William Rowan Hamilton

William Rowan Hamilton and Kant

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A view of the bridge at Broombridge, featuring the plaque commemorating the discovery of quaternions by Hamilton.

I have written before about Hamilton’s interest in philosophy, particularly Berkeley and idealism. This post will give some detail of William Rowan Hamilton’s interest in and understanding of Kant.

In this post on the discovery of quaternions I mentioned that the project which had his children asking each morning “Well, Papa, can you multiply triplets”? started with a paper : “Theory of Conjugate Functions, or Algebraic Couples; with a Preliminary and Elementary Essay on Algebra as the Science of Pure Time”, read to the Royal Irish Academy on November 4th, 1833, and June 1st, 1835, and published in 1837 (pdf from TCD).

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The discovery of quaternions

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But on the 16th day of the same month – which happened to be a Monday, and a Council day of the Royal Irish Academy – I was walking in to attend and preside, and your mother was walking with me, along the Royal Canal…An electric circuit seemed to close; and a spark flashed forth, the herald (as I foresaw, immediately) of many long years to come of definitely directed thought and work, by myself if spared, and at all events on the part of others, if I should even be allowed to live long enough distinctly to communicate the discovery. Nor could I resist the impulse – unphilosophical as it may have been – to cut with a knife on a stone of Brougham Bridge, as we passed it, the fundamental formula with the symbols, i, j, k; namely,
i2 = j2 = k2 = ijk = -1

Letter dated August 5, 1865 from Sir W. R. Hamilton to Rev. Archibald H. Hamilton.

The classic account of the discover of quaternions. Hamilton also notes in this letter that the Council Books of the Academy record that he had obtained leave to read a paper on quaternions, which reading took place on the 13th November 1843.

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What has Hamilton to do with philosophy?

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William Rowan Hamilton Wikimedia, Public Domain
William Rowan Hamilton
Wikimedia, Public Domain

[T]he visible world supposes an invisible world as its interpreter, and […] in the application of the mathematics themselves there must (if I may venture upon the word) be something meta-mathematical. Though the senses may make known the phenomena, and mathematical methods may arrange them, yet the craving of our nature is not satisfied till we trace in them the projection of ourselves, of that which is divine within us

From a lecture to astronomy students given by William Rowan Hamilton in 1833 (Graves, 1882-9, vol. 2, p. 68).

Hamilton differed from other mathematicians of his time in his focus on abstract mathematical laws, and in finding inspiration in idealist philosophers such as Immanuel Kant and Samuel Taylor Coleridge,  as can be seen from the quote. “Hamilton often argued that certain metaphysical views were the primary motivation for his work in mathematics” (Attis, 2004).

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Root and STEM

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Taming the Electric Fluids (c) PhotoAtelier/Flickr (CC BY 2.0)
Taming the Electric Fluids
(c) PhotoAtelier/Flickr (CC BY 2.0)

In the general consciousness, philosophy is more associated with the arts than with science. The nesting of philosophy under “literature” in the Oxford Reference timeline tool is one example. In the case of Irish philosophy it’s understandable given great writers such as Swift, Wilde and Yeats fit into the category of Irish philosopher. But Irish philosophy (as all philosophy) also includes people who are interested in the natural world, mathematics and technology.

AE wrote in 1925 (Irish Statesman): “Ireland has not only the unique Gaelic tradition, but it has also given birth, if it accepts all of its children, to many men who have influenced European culture and science, Berkeley, Swift, Goldsmith, Burke, Sheridan, Moore, Hamilton, Kelvin, Tyndall, Shaw, Yeats, Synge and many others of international repute.” Four of those names unequivocally played a role in the history of STEM. Three of those were also philosophers.

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Quaternion Bridge

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The quaternion plaque on Broombridge © Cliff Bilbrey on Flickr (CC BY-NC 2.0)
The quaternion plaque on Broombridge
© Cliff Bilbrey on Flickr (CC BY-NC 2.0)

This plaque commemorates the discovery of the quaternion formula (i2=j2=k2=ijk=-1) by Sir William Rowan Hamilton on 16th October 1843, as he walked along the canal from Dunsink on his way to a meeting in Dublin. Without paper to hand he scratched the formula into one of the bridge’s stones.

There is a commemorative Hamilton Walk organised by the Maynooth University Maths department every year. There is also a virtual version here.

For a Storify of Hamilton Day 2015 and the 25th Hamilton Walk, click here.