There is a lot of neat stuff connected with the quaternions, octonions and sedenions (see the external link in Octonions, for example). Saying that things would be more interesting if they were fields is missing the point. --Zundark, 2001 Dec 20
I don't think so. They'd be more interesting, (and a darn sight more useful for things like 3-dimensional versions of complex-analytic inviscid 2D fluid dynamics) and it is unfortunate that they don't.
They wouldn't be themselves if they were fields. And they wouldn't be any more useful, as they would be incorrect. This 'unfortunately' is ridiculous. --Taw