A New Algebra

 

Sir Robert Ball

Ball (1840-1913) came from a Dublin scientific family. He worked at Birr Castle as tutor to the Parsons family and as assistant on the great telescope. He spent nearly 20 years as professor at Dunsink Observatory before moving to Cambridge University. He was a gifted photographer, despite being blind in one eye, and took wonderful photographs of lighthouses and lighthouse keepers when he went on inspections with the Commissioners of Irish Lights. He also gave successful lecture tours in the USA.

Sir Robert Ball

Sir Robert Ball

Ball (1840-1913) came from a Dublin scientific family. He worked at Birr Castle as tutor to the Parsons family and as assistant on the great telescope. He spent nearly 20 years as professor at Dunsink Observatory before moving to Cambridge University. He was a gifted photographer, despite being blind in one eye, and took wonderful photographs of lighthouses and lighthouse keepers when he went on inspections with the Commissioners of Irish Lights. He also gave successful lecture tours in the USA.

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Sir William Rowan Hamilton

Hamilton (1805-65) was arguably the greatest Irish scientist. He made many contributions to physics, especially in mechanics and optics, as well as inventing quaternion algebra. His greatest work is his general theory of dynamics. His Hamiltonian operator (H) was crucial to the development of quantum mechanics, and today it is used by physicists, engineers and even economists. Hamilton spent all his working life as Astronomer Royal at Dunsink Observatory.

Image: Sir William Rowan Hamilton, MRIA, 1805-1865 (© RIA)

Sir William Rowan Hamilton
Image: Sir William Rowan Hamilton, MRIA, 1805-1865 (© RIA)

Sir William Rowan Hamilton

Hamilton (1805-65) was arguably the greatest Irish scientist. He made many contributions to physics, especially in mechanics and optics, as well as inventing quaternion algebra. His greatest work is his general theory of dynamics. His Hamiltonian operator (H) was crucial to the development of quantum mechanics, and today it is used by physicists, engineers and even economists. Hamilton spent all his working life as Astronomer Royal at Dunsink Observatory.

Image: Sir William Rowan Hamilton, MRIA, 1805-1865 (© RIA)

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In 1843 an Irish scientist invented a revolutionary form of algebra, called quaternions because it had four components. The great physicist Sir William Rowan Hamilton invented it to describe how objects rotate in three dimensions.

Controversially, it broke the fundamental commutative law of multiplication, which says that A times B is the same as B times A (AB=BA). In three dimensions, though, the order (or direction) is important, and commutativity no longer holds, as Hamilton discovered. His quaternions are now widely used in computer graphics and even to orient spacecraft.

Hamilton's day job was Astronomer Royal for Ireland at Dunsink Observatory. His successor, Sir Robert Ball, was another mathematically minded physicist. Physicists rely on mathematics to describe things, and many of the major Irish contributions to mathematics came from physicists, such as Hamilton, Ball and George Gabriel Stokes.

Like Hamilton, Ball used mathematics to describe movement, but he was interested in twisting and wrenching rather than rotation. In 1878 he developed a mathematical theory of screws, which was rediscovered in the 1970s and is now used by robotics engineers.

George Gabriel Stokes from Co Sligo was one of the towering figures of 19th-century science. He came up with powerful new mathematics to describe fluids and sediments, but is better remembered for his many contributions to physics.

Guinness's contribution to statistics came in 1900 from an English brewer working at the St James's Gate Brewery. William Sealy Gosset developed a powerful statistical test to compare the results of small trials of new barley varieties. Guinness staff could not publish under their own name, so Gosset used the pseudonym Student. His Student's t-test for small samples is still widely used.