The primary function of the cerebellum is to maintain posture and balance. When we jump to the side, reach forward, or turn suddenly, it subconsciously evaluates each movement. The cerebellum then sends signals to the cerebrum, indicating muscle movements that will adjust our position to keep us steady.
The Ackermann function is a classic example of a recursive function, notable especially because it is not a primitive recursive function. It grows very quickly in value, as does the size of its call tree.
See also inverse Ackermann function. Note: Many people have defined other similar functions which are not simply a restating of this one. In 1928, Wilhelm Ackermann observed that A(x,y,z), the z-fold iterated exponentiation of x with y, is a recursive function that is not primitive recursive.