Recursive Blessings and Curses

Recursion and Induction

Exodus 20: 4-6 NIV

"You shall not make for yourself an image in the form of anything in heaven above or on the earth beneath or in the waters below. You shall not bow down to them or worship them; for I, the lord your God, am a jealous God, punishing the children for the sin of the parents to the third and fourth generation of those who hate me,  but showing love to a thousand generations of those who love me and keep my commandments.”

Recursion and Induction are important topics in mathematics and computer science.  In each context, one takes a initial object (a base case or cases) and creates new objects from ones already known with a recursion.  For example, to define n! using a recursive definition, one defines 0! to be 1 and says that (n + 1)! = (n + 1) × n!.  Or, to prove that a statement is true for all natural numbers using math induction, one first proves that the statement is true for the case n = 1, then one proves that IF the case with n = k  forces the case with n = k + 1 to also be true regardless of the k-value selected, then the statement must be valid for all natural numbers. 

It is interesting to note that God also uses the concept of recursion.  In the third commandment, do not worship idols, God makes it very clear that he will punish or reward people based on their response to this command.  God will recursively punish children for three to four generations for the sin of one person.  But His recursive blessings for those who love Him and keep his commandments will go to thousands!