>>10428402 lb

CS person here.

>It seems that the operation time of the algorithm can greatly differ based on the SIZE OF THE INPUT FUNCTION. (variable)

Not always. A O(n!) algorithm with 100 possible output values will take vastly longer to run than a O(n) algorithm with 100,000 possible output values.

>What if there is an algorithm governing the timing of certain events? And the "input function" is HUMANITY?

I'd wager this exists, at minimum in a limited form. At the quantum level, particles are non-deterministic (unless they become entangled), but at the macro level, matter acts predictably. Individually, humans will act random. Form people into a more coherent body (that is, devalue personal identity and thought), and you'll find social sciences become useful.

Asimov explored this idea in the "Foundation" series with psychohistory.

>What if there is a mathematical limit that can be expressed as a function, where the Great Awakening grows at an exponential pace?

The important metric here is branching factor. At any given time step, what is the branching factor, and what is it dependent on? At successive time steps, does the branching factor change? For example, a post on this board has an immediate branching factor of the number of people who read the post. However, few people will ever take that content and share it with an equally large audience, so the successive branching factor may drop, but it could potentially increase (think a big celebrity). This process continues ad infinitum.

Exponential growth starts slow, but it eventually accelerates quite rapidly. At some point, the amount of people (to use Q as an example) who are unaware of Q may dwarf those who are. Once that happens, the growth rate will decrease.

Look into social network theory. You'll probably have fun over there. See the attached PDF for a formal treatment of it.