Erdogan was blunt; if the YPG pushes west of the Euphrates, it’s war. Well, looks like war then. The YPG is getting ready to attack the crucial towns of Jarabulus and Manbij. Russia most certainly will aid the YPG to reconquer Jarabulus. And that will directly pit – once again – Turkey against Russia on the ground.

In fact they don’t account for a changing population at all, as I discovered when I wrote a simple computer simulation to test his model. Thanks to a very basic calculus error, the lines actually show what the cumulative probability would have been if the population had started at the current level and stayed constant. So if we take the orange line at 10 years, instead of telling us the cumulative probability if the population had started at 5000 and fallen to 2500 over time, it gives us the value if the population had started at 2500 and stayed constant. Since this error occurs in equation 1, which the rest of Grimes’s equations are derived from… well, you get the idea.