ERGODICITY: The Ergodic Property, a Simplified Explanation of the Most Important Property to Understand in Probability, in Life, in Anything. You can estimate the life expectancy of a given single human that is, *over time*, using the average of all humans over a *given moment in time* (snapshot), by looking at a given day, say yesterday, the age of people who are alive/died, sometimes called a cross-section. The *time average* is similar to the *space average*. Otherwise it would be impossible to understand humans. Clearly, if there are a few 1000 year old persons in yesterdays sample, you can assume that your great uncle might live that long, and delay plans for spending his inheritance. A day in all the casinos should resemble the life of a given casino. Likewise you can see how books, companies, etc. fare over time by taking a given snapshot, in the absence of systemic risks or contagions that effectively eliminate ergodicity. Assuming ERGODICITY, we can look at nature, and consider the various species at a different stages in their cycles, and say that the future for a *given* species will resemble (that is for specific statistical properties) that of all other species. ---- Philosophically, the problem of (enumerative) induction is circumvented in our wisdom; we do not say Greenspan never died and infer that he could be immortal, so such wisdom includes the detection of ergodicity where applicable. But we fail to use it properly in social science because of BS-artists who use mechanistic statistics a-la-Pinker, with claims of the style it never happened before for a given company, asset class, etc. ---- This is much, much, much more technical, but we can go in the reverse direction: imply ergodiciy from long-term survival of a high dimensional system (say the planet), with no terminal blow-up. In the Precautionary Principle paper, we can use the argument of absence of ruin of the planet on a given day to assert ergodicity, i.e., to say that there are enough independent dynamics of sub-components on earth to warrant that had the earth produced systemic risks endogenously, it would have blown up already, on a single day. And we have several billion of such days! In other words, the Markov Chain does not produce absorbing states. https://en.wikipedia.org/wiki/Ergodicity or, clearer, https://en.wikipedia.org/wiki/Ergodic_theory
Posted on: Mon, 14 Jul 2014 12:32:23 +0000
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