Computational Information Geometry Wonderland

Hamilton's bridge and the birth of quaternions as 4D normed division algebra. It cannot exist for 3D vectors...
See also octonions and 2**n Caley constructions. There are also called hypercomplex numbers.

For the small story, here is the inscription plate:

Here as he walked by on the 16th of October 1843 Sir William Rowan Hamilton in a flash of genius discovered the fundamental formula for quaternion multiplication i2 = j2 = k2 = ijk = -1 & cut it on a stone of this bridge

How much progress has been done in a century! (eg., Lie groups and algebras)
Frank.