re: #1050 Pythagoras

… The video, like lots of things, constrains itself by avoiding the vocabulary of Calculus. …

Suppose temperature is falling and then some trigger reverses it. While it was falling, CO2 was also falling and passed through a value X. This value X is part of the feedback and is driving the temperature lower.

After the trigger, temperature rises and then CO2 starts to rise too. Eventually it gets back up to X but now the theory says that a CO2 level of X is driving temperature UP. That’s a problem as X cannot do both. At this point I can only go on using Calculus.

The feedback term in the differential equation is that the derivative of temp with respect to time (dT/dt) is a function of X, not dX/dt. I think the technical folks here who are not skeptics/deniers will confirm this. There are other forms of feedback beside dT/dt being a function of X but this is the one everyone’s thinking of. So, Houston, we gotta problem. …

I appreciate the calculus reference, but this is clear as mud. For one thing, you define X as a threshold (which would be a constant), and then refer to dT/dt as a function of it, and also refer to dX/dt.

What “positive feedback” implies is that dT/dt = +k * T (at least in a linearized, incremental sense. With my “+”, I’m indicating that the costant of proportionality, “k”, is positive. So what this equation says is that the higher the temperature is, the faster the temperature will increase (because of increased GHGs caused by the increased T).

The solution to that differential equation is T(t) = T(0)*exp(k*t). In other words, the system is unstable, and the temperature increases exponentially without bound.

In the real world, all it takes is the least little blip to set off an unstable mode like this one. Since even 1998 didn’t set it off, it clearly doesn’t exist (and, therefore, those end-of-the-world models that rely on this effect are clearly wrong).