One of the fun things about literature, for mathematicians, is picking on the faults, impossibilities, and grotesqueries of math and science exploited, as if real, to push an otherwise infeasible plot. Okay, so I'm probably overstating the entertainment factor, but who has never encountered a curmudgeon telling us what is wrong with Star Trek, the hyperdrive on the Millennium Falcon, or pointing out that Batman weighs to much for some stupid bat-contraption to work like it did on the screen? Meanwhile, it is said that Jonathan Swift, perhaps accidentally, accurately described the properties of Phobos and Deimos long before they were discovered. Arthur C. Clarke and Isaac Asimov were well-known for their scientific scruples; the cotton-candy fluff of Ray Bradbury need not apply. My point being, of course, that math and literature are not incompatible, no matter what surveys of university students might otherwise suggest. Part of the reason, though, that even legitimate writing suffers certain mathematic and scientific shortcomings is that the form, genre, or basic art attends the larger story. If people might worship gods, why not pretend we can break the light barrier? To the other, sometimes the math is just more than it's worth. An example: The Scene John awakens after an impossible sleep in an impossible suspended animation chamber to find himself in the custody of seemingly benevolent aliens. His hosts require the continued existence of humanity, and dismissing the reality that two organisms are a problematically low number for developing a species, he is presented to the only other living human Earthling in the Universe ... his ex-girlfriend. The Line John turned to the Governor. "Now wait a minute," he said. "You've been watching Earth for how long?" The Governor shrugged, inasmuch as a being of his design could. "Five hundred years. We arrived in 1510, by your calendar. "Okay." John thought for a moment, frustrated. Diplomacy, he knew, required a certain caution. Still, he could see no way around the problem. "And during that time, how many people walked the Earth?" Governor Shmaltzoid thought for a second. "_____," he replied. "Alright." This was the hard part. John glanced at Amy, and then again, letting his eyes rove up and down her delicate, porcine figure. "So, out of _____ people, over five hundred years, the only other human you saved had to be her?" The Math That blank can be represented, as such, by N. This unknown sum represents the total number of human individuals who existed on Earth during the period the aliens observed the Earth. In other words, it is the number of people who existed during a given period (P). The easiest starting point is simply the living (L), plus the born (B), less the died (D), but that is clearly inaccurate even before we apply the dynamics of reality. Still, how do we find N? Quite obviously, there are more factors to account for than just those, and D falls away as irrelevant except within the context of specific methods that only produce a general range; that is, if we choose to use periodic benchmarks in order to obtain a rough sum, yes, we need to know how many people accounted for in a prior period are no longer present in a later one. The obvious answer is to live five hundred years, have a billion eyes, and count. But in searching for something more real and efficient, there must be a way to start figuring how many people lived during a given period. To wit, a population estimate pulled not quite at random from a search result suggests a worldwide human population of 500 million in the year 1500. This particular estimate suggests we crossed the one-billion mark in 1810, achieved 1.6 billion by 1900, 6.5 billion by 2005, and estimates 6.8 billion this year. How many people, then, actually lived during that time? I mean, look at that math. That's a lot to put into a flaccid joke, eh? ____________________ Notes: Aubuchon, Vaughn. "World Population Growth History". Vaughn's Summaries. June 13, 2010. Vaughs-1-pagers.com. August 6, 2010. http://www.vaughns-1-pagers.com/history/world-population-growth.htm
Well, it seemed interesting at the time .... Nothing's wrong with "billions". Left to a question, I'd probably go with something like, "how many millions?" but I was high and it seemed like an amusing question. I mean, there must, somewhere, be an answer. I highly doubt I'm the first person in history to have proposed the question. Indeed, it's one of the few things in the Universe I can be certain of according to the confines of the cogito, or that I can be certain of insofar as whatever arcane doubt might exist is completely irrelevant. To the other, not being a mathematician, I wouldn't know how to even start looking for that answer. :m:
