Got your attention, did I?
You know what got mine? Noticing, a while ago, the apparently inexorable growth of interest in what I thought was a fairly dull* post, Friends Don’t Let Friends Use “cf.”, first published here in June 2016. That post got a bunch of views when I first posted it, which isn’t unexpected. Then it was largely ignored for a year or so, which isn’t unexpected either. Then something odd happened: exponential growth.
That’s what’s shown in the graph above: month-by-month readership statistics for Friends Don’t Let Friends Use “cf.”. It’s a lovely curve, isn’t it? Let’s ignore the first year (which is dominated by novelty; every post gets a spike when first published). Let’s make a semilog plot of the remainder, because that seems right for a curve like that. And let’s fit a line to that semilog plot, because we’re scientists and we like to do that kind of thing.
And now we can polish up our crystal ball. We can use that linear fit** to predict some things, right?
- By November of this year, Friends Don’t Let Friends Use “cf.” will be read 1,000 times every month.
- By March 2023, it will account for half of all visits to Scientist Sees Squirrel.
- In August 2025, it will account for 95% of all visits to Scientist Sees Squirrel. Then I can stop writing new posts, and it’s nice to have a retirement date.
- By August 2032, every human on Earth will read Friends Don’t Let Friends Use “cf.” once a year.
- By June 2035, every human on Earth will read that post every day.
- By January 2056, the post will have more monthly reads than there are stars in the universe.
- Sometime in the 2100s, the energy used to store, transmit, and display copies of the post will exceed the latent energy content of all matter in the universe – leading to its immediate heat death.
Now, that was pretty silly (I did warn you). But it’s also not-silly in two important ways.
First, this isn’t the first time you’ve seen someone make the mistake of extrapolating a fit beyond the data – and it won’t be the last. Be cautious with models, and especially so of models that are merely descriptive (like mine).
Second, the startling power of exponential growth (as in my linear-fit-in-semilog-space) has very important consequences for my own field, and for our natural world. Among other things, it’s why all natural populations experience density-dependent regulation at some point***; and it’s why natural selection (given heritable variation) is such a powerful force.
See, no matter how silly something gets, I can find a lesson in it. Or at least, I’ll be able to until that darned post brings the universe to its doom.
© Stephen Heard July 7, 2020
**^Which has r2=0.93, and as an ecologist may I just point again that it has r2=0.93, which is pretty much to die for?
***^For those interested in this, read about the debate sparked in the 1950s by the publication of books by David Lack (arguing for ubiquitous density-dependent regulation) and by Andrewartha and Birch (arguing against). To cut to the debat’es resolution: all populations experience density-dependent regulation at least some times, but it can be complex and subtle, and its detection is logistically and mathematically difficult. And yes, I just wrapped up 70 years of population ecology in one sentence. You’re welcome.