Royal Canal bridge stands as an old unique mathematical shrine

Many men have been guilty of being distracted while listening to their wives, but perhaps none more famously than Sir William…

Many men have been guilty of being distracted while listening to their wives, but perhaps none more famously than Sir William Rowan Hamilton, the great Irish 19th century mathematician and one of Ireland's most eminent scientists.

Hamilton had been grappling with the problem of complex number multiplication for many years. The laws governing addition and subtraction of complex numbers were well known, but those governing their multiplication had still not been cleared up.

Complex numbers are used to define points in a three dimensional space, and such numbers are referred to as triples. He introduced a fourth dimension so the complex numbers could describe points in four dimensional space not possible for us to relate to our own world - otherwise quaternions.

On October 16th, 1843, Hamilton set out from Dunsink observatory and met his wife for a walk along the Royal Canal. He was going to attend a council meeting of the Royal Irish Academy. In a letter to his son Rev Archibald Hamilton, he recounts the details.

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". . . and your mother was walking with me, along the Royal Canal, to which she had perhaps driven; and although she talked with me now and then, yet an undercurrent of thought was going on in my mind, which gave at last a result, whereof it is not too much to say that I felt at once the importance. An electric circuit seemed to close, and a spark flashed forth, the herald - as I foresaw immediately - of many long years to come of definitely directed thought and work by myself if spared."

Continuing, he wrote: "Nor could I resist the impulse - unphilosophical as it may have been - to cut with a knife on a stone of Brougham Bridge as we passed it, the fundamental formula . . ."

He wrote this letter to his son, 22 years after the actual event, the inscription had "mouldered away". The bridge referred to is now known as Broome Bridge. Hamilton's spelling may have been an Irish language version of the name, as he was quite a linguist being proficient in Latin, Greek and even Persian from an early age.

Hamilton was somewhat ashamed of his graffito, regardless of how learned it may have been. In a letter to Prof Tait, seven years before the letter to his son, he recounts the events of the Royal Canal stroll but he omitted the pocket knife account, writing: "I pulled out on the spot a pocket- book, which still exists, and made an entry."

The Broome Bridge has become a site of pilgrimage for the mathematical community. Each year on October 16th the students and staff of NUI Maynooth Mathematics Department organise a visit to the bridge followed by some Hamilton-related event such as a visit to the house near Trim where he lived in his early years with his uncle and tutor, the Rev James Hamilton.

Although born in Dominic Street in Dublin's north inner city, Hamilton spent most of his childhood with his uncle in Trim from whom he received a remarkable education. At 18 he was sent to Trinity College to read in classics and mathematics. During this time he predicted the phenomenon of conical refraction in birefringent crystals.

The subsequent demonstration of this type of refraction in the laboratory brought Hamilton great renown, so much so that when the astronomer royal in Ireland, Dr Brinkley retired, Hamilton was pressed to allow his name go forward for the post. As a result, while he was still an undergraduate, he was appointed Andrews' Professor of Astronomy at Trinity and astronomer royal in Dunsink.

A plaque commemorating the canal stroll has been set into the wall close to the bridge, which is a potential focus of interest for tourists. Unfortunately, the canal at this point is littered with discarded shopping trolleys amongst other jetsam.

The archway underneath the bridge is also covered with spray-painted graffiti, and if Hamilton were alive today he might be shocked, but he would hardly be in a position to complain.

Fintan Gibney is an IT consultant with SmartForce.