*le dernier grand savant universel*). As I quoted J.B.S Haldane earlier "

*Keats and Shelley were the last two poets who were at all up to date with their chemical knowledge*” so Poincaré knew

**the then available mathematics. Einstein was writing his key papers before Poincaré died and after his death things mathematical went exponential so that no single brain could retain it all. As well as making major contributions to several different fields of mathematics, Poincaré was also a philosopher of science with a notable interest in the where ideas spring from. In his 1908 book Science and Method he describes one of his own experiences getting onto a bus in Coutances in Normandy: "**

__all__*At the moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformation that I had used to define the Fuchsian functions were identical with those of non-euclidean geometry."*I can see that I'm going to have to come back to Poincaré later, because he is really so interesting.

__and__there was much less maths. He was appointed Professor of Astronomy at Trinity College Dublin at the ripe old age of 22; the position came with a house at the Dunsink Observatory NW of Dublin. On 16th October 1843 he went for a stroll with his wife along the Royal Canal, and as he passed under Broom/Brougham Bridge on the tow path he had an amazing revelation about mathematical relationships, which he hastily scratched into a stone on the bridge:

i^2 = j^2 = k^2 = ijk = -1

NUI Maynooth hosts an annual pilgrimage walk from Dunsink Observatory to Broom Bridge
or you can just go out on the Maynooth commuter rail and descend at
Broombridge. When I was last there 20 years ago, on pilgrimage with a
friend of mine who had a degree in Mathematics from Cambridge, the area
was all derelict rough meadows filled with old bedsteads and piebald
horses. Now, as you see from Google maps, the Celtic Tiger has passed
through depositing now derelict rough sheds and warehouses.

From the table it says that i x j .ne. j x i . It

__does__matter which order you multiply the elements in quaternion mathematics. You can, idly, use the table to verify Hamilton's bridge-scratching "

*ijk = -1*" (it's the same as i x j x k = -1) can be processed in two steps: i x j = k ; k x k = -1.

"

*So far, so what*?" I hear you say, and for 100 years that was the consensus. Quaternions were a clever game that mathematicians used to play with, trying to discover inconsistencies and mapping the results onto other weird branches of mathematics. Then it turned out that they were an extremely powerful, compact and useful way of representing 3-D movement, particular turning. Where did we need to mobilise that insight? First in space travel, controlling the yaw, pitch and roll of Gemini, Soyuz and Apollo with minimal expenditure of fuel. Latterly, quaternions are key to being able to write code for computer graphics that is compact enough to execute in real time. Without William Rowan Hamilton's insight 170 years ago there would be no Lara Croft, and the world would be a far duller place for 13 year old boys.

If you like maps, and as you live in Ireland, you will doubtless also be a fan of the awesome Tim Robinson.

ReplyDeletehttp://en.wikipedia.org/wiki/Tim_Robinson_(cartographer)

Glad you mentioned Poincaré.

And thanks for the excellent and eminently readable posts on women in STEM for Ada Lovelace Day.

Thanks. I am indeed in awe of Tim Robinson who refused to see the landscape as only in the now. But also recognised that it came from somewhere, that it had been walked by other feet and, regardless of time, was a coherent, internally consistent thing. Robinson's work has some commonality with http://blobthescientist.blogspot.ie/2013/08/prairyerth.html

DeleteAs I say, I'll return to Poincaré later.