Freedom, Stewardship, and Creative Powers via Mathematical Flashback

Today's pondering of freedom, stewardship, and creative powers has lead me through an interesting recollection and mental exploration of the concepts of continuity, differentiability, elastic and inelastic spiritual collisions, and behavior at infinity. Unfortunately (or fortunately), my fingers do not type as fast as these ideas raced through my head, but I will at least attempt to get some of my out there thoughts out there for the fortunate reader.

During my undergraduate years, I took a math class, Introduction to Number Theory, which completely fascinated me. Numbers, after all, are merely abstract ideas used to represent the world in which we live, and our experiences in it, in an organized manner, allowing us to gain insights and make discoveries about our world. One of the topics covered in my introductory Number Theory course that I found particularly poignant, and spiritually enlightening, was the concept of behavior at infinity of different sequences of numbers, and in particular, how these sequences behaved in relation to each other as they approached infinity.

Take, for instance, the two sequences A(n)=n, and B(n)=2n. No matter how big n gets, B will always be twice as big as A, which itself is going to get very large as n approaches infinity. On the other hand C(n)=n-1 will only ever be 1 unit away from A, which, as n gets larger, becomes a completely insignificant difference. One might say that C is practically the same thing thing as A as n approaches infinity. While the limitations of this text editor (or possibly of my knowledge of it) prevent me from displaying such, there are other sequences, the ratio of which gets exponentially larger and larger as n approaches infinity. So, there appear to be three options for monotonic sequences of numbers: either (1) they are practically the same thing in the eternities (because their rates of change are equal, and therefore the difference between them becomes minuscule over time), (2) one stays a certain number of times larger than the other, no matter how large they both get, or (3) the ratio of their "sizes" becomes unboundedly larger (or smaller) over time.

For all of you non-mathematically-minded people out there, stay with me. I am going somewhere with this. The practical application of this concept of behavior at infinity that I've been thinking about this morning is the possibility of different options for the relationship between production and consumption (or asset/liability) trends of an individual, a family, or a society. I've come to the conclusion that an important step toward godhood and maximizing creative powers (and liberty) is to learn how to place my production-consumption ratio in the third category, so that it becomes unboundedly large as time tends toward infinity. That would definitely lend toward perpetuating the creation of worlds without end, and the ability to do this seems to be a characteristic of God.

This leads to an appropriate discussion of continuity and differentiability (I apologize for any flashbacks the mention of these two words may have caused of the nightmares you experienced while studying for your calculus final in college, but hopefully these nightmares have been replaced by now with an overwhelming gratitude for the usefulness of calculus - if not, maybe you didn't really 'get it' and should take the course again!) - how changes in production-consumption ratio occur, and the feasibility or likelihood of such a change. However, being hungry, hair wet, and having presents yet to wrap, I'll save that discussion for another day!