Happy Canada Day π¨π¦π𦫠to all my fellow Northern followers. To all our Southern neighbours happy 4th of July πΊπΈπ½π¦ ! Here are some brief thoughts on non-ergodic systems to ponder during the celebrations.
An ergodic system has the special property that its time averages look the same as its ensemble averages. For example, if you were to average the temperature of the world's oceans across the globe at a particular point in time or average the temperature of a particular part of the ocean over the course of a year you would - barring some minor annual fluctuations - see very similar results.
Most of the systems we interact with on a daily basis, however, are non-ergodic. If you look at a country and find that 1% of its population are lawyers it would be a mistake to think that each person in the country spends 1% of their life as a lawyer. Complex systems like this follow path dependent routes. As one event occurs its effects on the systemβs state downstream compound in non-linear ways, leading to results that are never observed at an ensemble level.
If we want to understand systems like this - and we should, since our lives are non-ergodic - then we must learn to think of each situation as unique. When encountering non-ergodicity our usual tools of universal laws and randomised control trials offer little help for prediction. Better, through observing the system across time, we may learn from its past and present the patterns that govern its behaviour and as such, where it may be going in the future.
Thanks to Casey Li for reading a draft of this essay
This understanding of ergodicity and its import was much informed by this excellent paper by Matti Heino et al.