’s quaternions go against the rule in arithmetic that, if you multiply three times two, it’s the same as two times three. His new system of numbers didn’t have that property. So if you multiply two quaternions, A times B doesn’t necessarily give you the same result as B times A. That’s why he’s called The Liberator of Algebra. He freed algebra from the shackles of arithmetic.”
Hamilton’s quaternions have played a seminal role in the development of computer games and animation. More importantly perhaps, in the greater scheme of things, Hamilton seems to be thought of with great affection in Cabra. As Aodhán Perry of Cabra Community Council remarked at the 2009 Hamilton walk, “It has gone way beyond just being a walk because all the local school children and the community are extremely proud of Hamilton and their local connection with him. The walk really has touched the local people in a big way.”
If you’d like to connect with Hamilton for yourself by taking part in this year’s walk, you should register in advance with Fiacre Ó Cairbre by calling 01-7083763.
October 15th to 22nd is Maths Week Ireland.