Complexity threshold

The complexity threshold is a theoretical limit implied by various theological arguments which attempt to claim that the universe, the planet, or life are too complex to have come about by chance. Such complexity arguments are made to lay the groundwork for the claim that if something could not have come about by chance, then it requires a designer.

The complexity threshold, then, is the point at which a system is too complex to have come about by chance, and anything less complex than the threshold could, by definition, have come about by chance. Chance, in terms of the argument, implies a process by which a system of greater complexity could result from a system of lesser complexity.

Complexity arguments begin with the unproven premise that the universe exceeds the complexity threshold, and that it therefore must have been designed by an external creator. The complexity threshold counter-argument poses the following question: how complex is a creator that must have designed the universe?

Three answers are possible:
 * 1) A creator is more complex than the universe.
 * 2) A creator is as complex as the universe.
 * 3) A creator is less complex than the universe.

Because chance has been defined as illogical, 3 is impossible. If a creator is one of lesser complexity than the universe, then the universe could not have resulted from that creator. To assert that it did is to assert that a system of greater complexity (the universe) resulted from a system of lesser complexity (the creator), which is the definition of "chance."

However, because the initial premise claims that anything which exceeds the complexity threshold requires a creator, 1 and 2 are problematic. If a creator is one of equal complexity to the universe, or if a creator is one of greater complexity than the universe, then that creator itself exceeds the complexity threshold, and therefore requires a creator of its own.

Further, the necessary creator-of-the-creator, by definition, either meets or exceeds the complexity thresshold (since 3 is, again, impossible), and therefore also requires a creator of its own. Thus, the result of answers 1 or 2 is an infinite regress of increasingly complex creators.

Notation

 * level of complexity = x
 * system = S
 * complexity threshold = z
 * chance = x(S1) < x(S2) = h

If x(S2) > z, then h is defined as impossible.


 * universe = S2 = V
 * creator = S1 = C

If x(V) > z, then C


 * 1) if x(C) < x(V) = h
 * 1 is defined as impossible


 * 1) if x(C) = x(V), then x(C) > z
 * 2) if x(C) > x(V), then x(C) > z
 * if x(C) > z, then C(C)
 * if x(C) > z, then x(C(C)) > z
 * if x(C(C)) > z, then C(C(C))
 * if x(C(C)) > z, then x(C(C(C))) > z
 * if x(C(C(C))) > z, then C(C(C(C)))
 * ad infinitum