The Point I Was Making

Some people really didn't understand the point of the last post, so I'll explain.

First of all, it's my non-expert opinion that climatologists by and large do not understand the mathematics of the system they wish to characterize. And, in my limited experience, when you move on the spectrum from "folks who look at glacers" to "folks who write and simulate the actual dynamics of climate," you move from the people shouting "IMMINENT CATASTROPHE" to much more non-committal type answers like "Yes, humanity affects the climate in some way, but, really, there's a lot we don't know." And, unsurprisingly, those additional "rogue voices" saying that climate change may be due more to some factor other than CO2 come almost exclusively from the dynamicists.

Now let's talk mathematics. From the time you first learn algebra in middle school to the very end of your college career, your whole math education is governed by the assumption of linearity. Unless you actually get a degree in math. It's sort of like how unless you're an actual physicist, your whole engineering approach to physics will probably be Newtonian. That's because just like how Newtonian physics works for 99% of the situations most engineers will ever encounter (the exception being people who design microchips), the linearity assumption works for 99% of the mathematics most people will ever encounter.

The assumption of linearity is, in layman's terms, the assumption that every mathematical function behaves in a smooth manner if you look at it on a small enough scale. It's the governing assumption of calculus and engineering differential equations. One way this shows up in the sciences is regression correlation, which looks for "best fit" curves correlating the different variables and treats everything not lying on the curve as unpredictable "noise." Allow me to illustrate with the previous data, edited by me. This is what a lot of scientists see:
Your typical scientist looks at the above system and sees this black line as the "predictable part" and the red wiggly stuff as the "noise." His goal is to come up with an adequate model that will predict the black trend line without having to really even deal with all that crazy noise. The current wisdom is to say that black line is governed mostly by human-produced CO2.

The purpose of my little random walk example was to illustrate how it is possible (quite easy, really) to construct a mathematical system in which the the "noise" itself is the cause of the observed trend--it has both predictable and unpredictable statistical properties (with a random walk, one can predict the average fluctuation and establish an approximate bound on the growth; one simply can't predict the average value of the walk itself or any kind of growth trend). That's the only thing you should take from it. As I said before, climate isn't random. However, the reason I chose a random walk as my illustrative example is that my average reader is probably not mathematically sophisticated enough to be able to understand the concept of a dynamical system with sensitive dependence on initial conditions and a multifractal system of attractors, which would have much more direct relevance on the mathematics of climate. But like our random walk, such a dynamical system has some unpredictable stochastic properties governed by the small fluctuations themselves that will always defy our attempts to predict them due to the fundamental mathematics governing the system, not due to the inadequacy of our understanding of said mathematics.

Contrary to the beliefs of many, scientists and mathematicians don't do a lot of talking. There's lots and lots and lots of bad mathematics out there in even the best science journals. I partly blame mathematicians for being too aloof to concern themselves with trivial things like the "physical world," and partly blame scientists for (mostly) thinking that they don't really need to know any more more math than some statistics and ODEs. But with my background, and knowing what I do about the dynamics of the PDEs governing the climate, I look at data like the above and don't see a black trend line separate from the red noise. I say to myself, "Hey, I've seen similar dynamical systems do this sort of behavior before, and it definitely wasn't the sort of thing climatologists say that this behavior is."

Does it mean I'm right and they're wrong? No, of course not. I'm not even a full naysayer; I'm simply on the end of the spectrum responding to the doomsayers, "I don't think you can conclude as much as you wish to conclude," and the goal of my random walk experiment was to give the rest of you some idea of why using ideas you're familiar with instead of writing a 17-post series on chaos, fractals, and strange attractors.