Thanks to another reader for their suggestion for this comic's topic! Although they might not have had this particular aspect of vector calculus in mind, we couldn't resist once once we started looking into vector calculus and how it came about. It's also a good way to launch our "A brief history of" series where we will cover more math history.
Here are a few more interesting historical tidbits that didn't make it in:
- Frenchman Olinde Rodrigues had worked on representing rotations in space in 1840 before Hamilton discovered quaternions.
- Hamilton wasn't looking for quaternions per se; he was trying to extend the concept of complex numbers to three dimensions. As it turns out, this construction only works for dimension 1, 2, 4 and 8.
- Hamilton came up with the fundamental formulas for quaternions while he and his wife Helen Marie Bayly were strolling across Brougham Bridge . He was so excited by his flash of inspiration that he used his pocketknife to carve the formulas into a stone of the bridge. Although his original carving has disappeared, the moment is commemorated by a plaque which people can still visit today.
- Melanie Bayly, who holds a PhD in English Literature from Oxford University, has argued that the Mad Hatter scene from Lewis Carroll's Alice in Wonderland is meant to poke fun at Hamilton's quaternions. Carroll (a.k.a Charles Dodgson), like many other mathematicians at the time, had trouble digesting the fact that quaternionic multiplication is not commutative and that Hamilton treated time (the scalar part of the quaternion) separately from the three spatial dimensions. You can read her analysis here.
If you're interested in learning more about the history of vector calculus, Michael J. Crowe's A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (Dover, 1967) is a great resource and provided us with most of the information included in the comic.
Most of what the characters say is in their own words. Here are the works we cited in order of appearance in the comic:
- Sir William Rowan Hamilton, "Theory of Quaternions" in Proceedings of the Royal Irish Academy, vol. III (1845-1847), 3.
- James Clerk Maxwell, A treatise on electricity and magnetism, vol. I (1st ed.), (Oxford, 1873), 28.
- Lord Kelvin as quoted in Silvanus P. Thompson, The Life of William Thomson, vol. II, (London, 1910), 1138.
- Oliver Heaviside, Electromagnetic Theory, vol. I (New York, 1925), 301.
- Josiah Willard Gibbs, "Quaternions and the 'Ausdehnungslehre'", in Nature, vol 44, (1891), 79–82.