Ergodicity is the condition wherein a sample is representative of the whole vis-a-vis some statistical parameter. An ergodic system is one that visits all possible states of its existence as it evolves. Axiomatically, a non-ergodic system is one that does not. Stuart A. Kauffman, a scientist at the University of Calgary, wrote on Edge a year ago:
… the evolution of life in our biosphere is profoundly “non-ergodic” and historical. The universe will not create all possible life forms. This, together with heritable variation, is the substantial basis for Darwin, without yet specifying the means of heritable variation, whose basis Darwin did not know.
This is a very elegant description of history that employs a dynamism one commonly encounters in physics and the language of physics. If the past encapsulated everything that could every happen, it would be an uninteresting object of study because its peculiarities would all cancel out, leaving a statistical flatland in its wake. Instead, if the past contained only a specific set of events connected to each other in unique ways – i.e. exhibiting a distinctly uncommon variation – then it becomes worthy of study, as to why it is what it is and not something else. As Kauffman says, “Non-ergodicity gives us history.”
A billiard ball in a rectangle with two circular ends: slight changes in initial conditions make such a big difference that eventually it could be anywhere. To be precise, we say its motion is "ergodic".
This animation was made by @roice713.
(to be continued) pic.twitter.com/rQPS0OOdXH
— John Carlos Baez (@johncarlosbaez) July 28, 2018
Though today I know that the concept is called ‘non-ergodicity’, I encountered its truth in a different context many years ago: when I had written an article that appeared in Quartz about how Venus could harbour life and that that should encourage us to look for life on Titan as well. I had quoted the following lines from a 2004 paper to strengthen my point:
The universe of chemical possibilities is huge. For example, the number of different proteins 100 amino acids long, built from combinations of the natural 20 amino acids, is larger than the number of atoms in the cosmos. Life on Earth certainly did not have time to sample all possible sequences to find the best. What exists in modern Terran life must therefore reflect some contingencies, chance events in history that led to one choice over another, whether or not the choice was optimal.
Somehow, and fortunately, these lines have stayed with me to this day four years on, and I hope and believe they will for longer. They present a simple message whose humility seems only to grow with time. They suggest that even life on Earth may not be the best (e.g. most efficient) it can be after billions of years of evolution. Imagine the number of evolutionary states that the whole universe has available to sample – the staggeringly large product of all the biospheres on all the planets in all the time…
The search for a ‘perfect lifeform’ is not a useful way to qualify humankind’s quest. Against such cosmic non-ergodicity, every single alien species we discover could, and likely will, stand for its own world of contingencies just as peoples of different cultures on Earth do. Perhaps then our xenophobia will finally become meaningless.