Map of a Nation (48 page)

Hamilton was fascinated by geometry. He had long felt that it was ‘an
essential
requisite’ for all mathematicians and scientists and the keystone of all other
disciplines. In the 1850s, he would attempt to sell a game based on geometry and algebra on the commercial market, to a largely uncomprehending audience. (One instruction read: ‘the only operations employed in the game are those marked λ and μ; but another operation, ω = λ μ λ μ λ = μ λ μ λ μ, having the property that ω
²
= 1; was also mentioned’. No wonder one purchaser of Hamilton’s game reported back to its creator that ‘none of her family would play it’!) Hamilton was entranced by one geometric form in particular: maps. The leaves of his notebooks were scrawled over in places with sketch maps, somewhat like Coleridge’s, with whom he would enjoy a correspondence. In one notebook entry, Hamilton recalled ‘how much pleasure’ he derived from helping his younger sister Eliza ‘to find out on the maps the several counties of England & Wales’. This enjoyment grew even more profound when, on reading a short story that was set in Merionethshire, in Wales, he ‘recognis[ed] it as a county which I had lately seen marked in the Map. From this little circumstance,’ Hamilton continued, ‘I was led to reflect on the constant source of pleasure which would be opened to me by an extensive knowledge of Geography.’

In 1824, when the Ordnance Survey of Ireland was first being mooted, Hamilton was introduced to the 57-year-old novelist Maria Edgeworth, the daughter of the amateur map-maker Richard Lovell Edgeworth, who had died seven years previously. The meeting between the two was a great success, despite an age gap of nearly forty years. Maria wrote to her sister Honora soon after this first acquaintance, describing Hamilton as ‘an “Admirable Crichton” of eighteen’, a highly favourable comparison to the extraordinary Scottish polymath James Crichton. Hamilton, Maria continued, was ‘a real prodigy of talents,
who
,
Dr
[John] Brinkley [the astronomer] says, may be a second
Newton
– quite gentle and simple’. The approval was mutual. Hamilton also wrote to his sister Grace about ‘[she] who forms the great and transcendent interest of the place’. ‘Miss Edgeworth!’ he cried, ecstatically. ‘She far
surpasses
all that I heard or expected of her.’ William Rowan Hamilton and Maria Edgeworth formed a friendship that endured until the latter’s death in May 1849, and many of their discussions were concerned with maps. Hamilton described his delight upon arriving at Maria’s to be ‘carried off’ to consult ‘William [Edgeworth]’s maps and plans, which were just about to be rolled up for departure, as Mr W.E. was to go the next morning on an
engineering expedition’. They also talked about geometry and together designed an educational tour of the Lake District to help Maria’s younger brother Francis brush up on his knowledge of Euclid’s
Elements
. (It is
interesting
that they considered the Lake District the most apposite location for a geometrical education. Wordsworth and Mudge were clearly not the only ones to imagine that region imprinted over with trigonometrical shapes. In fact, in the late nineteenth century, the map-publisher Bartholomews would produce a series of educational maps for schools, which were based on the Lake District’s latent geometry.)

When the Ordnance Survey arrived in Ireland in the mid-1820s, Hamilton welcomed the project with delight. In April 1828 he secured ‘a situation among the calculators of the Trigonometrical Survey’ for a young assistant who was working under him at Dunsink Observatory, ‘thro’ the interest of Captain [Richard Zachariah] Mudge’. And when the Ordnance Survey came to Lough Foyle, Hamilton was eager to witness the map-makers in action. He travelled to the site, more ‘with the intention of reconnoitring the ground, than with much hope of seeing the base and the officers’, as he later wrote to a friend. But Hamilton was lucky enough to find some engineers there, among them ‘Lieutenant Drummond at home, and after eating in a tent, for the first time in my life, I took a walk with them along the base line to Roe, and then back again by the shore of Lough Foyle; on our return,’ he continued gleefully, ‘we found Colonel Colby, and had a pleasant evening, closed by my sleeping under canvas, a novelty which I enjoyed extremely.’

In the summer of the following year, Hamilton received a famous house guest who was connected to the Ordnance Survey: ‘Captain Everest, who has been superintending a great triangulation in India, and is going out again for that purpose.’ The upright, mutton-chopped and rather
humourless
George Everest had been appointed assistant to the Great Trigonometrical Survey of India in 1817, and acted as its superintendent from 1823 to 1843. (His surname was given to the Himalayan mountain, but it should be pronounced ‘Eve-rest’, not ‘Ever-est’: he would probably not have taken the wrong inflection in good spirits.) The backbone of the Indian Trigonometrical Survey was the longest meridian arc to be measured
anywhere
in the world, and this ‘Great Arc of India’ stretched over 1600 miles
of the Indian subcontinent. Begun under the aegis of the East India Company, and later taken over by the Crown, the triangulation was designed as the foundation for topographical surveys that would delineate British
territories
in India, and it was also a vital contribution to geodetic research into the shape of the earth. Everest’s dedication to his task was such that
contemporaries
referred to him as ‘Never-rest’ (a joke that relied upon the mispronunciation of his name).

George Everest came to Ireland in the summer of 1829 on sick leave from India, to observe the Ordnance Survey’s work and to talk with Thomas Colby, whilst staying with Hamilton. The two map-makers had much to
discuss
, not least the experience of surveying in a colonial territory. Everest noted the huge scale – six inches to the mile – on which the Irish map was being conducted, as well as its wealth of employees and its highly
sophisticated
instruments. After conversations with Colby, Everest resolved to request more personnel and funding for his own endeavour, as well as a double set of Compensation Bars, and he would also demand that the Indian Survey should be allowed to prioritise the Trigonometrical Survey above the interior maps, just as the Ordnance Survey did. Hamilton had long declared himself fascinated by the ‘work on the Meridional Arc of India’, and we can imagine that during Everest’s visit the two engaged in animated discussion about geometry, triangulation and map-making.

Over the following months and years, Hamilton maintained a fascination with the Ordnance Survey’s endeavour. He dined regularly with Larcom and Colby and during a brief interlude, in which Hamilton found himself too busy to visit the engineers’ camp, Colby lamented to the mathematician that ‘you are so wrapt up in your luminous pursuits that I can never get you to come and see our humble efforts to represent the surface of Ireland as it is. But,’ he continued, ‘I can assure you my assistant L[ieutenant] Larcom is managing a work here which would repay you for the time of coming to see it.’ Hamilton never doubted the merits of Larcom, whom he considered to be ‘somewhat of a universalist’, and in 1833, he recommended that
map-maker
as a member of the Royal Irish Academy (of which he, Hamilton, would be president from 1837 to 1845), from his ‘own personal conviction of his merits’. And the warmth was mutual, Larcom allowing Hamilton to
share in the Ordnance Survey’s adventures. Hamilton and Thomas Romney Robinson collaborated in discovering the longitudinal difference between the Dunsink and Armagh Observatories, to assist the Ordnance Survey. A few years later, Larcom provided Hamilton with compass bearings and
instructions
that enabled him to put his ‘telescope correctly on the spot’ at home or at the Observatory, and to mimic the map-makers’ own observations. ‘There can be no harm in your having an eye in the direction every night,’ Larcom assured Hamilton, and he even lent the Ordnance Survey’s theodolite to the curious mathematician. A Victorian biographer of William Rowan Hamilton described Larcom as ‘one of the friends who took most interest in his pursuits both scientific and philosophical’.

From the late 1820s, around the beginning of his friendship with the Ordnance Surveyors, Hamilton’s letters and notebooks show that he started thinking much harder about the precise nature and significance of geometry than he had done previously. The Scottish ‘common sense’
philosopher
Dugald Stewart had specifically mentioned the Ordnance Survey’s triangulation of Britain in the second volume of his
Elements of the Philosophy
of the Human Mind
(1814), describing the Trigonometrical Survey as almost the only example in ‘the real world’ of the perfect logic that is normally reserved for pure mathematics and abstract geometry. The Ordnance Survey’s
instruments
were so sophisticated, Stewart felt, that they ensured ‘we are not liable to be disturbed by those physical
accidents
, which, in the other
applications
of mathematical science, necessarily render the result, more or less, at variance with the theory’.

Hamilton likewise decided that geometry was a branch ‘of the philosophy of mind’, a product of the extraordinary powers of independent creation that were possessed by the intellect and which operated quite separately from the world of materiality and sensation. For Hamilton, geometry was ‘a language of pure space’, and the young mathematician enjoyed imagining the exact moment when the first triangle was ‘invented’, when ‘a new light flashed upon the mind of the first man … who demonstrated the properties of the isosceles triangle’. ‘The true method’ of devising geometrical figures, Hamilton felt, was to ‘bring out’ an idea that was already lodged in the intuition, rather than following long lists of mathematical rules. The
drawing 
of a triangle should be like a divine act of creation of ‘something simple, perfect, and
one
’. Hamilton had a penchant for idealist philosophy, especially the works of Immanuel Kant, and he embraced Kant’s suggestions that geometry was an image of the internal, not the external, landscape. This was a very different view to the conviction of many Enlightenment
philosophes
that geometry was a manifestation of empirical reason.

In 1829, shortly after George Everest’s departure from Hamilton’s
residence
, another famous friend came to stay with the mathematician. William Wordsworth had first made Hamilton’s acquaintance in the summer of 1827, when the young mathematician had been taken to the Lake District to meet Wordsworth by the writer Caesar Otway, author of
Sketches in Ireland
. After climbing Helvellyn, Otway and Hamilton visited the poet at home. Hamilton and Wordsworth instantly liked one another and when they came to part that evening, Hamilton described how the poet ‘walked back with our party as far as their lodge’. But, wanting to prolong their conversation further, Hamilton suggested that after dropping off his friends he would ‘walk back with [Wordsworth], while my party proceeded to the hotel. This offer he accepted,’ Hamilton continued, ‘and our conversation had become so interesting that when we arrived at his house, a distance of about a mile, he proposed to walk back with me on my way to Ambleside, a proposal which you may be sure that I did not reject; so far from it, that when he came to turn once more towards his home, I also turned once more along with him.’ ‘It was very late when I reached the hotel after all this walking,’ Hamilton added.

In the late summer of 1829, Wordsworth paid his only trip to Ireland, to stay with Hamilton. He was introduced to Maria Edgeworth, who found the poet ‘very prosing – as if he were always speaking
ex cathedra
for the instruction of the rising generation and never forgetting that he is
MR WORDSWORTH
the author and one of the poets of the lake’. But
Wordsworth
got on much better with the Ordnance Surveyors in Ireland, many of whom he was introduced to by Hamilton. The mathematician presented Words-worth to Thomas Drummond, and the poet thereafter referred warmly to his acquaintance with ‘Mr Secretary Drummond’ of ‘calculating celebrity’. He also met Thomas Spring Rice, chairman of the committee that had founded the Irish Ordnance Survey, and was still in touch with him ten
years later. And, during his ‘short tour’ of Ireland, Wordsworth threw
himself
into political debate with the Irish map-maker and sometime adviser to the Ordnance Survey, William Edgeworth. This Irish visit clearly
reinvigorated
Wordsworth’s earlier interest in the Ordnance Survey’s endeavours in the Lake District. When in 1837 Colby and Larcom published a memoir of the
Ordnance Survey of the County of Londonderry
, Wordsworth made sure to buy one of the 1500 copies printed.

During his Irish trip, Wordsworth enjoyed numerous conversations with Hamilton about the nature of geometry and the relationship between
literature
and science. And it is telling that the poet revised passages in his poetry where he had initially been rather scathing and sceptical about geometry and maps. In his long poem
The Prelude
, Wordsworth erased his denigratory description of the rational child’s dependence on telescopes, crucibles and maps. And he significantly expanded a section which encouraged his reader to ‘not entirely overlook/ The pleasure gathered from the rudiments of
geometric
science’, but to try to imagine ‘the relation those abstractions bear/ To Nature’s laws … / From star to star, from kindred sphere to sphere,/ From system on to system without end.’ It would be nice to think that his contact with Hamilton and the Irish Ordnance Survey may have been partly responsible for Wordsworth’s depictions of the joys of geometry in his later poetry and revisions. He clearly came to realise that maps could be
interpreted
in different ways than purely as exponents of Enlightenment rationality, and was attracted to Hamilton’s association of geometry with the independent powers of creation that were possessed by the imagination.