Quaternions and spatial rotation around the "z" axis, then flip it 180 degrees around the "x" axis. Take the other book, flip it 180° around "x" axis first, and 90° clockwise around "z" later. The two books do not end up parallel. This shows that, in general, the composition of two different rotations around two distinct spatial axes will not commute. The vector cross product, used to define the axis–angle representation, does confer an orientation ("handedness") to space: in a three-dimensional vector space, the three vectors in the equation will always form a right-handed set (or a left-handed set, depending on how the cross
Omnipotence paradox Paul the Apostle and Elymas the Magician mentioned in Acts 13:8, but it is phrased in terms of a debate as to whether or not God can "deny himself" ala 2 Tim 2:13. In the 11th century, Anselm of Canterbury argues that there are many things that God cannot do, but that nonetheless he counts as omnipotent. Thomas Aquinas advanced a version of the omnipotence paradox by asking whether God could create a triangle with internal angles that did not add up to 180 degrees. As Aquinas put it in Summa contra Gentiles: This can be done on a sphere,