One of biases that are extremely prevalent in science, but are rarely talked about anywhere, is bias towards models that are mathematically simple and easier to operate on. Nature doesn't care all that much for mathematical simplicity. In particular I'd say that as a good first approximation, if you think something fits exponential function of either growth or decay, you're wrong. We got so used to exponential functions and how convenient they are to work with, that we completely forgot the nature doesn't work that way.
But what about nuclear decay, you might be asking now... That's as close you get to real exponential decay as you get... and it's not nowhere close enough. Well, here's a log-log graph of Chernobyl release versus theoretical exponential function, plotted in log-log.
Well, that doesn't look all that exponential... The thing is that even if you have perfect exponential decay processes as with single nucleotide decay, when you start mixing a heterogeneous group of such processes, the exponential character is lost. Early in time faster-decaying cases dominate, then gradually those that decay more slowly, somewhere along the way you might have to deal with results of decay (pure depleted uranium gets more radioactive with time at first, not less, as it decays into low half-life nuclides), and perhaps even some processes you didn't have to consider (like creation of fresh radioactive nuclides via cosmic radiation).
And that's the ideal case of counting how much radiation a sample produces, where the underlying process is exponential by the basic laws of physics - it still gets us orders of magnitude wrong. When you're measuring something much more vague, and with much more complicated underlying mechanisms, like changes in population, economy, or processing power.
According to IMF, world economy in 2008 was worth 69 trillion $ PPP. Assuming 2% annual growth and naive growth models, the entire world economy produces 12 cents PPP worth of value in entire first century. And assuming fairly stable population, an average person in 3150 will produce more that the entire world does now. And with enough time dollar value of one hydrogen atom will be higher than current dollar value of everything on Earth. And of course with proper time discounting of utility, life of one person now is worth more than half of humanity millennium into the future - exponential growth and exponential decay are both equally wrong.
To me they all look like clear artifacts of our growth models, but there are people who are so used to them that they treat predictions like that seriously.
In case you're wondering, here are some estimates of past world GDP.
My computer is biased toward not running at 100 petahertz and having 70 petabytes of RAM. My brain is biased toward not using so many complicated models that it needs 1 trillion neurons each with 1 million connections and firing up to 10,000 times per second.
And now for something perhaps more useful than sarcasm, it seems to me that people tend to simply come up with the consistent model that is either the easiest one to compute or the simplest one to describe. Are heuristics for inconsistency, such as "exponential growth/decay rarely occurs in nature", quickly spread and often used? How about better approximations such as logistical growth?
Hahaha, anthropic Occam's Razor! If a science allows simple theories that can fit in our tiny brains, we call it a good science and observe with satisfaction that it "obeys Occam". If a science doesn't allow simple theories, we call it a bad science and go off to play somewhere else!
Come to think of it, physics seems to be the only science where Occam's Razor actually works. Even math is a counterexample: there's no law of nature saying simple theorems should have short proofs, and easy-to-formulate statements like 4-color or Fermat's last can ca... (read more)