Detour: Chaotic dynamics
This is actually an example of something called "chaotic dynamics." The population size is not actually unpredictable (after all, we're using an equation to calculate population size, so by definition we are predicting it) but it appears unpredictable. Even stranger, if two populations start out with only slightly different sizes, their population dynamics will get more and more different over time. Eventually knowing the size of the first population will tell you nothing about the size of the second population! This is called "sensitive dependence on initial conditions" (SDIC, not to be confused with the Vulcan motto IDIC, for any Trekkies out there).
Hallmark of chaotic dynamics SDIC =
"Sensitive Dependence on Initial Conditions"
Vulcan motto IDIC =
"Infinite Diversity in Infinite Combinations"
Whew, you've made it this far, which is through a lot of math. Here's the detective notebook:
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