Inscription on Brougham Bridge
Commemorating William Rowan Hamilton's 1843 DiscoveryBrougham (pronounced Broom) Bridge, sometimes known in later days as Hamilton Bridge, or even as Quaternions Bridge, lay on the road which Hamilton was taking from his residence at the Dunsink Observatory to preside over a meeting of the Royal Irish Academy. He thus described the incident in a letter of 1858:
"Tomorrow will be the fifteenth birthday of the Quaternions. They started into life, or light, full grown, on the 16th of October, 1843, as I was walking with Lady Hamilton to Dublin, and came up to Brougham Bridge. That is to say, I then and there felt the galvanic circuit of thought closed, and the sparks which fell from it were the fundamental equations between i, j, k, exactly such as I have used them ever since. I pulled out, on the spot, a pocketbook, which still exists, and made an entry, on which, at the very moment, I felt that it might be worth my while to expend the labour of at least ten (or it might be fifteen) years to come. But then it is fair to say that this was because I felt a problem to have been at the moment solved, an intellectual want relieved, which had haunted me for as least fifteen years before."
" Nor could I resist the impulse — unphilosophical as it may have been — to cut with a knife on a stone of Brougham Bridge the fundamental formula with the symbols i, j, k: i² = j² = k² = ijk = -1."
In a noncommutative algebra, the commutative law of multiplication (ab = ba) does not hold. In the case of Hamilton's new algebra, instead ab = -ba. The bridge and the inscription are not in the best of shape at the present moment, but noncommutative algebra is still as fresh as it was in 1843.
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