As the bi centenary of the birth of Ireland's greatest scientist, William Rowan Hamilton, gets under way, Mary Mulvihill takes a look at some of his achievements
Question: what does Lara Croft have in common with the Huygens spaceprobe? Answer: both can move thanks to unusual mathematics invented by an Irishman, William Rowan Hamilton, who was born 200 years ago.
Hamilton is arguably Ireland's greatest scientist, and to mark his bicentenary, 2005 has been designated Hamilton Year. Happily, this is also Unesco World Year of Physics, marking 100 years since Einstein hit the scene in 1905.
Ironically, Irish people are probably more familiar with Einstein than with Hamilton, something the Hamilton 2005 team hopes to change, though older folk may know of quaternions, a new algebra Hamilton invented in 1843. Eamon de Valera, the former taoiseach and one-time maths teacher, ensured that stamps were issued for quaternion's centenary in 1943, and the term entered the Irish psyche.
Hamilton may not be in the same league as Einstein - though Google.ie registered 3.3 million hits for Albert Einstein and a respectable 2.4 million for Hamilton-related sites - yet he made important contributions to physics and mathematics, especially quantum mechanics. Today his quaternions are used in computer graphics (Go, Lara!) and to control the orientation of spacecraft.
Born in Dublin, Hamilton was a child prodigy. Fostered to his uncle, Rev James Hamilton, a schoolmaster and linguist in Trim, he knew Latin, Greek and Hebrew aged five, and by 17 had mastered a dozen more languages, including Hindustani and Sanskrit. He was also writing poetry (a habit that would last a lifetime), but his interest in mathematics was not sparked until his teens.
Hamilton studied Classics and mathematics at Trinity College, Dublin, and was so outstanding that, before he had graduated, TCD appointed him professor of astronomy at Dunsink observatory. He held the professorship, and lived at Dunsink, until his death in 1865.
Hamilton made major contributions to mechanics, optics, geometry and algebra. When mathematicians struggled to accept such artificial and seemingly illogical concepts as imaginary numbers (involving i, the square root of -1), Hamilton helped the transition to the modern illogical mathematics.
His early work was in optics, and in 1832 he made a daring prediction based purely on a mathematical analysis of the laws of light: that a single ray of light will sometimes be refracted in a crystal to generate a cone of refracted rays. Such a theoretical prediction was unprecedented. So when his conic refraction was experimentally proved two months later, the news shook the scientific world. Hamilton was knighted and granted a royal pension.
Probably his greatest contribution was his general theory of dynamics. These Hamilton equations and the accompanying Hamiltonian are well known to physicists, and were crucial to Schrödinger's development of quantum mechanics.
Quaternions, invented in 1843, were a way of describing rotations in three dimensions. He got the idea in a classic eureka moment, while walking by Broom Bridge on Dublin's Royal Canal. Hamilton scratched his new equation on the bridge, and later wrote that an electric circuit seemed to close, and a spark flashed forth.
Significantly, quaternions dispense with a cornerstone of arithmetic, the commutative law, which says that A times B is the same as B times A (AB=BA). This creative leap paved the way for vectors. Hamilton spent the rest of his life looking for an application for quaternions, but they were clumsy to use and vectors proved more popular. Now, however, quaternions are used in high-tech computer graphics.
Hamilton received numerous honours - the American National Academy of Science, for instance, made him their first honorary overseas fellow. More recently, a crater on the Moon was named after him.
He retained his love of poetry, writing sonnets for his friends, who included the writers Wordsworth (who advised him to stick to mathematics), Coleridge and Maria Edgeworth. He could lose himself in work, often forgetting to eat, and suffered with double vision and a voice that alternated between a high treble and a deep bass.
Spurned by his first two loves, he married a friend, Helen Bayly, but it was not a happy union, and he later sought refuge in drink. A board game he invented also failed commercially. Plagued by gout, he died at Dunsink and was buried at Dublin's Mount Jerome cemetery.