Expo 2020 Dubai: Why Hamilton's equation is on the Ireland Pavilion facade

Under the sub-theme of Mobility, the Ireland Pavilion is honouring its past discoveries and ingenuity, tracing the innovative spirit of the Irish people all the way back to 5,000 years ago. Be it the principles of motion in physics or the sun's path across the sky, something unique is always born out of the well of Irish creativity. And now, come October, curious eyes and minds can see it all reflect in the country's pavilion at Expo 2020 Dubai.

When you visit the Irish Pavilion, look carefully at the facade. Here, a duplicate pair of equations and their corresponding mathematical diagrams signal the entrance to the pavilion. Engineers and students of quantum mechanics alike might recognise it from their lessons – this is the Hamiltonian equation of quaternions.

Dublin-born mathematician Sir William Rowand Hamilton had his own 'eureka' moment on the way to a Royal Irish Academy meeting in 1843. He had been troubled with the two-dimensional computation of complex numbers (a composition of real numbers such as 1, 2, 3 and numbers that have imaginary units such as 2i). Hamilton's use of triples proved difficult for charting in a three-dimensional space before he upended the rules of algebra and discovered quaternions.

‘i2=j2=k2=ijk=−1’ was what a thrilled Hamilton carved into the stone of the Broom Bridge (then the Brougham Bridge) as Helen Maria Bayly, Hamilton's wife, watched from the sidelines on October 16, 1843. In introducing a fourth dimension, the 19th-century mathematician described the geometry of vectors in a 3D space through quaternions, which are quadruples of real numbers. His unconventional discovery that bent the laws of ordinary arithmetic and would go on to revolutionise quantum mechanics, robotics, navigation and animation was commemorated on the same bridge by the Royal Irish Academy in 1958.

Another ode to the country’s mathematical prowess is the pavilion’s Neolithic solar clock. The Oculus, one of the two interlinked structures that make up the pavilion, pays homage to a monument older than the Great Pyramids and the Stonehenge themselves while offering visitors a journey into Irish history through a 360-degree film featuring audio-visual projections.

The pavilion's oculus takes inspiration from a passage tomb in Ireland called the Newgrange, built by prehistoric farmers on an area of one acre. What the structure mimics is the rectangular opening above the tomb's entrance, through which sunlight would pour in every winter solstice in December to symbolise the prevalence of life over death.

One wonders if the pavilion's skylight would, too, capture the sun's rays on winter solstice, to which Patrick Hennessy, Commissioner General of the Ireland Pavilion, says the visitors will have to find out for themselves. Also described as an ancient temple, Newgrange is a World Heritage site under the United Nations Educational, Scientific and Cultural Organization (Unesco).

Plenty of sunshine will illuminate the performance venue-slash-garden of the pavilion, casting fascinating patterns on the ground as the sun sinks below the horizon. A square within a square perimeter, the garden is Ireland’s take on a fusion of the European cloister and the Arab garden. From façade to the interior, the Irish pavilion integrates the various facets of mobility, which visitors will find rooted in the country's rich history of ceaseless inspirations.