Chaos Theory

These theories provide one certainty, that in an expanding and evolving system there is a point where order goes back into chaos. When considering infinity, this would be an infinite state in where the system would fluctuate alternatively form order into chaos and back into order infinitely. Some logic would indicate that chaos and order are one and the same only different states of the same system.

This view would predict that what we today perceive as order will in time fall into what we perceive as chaos.

From http://www.pbs.org/kcet/wiredscience/blogs/2007/10/climate-chaos-and-con...

See also... historyreligionandtruth.com/?q=Chaos%20Theory

Climate, Chaos and Confusion by Michael Tobis

theory and conclusions

We climate scientists often hear the case made "If you can't predict the weather next week, how could you predict the climate in a hundred years?" The answer to the question is hidden in the question. The weather and the climate are not exactly the same thing, and so what you can say about the one and what you can say about the other are also different.

Everyone knows what weather means. Sometimes we even speak of the weather as "it". What will "it" be like tomorrow? "It" will probably rain in the afternoon. Clearly the weather must be important, since we call it "it"!

Suppose you ask me today, in mid-October, whether it will snow in your home town on Christmas Day. I have very little information to offer; that would be a ten week weather prediction. On the other hand, suppose you ask me whether the next Fourth of July will be warmer than the next Christmas. Here (assuming you live somewhere like the US mainland) I will have very little hesitation in making a prediction. The first prediction is a weather prediction, but the second is simply a climate fact: it is extremely unlikey for an early July day to be colder than a late December day.

That's an easy one. There's a closely related question which is much harder.

It's asked by people who are somewhat interested in science. We hear "doesn't chaos theory mean you can't predict the climate"? Or "isn't climate chaotic"? Here I have to get very careful with language, because a few things are getting confused. There is a way of thinking about these questions that makes sense, but not everybody who talks about them knows it.

Let's start by thinking about what "chaotic dynamics" means.

The discovery of chaotic dynamics in any scientific application is often attributed to Ed Lorenz, one of the founders of the field of physical climatology. There's a nice description of the discovery as well as some of the consequences at this link. It's interesting, though, that Lorenz was making an early effort at getting a computer to model weather when he ran into this phenomenon.

Chaos is a property of some (not all) nonlinear systems of evolution. Here the word "evolution" has nothing to do with biology, but simply the nature of the system we are modeling. These systems change gradually and in completely well-defined ways; their state at any given instant of time depends only on their previous state and the inputs. There is no randomness in this system, and so the behavior of the system is in principle predictable. What Lorenz discovered was an unanticipated behavior of the system that, among other things, greatly liimits the extent to which such a system can be predicted in practice. It turns out that this behavior is quite common in nonlinear systems of evolution. The best mathematical descriptions of fluids behave in just this way, and the atmosphere and the ocean are fluids.

If you've heard of this topic, you've probably also seen a diagram like this one.

Let's review what this picture: Lorenz.pngis showing us. What you see is the trail of the state of a mathematical model plotted on two axes. The vertical axis represents one physical quantity and the horizontal another. What we see is a system that has two separate behavior pattern, and can jump from one to the other. The locations of the jumps are systematic, but there are non-jumps very close, indeed as close as you specify, to jumps. So if you have the state of the system even very slightly wrong , if you want to predict the system into the future your model will take the wrong branch. The weather of the system is unpredicatable.

Is the climate of this system unpredictable? What does the word "climate" even mean/ Everyone knows it intuitively. Austin, Texas has a warmer climate than Madison, Wisconsin. This doesn't mean that it is impossible that Madison is warmer than Austin on a given day, just that it is unlikely. Once we use the word "likely" oir "unlikely" we have moved into the domain of statistics and must tread very carefully lest the statisticians mock us for our crude misuse of their delicate concepts. And indeed, we are sometimes a little bit sloppy when we define "climate" as "the statistics of weather". Whether that definition is adequate or simply hides some difficulties under a rug depends on exactly what topic we are pursuing.

For the Lorenz case, though, it's simple. The weather is the present position of the dot. The climate is the whole picture, both sets of loops. They define the behaviors that the system is prone to. They are the climate of the system. Is that climate predicatble? Yes. It is more than predictable. It doesn't change at all. In the long run, the moving dot will be somewhere on those loops, and not anywhere else!

The real climate of the world is a much more complicated system of evolution than Lorenz's example, and there are lots of difficulties in getting it right. I'll talk about this some more next time. For now, what I'd like you to appreciate is that chaotic weather is entirely consistent with totally predictable climate.

Let's be careful. I haven't proven that climate is predicatble.

I have shown that the long term aggregate behavior of a system can be known (the shape of the two loops in the far future) even if the long term dynamic prediction (where on the loops the dot will be at some time in the far future) cannot.

In other words, I've shown that chaos in weather doesn't demonstrate chaos in climate. Which is practically the same thing as saying that I can't tell you whether you'll have a white Christmas, but I can still tell you whether you'll have a hot July. It just took a lot longer, because a little knowledge is a dangerous thing.

Turing machine