Edward Norton Lorenz (1917–2008), the American mathematician and meteorologist, apparently thought that earth’s climate system displayed both ergodic and non-ergodic elements:
“… let us recall that a dynamic system is termed ergodic if the equations describing its evolution at random initial conditions and fixed external parameters have a unique possible stationary solution. If the dynamic system is not ergodic, then its behaviour over an infinitely large time interval will depend on the initial conditions. As applied to the climatic system this is equivalent to the fact that external parameters uniquely determine climate in the first case and non-uniquely in the second case.The climate system is highly complex and the further into the future one goes, the greater the uncertainty associated with what the weather will be like on any particular day. In fact, one might argue that, as soon as one goes from the very short term future (say, hours, days and weeks at most), it must become extremely difficult if not impossible to predict the weather. Certainly, predictions cannot yield objective probability scores, and there are high degrees of increasing uncertainty involved as one moves to the future.
The idea of the non-uniqueness of Earth’s climate was first put forward by Lorenz (1979), who termed ergodic systems transitive, and those systems which do not have the property of transitivity intransitive. The real climatic system, according to Lorenz, is almost intransitive, that is, it shows signs of transitivity and intransitivity simultaneously. Alternation of glacial and interglacial epochs over the last 3.5 million years of Earth’s history testified to this. (Kagan 1995: 15).
Nevertheless, there are certain predicable cycles: the changes caused by days and nights, the changes of seasons, and (generally speaking) Ice Ages.
So the system seems simultaneously ergodic and non-ergodic, and one must wonder whether in economic life we also face a number of such complex processes that have the property of being both ergodic and non-ergodic. For example, business cycles are a real and repeated empirical regularity in modern capitalist systems. Asset bubbles and their collapse appear in an admittedly highly irregular but cyclical way on unregulated or poorly regulated secondary asset markets, even though strict prediction of quantities and turning points with mathematic probability is not possible and movements of specific prices on secondary asset markets are surely non-ergodic.
BIBLIOGRAPHY
Kagan, B. A. 1995. Ocean-Atmosphere Interaction and Climate Modelling (trans. Mikhail Hazin), Cambridge University Press, Cambridge.
Lorenz, Edward N. 1979. “Forced and Free Variations of Weather and Climate,” Journal of Atmospheric and Oceanic Science, 36.8: 1367–1376.
I think you're seeing where I'm coming from, LK. (You could have also discussed the infamous Medieval Warm Period...). However, you do end with a contradiction. A system cannot be both ergodic and non-ergodic. To say that is to destroy the meaning of both words (like "blackwhite" or "goodbad" in Orwell). The only viable solution to this inherently philosophical problem is to recognise that reality itself -- as Davidson has hinted at many times -- is non-ergodic. And what appears as ergodic processes are really just regularities (I would say: repetitions) with long time horizons.
ReplyDeletePerhaps I have phrased myself badly.
DeleteTo re-phrase: it is possible for some complex general process or phenomenon to have individual elements or attributes that are ergodic and others that are non-ergodic?
Whether one characterizes the whole process/phenomenon as nonergodic depends on the extent and importance of the non-ergodic elements in relation to the ergodic ones.
As Lorenz argued, the climate system looks like such a process (being almost nonergodic).
After all, what can you call the regular change from day to night as anything but ergodic?
"And what appears as ergodic processes are really just regularities (I would say: repetitions) with long time horizons."
But is there really any difference between this and a system that in fact yields stable, long-run relative frequencies? If you have the latter, surely you have an ergodic process.
This is where I disagree. I think that everything is non-ergodic. And, actually, I think this is captured in Keynes' famous phrase "In the long-run we are all dead". It is also captured in the second law of thermodynamics (the entropic law). (The idea of true ergodicity in this regard is identical philosophically to the idea of a perpetual motion machine).
DeleteThe regular change from day to night is only regular over a finite time horizon. Will you or I ever see this change? Not really, no. But we are but a speck in the great hourglass of time. Eventually the sun will burn out or the earth will lose its orbit or whatever. Day to night will come to an end.
I think it's really a rather deep philosophical question: are there things in the finite universe that stay the same? I do not think that there are. I think that we can call certain regularities (day to night etc.) ergodic for the sake of convenience. But nothing more. The reality of the situation is that everything is always and everywhere changing. And the question is only how fast or how slow.
Economic and social systems change with great rapidity and that seriously and fundamentally impedes our study of them. While the rotation of the earth around the sun changes rather slowly -- but it still changes.