The science or calculus of quaternions is a new mathematical method Not so new. Quaternions were invented (discovered?) by the Irish mathematician and philosopher Sir William Rowan Hamilton in the 1800's. Quaternions can be used to mathematically describe rotations. For most purposes the quaternion method was replaced by the matrix method when that was later invented. Technically, quaternions are a 4-dimensional number system, just as the complex numbers are a 2-dimensional number system. I think the use in Poser is for interpolating in animations: if the position of some morph is given in two key frames, how should it be filled in between? Try the quaternion method if you do not like the default way that it was filled in.