I don't normally post twice in one day, but I didn't want to lose the thought.The past three Keep the Joint Running columns have been based on Jared Diamond's Collapse: How Societies Choose to Fail or Succeed (see "Collapsible business lessons," 11/6/2006). A friend, reading them, suggested that usually, negative feedback loops will act to prevent collapse.That's when it occurred to me: The mathematics of negati I don’t normally post twice in one day, but I didn’t want to lose the thought.The past three Keep the Joint Running columns have been based on Jared Diamond’s Collapse: How Societies Choose to Fail or Succeed (see “Collapsible business lessons,” 11/6/2006). A friend, reading them, suggested that usually, negative feedback loops will act to prevent collapse.That’s when it occurred to me: The mathematics of negative feedback covers the Collapse effect nicely. It works like this: If you take the basic logistics equation (x at time (n+1) = max(rx(1-x),0)) and play with the parameters, you’ll find that for a wide variety of conditions (so long as x is a fraction and r is less than 2.2 or so) you’ll end up with a stable system. Now, delay the feedback (make it x at time (n+2) or (n+3) = the formula). The result is that the system destabilizes – it grows unpredictably and wildly, then crashes to zero.This is exactly what happens in Collapse situations: The factors that should lead to moderation of population growth don’t happen immediately, and so they go unrecognized. The feedback is delayed, and the result is chaos and collapse.The lesson is clear, really pretty obvious, and applies to a wide variety of situations: Make decisions based on current information, not what was true a year or two ago. Situations change, and if you don’t notice the change, what you “know” is what used to be true, not what’s true right now. – Bob Technology Industry