The mathematical function (f) exists iff there exists a domain (S) associated with a codomain (T) usually called the range. Furthermore, S and T are both non-empty sets. In this context, the elements of both are the real numbers. There exists a rule of transformation or mapping (f) that relates an element of S a unique element of T. That is if x is an element of S (x Î S) then y=f(x) is the image of x by the transform of f. The subset of T are some elements that are images of some elements of S:{y|y=f(x), for some x in S}. For a 1 to 1 correspondence, one element of S relates to exactly one element of T. For many to 1 correspondence, 1 or more elements of S relate to just one element of T. For 1 to many correspondences, 1 of S relates onto many elements of T. Consequently, many to many correspondences can also exist. Mathematically speaking, only the first and the second define a functional relation while the third and fourth can define a dysfunctional relation.


In view of these 4 correspondences, the question can be asked which of them would correspond to the evolution of the physical universe. The big bang theory suggests the 3rd correspondence, from a singularity to everything comprising the states of the presence. What exist now must already exist in the beginning, meaning that creation is not a continuous process. Everything was created at one time from one thing. However, the relatively localized varieties of things: atoms, planets, stars, and galaxies all seem to correspond to the second correspondence (many to one) while some of the localized planetary human affairs: marriages, personal, national, international relationships can correspond to any of the four correspondences thus giving meaning to monogamy, polygamy, monotheism, polytheism, united nations, united states, companies, corporations, limited partnerships, and students to teacher functional classroom. All hell breaks loose if there were more than one teacher in the classroom, talking simultaneously. The same would apply to the leaderships of nations and the rules of governments. Making the long story short, a functional universe would definitely require a theory of everything. On the other hand, a dysfunctional universe would require no theory at all which is the same as many contradicting theories working against each other with equal validity and the world evolves without any constructive interference, approaching the ultimate state of absolute chaos. This is analogous to a scattered plot with neither positive nor negative correlation. Fortunately, an absolute theory of complexity would still assert that perfect order can emerge from a state of absolute chaos but not from states of relative chaos, from absolute (genuine) randomness not from pseudo (artificial) randomness.