In July and August of 2009 my wife and I went on a four-week trip to Scotland and Ireland. We would be visiting Dublin, so I decided that we should visit the famous bridge where William Rowan Hamilton carved the equations for the quaternions. The task was not as simple as I had assumed. This paper gives some details of the search

Gossett, Eric

English

Pillars at Taylor University

The Search for HamiltonEric GossettBethel University, St. Paul, MNEric Gossett earned his M.S., and Ph.D. in mathematics fromthe University of Arizona while specializing in combinatorics. Hehas pioneered the use of Mathematica within the curriculum andpublished the textbook Discrete Mathematics with Proof, SecondEdition. He developed Bethel’s first generation of web services.He is an avid racquetball player and is the faculty sponsor of theBethel Anime Club.1. IntroductionIn July and August of 2009 my wife and I went on a four-week trip to Scotland and Ireland. Wewould be visiting Dublin, so I decided that we should visit the famous bridge where WilliamRowan Hamilton carved the equations for the quaternions.Hamilton had been struggling to find a good way to multiply and divide points in three dimen-sions but was making no progress. On October 16, 1843 he was walking with his wife along theRoyal Canal in the outskirts of Dublin. He had a flash of insight which lead to the now-famousequations that defined the quaternions:i2 = j2 = k2 = ijk = −1.Hamilton was evidently so excited that he carved the equations in the stone of the Broom Streetbridge which crossed the canal. (The carving has long since vanished, but a commemorativeplaque was added in 1958.ACMS 18th Biennial Conference Proceedings, Westmont College, 2011 Page 66I teach a course in Discrete Mathematics so my interest in Hamilton is actually related to thetopic of Hamiltonian cycles in graphs. A Hamiltonion cycle is a walk in the graph that visitsevery vertex exactly once (except that it starts and ends with the same vertex).2. The JourneyI had the following useful information from Wikipedia:Broom Bridge, also known as Brougham Bridge, is a bridge along BroombridgeRoad which crosses the Royal Canal in Cabra, Dublin, Ireland:http://en.wikipedia.org/wiki/Broom_Bridge.When we arrived at our hotel in Dublin, I asked the desk clerks if they knew where the famousbridge was located. They had never heard of the bridge, In fact, they had never heard of afamous Irish mathematician named Hamilton. Our tour guide, bus driver, and city guide werealso not very helpful. The bus driver did think that he knew the bridge, but it was in a suburbthat was too far to walk to and the tour was not going near that area.We did have a nice walking map of Dublin which contained the cryptic message:Site of No. 36 Sir William Rowan Hamilton World-Famous Mathematician.The site was part of a row house. We asked several people in the area about the house butnone of them had heard of Hamilton. The best I can figure is that Hamilton lived there at onetime. The house has been a teacher’s club for many years.Our hotel was next to Trinity College, so we decided to see if the math department there had adisplay about Hamilton. We started on one end of campus and walked a very long way to getto the math department. It is a small, old building which is surrounded by large, new buildingsfor departments such as chemistry and pharmacology. It was a weekend and nobody was in themath building. We were unable to find any displays about Hamilton.ACMS 18th Biennial Conference Proceedings, Westmont College, 2011 Page 67We left Dublin in defeat. However, we did find the famous statue of Molly Malone,saw the Book of Kells,and attended a Sunday Evensong service at St. Patrick’s Cathedral. The service featured aguest choir from America.ACMS 18th Biennial Conference Proceedings, Westmont College, 2011 Page 68We were also able to visit Glendalough which is the site of a famous 6th century Irish monasticcommunity. The tower on the left was for protection from Viking raiders - entry was throughthe hole about 12 feet from the bottom using a rope ladder which could be retracted.We wandered around Ireland for several days, then crossed into Northern Ireland. The borderreally surprised me. The American-Canadian border has armed guards on the American sideto keep out attacking hoards of Canadians and to stop foreign terrorists from sneaking intothe country. On the Canadian side are armed guards who are desperately trying to keep outAmerican culture. The border between the Republic of Ireland and Northern Ireland has noguards (not even the remains of guard houses), no lines on the road, not even a sign saying“Welcome to the UK” or ”now leaving the Republic of Ireland”. The only way to tell you havecrossed the border is that signs in Ireland use kilometers and kilometers per hour and list placesusing Gaelic followed by English. In Northern Ireland they use miles and miles per hour andonly list places in English.The image is of a wall mural in Derry/Londonderry Northern Ireland. (The Catholics call thetown Derry, the protestants call it Londonderry, and tourists who are unsure about who theyare talking with refer to it as “your fair city.”ACMS 18th Biennial Conference Proceedings, Westmont College, 2011 Page 69We eventually crossed into Scotland and wandered around there for several days. The imageis of Brig O’Doon (the bridge over the river Doon). The bridge is famous for the Broadwaymusical and also because of the Robert Burns poem “Tam O’ Shanter.” Tam and his horseescape a group of angry witches by crossing the river via the bridge. Remember the Broomstreet bridge? We were having a good time, but at the back of my mind I was still disappointedthat I missed it.We eventually ended in Edinburgh, said goodbye to one tour group, then a day later joined asecond tour group. After wandering around to more places in Scotland, Northern Ireland, andIreland, we ended up back in Dublin. Here is yet another bridge: a new bridge across the riverLethe shaped like a celtic harp (the national symbol).In Dublin we connected with another city guide. This time the city guide and bus driver wereconfident that they knew how to get to the Broom bridge, The next morning was a free time,so we walked 2 minutes from our hotel and got on a commuter train heading to the suburbs.One train change later we exited onto the Broombridge Station—a bare platform surroundedby weeds and some liter.ACMS 18th Biennial Conference Proceedings, Westmont College, 2011 Page 70Up ahead was a graffiti-covered bridge over the railroad tracks. We walked up the ramp andasked a pedestrian where the Broom bridge was. He said “this is it.” I told him about theHamilton plaque and he said he thought this was the bridge some people were interested in.Enter the following coordinates into Google Maps to see a satelliteimage of the bridge and station: 53.373023,-6.299992.We walked across the bridge and noticed the canal running parallel to the train tracks. Therewas a walking path next to the canal, so we exited the road and went under the bridge, Andthere it was: the long-lost plaque.ACMS 18th Biennial Conference Proceedings, Westmont College, 2011 Page 71There was no graffiti on this side of the bridge, but there was some white paint that had beenthrown onto the wall and plaque.The following heavily photo-manipulated image shows the plaque. The contents read:Here as he walked by on the 16th of October 1843 Sir William Rowan Hamilton ina flash of genius discovered the fundamental formula for quaternion multiplicationi2 = j2 = k2 = ijk = −1and cut it on a stone of this bridge.ACMS 18th Biennial Conference Proceedings, Westmont College, 2011 Page 72This bridge, so dearly loved by mathematicians, is clearly not on the Dublin Tourist Board’slist of places to visit. The site is pretty much off the radar of both the city of Dublin and thenation of Ireland. However, there is one group that is attempting to keep the memory alive:the Mathematics Department at the National University of Ireland at Maynooth.In 1990, we (the Department of Mathematics at NUI Maynooth) initiated the annualcommemoration on the anniversary of the discovery, in the form of a walk fromDunsink observatory to Broom Bridge. Since then, a growing number of people havebeen participating. In 1993, the sesquicentenary, the first New Yorker appeared. Hehad flown across just for the day. http://www.maths.may.ie/hamiltonwalk3. EpilogueThere is an even happier ending to the story. Two months after our visit, a restored plaquewas installed during the 2009 annual walk.All images except the portrait of Hamilton and the image from the Book of Kells were taken by EricGossett and can be used with permission. The exceptions are already in the public domain and canbe found on Wikipedia.ACMS 18th Biennial Conference Proceedings, Westmont College, 2011 Page 73

The Search for Hamilton

https://pillars.taylor.edu/cgi/viewcontent.cgi?article=1004&context=acms-2011

The Search for Hamilton

Abstract

Similar works

Full text

Available Versions

Pillars at Taylor University